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## Uniqueness in PostgreSQL: Constraints versus Indexes

While doing a bit of database cleaning, I noticed many tables with more than a few indexes and constraints. In particular, a few tables had both a unique index and a unique constraint for the same column. Constraints and indexes come at a cost: they add write overhead with each INSERT and UPDATE and they can take up significant amounts of space. Since a unique constraint and a unique index both enforce uniqueness, which one should we prefer? And are they different?

#### The Set-Up

lauren=# \d examples
Table "public.examples"
Column        |  Type   | Modifiers
---------------------+---------+-----------
a_constraint        | integer |
b_unique_idx        | integer |
c_non_unique        | integer |
Indexes:
"examples_a_unique_constraint" UNIQUE CONSTRAINT, btree (a_constraint)
"examples_b_unique_index" UNIQUE, btree (b_unique_idx)

#### The Test

A unique constraint enforces that the specified columns are unique across all rows in the table. Importantly, a unique constraint allows nulls, and null values compared against each other are not considered equal. A unique index and a unique constraint return the same error when violated “duplicate key value violates unique constraint.”

lauren=# INSERT INTO examples VALUES (0,0,0);
INSERT 0 1
lauren=# INSERT INTO examples VALUES (null,1,0);
INSERT 0 1
lauren=# INSERT INTO examples VALUES (null,2,0);
INSERT 0 1
lauren=# INSERT INTO examples VALUES (0,3,0);
ERROR:  duplicate key value violates unique constraint "examples_a_unique_constraint"
lauren=# INSERT INTO examples VALUES (1,4,0);
INSERT 0 1
lauren=# INSERT INTO examples VALUES (2,null,0);
INSERT 0 1
lauren=# INSERT INTO examples VALUES (3,null,0);
INSERT 0 1
lauren=# INSERT INTO examples VALUES (4,4,0);
ERROR:  duplicate key value violates unique constraint "examples_b_unique_index"

Note that we were able to add multiple null values for column a_constraint and column b_unique_idx, and we have validated that uniqueness is sufficiently enforced in both cases.

#### The Documentation

“Adding a unique constraint will automatically create a unique B-tree index on the column or group of columns listed in the constraint.”

PostgreSQL Documentation - DDL Constraints

“Note: The preferred way to add a unique constraint to a table is ALTER TABLE … ADD CONSTRAINT. The use of indexes to enforce unique constraints could be considered an implementation detail that should not be accessed directly. One should, however, be aware that there’s no need to manually create indexes on unique columns; doing so would just duplicate the automatically-created index.”

PostgreSQL Documentation - Unique Indexes

The documentation for unique constraint specifies that a unique index is created under the hood upon creation of a unique constraint. This means we’re already getting a unique index with each unique constraint, and adding another unique index is simply duplicating the one underneath our unique constraint. If you think about it, this makes perfect sense from a performance perspective; a constraint needs to quickly look up all values in a column upon insert or update in order to verify duplicates have not been introduced. The fastest way to do this lookup is to have these values in an index, ergo an index is automatically created upon creation of a constraint.

The documentation for unique index specifies that we should be using a constraint to enforce uniqueness. The fact that a unique index will also be constrained in the same way is an “implementation detail,” with the recommendation being to directly create a constraint.

#### The Conclusion

The difference between unique constraints and unique indexes causes quite a bit of confusion. My personal suspicion is that while most developers understand indexes, constraints are often enforced in the code base rather than in the database (through a Rails :validates_uniqueness_of or other methods). Often times these code level constraints can’t actually guarantee uniqueness because multiple threads may be attempting to insert into the database at the same time. Database level enforcement is preferred, but for many web developers it is not the natural tendency. Plus, most constraints don’t create indexes, which helps add to the confusion around what’s happening underneath the hood. Anecdotally, I find indexes to be more of an accessible concept (speed!), and many people err on the side of indexes rather than constraints.

But in this case, the clear preferred method is a unique constraint, with which you still get an automatic unique index. If you are creating a table from scratch, this is absolutely the way to go. If you are adding a uniqueness constraint to an existing table, you may still find yourself erring on the side of a unique index, if only because an index can be created concurrently while a constraint cannot. Should you choose a concurrent index in this case, you can add a unique constraint that depends on that index, effectively doing manually what PostgreSQL would have done automatically on a new table:

CREATE UNIQUE INDEX CONCURRENTLY examples_new_col_idx ON examples (new_col);
ALTER TABLE examples
ADD CONSTRAINT examples_unique_constraint USING INDEX examples_new_col_idx;

PostgreSQL Documentation - Alter Table

This method will in effect create a unique constraint while capitalizing on the ability to add an index concurrently.

In the meantime, I’ll be dropping our extra unique indexes, as both a unique index and a unique constraint are taking up extra space and extra write overhead with no extra gain. In a quick test of one million integer inserts, time to insert was 60% higher into a column with a unique constraint and a unique index, and having both a unique constraint and a unique index consumed twice as much space.

Thank you to contributors, reviewers, and editors: Rohit Parulkar, James Dura, Ann Jaskiw, and Dan Eisenberg


text: Additionally, you always just enter the text "sqrt." What easier way to insert a square root symbol than using a simple keyboard shortcut. In the Radicals list choose Square root: 4.2. Option-V used to create the square root symbol. You also can use keyboard shortcuts to enter special characters and symbols. It is not on your keyboard, but a good representation of a square root is: sqrt(of some #). Here are the easiest five ways in which you can insert the square root symbol in MS Excel. For example, if you were take the square root of 4 you could say: sqrt(4)= 2 Use a Keyboard Shortcut. Any ideas what keyboard combination will create the square root symbol - â ? When you're answering questions in a player, you can cut, copy, and paste using the keyboard. Poor there are six key internal organizationallevel characteristics. Step 2: Hold down the Alt key on your keyboard, then press 8730. With this tool, you can adjust the size, color, italic, and bold of Square Root(symbol). Option 1 â Using a Keyboard Shortcut to Add a Square Root Symbol in Word. Use a slash (/) for division. Use an asterisk (*, Shift + 8 on an American keyboard). I have photos on my samsung phone, i go to gallery ,select the picture and choose share, then fb,,select postand a red triangle appears on my fb page ; Microsoft Office applications offer a Symbol utility that you can use to insert square symbols. A simple way to add a square root symbol is the shortcut key and the shortcut is Alt + 251. 1 decade ago. I am doing an algebra project and have to type out all work. 0178) using the numeric keypad. Jay p galbraith, an expert explanation of the poetry module this year. Release the buttons. Division. Root Symbol Root Name Decimal Hex â Square Root √ √ â Cube Root ∛ ∛ â Fourth Root ∜ ∜ Copy and paste the Root symbol or use the unicode decimal, hex number or html entity in social websites, in your blog or in a document. 0 0. raaj. For an Android, this is where you will find the Squared symbol. The symbol will now be copied to your clipboard and you can paste it like this: â In Windows, go to Start->all programs -> accessories -> system tools and click on Character Map. To put the square root symbol, you must enter the following key combination: Option + V key Square root symbol in word. You can also type "sqrt" in the expression line, which will automatically convert into â This is the basic square root symbol (â), so you might want to consider other options depending on the purpose of your document. Enter 2. How do I type the square root symbol (â) in Windows? Layout creator Then click on select and copy. If that doesn't work, you could copy and paste it. Cube Root; This is how the square symbol will look like. Keyboard layout (functional) - is the keyboard-meaning associations arrangement of all the keys of a keyboard, determined in software (Windows in our case). Long press the number 2 as showing on your keyboard. I need to know how to represent the square root symbol. When you want to type square root, cube root and fourth root symbols on your documents then the easy way is to use alt code shortcuts. This method lets you simply press a sequence of keys on your keyboard to add the square root symbol. I'd appreciate it if anyone could tell me where to find the square root symbol for my math note taking.....I know of the #+= section on the keyboard but it's not there. Click it and then click "Insert" to put it in the body of your document. A superscript 2 will appear. the square root symbol appears: This is an easy way to insert symbols in Excel as keyboard shortcuts may not work well in spreadsheets. Tested in Excel 2016 2nd Method * Go to Insert Tab and click the Symbol from the Symbols group. All you need to do is to hold down the Alt button and then type in the corresponding code for this character. Facebook Twitter. Five Easy Ways to Insert the Square Root Symbol in MS Excel. Add a SQUARE Root Symbol by Applying Custom Formatting. Try it. The mathematical square root symbol is called radical. Basically got the iPad for note taking and other things. You can also copy the symbol and paste it again for subsequent uses. Since the iPhone/iPad keyboard does not have the ability to input the squared symbol, you'll need to install a third-party keyboard like Gboard to get the job done. #2. Press 2, 5 and 3 on the alpha-numeric part of your keyboard while you are holding the Alt key. That's what I do. To type the square root symbol on ypur keyboard press and hold alt and type 251. Under Equation Tools, on the Design tab, in the Structures group, click the Script button. Hold down ALT and key in 0178 and let go of ALT. Choose the one that you require. If you have a Mac computer, its procedure is different. (note: you must use the number pad to type 251 and not the number buttons above the letters on your keyboard) Unfortunately, some laptop computers do not have a number pad. Under Equation Tools, on the Design tab, in the Symbols group, click the More button: In the list of symbols choose: 4.4. [goldberg s note] pat seemingly precise. You can insert a square root symbol in Excel using only your keyboard, without any additional steps. You need to hold down the Alt key as you type 251 on the numeric keypad. in some word processors, you can type in 221A and then press the [Alt] and X buttons at the same time which will convert the 221A into the square root symbol. In some cases, there is no special keypad, and it may not be obvious how you should type a math symbol. If you want to be able to type â , just copy and paste the symbol. ... a. use Tools->Customize Keyboard, select Category Insert, find InsertEquation in the list of commands, and assign a new keystroke (e.g. When A 2= B then A is the square root of B indicated as âB = A. Alt Code Shortcut for Square Root Symbol. Square root symbol on Mac. Square root symbol on keyboard on a dell. You can sometimes get the square root symbol by holding down alt and pressing 2 then 5 then 1 (or alt + 251). Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Here's the breakdown on how to enter some common math symbols: Multiplication . â (that square root sign is from pressing alt + 251) To make it on Windows itâs, Alt+23CD. This tool is very convenient to help you preview the symbol, including viewing the details of the symbol display and the effect displayed on the web page. #Ms_word #square_rootFor typing square root In MS Word 20161. Go to Equation, it is in the Symbols section, at the end3. To do this, press and hold the Alt key whilst pressing the Squared Alt code (i.e. This will open the other options for this key on the keyboard. I found reference to exactly the symbol you describe on an AutoCAD forum from 2002 that mentioned itâs Unicode character U+23CD. Because of these associations, when you press buttons on your keyboard, you get some corresponding text and things happening. For example to take the square root of 25, you would enter sqrt(25). For example, â4 = 2. Like getting some text typed in, etc. Select the font "symbol" and then click on the square root symbol. square root symbol: The square root symbol ( ) is used to indicate the quantity or quantities which, when multiplied by itself or themselves, results in the quantity encompassed by the symbol. That's not working for me any more. However that source clearly shows a square with a tick mark thru the top, so not exactly what youâre looking for. 1st Method =UNICHAR(8730) gives the square root symbol in Microsoft Excel. Root Symbol Preview Variations. Click on Insert from the top menu2. Many times when you place your mouse in the answer box you will see another "window" that will pop up that will allow you to click on the radical sign. Square root or principal square root symbol â does not have 2 on the root. Use keyboard shortcuts. 4.3. Even though this Symbol has no dedicated key on the keyboard, you can still type it on the keyboard with the Alt code method. Source(s): write type symbol square root computer keyboard: https://biturl.im/DL1fp. Square Root (Symbol/sign/mark) Preview and HTML-code. Using Symbol Utility or Character Map. This will open Symbol utility, Step 1: Click at the point in the document where you want to add the symbol. If you needed 'cubed' then type 0179 and you'll get a superscript 3. To insert a square root (a radical), you can click on the "â" button next to "A B C" on the Desmos keyboard. In this case, while holding down the Alt key, press 251 to add a square root.. These analysis my symbol the type i how do square root on keyboard of engineering systems consult sustainablefuture, here s the deal closes. However itâs not a very common symbol in most fonts. After you press the necessary numbers, release all the keys, and the "squared 2" symbol should appear in the text area, portrayed as "²". For example, if you enter: \sqrt. Using the Squared Symbol Alt Code (Windows Only) The Squared Symbol alt code is 0178. Open any Office application and go to âInsert > Symbolsâ menu. There is no single Square root button on a keyboard. Below is the Alt code keyboard shortcut for inserting the squared symbol.If you are new to ALT codes and need detailed instructions on how to use them, please read How to Use ALT Codes to Enter Special Characters.. For the the complete list of the ASCII based Windows ALT Codes, refer to Windows ALT Codes for Special Characters & Symbols. For example, 3 times 4 is "3*4." The square root symbol is visible right away. This wikiHow will teach you how to type a squared symbol (²) on a keyboard on a Windows PC, Mac, Android, iPhone, or iPad. Now Option-V pauses, allowing me to accent the next character with a Ë. You can also use a Cube symbol by long-pressing the number 3. how do you make a square root symbol on the keypad? Alt Code. Many thanks, and once you release the Alt key, and the symbol appears. 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format: plain


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# Fermat Equation (noch nicht übersetzt)

Problem 753

Fermat's Last Theorem states that no three positive integers $a$, $b$, $c$ satisfy the equation $$a^n+b^n=c^n$$ for any integer value of $n$ greater than 2.

For this problem we are only considering the case $n=3$. For certain values of $p$, it is possible to solve the congruence equation: $$a^3+b^3 \equiv c^3 \pmod{p}$$

For a prime $p$, we define $F(p)$ as the number of integer solutions to this equation for $1 \le a,b,c < p$.

You are given $F(5) = 12$ and $F(7) = 0$.

Find the sum of $F(p)$ over all primes $p$ less than $6\,000\,000$.


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# Chapter 4 Institutional Analysis of Healthcare Systems in Selected Developed Countries

Author:
Julian Smółka
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## Abstract

The aim of this chapter is to search for common institutional traits that improve the efficiency of healthcare systems in developed countries. The study joins the broad discussion on the topic of limiting costs and accelerating effects of healthcare systems. An extensive review of the literature and statistical sources is used to create the institutional framework for healthcare systems in the United States, the United Kingdom, Germany, Sweden, Singapore, and Poland – developed countries selected for differences in socio-economic conditions of health care as well as diverse models of capitalism. Based on the characteristics specified during research, a comparative analysis of institutional traits was performed. This allowed the identification of similarities that improve the efficiency of healthcare systems in developed countries (as measured by the provision of satisfactory services at acceptable levels of cost). The institutional traits and patient navigation within the healthcare systems of Singapore and Sweden appear to be most effective in increasing system efficiency. Other selected features from the remaining countries were also brought up. Wide implementation of the presented institutional traits may help reduce the burden of health care costs while maintaining high quality services.

## 1 Introduction

The World Health Organization defines the health system as all the activities whose primary purpose is to promote, restore and maintain health (WHO, 2000, p. 5). However, this broad definition is not applicable when studying and comparing the systems of individual countries; hence, this chapter deals with the healthcare system, meaning one providing medical care, as it is also understood in everyday language (Libura et al., 2018, p. 11).

The primary goal of the healthcare system is to ensure an appropriate scope and level of health services that the state provides guided by concern for public health. This is because health is not only an individual value, but it also constitutes a social resource that guarantees the long-term development of a community (Frączkiewicz-Wronka, 2009).

Demographic and epidemiological changes, as well as technological progress, pose new challenges to the healthcare system. An aging population, rising costs of chronic disease management, and expectations of access to new medical technologies also give rise to pressure for increased funding and better quality of services, to which the state, with its limited resources in the face of unlimited needs, must somehow respond (Libura et al., 2018, p. 7). The following chapter was born out of the question of what that response should look like.

There is no doubt about what a healthcare system should be: accessible, cost-effective, and enabling the use of modern therapies and treatments. However, there is no consensus on what a system that achieves all these expected components should exactly look like. The aim of this chapter is an institutional analysis of healthcare systems in six selected developed countries in order to point out the advantages and disadvantages of the solutions found in each of them and, on this basis, formulate conclusions about the best practices in shaping health care.

For the purposes of this analysis, the selected countries are overviewed in terms of specific socio-economic input and output measures, while characterizing their healthcare systems. Then, by comparing the parameters of each system, an attempt is made to compare them and select the best replicable elements.

This article claims that that the institutional analysis of individual countries will show that the most effective healthcare traits include its public nature (Basu et al., 2012), with decentralized decision-making based on centrally defined processes (James et al., 2019), a central patient registry for knowledge management and extensive research (Gliklich, Dreyer, & Leavy, 2014), and elements of competition between different institutions (Barros et al., 2016) with an extensive ecosystem of cooperation. Digitalization is also believed to be an additional element which plays an increasingly important role.

## 2 Theoretical Overview

For a complete analysis of healthcare systems, it is necessary to understand the models on which they are based, as well as their historical, cultural, and social conditions.

### 2.1 Theoretical Healthcare Models and Their Historical Context

The literature usually distinguishes four models of healthcare. Three of them, although their roots go back as far as the 19th century, still represent an ideal/typical model for contemporary solutions (Beveridge, Bismarck, and residual), and the fourth, although strictly historical in nature (Semashko), is still a source of inspiration for decision-makers in shaping health care (Suchecka, 2010, p. 46). Some sources also mention separately the National Health Insurance Model, which is a combination of the Beveridge and Bismarck models, but due to the lack of independent elements distinguishing them from the other models, it is not the subject of analysis here (Chung, 2017).

The Bismarck Model (public contract model), was the first universal healthcare model. Introduced in 1883 by Reich Chancellor Otto von Bismarck, revolutionary in its nature, it established compulsory health insurance (Łagowski, 2012, pp. 82–83).

The Beveridge Model (public integrated model) was introduced in the United Kingdom in 1948 based on William Beveridge’s report “Social Insurance and Allied Services” (Beveridge, 1942). It combines elements of universal health coverage with a public guarantee of access to health care. Underlying the system is the belief that health is a human right (Chung, 2017).

The residual model (a private insurance provider, mixed system) is based on private health insurance and is market-based. The majority of entities involved in the system operate on for-profit basis – the model provides for domination of the private sector. In most cases, the costs of services are covered by insurance institutions; if there is no insurance, the patient has to cover the costs. This rule does not apply to certain categories of people (e.g. disabled persons and veterans) who are covered by public programs (Białynicki-Birula, 2010, p. 4). The only developed country in which such a system exists today is the United States.

The Semashko model (central planning model – historical) of primary healthcare was introduced as a result of the October Revolution of 1917 in the Soviet Union. It was based on five-year plans of the central apparatus responsible for coordinating all system activities, starting with financing, creating and managing infrastructure, and training medical personnel (Libura et al., 2018, p. 13). From the 1950, Semashko’s model began to be implemented in different versions in other countries, mainly under the rule of “people’s power”.

The abovementioned model solutions are not used nowadays in their pure form in any developed country, which is a result of continuous social and cultural changes, as well as an ongoing reform of healthcare systems around the world, as if in response to the pressure mentioned in the introduction to this chapter.

### 2.2 Contemporary Models of Healthcare

The models presented in Section 2.1 are predecessors to the contemporary ones and much has changed in the study of health systems since their inception. It has been shown that health plays an important role in the creation of the welfare state, and this role has been steadily increasing for many years. This was the view of renowned Danish sociologist Gøsta Esping-Andersen – author of the most famous classification of welfare states presented in his book “The Three Worlds of Welfare Capitalism” (1990). His work became the basis for numerous subsequent studies on the empirical classification of healthcare systems. In 2000, to emphasize the role played by health in the welfare state, Michael Moran (Moran, 2000) proposed the term “health-care state”, which was supposed to show its inherent connection with the “welfare state”. He also analyzed the direction in which healthcare systems are changing and proposed a new classification of them into four “families”:

• entrenched command and control states,

• supply states,

• corporatist states,

• insecure command and control states.

The name of the first “command and control” family is taken from the work of Saltman and von Otter (1992). Moran calls it “entrenched” because in the family of states considered here (which includes Scandinavia and the United Kingdom) the institutions of command and control are well established. The state plays a dominant role on both the “production” and “consumption” sides. It holds a vast majority of the means of production are in its hands. Decisions are made by democratically elected decision-makers at national (UK), state and regional (Sweden, Denmark, Norway), or national and municipal (Finland) levels. The state uses its power to manage resources through the tax system and allocates the resources raised through administrative mechanisms. The only area in which the state has relatively little involvement is the technology sector, which, however, is strongly supported by the regulatory and institutional framework.

The “supply states” family actually consists of one country – the United States. The source of this system is quite easy to reconstruct. An extensive private system arose naturally so quickly and its structures became so stagnant that by the time the foundations of modern healthcare systems were being laid in Europe, it was already difficult to change anything in the States. In the early stages, before Medicaid and Medicare, the state focused on financing the construction of hospitals and on research activities. This contributed to the emergence of the best scientific community in the world, but the rampant costs of the system make medical care extremely far from universal.

The corporatist system, of which Germany is the best example, relies on a relatively minor role of the state, which is limited to providing a public legal framework, while real decisions largely fall within the remit of corporations, which dominate the medical technology sector, or physicians’ associations, which own the real decision-making process in matters of outpatient care, for example. However, there is growing public pressure to change this, and action is being taken to do so, so one can conclude that if the German model of such system is changing, it is possible that similar systems will also be displaced.

The family of “insecure command and control systems” is a recent creation. It consists of four remarkably similar Mediterranean countries: Portugal, Italy, Greece, and Spain. Their healthcare systems are based on the same foundations as those of the “entrenched command and control” family and were modeled on them. In none of the countries, however, have the systems been rooted in the Northern European model. In all of the “insecure” systems, despite the existence of a formal set of citizenship-based health entitlements, there is in fact no universal health coverage. In Portugal and Greece, the system has never succeeded in crowding out the large private insurance sector. In Italy, fiscal pressures have significantly weakened the universal system to the point where co-payments (which are marginal in most European systems) have become the largest single source of funding for the system. Despite formal guarantees of public health care, many services continue to be offered privately. This also applies to the most problematic group in this regard, namely physicians, who in large part run private practices. This is largely due to a distinct culture that is not entirely characterized by Weberian administrative rationality (Moran, 2000, pp. 138–158).

Little seems to have changed in this area since 2000, when Moran proposed his classification, and his observations and diagnoses remain valid. The reader will be able to see some of this in the next part of this chapter.

## 3 Characteristics of Selected Countries and Healthcare Systems

For the purposes of this chapter, the analysis has been narrowed down to six selected developed countries. This is due primarily to the desire to maintain the clarity of the argument, as well as the article word count limit. By adopting the assumed differentiation criteria, the comparison can reflect the global situation of the healthcare systems in developed countries and allows the determination of the directions in which they should move to achieve the highest degree of efficiency.

Based on a review of theoretical and contemporary models of healthcare systems, discussed in the first part of the chapter, an attempt has been to select countries so as to best reflect the totality of their diversity. Guided primarily by the criteria of the healthcare system in place, the expenditures it incurs and its effectiveness, the following countries have been selected on the basis of my own analysis:

1. United States of America

2. United Kingdom

3. Singapore

4. Germany

5. Sweden

6. Poland

As part of the discussion on the individual countries selected for analysis, the categorized criteria related to the healthcare system have been compiled and compared. The measures and data analyzed and compared are presented in Table 4.2.

### 3.1 United States of America

The healthcare system in the US is an example of a residual healthcare financing model. Private financing plays a key role in the structure of the US healthcare system. The system is among the most expensive as well as the most complex in the world (Lewandowski, 2010, p. 64). Healthcare is the most regulated sector in the US (Owoc et al., 2009), which translates into extraordinarily high administrative costs, estimated to be as high as 30% of total health care costs (Cutler, 2018, p. 2) – twice as much as is spent on heart disease treatment and three times as much as on cancer treatment (Cutler, Wikler, & Basch, 2012, p. 1876).

In 2018, 90.6% of the US population had some form of insurance coverage; the number of uninsured was 30.7 million (CMS, 2019b). However, it is important to keep in mind that even among the insured, in many cases the amount of insurance is insufficient to cover major health expenses.

In 2017, US health care spending grew 4.6%, reaching $3.6 trillion ($11,172 per capita) in 2018. The increase was 0.4 percentage points faster than in the previous year and more than double the average growth rate of 1.9% per year between 2000 and 2017. Health spending as a share of GDP was at 17.7%, falling by 0.2 p.p. y-o-y.

The share of health spending in total budget expenditures was 22.6% in 2017, as much as 6.4 p.p. higher than in 2000. This shows how large and growing a burden the healthcare system is on the US budget.

The US spends the most on hospital treatment, on which as much as every third dollar is spent. A large share is also spent on specialist services (20%), as well as funds allocated to drugs, on which the US spends the most in the world in absolute terms (Statista, 2019).

The healthcare system in the US is one of the most expensive and inefficient in the world (Kumar, Ghildayal, & Shah, 2011, p. 366). The country is notable for having shorter life expectancy, a higher suicide rate, and more than twice the rate of obesity and long-term disease burden relative to the OECD average (Tikkanen & Abrams, 2020).

US residents are among the most dissatisfied with their healthcare system among developed countries in the world. An IPSOS survey from late 2019 shows that 30% are satisfied with the current system, 25% are neither satisfied nor dissatisfied, and as many as 43% express dissatisfaction (IPSOS, 2020).

### 3.2 United Kingdom

The UK healthcare system based on the Beveridge model consists de facto of four separate healthcare systems: National Health Service in England, Health, Social Services and Public Safety in Northern Ireland, NHS Scotland, and NHS Wales.

In each of the UK countries, the NHS has its own distinct structure and organization. The system consists of two broad parts: one dealing with strategy, policy and management, and the other with actual medical care, which is divided in turn into primary (community care, GPs, dentists, pharmacists, etc.), secondary (hospital care available by GP referral), and tertiary (specialist hospitals). The distinction between these two parts has become clearer over the years (Grosios, Gahan, & Burbidge, 2010, p. 529).

The UK government sets the total budget for the NHS in England, which includes subsidies for the other three countries, where their legislatures determine how much of that subsidy can be spent on healthcare (Tunstall, 2016).

In 2018, healthcare spending in the UK was £214.4 billion, equating to £3,227 spent per person. This spending represents 10% of the UK’s GDP in 2018 and its share of GDP increased by 0.2 p.p. from the previous year, which was due to healthcare spending growing faster than GDP. Between 1997 and 2018, health spending grew at a nominal annual rate of 5.8%.

The Department of Health and Social Care (DHSC) is the main funder of healthcare in the UK. For 2019/20, the largest part of its budget, £121 billion, was allocated to the NHS in England, with the remaining £17 billion split between other DHSC agencies and programs.

The healthcare system in the UK is considered relatively efficient, achieving average health outcomes with moderate expenditure. Depending on the set of selected indicators, it ranks either slightly above or slightly below the average efficiency among developed countries. The challenges identified earlier create pressure for increased investment and further reforms to maintain current performance (Papanicolas et al., 2019, p. 11). The strengths of the UK’s institutional healthcare ecosystem include a highly developed clinical research sector, in which the UK is one of the global leaders.

It is worth noting that a majority of UK residents (51%) believe the NHS wastes resources, with only 7% believing it never does. 37% believe that, in general, the UK health system does not waste resources (Gershlick, Charlesworth, & Taylor, 2015, p. 18). In another survey, 69% cited the creation of the NHS in 1948 as the greatest British achievement in history (Duncan & Jowit, 2018).

The NHS faces a number of financial and demand challenges, largely as a consequence of a growing and ageing population, and the rising cost of new drugs and treatments. This primarily translates into greater strain on hospitals and longer waiting times for tests and treatment (Powell, 2020, p. 11). Interestingly, awareness of the worsening situation is not widespread. In a 2015 survey, 43% of respondents agreed that the situation in the healthcare system had not changed significantly over the past 5 years, and improvement and deterioration were indicated by almost equal portions of the population – 26% of the respondents diagnosed the situation as better and much better, 28% as worse and much worse (Gershlick, Charlesworth, & Taylor, 2015, p. 13).

A vast majority of UK respondents agree with the current formula of the health system as being tax-funded, free at the point of use, and providing comprehensive medical care for all citizens (Gershlick, Charlesworth, & Taylor, 2015, p. 10). This translates into high rankings in satisfaction – the UK is ranked 4th in the world with 53% of residents satisfied with the current form of the system, 24% neither satisfied nor dissatisfied and 22% dissatisfied (IPSOS, 2020).

### 3.3 Singapore

Singapore’s healthcare system is one of a mixed type, in which the organizing role is assigned to the government, but the state’s main safety net program, MediShield Life, only covers large bills for inpatient care and some outpatient procedures. Supplementing MediShield Life are government subsidies, as well as a mandatory medical savings account called MediSave, which can help residents pay for inpatient care and selected outpatient services. In addition, individuals can purchase additional private health insurance or obtain it through their employer.

A central tenet of Singapore’s healthcare system is the belief that all stakeholders share responsibility for achieving sustainable and universal health insurance coverage. Singapore’s healthcare framework is multi-layered, where a single procedure may be captured in several systems and have several payers, often overlapping. The overall system, commonly referred to as the 3Ms, is based on three programs:

• MediShield Life: a mandatory health insurance program for citizens and permanent residents that provides lifetime medical care and coverage for high-cost hospital stays and selected outpatient procedures.

• MediSave: a medical savings program to help cover out-of-pocket payments. Contributions to MediSave are mandatory for all citizens and permanent residents in the amount of 8.5–10% of salary depending on age. The individual accounts in which the premiums are held are tax-free and interest-bearing, and the funds in them can only be used to pay for the health care expenses of the insured and their family.

• MediFund: a government fund to cover medical expenses for poor residents whose medical costs are not covered by the funds accumulated in their MediSave accounts.

Singapore is among the countries that spend the least on the health system. In 2017, it was only 4.44% of GDP, which is the highest historical result, preceded by 7 years of a continuous growth in expenditure. In per capita terms, the result is no longer so low, but it is still not high – in 2017, it was $4,270 measured in purchasing power parity. The mixed structure of the health system also translates into the fact that the share of health spending in total budget expenditure is also extremely low. It was only 12.6% in 2017, albeit this share had almost doubled since 2000. In overall health spending, the share of public spending is also extremely low, accounting for only a third of the total. The remainder consists of spending from private savings, funded by private insurance or charities (Lim, 2017, p. 103). Singapore’s healthcare system is considered one of the most efficient in the world, achieving remarkable health outcomes and treatment efficacy at half the cost of any comparable country (Ramesh & Bali, 2019, pp. 42–45). In Singapore, the national healthcare system is highly regarded, which is reflected in high satisfaction scores in surveys. As many as 60% of residents are satisfied with their healthcare system, 22% are neither satisfied nor dissatisfied, and only 18% are dissatisfied in some form. This gives Singapore a second place ranking for satisfaction with its healthcare system (IPSOS, 2020). This result is particularly interesting when compared with the results of a 2012 survey in which 72% of Singaporeans indicated that they “cannot afford to get sick due to high medical costs” (Lim, 2017, p. 103). ### 3.4 Germany The German healthcare system is based on the Bismarck model and was the world’s first universal health insurance system. Two years after the program was introduced, in 1885, it covered 10% of the population. Over time, the coverage rate of the population increased. Currently, state insurance, which provides coverage for inpatient, outpatient, mental health care and prescription drugs, covers approx. 86% of the population. Individuals earning more than$68,000 per year can opt out of state health insurance premiums in favor of private insurance – which is then not subsidized in any way (Tikkanen et al., 2020a).

The German healthcare system is complex, and responsibility for it is distributed across different levels of government. Decision-making competencies are traditionally divided between the federal and state levels, with many powers delegated to local government bodies. Health insurance is mandatory for all citizens and permanent residents in the form of either statutory or private insurance (Busse & Blümel, 2014, p. 18). The administration and financing of the healthcare system is handled by regional health insurance funds. The delegation of responsibilities to local authorities ensures better informed decisions adapted to local circumstances but also contributes to a fragmented system structure with a plurality of payers and providers (OECD/European Observatory on Health Systems and Policies, 2019a, p. 22).

Germany boasts the highest rate of hospital beds per capita in the European Union. However, due to the impressive number of more than 3,000 hospitals, services are provided in many small and often under-equipped facilities, resulting in reduced quality. There is political awareness of the problem and discussions are in progress on changes to move towards increasing the degree of centralization of care and specialization of hospitals (European Commission, 2019).

The primary spending institution in the German healthcare system is a network of health insurance funds financed through general wage contributions (14.6% of salary) and a special additional contribution (averaging 1% of salary) shared between employers and employees. Co-payment mechanisms are an additional source of funding, but these are limited to 28 days of co-payment for inpatient care per year and to 2% of household income (1% for the chronically ill). Persons under 18 years of age are excluded from co-payment mechanisms. Individuals earning more than €62,550 per year can opt out of universal insurance in favor of private insurance. However, this is not subsidized in any way from public funds (Tikkanen et al., 2020a).

The share of healthcare expenditure in total budget expenditure in Germany has remained at a similar relatively high level for more than 20 years, with only a relatively small increase from 17.2% in 2000 to 19.9% recorded in 2017. A similarly small increase is seen in the share of health expenditure in GDP from 9.9% at the beginning of the first decade of the 20th century to 11.2% in 2017. (World Bank, 2020a). Per capita spending has more than doubled over that time from $2,687 to$5,923 (World Bank, 2020b), putting Germany in second place in Europe (OECD/European Observatory on Health Systems and Policies, 2019a, p. 10).

The German healthcare system is considered to be moderately effective, given its high expenditures and significant human and infrastructural resources. The costs of the healthcare system in Germany do not fully translate into health outcomes. Elements for improvement include reducing avoidable hospital admissions that generate high costs without translating into health outcomes (OECD/European Observatory on Health Systems and Policies, 2019a, p. 14).

Germany is around the middle of the ranking among all countries surveyed in terms of satisfaction with its healthcare system. 39% are satisfied with its current design, a third are neither satisfied nor dissatisfied, and 26% express dissatisfaction (IPSOS, 2020).

### 3.5 Sweden

The Swedish healthcare system is universal, and coverage is automatic. The organizational structure is highly decentralized and has three levels:

1. the national level, where the Ministry of Health and Social Policy is responsible for shaping health policy and allocating resources among government agencies and the country’s regions;

2. the regional level, where 21 regional bodies are responsible for financing and delivering health services;

3. the local level, where 290 local government bodies are responsible for elderly and disability care (Tikkanen et al., 2020b).

Local and regional authorities at the national level are represented by the Swedish Association of Local Authorities and Regions (SALAR).

The decentralization of the Swedish healthcare system contributes to regional differences in access to care and outcomes across regions, which is contrary to the goal of equality of access to health care in Sweden. In an effort to change this situation, additional funding has been introduced in recent years to reduce these disparities and to improve access in rural areas (European Commission, 2019, p. 82).

With universal medical insurance covering 100% of the population, private insurance is not very popular, with only 6% of the population using it. However, this proportion is increasing due to faster access to private than public services. For the most part, private insurance is covered by employers.

Sweden has the third highest health care expenditure in Europe. Swedes spend 11% of their GDP, including 18.7% of their national budget, on health care. Per capita, this amounts to $5,699 annually. Public spending accounts for 84% of total health care spending. The remaining expenditure consists of 15% private out-of-pocket payments and 1% private medical insurance (OECD/European Observatory on Health Systems and Policies, 2019, pp. 16–17). The average health care expenditure is less than 2% of the household budget (Borg and Sixten, 2019, p. 30). The Swedish healthcare system is considered to be one of the best in the world in terms of organization. Despite high costs, efforts to minimize hospital treatment in favor of primary care are appreciated. The high scores on health outcomes of the health system, however, do not seem to be appreciated by the residents themselves, who are moderately satisfied with their system. Only 34% say they are satisfied with its design, 30% are neither satisfied nor dissatisfied, and another 34% would like to see a change (IPSOS, 2020). ### 3.6 Poland The main payer in the Polish healthcare system is the National Health Fund, financed partly by health contributions and partly by a dedicated budget subsidy. In Poland, 91% of the population is covered by mandatory health insurance, and most of the uninsured are those living abroad but registered as residents in the country. The genuinely uninsured make up a negligible proportion and are mainly those employed under casual or atypical employment contracts and informally employed (OECD and European Observatory on Health Systems and Policies, 2019). Of the countries analyzed, Poland is by far the poorest, which is reflected in the underfunding of the healthcare system. Three basic public sources of funding can be distinguished: 1. health contribution, 2. specific budgetary subsidy, 3. expenditures of local governments. Only persons paying the contribution are covered by insurance. The health insurance contribution amounts to 9% of the salary (contribution base) (Pietryka, 2018, pp. 233–235), and it accounted for 57.6% of the total revenue of the healthcare system in 2017 (Statistics Poland, 2019, p. 114). Despite the constant increase in spending on the health system, Poland spends very little on health compared to countries with a similar level of development, only 6.5% of GDP, in which the share of public spending is about 70% (4.4% of GDP) (Tambor, 2018). The share of health care financing in total budget expenditure is well below the European average and accounts for only 10.9%. In per capita terms, the amounts look even worse, as they amount to only$1,958 per citizen per year (World Bank, 2020a, 2020b).

In overall spending, the National Health Insurance Fund functions as the main payer, accounting for 85% of total public spending on health in 2018. The central government budget financed 11% of expenditures, and local and regional authorities (LRAs) financed 4%. Among the LRAs, cities with county rights spent the most, as they covered almost 1/3 of the total health expenditures at the local and regional government level (Statistics Poland, 2019, p. 119).

The Polish healthcare system is considered moderately effective. In recent years, however, improvements have been noticeable and the current direction of development seems to be increasing the effectiveness of the system, although primarily in organizational and economic terms. This is mainly due to the progressing digitalization; however, much still remains to be done in this area as well.

Among the problems facing the Polish healthcare system, the Polish Supreme Chamber of Control mentions the following:

• lack of a target vision for the system and a health policy strategy,

• uneven distribution of medical entities, inadequate to the health needs of the population,

• limited coordination of activities between particular participants of the healthcare system,

• lack of an adequate number of staff,

• decapitalization of assets, failure to meet current standards for buildings and equipment (NIK, 2019, pp. 24–140).

The issues of underfunding of the healthcare system and lack of adequate staff are widely recognized as the most important of these.

Poland is one of the countries whose inhabitants are among the most dissatisfied with their healthcare system. Only 13% are satisfied with its current shape, 13% are neither satisfied nor dissatisfied, and as many as 74% are dissatisfied (IPSOS, 2020).

## 4 Comparative Analysis of Healthcare Systems of Selected Countries

The comprehensive analysis of healthcare systems in six developed countries selected in this chapter is the basis for comparing and contrasting them, which allows conclusions to be drawn on the effectiveness of individual systems and solutions applied in them.

### 4.1 Previous Comparative Analyses

Before comparing the countries, it is worth starting with a presentation of existing quantitative summaries classifying healthcare systems and their effectiveness. Five most significant rankings developed by leading institutions have been selected as presented in Table 4.3.

Research on the efficiency and effectiveness of healthcare systems was pioneered by the World Health Organization, which launched a global discussion in this area with the publication of its ranking of systems in 2000 (WHO, 2000). It analyzed 191 countries and ranked them according to eight indicators.

Since 2005, a Swedish think-tank, the Health Consumer Powerhouse, has been publishing its own ranking as a supplement to existing evaluations, with the first edition analyzing health systems in 12 major European economies, expanded to 34 in the 2018 edition (Björnberg & Phang, 2019). The ranking itself (coupled with a comprehensive report discussing its findings), is meant to distinguish itself from others in that it takes a different perspective – it tries to rank countries by the user-friendliness of the system, and analyzes more outcome indicators than any other of the selections discussed here (Health Consumer Powerhouse, 2005).

The institutions that analyze country performance also include two leading publications – The Economist and Bloomberg. The analytical department of the first one – The Economist Intelligence Unit (2014) took a look at healthcare systems in 166 countries, dividing them into six tiers. Countries were ranked in terms of population health outcomes, which consisted of indicators including DALYs (disability-adjusted life years), HALE (health-adjusted life expectancy), life expectancy at age 60, and adult mortality, composed in such a way that the scores range from 0 to 100, where a higher score indicates better health outcomes. The countries were also ranked by their per capita health spending and the cost per outcome point.

In its ranking, Bloomberg chose to consider only countries where life expectancy exceeds 70 years, GDP per capita is greater than \$5,000, and population exceeds 5 million. There were 56 such countries. The design of the ranking itself was much simpler than the others analyzed, because it only took into account life expectancy at birth and the share of health spending in GDP (Miller & Lu, 2018). It is this oversimplification that is the biggest drawback of the Health Care Efficiency Index. Life expectancy is influenced by many other factors in addition to health system expenditures, and without taking them into account, we really still know little about the actual efficiency of the systems compared in the ranking.

The last of the selected rankings is the one developed by The Commonwealth Fund. Prepared by the American foundation in 2017, the analysis covers only 11 high-income countries (Schneider et al., 2017) and its goal is to present the best global solutions in order to find the optimal one for the US. Its results differ significantly from other rankings mentioned. The Commonwealth Fund considers quality, accessibility, value for money and equity of health care as the most important criteria. These criteria are defined by the sets of indicators chosen to determine them. With its emphasis on accessibility and per capita spending, the US was ranked just last, despite its above-average performance in health prevention, patient-centered care and innovation. The United Kingdom came in first, while performing worse in many indicators.

These examples of rankings, all produced by reputable organizations and institutions, and the differences in the performance of health systems from different countries, show how difficult it is to compare them with each other. Due to the lack of accepted standards in this area, methodological assumptions of the authors have a very high impact on the final results for individual countries. This is also indicated by the editors of The Economist (2014) in their commentary on The Commonwealth Fund’s report. The above issues must be kept in mind both when trying to compare countries and when using and interpreting existing rankings.

The rankings that come closest to each other in terms of country performance are certainly those of the WHO (2000) and The Economist Intelligence Unit (2014). The rankings that differ most from the others are those of Bloomberg (Miller & Wei, 2018) and EHCI (Björnberg & Phang, 2018), due to the uniqueness of the criteria adopted.

The US scored best in the WHO ranking, in which it was recognized for high innovation of the system and good strictly medical effects (in this case they do not translate into population health). It fared the worst in The Commonwealth ranking, which, as The Economist (2014) points out, is partly the result of a very unfavorable selection of indicators for the US. The main reason for the worse performance in the rankings than the economic position and size of inputs would indicate is the extreme disproportionality of inputs to medical outcomes. This was most evident in the Bloomberg ranking, in which the US ranked third from last.

The UK ranked first in The Commonwealth Fund’s ranking, which was meticulously noted by British journals (Duncan & Jowit, 2018). In other rankings, however, the UK performs worse. Just like the United States, the country scored worst in the Bloomberg ranking, allowing itself to be overtaken by 60% of the analyzed countries. It did not do much better in the EHCI ranking, where it was rated very low for the accessibility of the healthcare system, understood as waiting time for treatment.

Singapore, although included in only three of the analyzed rankings, took one of the highest positions in all of them. One of the world’s longest life expectancies combined with low spending on health care could not have produced a different result. In The Economist’s ranking, in which Singapore ranked second, the Lion City achieved the largest positive discrepancy between health outcomes and inputs.

Germany, like the US and the UK, scored the worst in the Bloomberg ranking, coming in at number 45. Relatively speaking, it ranked highest in the EHCI ranking, which recognized a strong emphasis on the patient work system and access to information, short waiting times in most cases analyzed, and good treatment outcomes.

Sweden ranked first or second in all of the rankings among the six countries analyzed. Sweden ranked highest in the EHCI, gaining approval for most indicators. Sweden is the only country in the EHCI to score maximum points in the accessibility of health care services category. In the Bloomberg ranking, Sweden is ranked 22nd, and in The Economist it is in the top 10.

Poland was by far the worst performer in all the rankings except Bloomberg, which placed it just two positions behind Sweden, thanks to its decent health outcomes for low investment. Poland was ranked fourth from last in the EHCI, ahead of only Albania, Romania, and Hungary. The availability of services for patients was rated lowest, but cardiological care and its effects were distinguished.

### 4.2 Objectives and Methodology of Efficiency Analysis: Sources of Inefficiency

The goal of measuring, reporting, and comparing health care outcomes is to achieve the triple aim of health care:

• improve population health,

• increase the quality of individual care,

• reduce costs per person (Czerska, Trojanowska, & Korpak, 2019, p. 206).

These goals were proposed by Berwick, Nolan, and Whittington (2008) for the US and gained rapid popularity, and are nowadays also expanded to include a fourth goal: reducing staff burnout (Bodenheimer & Sinsky, 2014). Achieving the so-called Quadruple Aim is not easy and requires a highly effective organization of the healthcare system (Sikka, Morath, & Leape, 2015, p. 608).

A study published in 2009 analyzing available methods for measuring performance in health care identified 265 different indicators used in all kinds of peer-reviewed texts in the US alone (Hussey et al., 2009, pp. 789–790). From the methodological side, two basic types of comparisons can be distinguished:

• economic evaluation: consists of comparing individual components of the healthcare system in terms of their costs and benefits,

• benchmarking: compares individual health care service providers (countries, institutions) with regional or global best practices.

Based on the above methods, Section 4.4 seeks to compare the developed countries discussed in this chapter, indicating the best solutions and directions in which the healthcare systems should be reformed.

However, before comparing healthcare systems looking for sources of efficiency, it is worth considering the sources of inefficiency themselves. The OECD (2017) identifies three categories of these:

• resource-wasting clinical care,

• operational waste,

• managerial waste.

Resource-wasting clinical care refers to patients who do not receive appropriate treatment. This includes both preventable medical events resulting from errors, suboptimal decisions, and organizational factors, as well as inefficient and inappropriate low-value care caused primarily by poor staff motivation. Resource-wasting clinical care also includes unnecessary duplication of services.

Operational waste occurs when medical care could be delivered with fewer resources within the system while maintaining benefits. Examples include purchasing resources at higher prices than can be obtained, or using more expensive resources without additional patient benefit. Also falling into this category are unused resources. Operational waste most often involves individuals at managerial levels and reflects poor organization and poor coordination of processes in the healthcare system.

Managerial waste includes losses that are not directly related to patient care and take place in the process of administration and management of the healthcare system. It involves administrative waste (e.g., inefficient use of human resources in administration, excessive bureaucracy) and misuse of resources through fraud, abuse, and corruption (Expert Group on Health System Performance Assessment, 2019, p. 11).

All of the above-discussed examples of inefficiencies in the health system contribute to why the cost of maintaining it is so high. The lack of optimization in each of the areas also contributes to further increases.

### 4.3 Determinants of Efficiency

The healthcare systems analyzed in this chapter are extremely diverse. They differ in their inputs, organization, and outcomes. However, there is no one simple and universal solution (Helgesson & Winberg, 2009; Keller, 2017), which would allow an effective system to be constructed under any conditions, eliminating the identified sources of inefficiency. However, it is possible, on the basis of the extensive analysis made, to indicate the directions in which country-specific solutions should be sought, as well as the factors that should be taken into account when formulating such recommendations.

The factors affecting the efficiency of the healthcare system can be divided into three categories:

• input,

• political-institutional,

• cultural and social.

They are discussed in detail in the following subsections.

#### 4.3.1 Input Factors

Input factors are the most obvious category. Research clearly shows a clear positive relationship between health care inputs and outcomes such as life expectancy or infant survival. The relationship is evident around the world, regardless of the level of economic development, ranging from South Africa (Bein et al., 2017), through various developed countries, and even for individual health programs in the United Kingdom (Martin, Rice, & Smith, 2009, p. 46). However, the role of inputs alone should not be overstated. A meta-regression study published in 2017, using 65 studies published between 1969 and 2014 in this area, indicates that other factors, such as income, demographic structure, and lifestyle choices of the population, for example, also play a large role (and collectively possibly even a larger role). These were included here under the category of cultural and social factors. The study also argues that higher expenditures have a much greater effect on decreasing infant mortality than on life expectancy (Gallet & Doucouliagos, 2017), which is especially important to consider when making recommendations for developed countries, where additional expenditures might not produce the desired effect and scale.

#### 4.3.2 Political-Institutional Factors

Arguably, the second category should include political and institutional factors together. It is particularly important to combine them, because despite a certain institutional resistance, which is the effect of change-resistant institutional mechanisms and habits of people creating an institution, the latter directly result from the former. As research confirms, the policies pursued by the ruling party have a direct impact on the performance of the healthcare system. Policies aimed at leveling the playing field and redistributing income fare best in this comparison in terms of health outcomes, such as infant survival, and liberal policies fare worst (Navarro et al., 2006). Also important in this context is the evidence of a positive relationship between public and private sector efficiency and the impact of government capacity and organizational effectiveness on health system performance. This is influenced by factors such as the type of patient who goes to the private sector, the level of education of the health workforce, and the regulation and organization of the health system shaped by the development of the public sector (Morgan, Ensor, & Waters, 2016).

#### 4.3.3 Cultural and Social Factors

Cultural and social factors also have a significant influence on the effectiveness of the healthcare system, although this influence may not be as obvious as the amount of money spent or the political decisions and efficiency of institutions. Cultural and social factors largely determine political and organizational behavior, as well as the propensity to support the allocation of public resources to healthcare. Perceptions of healthcare systems and satisfaction with them, as well as perceptions of corruption, also depend on cultural and social factors. They also influence the extent to which resources are wasted and even public perceptions of waste. For example, in the UK, Conservative and UKIP voters are 20% more likely, relative to the Liberal Democrats, to say that the NHS wastes money (Gershlick, Charlesworth, & Taylor, 2015).

### 4.4 Comparison of Healthcare Systems in the Countries Analyzed

Among the analyzed countries, the US has the highest share of health expenditures in GDP (17.1% of GDP in 2017), surpassing second-ranked Germany by more than 50% (6.9 p.p.). Sweden ranks next, just behind Germany, with spending at 11% of GDP. The UK spent 9,6% in 2017. Less was spent by Poland (6.5% of GDP) and Singapore, which, with 4.4% of GDP, is one of the lowest spenders among developed countries.

The US, despite a theoretically private healthcare system, also has the largest share of health spending in total budget expenditures among developed countries. Germany is again in second place, with the UK and Sweden spending almost the same proportion of their budgets. In this category, however, it is not Singapore that is the least spender, as Poland spends as much as 1.6 p.p. less than it.

Satisfaction with medical care is a commonly used indicator in assessing the quality of treatment, and thus indirectly also makes its way into rankings of healthcare systems. Of the six analyzed in this respect, Singapore was the best, with 60% of its residents satisfied with its healthcare system. The worst performer in this respect was Poland, where almost three quarters of the population were dissatisfied with the national health system. Surprisingly low satisfaction scores were also achieved by Germany and Sweden. This can only be explained by cultural factors determining the level of patient expectations, which are much higher in Poland, Sweden, and Germany.

### 4.5 Conclusions and Recommendations

Taking into account the possible influence of the above-mentioned factors and based on the proven solutions from the analyzed developed countries, a universal set of recommendations is proposed that should be taken into account in the design and development of healthcare systems. Each of the proposed solutions will bring benefits to the system, but only when implemented together can they give the expected results. Relevant recommendations are presented in the following 4 subsections.

#### 4.5.1 Data and Analytics

Healthcare systems provide huge amounts of data, most of which is not managed at all (Raghupathi & Raghupathi, 2014). The use of big data in the US raises the possibility of reducing public spending on health care by 8% (through operational efficiencies) and for private insurers to increase operating margins by up to 60% (Manyika et al., 2011, p. 2). Through predictive models, it also provides opportunities to improve countries’ health outcomes. Sweden is a good example in the data management domain (Chipman, 2019, p. 5).

Data and analytics should also be used in revamping governance structures, which are suggested in the next section. A systematic and integrated evaluation of the different sectors and a study of their performance will allow a better understanding of the processes taking place and thus make it possible to redesign them more effectively.

#### 4.5.2 Reorganizing Management Structures

In order to stop further cost increases, a reorganization of the management structures of healthcare systems is necessary in many respects. The aim of such a reform would be to decentralize the system towards the Swedish model, where much of the decision-making has been transferred to local government. In Sweden, this translated into a better, more adequate and tailored spending of available resources. In order to avoid creating differences in access to medical care in particular regions, it would also be necessary, following the example of the latest Swedish solutions, to introduce additional subsidies for less wealthy and rural regions. In this area, priorities should also include a reduction in the number of hospital admissions in favor of better primary care, which, according to numerous sources, would contribute to reducing the costs of the healthcare system.

#### 4.5.3 Coordinated Care

As with the management structure, the treatment process itself needs to change in most countries. Chronic diseases account for an increasing share of all diseases worldwide (Institute for Health Metrics and Evaluation, 2017) – this generates costs and forces the search for new solutions. The direction that seems to be inevitable is coordinated care (Battersby, 2005, p. 662), which in its ideal form – at the sixth level – provides the patient with treatment and ensures an excellent flow of information between the physicians treating the patient. Although its implementation initially requires additional expenditures, in an amount that is difficult to estimate, its translation into health outcomes is expected to compensate for this and, in the long run, also bring savings to the system (Schrijvers, 2017, pp. 27–40). It is important to keep in mind that this has not always been the case when trying to implement coordinated care. In some cases, neither cost reductions nor improved outcomes or even satisfaction have followed.

The most important non-financial effects of implementing coordinated care include:

• the possibility of greater physician specialization, due to better case allocation by the coordinator,

• better use of human resources (doctors and nurses), by reducing the number of medical consultations in favor of nursing whenever possible,

• patient involvement in the treatment process, through direct and continuous communication between the patient and the coordinator (Consensus Health, 2019, p. 4).

#### 4.5.4 Co-payments for Medical Services

Co-payments in medical care are a debatable issue in terms of recommendations for healthcare systems, but their introduction is believed to be necessary. However, it is important to properly adjust this solution to the conditions in the country concerned. Singapore shows how to do this effectively and fairly, without losing the satisfaction of patients. When implementing such a solution, it is necessary to take into account the possibilities for individual financing of services, so that no one is excluded from access to medical services.

Comprehensive implementation of the presented solutions would arguably be of greatly help to developed countries in coping with the problem of high and growing costs of healthcare, using the best of the systems presented in this chapter.

In relation to the theses put forward in this article, it was not possible to prove the universal impact of coopetition on the effectiveness of the healthcare system. Although the solutions used in Singapore contribute to system efficiency, they are not replicable in other analyzed countries due to significant differences in area and population.

Developing countries should also draw extensively on the presented solutions, but always bearing in mind that the changes should be nuanced to the extent that they fit the culture and institutional order of the country concerned.

## References

• Barros, P. P. et al. (2016). Competition among health care providers: helpful or harmful? European Journal of Health Economics, 17(3), 229233. doi: 10.1007/s10198-10015-0736-0733.

• Export Citation
• Basu, S. et al. (2012). Comparative performance of private and public healthcare systems in low- and middle-income countries: A systematic review. PLoS Medicine, 9(6), doi: 10.1371/journal.pmed.1001244.

• Export Citation
• Battersby, M. W. (2005). Health reform through coordinated care: SA HealthPlus. British Medical Journal, 330(7492), 662665. doi: 10.1136/bmj.330.7492.662.

• Export Citation
• Bein, M. A. et al. (2017). Healthcare spending and health outcomes: Evidence from selected East African countries. African Health Sciences, 17(1), 247254. doi: 10.4314/ahs.v17i1.30.

• Export Citation
• Berwick, D. M., Nolan, T. W., & Whittington, J. (2008). The triple aim: Care, health, and cost. Health Affairs, 27(3), 759769. doi: 10.1377/hlthaff.27.3.759.

• Export Citation
• Beveridge, W. (1942). Social insurance and allied services. Report by Sir William Beveridge. Her Majesty’s Stationery Office.

• Białynicki-Birula, P. (2010). Wielowymiarowe porównania systemów zdrowotnych w krajach OECD w kontekście realizowanych modeli ochrony zdrowia. Prace Naukowe UE we Wrocławiu, PN Finanse Publiczne 112, 115.

• Export Citation
• Björnberg, A., & Phang, A. Y. (2019). Euro Health Consumer Index 2018 Report, Euro Health Consumer Index.

• Bodenheimer, T., & Sinsky, C. (2014). From Triple to Quadruple Aim: Care of the Patient. Annals of Family Medicine, 12(6), 573576. doi: 10.1370/afm.1713.Center.

• Export Citation
• Borg, A. H., & Sixten, G. (2019). Can people afford to pay for health care? New evidence on financial protection in Sweden. World Health Organization.

• Export Citation
• Chipman, A. (2019). Value-based healthcare in Sweden. Reaching the next level. The Economist Intelligence Unit. https://impact.economist.com/perspectives/VBHCSweden.

• Export Citation
• Chung, M. (2017) Health Care Reform: Learning from other major health care systems. https://pphr.princeton.edu/2017/12/02/unhealthy-health-care-a-cursory-overview-of-major-health-care-systems/.

• Export Citation
• Consensus Health (2019). Coordinated Care: Key to Successful Outcomes. Marlton. https://www.continuumhealth.net/coordinated-care-key-successful-outcomes/.

• Export Citation
• Cutler, D. (2018) Reducing Health Care Costs: Decreasing Administrative Spending [Testimony for US Senate Committee on Health, Education, Labor and Pensions]. https://www.help.senate.gov/imo/media/doc/Cutler.pdf.

• Export Citation
• Cutler, D., Wikler, E., & Basch, P. (2012). Reducing Administrative Costs and Improving the Health Care System. New England Journal of Medicine, 367(20), 18751878. doi: 10.1056/NEJMp1209711.

• Export Citation
• Czerska, I., Trojanowska, A., & Korpak, T. (2019). Przyszłość opieki zdrowotnej w Polsce – nowe horyzonty. E-Wydawnictwo. Prawnicza i Ekonomiczna Biblioteka Cyfrowa. Wydział Prawa, Administracji i Ekonomii Uniwersytetu Wrocławskiego, 153, 197214. doi: 10.34616/23.19.120.

• Export Citation
• Duncan, P., & Jowit, J. (2018). Is the NHS the world’s best healthcare system? The Guardian. Retrieved September 18, 2020, from https://www.theguardian.com/society/2018/jul/02/is-the-nhs-the-worlds-best-healthcare-system.

• Export Citation
• Esping-Andersen, G. (1990). The Three Worlds of Welfare Capitalism. Polity Press.

• European Commission. (2019). State of Health in the EU. Companion Report 2019. Publications Office of the European Union. doi: 10.2875/71887.

• Export Citation
• Expert Group on Health System Performance Assessment (2019). Tools and methodologies to assess the efficiency of health care services in Europe. Publications Office of the European Union. doi: 10.2875/77000.

• Export Citation
• Frączkiewicz-Wronka, A. (2009). Zarządzanie publiczne w teorii i praktyce ochrony zdrowia. Wolters Kluwer Polska.

• Gallet, C. A., & Doucouliagos, H. (2017). The impact of healthcare spending on health outcomes: A meta-regression analysis. Social Science and Medicine, 179, 917. doi: 10.1016/j.socscimed.2017.02.024.

• Export Citation
• Gershlick, B., Charlesworth, A., & Taylor, E. (2015). Public attitudes to the NHS: An analysis of responses to questions in the British Social Attitudes Survey. The Health Foundation. http://www.health.org.uk/sites/default/files/PublicAttitudesToTheNHS.pdf.

• Export Citation
• Gliklich, R., Dreyer, N., & Leavy, M. (2014). Registries for evaluating patient outcomes: A user’s guide: 3rd edition. Agency for Healthcare Research and Quality. https://effectivehealthcare.ahrq.gov/products/registries-guide-3rd-edition/research.

• Export Citation
• Grosios, K., Gahan, P. B., & Burbidge, J. (2010). Overview of healthcare in the UK. EPMA Journal, 1(4), 529534. doi: 10.1007/s13167-010-0050-1.

• Export Citation
• Health Consumer Powerhouse (2005). 2005 EuroHealth Consumer Index, Health Consumer Powerhouse.

• Helgesson, C.-F., & Winberg, H. (2009). Debate on future healthcare must go beyond easy solutions and answers. In H. Winberg, J. Rognes, & C.-F. Helgesson (Eds.). Leading Health Care – Organizing healthcare for greater value (pp. 151155). Stockholm School of Economics.

• Export Citation
• Hussey, P. S. et al. (2009). A systematic review of health care efficiency measures: Health care efficiency. Health Services Research, 44(3), 784805. doi: 10.1111/j.1475-6773.2008.00942.x.

• Export Citation
• Institute for Health Metrics and Evaluation (2017). Global Burden of Disease Study 2017. The Lancet, 2017(Gbd), 17.

• IPSOS. (2020). Percentage of respondents worldwide who were satisfied with their country’s national health system as of 2019, by country. Statista. Retrieved August 27, 2020, from https://www.statista.com/statistics/1109036/satisfaction-health-system-worldwide-by-country/.

• Export Citation
• James, C. et al. (2019). Decentralisation in the health sector and responsibilities across levels of government: Impact on spending decisions and the budget. OECD Journal on Budgeting, 19(3). doi: 10.1787/c2c2058c-en.

• Export Citation
• Keller, R. (2017). Health Care: A Universal Problem Without a Universal Solution, Stratfor. Retrieved September 18, 2020 from https://worldview.stratfor.com/article/health-care-universal-problem-without-universal-solution.

• Export Citation
• Kumar, S., Ghildayal, N. S., & Shah, R. N. (2011). Examining quality and efficiency of the U.S. healthcare system. Int J Health Care Qual Assur, 24(5), 366388. doi: 10.1108/09526861111139197.

• Export Citation
• Łagowski, P. (2012). Wybrane modele finansowania systemu opieki zdrowotnej. Studenckie Prace Prawnicze, Administratywistyczne i Ekonomiczne, 12, 8194.

• Export Citation
• Lewandowski, R. (2010). Modele systemów opieki zdrowotnej na świecie. In M. Kautsch, (Ed.) Zarządzanie w opiece zdrowotnej: Nowe wyzwania (pp. 5866). Wolters Kluwer Polska.

• Export Citation
• Libura, M. et al. (2018). Finansowanie i organizacja systemu ochrony zdrowia w oczach pacjentów. Fundacja MY Pacjenci. https://mypacjenci.org/wp-content/uploads/2018/08/Finansowanie-i-organizacja-systemu-ochrony-zdrowia-w-oczach-pacjentw.pdf.

• Export Citation
• Lim, J. (2017). Sustainable Health Care Financing: The Singapore experience. Global Policy, 8(March), 103109. doi: 10.1111/1758-5899.12247.

• Export Citation
• Manyika, J. et al. (2011). Big data: The next frontier for innovation, competition and productivity. McKinsey Global Institute. https://www.mckinsey.com/business-functions/mckinsey-digital/our-insights/big-data-the-next-frontier-for-innovation.

• Export Citation
• Martin, S., Rice, N., & Smith, P. (2009). The link between health care spending and health outcomes for the new English primary care trusts. The Health Foundation.

• Export Citation
• Miller, L. J., & Wei, L. (2018). These are the economies with the most (and least) efficient health care. Bloomberg, Retrieved August, 22, 2020, from https://www.bloomberg.com/news/articles/2018-09-19/u-s-near-bottom-of-health-index-hong-kong-and-singapore-at-top.

• Export Citation
• Moran, M. (2000). Understanding the Welfare State: The Case of Health Care. The British Journal of Politics and International Relations, 2(2), 135160. doi: 10.1111/1467-1856x.00031.

• Export Citation
• Morgan, R., Ensor, T., & Waters, H. (2016). Performance of private sector health care: implications for universal health coverage. Lancet, 388(10044), 606612. doi: 10.1016/S0140-6736(16)00343-00343.

• Export Citation
• Navarro, V. et al. (2006). Politics and health outcomes. Lancet, 368(9540), 10331037. doi: 10.1016/S0140-6736(06)69341-69340.

• OECD/European Observatory on Health Systems and Policies. (2019). Sweden: Country Health Profile 2019, State of Health in the EU. OECD Publishing. https://doi.org/10.1787/2dcb7ca6-en.

• OECD. (2017). Tackling Wasteful Spending on Health. Highlights. Tackling Wasteful Spending on Health. OECD Publishing. doi: 10.1787/9789264266414-en.

• Export Citation
• OECD and European Observatory on Health Systems and Policies. (2019). State of Health in the EU. Polska: Profil systemu ochrony zdrowia 2019. OECD Publishing. https://ec.europa.eu/health/sites/default/files/state/docs/2019_chp_poland_polish.pdf.

• Owoc, A. et al. (2009). System ochrony zdrowia w Stanach Zjednoczonych. Probl Hig Epidemio, 90(3), 403406.

• Papanicolas, I. et al. (2019). Performance of UK National Health Service compared with other high income countries: Observational study, The BMJ, 367, 112. doi: 10.1136/bmj.l6326.

• Export Citation
• Pietryka, E. (2018). Finansowanie systemu opieki zdrowotnej w Polsce w kontekście wprowadzenia systemu sieci szpitali. Journal of Management and Finance, 16(3/1), 229244.

• Export Citation
• Powell, T. (2020). The structure of the NHS in England. Briefing paper CPB 07206, doi: https://researchbriefings.files.parliament.uk/documents/CBP-7206/CBP-7206.pdf.

• Export Citation
• Raghupathi, W., & Raghupathi, V. (2014). Big data analytics in healthcare: promise and potential, Health Information Science and Systems, 2(3), 110. doi:10.1186/2047-2501-2502-3.

• Export Citation
• Ramesh, M., & Bali, A. S. (2019). The remarkable healthcare performance in Singapore. In M. E. Compton & P. T. Hart, (Eds.) Great policy successes: Or, a tale about why it’s amazing that governments get so little credit for their many everyday and extraordinary achievements as told by sympathetic observers who seek to create space for a less relentlessly negative view of our pivotal public institutions (pp. 4262) Oxford University Press. doi: 10.1093/oso/9780198843719.003.0003.

• Export Citation
• Saltman, R. B., & Otter, C. von (1992). Planned markets and public competition. Strategic reform in Northern European health systems. Open University Press. https://doi.org/10.1177/000169939303600205.

• Schneider E. C., Sarnak D. O., Squires D., Shah A., Doty, M. M. (2017). Mirror, Mirror 2017: International Comparison Reflects Flaws and Opportunities for Better U.S. Health Care. The Commonwealth Fund.

• Export Citation
• Schrijvers, G. (2017). Opieka koordynowana. Lepiej i taniej. Narodowy Fundusz Zdrowia.

• Sikka, R., Morath, J. M., & Leape, L. (2015). The quadruple aim: Care, health, cost and meaning in work, BMJ Quality and Safety, 24(10), 608610. doi: 10.1136/bmjqs -2015-004160.

• Export Citation
• Statista (2019). Pharmaceutical spending per capita in selected countries as of 2018. Retrieved August 23, 2020, from https://www.statista.com/statistics/266141/pharmaceutical-spending-per-capita-in-selected-countries/.

• Export Citation
• Statistics Poland (2019) Zdrowie i ochrona zdrowia w 2018 r. Retrieved March 11, 2022, from https://stat.gov.pl/obszary-tematyczne/zdrowie/zdrowie/zdrowie-i-ochrona-zdrowia-w-2018-roku,1,9.html.

• Export Citation
• Suchecka, J. (2010). Ekonomia zdrowia i opieki zdrowotnej. Wolters Kluwer Polska.

• Tambor, M. (2018). Ile i z jakich źródeł wydajemy na zdrowie w Polsce? Instytut Zdrowia Publicznego Wydziału Nauk o Zdrowiu Collegium Medicum Uniwersytetu Jagiellońskiego. Retrieved September 18, 2020, from https://izp.wnz.cm.uj.edu.pl/pl/blog/ile-i-z-jakich-zrodel-wydajemy-na-zdrowie-w-polsce/#.

• Export Citation
• The Economist (2014). How to compare health-care systems. Retrieved September 13, 2020, from https://www.economist.com/the-economist-explains/2014/06/29/how-to-compare-health-care-systems.

• Export Citation
• The Economist Intelligence Unit (2014). Health outcomes and cost: A 166-country comparison, The Economist. Retrieved March 11, 2022, from http://stateofreform.com/wp-content/uploads/2015/11/Healthcare-outcomes-index-2014.pdf.

• Export Citation
• Tikkanen, R. et al. (2020a). International health care system profiles: Germany. The Commonwealth Fund. Retrieved August 24, 2020, from https://www.commonwealthfund.org/international-health-policy-center/countries/germany.

• Export Citation
• Tikkanen, R. et al. (2020b). International health care system profiles: Sweden. The Commonwealth Fund. Retrieved September 10, 2020, from https://www.commonwealthfund.org/international-health-policy-center/countries/sweden.

• Export Citation
• Tikkanen, R., Abrams, M. K. (2020). U.S. health care from a global perspective, 2019: Higher spending, worse outcomes? The Commonwealth Fund. Retrieved September 9, 2020, from https://www.commonwealthfund.org/publications/issue-briefs/2020/jan/us-health-care-global-perspective-2019.

• Export Citation
• Tunstall, L. (2016). The UK health care system. Evidence Network. Retrieved August 18, 2020, from https://evidencenetwork.ca/the-uk-health-care-system/.

• Export Citation
• WHO. (2000). The World Health Report 2000. World Health Organization.

• WHO. (2007). Everybody’s business. Strengthening health systems to improve health outcomes. World Health Organization.

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