How Much Health Do we get in Return for Health Spending?

I

How Much Health do we get in Return for Health Spending?

A Case Study Using Stroke as an Example

Martin Andreas Furu

Supervisor: Hans Olav Melberg

Master Thesis submitted as a part of the European Master in Health Economics and Management

Faculty of Medicine

Department of Health Management and Economics UNIVERSITY OF OSLO

June 2016

II

How Much Health Do we get in Return for Health Spending?

-A Case Study Using Stroke as an Example

III

© Martin Andreas Furu 2016

How Much Health do we get in Return for Health Spending?

Martin Andreas Furu http://www.duo.uio.no/

Trykk: Reprosentralen, Universitetet i Oslo

IV

Abstract

Background Prioritization is a critical factor in the healthcare sector, and it is critical that prioritization be based on relevant criteria which facilitate the comparison of different interventions and health measures. When deciding whether or not to implement new interventions, typically projections of increased costs are weighed against expected benefits of the interventions. This comparison allows the calculation of quality adjusted life year gains, also known as a QALY, as well as the comparison of the new intervention to existing measures or other new interventions, through the current cost per QALY, or through the incremental cost per QALY of additional intervention.

Method This thesis is a case study of resource spending on patients recovering from stroke, using length of stay as a resource indicator and 30-day survival rate as health outcome. We compare all health enterprises and their differences in both length of stay and 30-day survival rate to determine whether there are any indications of correlation. We seek to answer the question of what the possible health effects would be of increasing length of stay by one day.

To measure this, a simple equation was made to help measure the cost of an incremental QALY.

Incremental cost

per QALY = Incremental cost (Δc)

= Cost of increasing one LOS Incremental benefit (Δb) Δp*Δy*Δq

In this equation Δp is the increased probability in 30 day survival rate, Δy is the expected life years by surviving a stroke, Δq is the quality of life a stroke survivor has after the stroke.

Results A linear regression model of a five year weighted average indicated a correlation of 0.18% increase in 30 day survival rate by increasing length of stay by one extra day for all Health Enterprises, resulting in a QALY of 372,802 NOK (the simulation yielded a 95%

confidence interval of [232,208 - 656,220]). Other relevant linear regressions also yielded similar results with different significance. The results also indicated a negative correlation between increasing length of stay and 30 day readmittance rate. While more research would be needed to reach a definitive conclusion, as other factors not taken into account here could possibly affect length of stay or 30 day survival rate, this research indicates that increasing length of stay by a single day could yield a larger benefit than other measures which demand more resources as measured by incremental cost per QALY.

V

Acknowledgements

Working with this thesis has been challenging and I have learned a great deal in the process of completing it. I certainly would never have been able to do this all on my own, and there are some people that deserve a big thank you for helping me throughout the process. I would like to thank my supervisor Hans Olav Melberg for his support and sharing of knowledge on the topic. Thank you Jeremy Banzhaf for taking your time to proofread this thesis, I am grateful. I would also hand out an extended thank you to friends and family for being there for me. I would not have been here without you. A big thank you to all my colleagues for fruitful discussions in this and other topics, for being helpful in times of struggle, and for being the social relief needed to keep up the long work of doing this thesis.

VI

Table of Contents

1 Introduction ... 1

2 Theoretical background ... 4

3 Methods ... 7

4 Description of data ... 10

4.1 Assumptions ... 15

4.1.1 Cost of Increasing Length of Stay ... 15

4.1.2 Average Age of Stroke Occurrence ... 16

4.1.3 Life Expectancy After Stroke ... 16

4.1.4 Quality of Life After Stroke ... 18

5 Results ... 19

5.1 Calculation ... 19

5.2 Data ... 22

5.2.1 Linear trend ... 23

5.2.2 Polynomial trend in the second degree ... 25

5.3 Regression analysis... 28

5.3.1 Single Year Regressions ... 29

5.3.2 Weighted Regressions ... 31

5.3.3 Regression Using Year as a Dummy Variable ... 32

5.4 Simulation ... 33

5.5 Length of Stay and Readmittance ... 35

5.6 Length of Stay and Complicating Diseases ... 37

6 Discussion ... 38

6.1 Summary of Results... 38

6.2 Length of Stay and Readmittance ... 39

6.3 Comparability Between Years ... 40

6.4 Comparability Between Health Enterprises ... 41

6.5 Coordination Reform and QBF ... 43

6.6 Limitations ... 44

6.7 Prioritization and Future Research ... 45

References ... 48

Appendix ... 50

Amount of DRG 14A and DRG 14B by Year ... 51

VII

Average Length of Stay DRG 14A and DRG 14B (days) ... 52

Average 30 day Survival Rate for Each Health Enterprise (%) ... 53

Average LOS DRG 14A and DRG 14B (67+) & Amount of DRG 14A and DRG 14B (67+) ... 54

Weighted Shares DRG 14A and DRG 14B (67+) (%) and Yearly Weight 2013-2014 ... 55

Probability of Readmittance of Elderly (67 +), Admitted for Stroke Within 30 Days After Discharge (%) ... 58

DRG 14A to DRG 14B Yearly Weight 2010 - 2014 ... 59

Yearly Weights Based on Activity 2010 - 2014 ... 60

Trend Charts ... 61

Regression Models ... 63

VIII

List of Tables and Figures

Figure 1: Hierarchy of the Norwegian health care structure...7

Figure 2: Example weighing DRG 14A and DRG 14B ... 8

Figure 3: Example of HE weighted LOS based on 14A-14B ratio ... 8

Figure 4: Table of the Health Enterprises used in this study ... 12

Figure 5: example of weighting between DRG 14A and DRG 14B ... 12

Figure 6: Example of yearly weighing for DRG 14A and DRG 14B ... 13

Figure 7: Example of how survival rate is weighted into a five year average ... 13

Figure 8: Distribution of Health Enterprises within survival ranges ... 14

Figure 9: Price municipalities pay not accepting patients ready for discharge ... 15

Figure 10: Age distribution for stroke occurrence ... 16

Figure 11: Key variables ... 20

Figure 12: Linear trend chart ... 23

Figure 13: Results from linear trend ... 24

Figure 14: Polynomial trend chart ... 25

Figure 15: Results from polynomial trend ... 27

Figure 16: Regression models ... 28

Figure 17: Data for simulation ... 33

Figure 18: Cost/Gain scatter plot 1000 simulations ... 33

Figure 19: Willingness to pay table 1000 simulations ... 34

Figure 20: Scatter plot chart Probability of readmittance and Length of stay ... 35

Figure 21: Regression model re-admittance and Length of Stay ... 35

Figure 22: Scatterplot LOS and percentage of complicating procedures ... 37

List of abbreviations

ABF Activity Based Financing (Innsatsstyrt Finansiering) DRG Diagnosis Related Groups

HE Health Enterprises (Helseforetak)

ISF see: ABF

LOS Length of Stay

NOK Norwegian Currency Krone QALE Quality Adjusted Life Expectancy QALY Quality Adjusted Life Years PEV Polynomial expected value

RHE Regional Health Enterprise (Regionalt helseforetak)

UH University Hospital

1

1 Introduction

In recent years there have been discussions about prioritization and where to spend resources.

In a society facing higher constraints the need is getting stronger for streamlining and increased efficiency, and we need to investigate the return on investment in health care spending. The question we face is how much we spend treating diseases. In an article by Ottersen (Ottersen, T et al. 2016) this topic was covered in depth. There is a need for priority setting in Norway, and Ottersen discusses the new framework for priority setting in Norway.

This framework has four general principles. The first principle sets the goal of “the greatest number of healthy life years for all, fairly distributed”. The second principle is that the prioritization should be based on clear criteria, third that the prioritization should be open, systematic, involve user participation, and the fourth that the prioritization should be supported by a coherent set of effective instruments (ibid).

The article states three criteria: that prioritization should be based on the expected health benefit of an intervention; resource usage, and loss of health. The first criterion means that the expected health benefit determines the level of priority of an intervention. The second criterion states that the fewer resources the intervention needs the higher priority the intervention will have. For the third, it states that the higher health loss a patient will suffer without the intervention, the higher the priority (ibid).

This is an important topic especially when resources are scarce, and it becomes necessary to question and prioritize existing thresholds. With a limited budget, one cannot introduce a new intervention without excluding an existing intervention, even if the existing intervention meets extant thresholds.

This naturally has a strong influence on prioritization. After this framework was published in 2014, there were discussions in the media about expensive cancer treatments, palliative treatments, and the introduction of new, expensive drugs often with limited research into health benefits. The resources for introducing such treatments and drugs have to be justified through research of their efficacy. There is also a question about prioritization, since the health care budget is both finite and scarce. The goal therefore has to be to spend the resources in a way that is fair, and seeks to maximize overall health outcomes. In relation to this, this thesis investigates whether an increase in resource spending would lead to a better

2

health outcome, and if this spending yields better value compared to other medical interventions. Because of limited time, this thesis will focus on stroke, a case study using all health enterprises in Norway. Stroke was chosen because it is highly relevant as one of the most deadly diseases in Norway, where in 2012 alone, 3116 people died after suffering from a stroke (FHI faktaark). The availability and quality was also an important factor in our decision to choose stroke as a focus of research. There is an abundance of available data for Norwegian HEs, both for data used as a variable to measure quality, and also for data used as a variable to measure resource spending.

Stroke is an acute disease that can have fatal consequences when not treated within a few hours after symptoms occur. About 16000 people every year suffer from stroke in Norway (LHL). The quality in treatment of strokes therefore relies on securing as high a survival probability as possible within a reasonable level of resource expenditure. The question of how much to spend on the treatment of stroke is relevant, but the decision should also be informed by the availability of newer measures to improve the quality to make sure that as many people as possible will survive after having had a stroke.

There are more people dying from stroke than from lung cancer or chronic obstructive lung disease. A stroke is the process wherein the brain suffers from reduced blood flow due to one of two causes dependent on the type of stroke. Ischemic stroke is a stroke where the blood flow in the blood vessel is reduced due to a blockage or a blood clot, resulting in death in the brain cells. The other type of stroke is called hemorrhagic stroke and occurs when a blood vessel bursts and blood flows out in the brain instead of flowing to the parts of the brain supplied by the blood vessel. This leads to a lack of oxygen in parts of the brain, causing the brain tissue to take, if not treated in time, irreversible damage (FHI hjerneslag). This thesis investigates if differences in resource spending through length of stay can be a factor for differences in health outcomes in terms of 30 day mortality.

The reason why the 30 day mortality statistics is considered the most relevant is that stroke most commonly affects the elderly, who often have other diseases or health risks. Examples of this are high blood pressure, diabetes, osteoporosis, dementia, and other factors, affecting their mortality in the longer term.

The need for efficient spending is highly relevant, and investigating potential cost-efficient areas of health care spending can provide health benefits for patients, savings in healthcare,

3 and guidelines for further prioritization. The occurrence of stroke is increasing in Norway, and therefore the need to improve survival rate is increasing in importance. Differences in the patient adjusted survival rate imply that there are factors affecting the differences in survival rates between different health enterprises. In this thesis we investigate one of the possible factors: differences in the length of stay. This thesis comes as a part of the question about how much should be spent on the treatment of stroke, compared to other diseases and treatments.

Different treatments yield differences in how much health value is achieved per NOK. When prioritizing between two or more treatments, it is important to know the yield, in a standardized, comparable unit. This thesis seeks to provide evidence and guidance for further research on the topic.

The research aim for this thesis is to find if there is a relationship between length of stay and survival rate. The data available has been gathered from public data sources. The results will yield the marginal cost per QALY for the increased health benefit.

The main hypothesis of this thesis is that differences in resource spending lead to differences in health outcomes. Resource spending is measured in length of stay for the DRGs including stroke, while health outcomes are measured in 30 day survival rate for stroke patients, and 30 day readmittance rate for stroke patients. The expectations are that a higher resource spending through length of stay will result in a higher 30 day survival. Other expectations are that longer lengths of stay will yield lower probabilities of 30 day readmittance.

This thesis will use these three datasets to see if resource spending through length of stay could be an explanatory factor for 30 day survival rate and probability of readmittance, and in that case, how much explanatory power it has.

4

2 Theoretical background

Available previous studies are very limited concerning case studies in spending and quality on a micro level. There are however studies on a higher level concerning general spending on diseases, but which do not consider where the resources are spent, simply assuming that those in charge will allocate the funds in such a way as to maximize health gains for the individuals concerned.

Most background theory is more extensive in studies compared to this, for example Martin (Martin, S. et al. 2008) addressed the lack of studies addressing whether “additional health expenditure yields patient benefits in the form of improved health outcomes”. They used spending of Primary Care Trusts and compared a development in the program budget introduced by the NHS in 2003, referencing ICD-10 codes, through chapters in ICD-10. As a variable of health outcomes, they used Standardized Mortality Ratio for the population under the age of 75, and as a variable of health care spending, estimated mean spending per category. (ibid)

They investigated circulatory diseases and cancer treatments. Their findings showed that there was a correlation: an increase of 1% in the per capita spending for cancer treatment, totaling

£0.751 per capita, was associated with 0.378% in life years lost, a reduction of 0.015 life years lost to cancer per person in the whole population. The implications lead to an estimation of the cost of 1 life year to total to £13,137 and to have a correlation coefficient of 0.304. The results for circulatory disease yielded a 1.4% reduction in life years lost, by increasing 1% in expenditure to circulatory diseases. Increased expenditure by £1.22 per person was related to a decrease of 0.056 days reduction in life loss. This means the cost of 1 life year was calculated to total to £7,979. The suggested cost per QALY saved were, within large confidence intervals, £11,960 for circulatory diseases and £19,070 for cancer. The paper still argues that within these confidence intervals, the yield of greater benefit outweighs the cost per QALY threshold of £30,000 set by NICE as acceptable for implementing new technologies (ibid).

Another study similar to Martin was conducted by Claxton (Claxton, K et al. 2015), which used two new datasets to estimate a link between mortality and spending within the NHS.

Their first dataset contained mortality rates for categories of diseases, at the Primary Care

5 Trust (PCT) level. The second dataset contains expenditure by the National Health Service.

Their model assumed that the primary care trusts receive a lump sum budget, which they then allocate to 23 categories or programs and try to maximize health outcomes within the programs. The study checks mortality in the 23 different funding programs, in the PCTs. One funding program is for example infectious diseases, another is cancers and tumors.

The model they used assumed that the PCTs allocated the funding so as to maximize health outcomes within the limits of the finances received. Their findings showed that the threshold in 2008 values for expenditure and 2008-2010 mortality £12,936 per QALY. They also conducted an uncertainty analysis, showing that the probability for the QALY threshold was less than £20,000 per QALY at 0.89, and less than £30,000 per QALY at 0.97 (ibid).

A similar study conducted in Canada by Cremieux (Cremieux et al. 1999) indicated a correlation between lower health care spending and an increase in infant mortality, and thus a decrease in life expectancy in Canada. The study conducted was based on data over a time span of 15 years and covered all the ten Canadian provinces. The study found this relationship independent of other factors, such as lifestyle or socio-demographic factors (ibid).

There are some significant differences between the study this thesis is conducting and the other studies, because the variable health care spending is not as specific as the case study used here. The other papers use health care spending in monetary terms, while this thesis focuses on health care spending for one specific disease through one specific resource post.

The data in this thesis is on a Health Enterprise level, with data from 60,000-200,000 people, much like the PCTs in England, but smaller than the study at the province level in Canada.

This thesis uses a single case study, focusing on stroke at the diagnosis level, with specific focus on varying resource usage. The other studies are not as detailed in the level of resource use, and only consider differences in actual spending, assuming that the PCTs are allocating their resources ideally. In comparison, this thesis looks at the differences in HE resource spending to see differences in health outcomes between different HEs, and to derive an estimation of health outcomes based on the prioritization of said resources. Another study on a more detailed level was done by Nixon (Nixon, J. and Ulmann, P. 2006); they investigated

“the relationship between health care expenditure and health outcomes”. They found that male life expectancy was significantly improved by increased health expenditure, increased number of physicians, improved nutrition, and lowered pollution (Nixon, J and Ulmann, P 2006). For

6

female life expectancy, increased health expenditure and increased number of physicians were significant determinants for health. From contributing factors to health outcomes, health expenditure accounts for of 3.53 % of male life expectancy coefficient equaling 2.6 years while for female it equals 3.46 % and 2.8 years (ibid). The paper investigates specific factors that may result in differences in health outcomes and are more similar to what this thesis is looking to explain.

7

3 Methods

This thesis seeks to determine whether variations in spending lead to variations in health outcomes, measured by 30 day survival rate and the probability of 30 day readmittance for stroke patients. The methodology is restricted to collecting data from available sources. The data has been collected from two different public providers, based on the same foundation.

The data collected is on a Health Enterprise level, seen in the figure below, showing the hierarchy. Each Health Enterprise has one or more hospitals underneath. For example, Sørlandet Sykehus Health Enterprise has three hospitals under its purvey: Clinics for Somatic Treatments in Kristiansand, Arendal, and Flekkefjord.

Figure 1: Hierarchy of the Norwegian health care structure

Data is collected at a Health Enterprise level because data from Health Enterprises are more concise, as hospitals may report data differently, and the best comparability would be at a level where all actors are equal.

To investigate the first hypothesis, some calculations needed to be made. The available data from ISF was calculated as the average LOS at DRG level from each Health Enterprise on a yearly basis and total number of procedures at DRG level from each Health Enterprise each year.

Department of Health Regional Health Enterprise

Health Enterprise Hospital Hospital

Regional Health Enterprise Health Enterprise

Hospital Hospital Hospital

Regional Health Enterprise Health Enterprise

Hospital

8

This study compares two datasets, and there are five years where the datasets coincide: 2010 – 2014. These five years are the only years available from the dataset involving health outcomes, while the data concerning resource spending also contained data from 2015.

The first data set was made available from the ISF cube. The data collected were average length of stay at DRG level and total number of treatments of stroke.

The stroke patients are divided into two DRGs. DRG 14A, and DRG 14B, with and without bi-diagnosis and/or complicating disease. The two DRGs are registered with different length of stay. Since 30 day mortality does not differentiate between these, the proportion between the two had to be calculated for a weighted average length of stay for each year. Below is an example of how to find the relationship between the two DRGs per year.

Total DRG 14 A 2010

Total DRG

14 B 2010 14 a % 2010 - Helse Møre og Romsdal HE 439 218 67 % Figure 2: Example weighing DRG 14A and DRG 14B

This means that the length of stay is weighted 67 % of the length of stay of DRG 14A and 33

% of DRG 14B.

To have a five year average of the different length of stays and 30 day survival rate, there was necessary to calculate the percentage of the accumulated relative DRGs for each Health Enterprise per year. By accumulating the number of DRG14A and 14B per year divided by the total accumulated amount of respectively DRG 14A and 14B in the five year period, we found the yearly weighted percentage that both the 30 day mortality and the length of stay would be based on. Under it is shown the average length of stay between DRG 14A and DRG 14B.

avg LOS 2010 14a

avg LOS 2010 14B

Weighted avg 2010

- Helse Møre og Romsdal HE 11.3 7.7 10.1 Figure 3: Example of HE weighted LOS based on 14A-14B ratio

To find the five year weighted average survival rate, the yearly proportion of DRG 14A and DRG 14B, is used to determine the weighted proportion of the yearly survival rate. The same procedure was used for the yearly weighted average length of stay data. These two data sets were then compared in a scatter plot chart, to check for a trend.

9 The number of procedures was also yearly weighted, so that the years with the most treatments had the highest proportion when estimating the five year weighted average. This will be used for averaging both the length of stay, and the 30 day survival rate.

To find the incremental cost per QALY the calculation is done as follows: incremental cost divided by incremental benefit. Incremental cost is defined as the cost of increasing one length of stay. Incremental benefit is defined as Δp*Δy*Δq whereas Δp is the incremental increase in 30 day mortality by increasing one length of stay, Δy is the life expectancy of a person having had a stroke. Δq is the average yearly QALY of a person who has had a stroke.

Incremental cost

per QALY = Incremental cost

= Cost of increasing one LOS

Incremental benefit Δp*Δy*Δq

In the “Økonomisk evaluering av helsetiltak – en veileder” IS-1985 from 2012, from the Directorate of Health, the reference value for economical evaluation in sector reaching public health measures using Cost Benefit Analysis, is set at 588 000 NOK (2012 value) for a statistical life year, or 1 QALY. By calculating using SSB’s change in consumer price index, it shows that 588 000 NOK in 2012 is worth 626 000 in 2015. If the calculation shows that the incremental cost per QALY is less than 626 000 NOK, this study can work as a possibility for further investigation of potential gains for stroke victims.

When investigating for a correlation between length of stay and readmittance probability, the same procedures were done, but with a two year weighted average for the readmittance probability and for length of stay, only including data from 67 years of age and older, through two weighted intervals, 67-79 and 80+, since the dataset on 30 day readmittance probability only contains data for patients 67 years of age and older. This yields a weighted two year average for both datasets which has then been compared through a regression and a scatter plot trend chart, and then analyzed.

10

4 Description of data

To conduct the research, three sets of data have been collected from two different sources.

The first set of data has been collected from the ASF cube through Cognos, and the other sets of data have been collected from helsenorge.no (Quality indicators).

The datasets from helsenorge.no were the 30 day survival rate after being admitted for stroke (Quality indicator 30 day survival after admittance for stroke) (see appendix), and the probability of being readmitted after being treated for stroke for elderly patients (Quality indicator Readmittance within 30 days for elderly patients after being treated for stroke) (see appendix). The 30 day survival rate after being admitted for stroke (abbreviated: 30 day survival rate) contained data for the years 2010 to 2014 on a hospital, Health Enterprise, and Regional Health Enterprise level. This thesis uses the data from the Health Enterprise level.

The Probability of being readmitted after being treated for stroke for elderly patients (abbreviated: Probability of readmittance) contained data for only two years, 2013 and 2014, on a hospital, Health Enterprise, and Regional Health Enterprise level. The data on a Health Enterprise level is used in this thesis.

The 30 day survival rate dataset measures risk adjusted survival, and is built upon “Inpatient Quality Indicators”. The method used is comparing actual deaths in a hospital to the national average. By risk adjusted, means that it has been adjusted for age, sex, diagnosis and condition on admission. This makes the data more comparable because the larger or specialized hospitals tend to receive the most difficult patients. Patient composition and transfer between hospitals has also been accounted for. The results show the probability of 30 day survival after the course of the hospital or the hospital stream has begun. (Quality indicator 30 day survival after admittance for stroke)

The method for calculating the Probability of readmittance dataset is a method based on one used by Sundhetsstyrelsen in Denmark (Quality indicator Readmittance within 30 days for elderly patients after being treated for stroke). Elderly patients are defined as patients at the age of 67 or older, and readmittance is defined as acute readmittance to a hospital, regardless of reason, between eight hours and 30 days after being discharged for stroke. The readmittance is also registered if the patient is admitted at another hospital than where they were treated for stroke. (ibid)

11 The second source containing data from the ABF cube (Cognos), the datasets concerning average length of stay for DRG 14A and DRG 14B 2010 - 2014(see appendix), average length of stay for DRG 14A and DRG 14B for patient aged 67-79 and 80+ 2013-2014 (see appendix), total number of procedures for DRG 14A and DRG 14B 2010-2014 (see appendix), total number of procedures for DRG 14A and DRG 14B for patients aged 67-79 and 80+ 2013-2014 (see appendix) were collected from this data cube.

The data in this data cube are the data included in the ABF arrangement from the Health Enterprises. The data is therefore excluding data that NPR, the Norwegian Patient Register, use, since their data also include other activity that is financed through projects and other types of funding.

The data collected from the ABF cube (Cognos) is:

2010 - 2014

Average length of stay per admission for DRG 14A Average length of stay per admission for DRG 14B

Total number of ABF stays (when more than 3) for DRG 14A Total number of ABF stays (when more than 3) for DRG 14B 2013 - 2014

Average length of stay per admission for DRG 14A for patients aged 67-79 Average length of stay per admission for DRG 14B for patients aged 67-79 Average length of stay per admission for DRG 14A for patients aged 80+

Average length of stay per admission for DRG 14B for patients aged 80+

Total number of ABF stays (when more than 3) for DRG 14A for patients aged 67-79 Total number of ABF stays (when more than 3) for DRG 14A for patients aged 80+

Total number of ABF stays (when more than 3) for DRG 14B for patients aged 67-79 Total number of ABF stays (when more than 3) for DRG 14B for patients aged 80+

The data from the two sources is gathered on the same level, on a Health Enterprise level. The datasets are gathered for the same population and in the same age groups as the corresponding dataset available from helsenorge.no. Data from all 19 public Health Enterprises in Norway were used, plus two ideal private Health Enterprises, Lovisenberg Diakonale and Diakonhjemmet sykehus. Below is a table of the Health Enterprises, and which Regional Health Enterprise they are under.

12

- Helse Nord RHE - Helse Sør-Øst RHE

- Finnmarkssykehuset HE - Akershus Universitetssykehus HE - Helgelandssykehuset HE - Diakonhjemmet sykehus AS - Nordlandssykehuset HE - Lovisenberg Diakonale - Universitetssykehuset Nord-Norge HE - Oslo Universitetssykehus HE

- Helse Vest RHE - Sykehuset i Telemark HE

- Helse Bergen HE - Sykehuset i Vestfold HE

- Helse Fonna HE - Sykehuset i Østfold HE

- Helse Førde HE - Sykehuset Innlandet HE

- Helse Stavanger HE - Sørlandet sykehus HE - Helse Midt-Norge RHE - Vestre Viken HE - Helse Møre og Romsdal HE

- Helse Nord-Trøndelag HE - St. Olavs Hospital HE

Figure 4: Table of the Health Enterprises used in this study

Since the dataset from helsenorge.no does not differentiate between stroke with and without complicating diseases and bi-diagnosis, the average length of stay had to be weighted based on the number of procedures at each Health Enterprise. The ratio between DRG 14A and DRG14B (see appendix) are calculated by:

DRG 14A ratio 2010 = total number of DRG 14A 2010 / total number of (DRG 14A + DRG 14B) also described as a weighted average between the two. Example:

DRG 14A Total DRG

14 A 2010

Total DRG

14 B 2010 14 a % 2010

- Helse Midt-Norge RHE 1 169 678 63 %

Figure 5: example of weighting between DRG 14A and DRG 14B

There was also a need to find yearly weights, to weigh the data differently depending on activity within both two and five year averages (see appendix). The calculations to find the yearly weights for two and five years respectively, were done based on the total number of procedures in the respective intervals. An example of how the 2010 portion of the 2010-2015 time periods was calculated:

2010 % = (14A 2010 +14B 2010) / ((14A 2010 +14B 2010) (14A 2011 +14B 2011) + (14A 2012 +14B 2012) + (14A 2013 +14B 2013) + (14A 2014 +14B 2014)).

An example of this in practice is shown on the next page:

13

2010% out of five year interval

DRG 14A 2010

DRG 14B 2010

Acc

2010-14 2010 % 2011 % 2012 % 2013 % 2014 % - Helse Midt-Norge RHE 1 169 678 9 110 22 % 20 % 21 % 18 % 19 %

Figure 6: Example of yearly weighing for DRG 14A and DRG 14B

For the two year weighted share, the calculations were as follows:

(Number of procedures for each group)/ (accumulated values both years, both DRGs, both age intervals)

Below is an example of the data available in the appendix showing each weight based on each segment’s activity.

DRG 14A DRG 14B

2013 2014 2013 2014

67-79 80+ 67-79 80+ 67-79 80+ 67-79 80+

- Helse Midt-Norge RHE 0.13 0.21 0.16 0.22 0.09 0.07 0.08 0.05

By accumulating the yearly weights between the two DRGs, we arrive to a weight used for the dataset from helsenorge.no.

Yearly weighted activity shares (%)

2013 2014

- Helse Midt-Norge RHE 0.49 0.51

The weighted yearly average was used combined with the yearly percentage of the total procedures to find the weighted 30 day survival average in five years. To find the weighted five year average 30 day survival rate, the yearly proportion of the total amount in the five year interval, together with the 30 day survival rate were used.

Total number of procedures 2010-14

Proportion 2010 %

30d survival

% 2010 30d survival

% 2011 30d survival

% 2012

30d survival

% 2013 30d survival

% 2014

Weighted avg 30d survival 5 years

9 110 22 % 86.8 % 86.8 % 86.8 % 87.4 % 88.0 % 87.1 %

Figure 7: Example of how survival rate is weighted into a five year average

14

Of the 30 day survival rate on a five year average, there are five Health Enterprises scoring a survival rate between 85.0 – 85.99, consisting of 32% of the total procedures in this five year period. In the interval 86.0 – 86.99, there are 10 Health Enterprises represented, consisting of a total of 48% of all procedures in the five year period. From 87.0 – 87.99, four Health Enterprises are represented consisting of 16 % of all procedures from 2010 – 2014. In the interval 88.0 – 88.99 there are two institutions, Lovisenberg Diakonale and Diakonhjemmet, which both are the two private, non-commercial Health Enterprises with long term contracts with Health South-East Regional Health Enterprise.

30 day survival rate 5 years avg

Number of Health

Enterprises Percentage

Cumulative proportion

85.00% - 85.99% 5 32 % 32 %

86.00% - 86.99% 10 48 % 81 %

87.00% - 87.99% 4 16 % 96 %

88.00% - 88.99% 2 4 % 100 %

Figure 8: Distribution of Health Enterprises within survival ranges

15

4.1 Assumptions

To compute the marginal benefit of increasing resource spending some assumptions needed to be made to find how much benefit patients get from surviving a stroke. There are not available data on a national level, so the assumptions are based on studies conducted in countries that are comparable to Norway.

The assumptions are:

Cost of Increasing Length of Stay Average Age of Stroke Occurrence Life Expectancy After Stroke Quality of Life After Stroke

4.1.1 Cost of Increasing Length of Stay

In the assumed cost of increasing length of stay, the cost presented to the municipalities in the 2012 coordination reform in Norway is used. The municipalities were presented with a given price for patients staying at a hospital, ready for discharge. The municipalities had the responsibility for the rehabilitation of these patients when they no longer needed to be observed in the hospital. The reason for using this cost is because a patient would not require a lot of resources in the extra stay, other than occupying the hospital bed. On the website of the Directorate of Health, there is a matrix showing the price the municipalities faced 2014 – 2016. (Utskrivningsklare pasienter)

Year Price per day

2016 4 505 NOK

2015 4 387 NOK

2014 4 255 NOK

Figure 9: Price municipalities pay not accepting patients ready for discharge

In this study, the 2014 price was chosen to make sure that in this study, the actual cost of one extra stay will not be underestimated.

16

4.1.2 Average Age of Stroke Occurrence

Because there are no relevant available statistics from Norway about the average age of having a stroke, this assumption will be based upon former studies about stroke, with a representatively sized study population.

A study conducted by Laditka (Laditka, J. et al. 2014) found that the average age for white males and females was at 78.9 and 82.9.

In another study, by Barclay-Goddard (Barclay-Goddard, R. et al. 2011) calculated an average age of participants at 68 years old with a SD of ± 14.8

In the data gathered in this thesis from the ABF cube we divide the age groups into 0 – 15, 16 – 49, 50 – 66, 67 – 79, and 80+. (Cognos) Within these age groups, the divisions are:

0 – 15 16 – 49 50 – 66 67 – 79 80+

0 % 10 % 29 % 33 % 28 % 100 %

Figure 10: Age distribution for stroke occurrence

This implies that the vast majority of the stroke incidences happen from age 50, onwards and that the age group with the highest percentage of stroke incidences is in the age group 67 – 79. This is also within the average ages of the other studies’ findings, and is enough to provide enough information to make an informed assumption.

Based on these three sources, 80.9 (n=1862), 68 (n=677), 73 (average of the main group having a stroke in the Norwegian statistics) (n=32 430).

Weighted this gives yields the age 73.3, which is an assumption based on studies from the US where the population is comparable, and on the data available from the Norwegian ABF cube.

4.1.3 Life Expectancy After Stroke

In terms of life expectancy after having had a stroke, the same study by Laditka (Laditka, J. et al. 2014) which was a very extensive research over a period of 10 years, yielded results from their population sample (n=1862) that the average life expectancy after having had a stroke was 11.6 for white males and 10.8 for females.

17 In a study investigating 13,004 people in the UK, they found that that the total life expectancy (TLE) at the age of 65 without getting stroke was 15.3 for males and 19.4 for females, where 12.1 and 11 of those years were disability free. Males aged 65 who suffered stroke had 4.8 years shorter TLE and 6.5 more years of disabilities. Females in the same situation had 4.6 years shorter TLE compared to the stroke free group, and 5.8 more years of disability.

(Jagger, C. et al 2007)

This averages to 10.5 TLE after having a stroke for males, and 14.8 TLE for females, after the age of 65. This implies that the LE after having had a stroke in this study is 75.5 for males and 79.8 for females. This study is not as accurate for this assumption as the study by Laditka, J et al. from 2014, where the age of getting a stroke was closer to the average in the dataset this thesis uses.

In the study “The Impact of Nonfatal MI or Stroke on Life Expectancy” Caro (Caro, J. et al.

2008) used a total of 81,785 patients whereas 6,154 of those suffered a non-fatal stroke. Their study concluded that the life expectancy at 80 years for males were 8.5 years, while having a stroke at 75 years reduced the life expectancy by 4.8 years for males and 6.7 years for females. (ibid)

This means that the total life expectancy for males having a stroke at 75 is at 83.7 years for this study. They did not disclose the same information for women, so an assumption based on the common knowledge that females have equal or longer life expectancy than the 8.5 years that they found for males is needed. Therefore, the number 83.7 will also be used for women, since higher life expectancy and a higher reduction will outweigh each other.

The results are then weighted by means of relevance and on number of participants. The weights are distributed following: 3/6 for the study conducted by Caro, 2/6 for the study conducted by Jagger, and 1/6 for the study by Laditka. This equals an average of 81.17 for males and 82.47 for females. To have a uniform number, the averages need to be weighted accordingly to the distribution in the sample populations, at an average of 55% male. The life expectancy after having stroke for both sexes then equals to 81.8.

18

4.1.4 Quality of Life After Stroke

In a 13 year follow up study in Quality-Adjusted life expectancy done by Lee (Lee, H. et al 2010) their results found that the mean QALY for the participants(n=486) who had suffered from a stroke, was 0.8.

In a study by Jia, H. et al. they were studying the effects of different diseases, including stroke on the QALE. The study included 15,264 people having suffered a stroke, and the reported life quality after having had a stroke were 0.704 QALY per year. (Jia, H. et al. 2013)

Based on these two studies, the average yearly QALY after having had a stroke is set to be 0.752.

19

5 Results

5.1 Calculation

The core of this thesis is to determine how much health we get for resource spending, and if increased resource spending leads to an increase in health outcomes. As a measure of resource spending, the length of stay at the Health Enterprise is used as variable, while health outcomes are measured through 30 day mortality rate also at the Health Enterprise level. Our hypothesis is that a marginal increase as Δc (marginal increase in cost) will lead to Δb (marginal increase in benefit). If that is the case, it should also be possible to convert the incremental cost/benefit into QALYs, and calculate the cost of each marginal QALY gained by the increased resource spending. The calculation can be shown as the following:

Incremental cost (Δc)

= Cost of increasing one LOS Incremental benefit (Δb) Δp*Δy*Δq

As this equation shows, the incremental cost is measured through the cost of increasing one day length of stay, while the incremental benefit is measured through the increased probability of surviving by increasing one day length of stay, multiplied by the incremental life expectancy by surviving a stoke, multiplied by the incremental quality of life after having survived a stroke.

In this equation, variables made from the assumptions based on former research are used. The equation is therefore:

Incremental cost

= Cost of increasing one LOS

= 4255

Incremental benefit Δp*Δy*Δq Δp*8.432*.752

From the assumptions, the incremental cost of increasing one LOS is 4255 NOK, the incremental life years is 8.432 years, while those life years are reported to have a quality of life of 0.752. The missing variable is therefore the increased probability of 30 day survival, by increasing one LOS. The comparing of the two variables in a five year weighted average indicates a correlation between the number of LOS and the 30 day survival rate. By comparing the pairs of values, for each year, using a linear scatter plot chart, we find differences in the linear trend chart (See Appendix).

20

As shown in the trend charts, the linear trend in four out of the five years studied, there is a positive correlation between length of stay and 30 day survival rate in the Norwegian Health Enterprises. In 2012 there is a negative correlation. 2012 represents a shift in the correlation, whereas in 2010 and 2011 there was a strong positive correlation between LOS and 30 day survival rate, while after 2012, in 2013 and 2014, there is still a positive correlation, but it is not as strong. The correlation between the two variables in 2010 using a linear trend is 0.31%, which means that the Health Enterprises with a higher length of stay, also is associated with having a higher 30 day survival, and considered to have an average of 0.31% per extra day LOS.

To have more accurate information about the correlation between 30 day survival rate and length of stay, a calculation for a weighted average over the five years where there is available data was conducted. The inclination of the curve will then give information about the correlation between the two variables. The hypothesis of this thesis suggests a positive correlation, and therefore expects a positive incline of the linear trend chart. The task will then be to investigate, with this correlation in mind, the potential benefit of increasing one day LOS for all Health Enterprises.

The relevant variables have been gathered in the figure below.

Average age of having a stroke 73.3 years

Total life expectancy after having had a stroke 81.8 years

Quality of life after having had a stroke per year 0.752 QALY/year Average total expected QALY after having had a stroke and survived 6.34 QALY

Cost of increasing one day length of stay 4,255 NOK

Five year average survival rate 86.34 %

Yearly average number of people being admitted for stroke 12161 Yearly average number of people survival after being admitted for stroke 10500 Figure 11: Key variables

21 These are the key variables needed, along with the five year trend chart, for calculating the potential increase in 30 day survival by increasing one day length of stay. There are two ways of resulting evidences for the hypothesis. The first would be to use a linear trend chart model, to see what the inclination of the linear trend is, to see the general potential increase in survival rate by increasing length of stay. Another way to investigate the correlation would be to use a polynomial trend, and use that for investigating which hospitals might have the highest yield of increasing LOS. Using polynomial trend is useful because it gives a dimension that the linear trend does not, the fact that there is a limit of correlation, that the correlation coefficient is not static, between 30 day survival and LOS. The linear trend, if it has a positive inclination, would suggest that a LOS of 20 would lead to a higher 30 day survival rate of y=20*x+b, (where survival rate is symbolized as y, length of stay is symbolized as x, and b represents a constant.) compared to for example 8 LOS would correlate to a 30 day survival rate of y=8*x+b. With the polynomial trend, the higher LOS will yield a decreasing correlation, because of the added dimension.

22

5.2 Data

A linear trend scatter plot chart is used to find the correlation, and to find the average increase of 30 day survival is correlated to the number of length of stay. It is useful to find the general average increase, but the increase does not necessary mean that an increase from 14 to 15 LOS will yield the same increase.

DRG 14A & 14B

Five year weighted average LOS

Five year weighted average survival rate

- Helse Midt-Norge RHE 8.6 87.14 %

- Helse Møre og Romsdal HE 8.5 86.20 %

- Helse Nord-Trøndelag HE 8.4 87.66 %

- St. Olavs Hospital HE 8.7 87.45 %

- Helse Nord RHE 10.6 87.17 %

- Finnmarkssykehuset HE 8.7 87.25 %

- Helgelandsykehuset HE 8.1 86.69 %

- Nordlandsykehuset HE 9.0 86.90 %

- Universitetssykehuset Nord-Norge HE 13.5 87.56 %

- Helse Sør-Øst RHE 8.1 85.98 %

- Akershus Universitetssykehus HE 11.4 86.76 %

- Diakonhjemmet sykehus AS 9.0 88.68 %

- Lovisenberg Diakonale 8.5 88.94 %

- Oslo Universitetssykehus HE 9.8 85.09 %

- Sykehuset i Telemark HE 8.7 85.62 %

- Sykehuset i Vestfold HE 6.8 85.58 %

- Sykehuset i Østfold HE 5.7 85.64 %

- Sykehuset Innlandet HE 6.1 85.69 %

- Sørlandet sykehus HE 8.5 86.13 %

- Vestre Viken HE 7.4 86.09 %

- Helse Vest RHE 9.6 86.83 %

- Helse Bergen HE 8.4 86.15 %

- Helse Fonna HE 7.8 86.42 %

- Helse Førde HE 10.1 86.94 %

- Helse Stavanger HE 12.3 86.72 %

23

5.2.1 Linear trend

When entering the data in a scatter plot chart with a linear trend, the model looks like this:

Figure 12: Linear trend chart

The formula of the linear trend is y = 0.0018x + 0.851. This linear trend indicates that in the five year weighted average, there is a positive correlation between LOS and 30 day survival rate of 0.18% per increased LOS. Using the variables from figure 11, we can go back to the former equation, and see that we now can compute the incremental benefit.

The incremental cost divided by the incremental benefit equals to 372,802 NOK. This is the price per incremental QALY that the linear trend yields by increasing one LOS given that the correlation for all Health Enterprises equals to 0.18%, or that the correlation totals to an average of 0.18% increase in 30 day survival rate by increasing one day LOS at all Health Enterprises. More details of the potential survival rate, and potential lives saved and number of QALYs gained, are shown in the next table.

Incremental cost

= Cost of increasing one LOS

= 4255

= 372,802 NOK

Incremental benefit Δp*Δy*Δq 0.0018*8.432*.752

y = 0.0018x + 0.851

0.84 0.85 0.86 0.87 0.88 0.89 0.9

5 6 7 8 9 10 11 12 13 14

30 day survival 2010 - 2014

Length of stay 2010 - 2014

Health enterprises 2010 - 2014

24

Percentage increase in 30 day survival by increasing length of stay (linear)

0.18 %

Potential survival rate by increasing one day length of stay 86.52 % Yearly potential average number of people survival after being

admitted for stroke 10522

Potential lives saved 22

Average yearly cost of increasing one day length of stay 51,746,757 NOK

Potential QALYs gained 138.8

Cost per incremental QALY 372,802 NOK

Figure 13: Results from linear trend

This trend shows the overall potential increase in 30 day survival rate is 0.18 %. This potential increase is an average of the total increase in 30 day survival by increasing one LOS at all the Health Enterprises, and does not necessarily mean that an increase in one LOS will increase the 30 day survival rate by 0.18 % at each and every one of the Health Enterprises, but expectedly a higher increase in survival rate at the hospitals with lower LOS than the average, and or a lower survival rate than the average. For example Sykehuset I Vestfold HE, Sykehuset I Østfold, and Sykehuset Innlandet are three Health Enterprises with both low LOS, around 6 days, and relatively low 30 day survival rate, registered between 85.58% and 85.69%. These three Health Enterprises would potentially have a higher increase in 30 day survival rate by increasing one LOS.

By using a polynomial trend chart, the results show which Health Enterprises potentially would benefit the most from the increased LOS, given that there is a correlation between the two variables. The potential gain of increasing one day LOS would decrease the higher the number of LOS. The polynomial trend will show this in a better way than the linear trend does. The expected value of the polynomial curve is a concave increasing graph line that will show a decreasing benefit for the hospitals with a higher number of LOS.

25

5.2.2 Polynomial trend in the second degree

The polynomial trend chart model looks like this:

Figure 14: Polynomial trend chart

The formula of the polynomial trend is y = -0.0005x² + 0.0107x + 0.8098. This shows that the potential increase in 30 day survival is higher by increasing the length of stay for the hospitals with fewer days’ length of stay than those with higher initial length of stay. An increase from six days to seven days would therefore equal a potential increase in 30 day survival rate by 0.42 %, based from the five year average overall survival rate. In the polynomial trend we are also dealing with the polynomial expected value, which is the value of the polynomial trend line. The deviations from the polynomial expected value will either mean a stronger or weaker possible increase in potential survival, while some of the Health Enterprises has a 30 day survival rate so high that the polynomial trend expects a decrease in 30 day survival rate by increasing one LOS. These include Helgelandssykehuset, Nord Trøndelag HE, Lovisenberg Diakonale, St Olavs Hospital, Finnmarkssykehuset, Nordlandssykehuset, Diakonhjemmet, Helse Førde, Akershus University Hospital, Helse Stavanger, UH Nord- Norge. This exposes some of the limitations of using a polynomial trend, since the 30 day survival rate will not necessarily decrease by increasing the stay by one LOS.

In the next table, the five year average length of stay is in column two. In column three is the polynomial expected value given the LOS. Column four shows the potential increase in 30 day survival rate based on the PEV. In the fifth column is their actual five year average 30 day survival rate, and the sixth is the potential increase from the actual survival rate, to the polynomial expected value by increasing one LOS. The seventh column is the potential 30

y = -0.0005x² + 0.0107x + 0.8098

0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88 0.885 0.89 0.895

5 6 7 8 9 10 11 12 13 14

30 day survival 2010 - 2014

Length of stay 2010 - 2014

Health enterprises 2010 - 2014

26

day survival rate, of increasing one LOS, given that there is a correlation. The polynomial trend shows that increasing one day length of stay at all Health Enterprises with an average length of stay of 8.4 or less would potentially yield a higher or equal 30 day survival rate benefit compared to the linear trend, based on the expected value of the polynomial trend. It also shows that there is an increasing benefit for increasing the length of stay until the initial length of stay equals 10.2 days. A higher initial length of stay than this results in a negative benefit in the potential length of stay. The sixth column shows the potential gain from increasing one LOS from the actual survival rate, to the potential expected polynomial survival rate. As shown, 14 out of 21 Health Enterprises perform better than their polynomial expected value, and 11 out of 21 Health Enterprises will have a negative increase (decrease) by increasing one LOS from the actual survival rate. Based on the polynomial trend, all Health Enterprises, except Helse Nord Trøndelag and Helgelandssykehuset, with an initial LOS average at 8.4 or below is expected to yield equal or higher potential increase from increasing one LOS compared to the polynomial expected value.

Health Enterprise

Avg LOS

Polynomial expected value

Actual survival rate

Increase from PEV

Increase from actual

Potential survival rate Sykehuset i Østfold 5.7 85.45% 85.64 % 0.45 % 0.26 % 85.90 % Sykehuset Innlandet 6.1 85.64% 85.69 % 0.41 % 0.37 % 86.06 % Sykehuset i Vestfold 6.8 85.94% 85.58 % 0.34 % 0.70 % 86.28 %

Vestre Viken 7.4 86.16% 86.09 % 0.28 % 0.35 % 86.62 %

Helse Fonna 7.8 86.28% 86.42 % 0.24 % 0.11 % 86.58 %

Helgelandssykehuset 8.1 86.36% 86.69 % 0.21 % -0.12 % 86.55 % Nord Trøndelag 8.4 86.44% 87.66 % 0.18 % -1.04 % 86.52 %

Helse Bergen 8.4 86.44% 86.15 % 0.18 % 0.47 % 86.52 %

Sørlandet Sykehus 8.5 86.46% 86.13 % 0.17 % 0.50 % 86.51 % Møre og Romsdal 8.5 86.46% 86.20 % 0.17 % 0.43 % 86.51 % Lovisenberg Diakonale 8.5 86.46% 88.94 % 0.17 % -2.31% 86.51 % Sykehuset Telemark 8.7 86.50% 85.62 % 0.15 % 1.04 % 86.49 % St Olavs Hospital 8.7 86.50% 87.45 % 0.15 % -0.79 % 86.49 % Finnmarkssykehuset 8.7 86.50% 87.25 % 0.15 % -0.60 % 86.49 % Nordlandssykehuset 9.0 86.56% 86.90 % 0.12 % -0.22 % 86.46 % Diakonhjemmet 9.0 86.56% 88.68 % 0.12 % -2.00 % 86.46 %

Oslo UH 9.8 86.66% 85.09 % 0.04 % 1.61 % 86.38 %

Helse Førde 10.1 86.68% 86.94 % 0.01 % -0.24 % 86.35 %

Akershus UH 11.4 86.68% 86.76 % -0.12 % -0.20 % 86.22 % Helse Stavanger 12.3 86.57% 86.72 % -0.21 % -0.35 % 86.13 % UH Nord-Norge 13.5 86.31% 87.56 % -0.33 % -1.57 % 86.01 %

27 The three Health Enterprises with the biggest potential increase in 30 day survival rate based on the PEV are also the three Health Enterprises with the shortest length of stay, all below seven days, Sykehuset I Østfold, Sykehuset Innlandet, and Sykehuset I Vestfold. Below is a table showing the potential marginal QALYs gained by increasing one LOS and where the potential 30 day survival then equals the PEV.

SiØ (PEV) SI (PEV) SiV (PEV)

Percentage increase in 30 day survival (polynomial)

0.26% (0.45 %) 0.37% (0.41 %) 0.70% (0.34 %) Current average 30 day survival rate 85.64 % 85.69 % 85.58 % Potential survival rate by increasing

one day length of stay

85.90% 86.06% 86.28%

Current number of survivals 2929 4921 2264

Potential number of people survival 2938 4942 2283

Potential lives saved 9 21 19

Accumulated costs of increasing one day length of stay

14,552,100 NOK 24,436,465 NOK 11,258,730 NOK

Potential total QALYs gained 56.4 134.7 117.4

Cost per incremental QALY 258,093 NOK 181,363 NOK 95,863 NOK Figure 15: Results from polynomial trend

There are hospitals performing better and worse than the PEV, and there can be other factors not taken into account in this thesis affecting the 30 day survival rate. Note that these expenses and QALY outcomes are accumulated for five years.

The polynomial trend shows that there are potential benefits, in the form of increased 30 day survival rate, achievable by increasing length of stay at the Health Enterprises with the lowest length of stay. The numbers are not precise, give an indication that the effect of increasing one day length of stay is higher at the Health Enterprises with a combination of a low length of stay and a low 30 day survival rate.

These results do not say that increased length of stay causes increased 30 day survival rate, but rather that there is indications for causation, where the models supports these theories.

This is rather supporting evidence whereas in the next part, regression analysis models will be presented and investigated to find more information about the strength of the relationship between the two variables.

28

5.3 Regression analysis

For the following data, I used Stata to find the level of significance at the individual years, and five years weighted average, to see if there is a significant correlation between the two variables. The different regression models are listed in the appendix.

Figure 16: Regression models

30 day survival rate Coefficient Standard Error P>|t| Prob>F Adj R-squared

Model single year 2010 0.0057 0.3028

Constant .8318765 .0103647 0.000

LOS .003107 .0009982 0.006

Model single year 2011 0.0168 0.2268

Constant .8388625 .0100897 0.000

LOS .0027704 .0010574 0.017

Model single year 2012 0.7994 -0.0490

Constant .8684373 .0095564 0.000

LOS -.0002837 .0011009 0.799

Model single year 2013 0.6069 -0.0377

Constant .8623116 .0094603 0.000

LOS .0005891 .0011259 0.607

Model single year 2014 0.6896 -0.0436

Constant .8689691 .0100092 0.000

LOS .0004814 .0011871 0.690

Five years weighted avg. 0.1446 0.0617

Constant .8510376 .0105328 0.000

LOS .0017757 .001167 0.145

All HE all years 0.0711 0.0219

Constant .858885 .0044836 0.000

LOS .0008966 .0004916 0.071

Weighted regression 0.0000 0.1815

Constant .8478135 .0001475 0.000

LOS .0018557 .0000166 0.000

Model year dummy 0.0036 0.1179

Constant .8485809 .0055265 0.000

2010 ref

2011 .00256 .003277 0.437

2012 .0052132 .0033602 0.124

2013 .0066328 .0033895 0.053

2014 .0124225 .0033918 0.000