Estimating the marginal cost of a life year in Sweden’s public healthcare sector

Although cost-effectiveness analysis has a long tradition of supporting healthcare decision-making in Sweden, there are no clear criteria for when an intervention is considered too expensive. In particular, the opportunity cost of healthcare resource use in terms of health forgone has not been investigated empirically. In this work, we therefore seek to estimate the marginal cost of a life year in Sweden’s public healthcare sector using time series and panel data at the national and regional levels, respectively. We find that estimation using time series is unfeasible due to reversed causality. However, through panel instrumental variable estimation we are able to derive a marginal cost per life year of about SEK 370,000 (EUR 39,000). Although this estimate is in line with emerging evidence from other healthcare systems, it is associated with uncertainty, primarily due to the inherent difficulties of causal inference using aggregate observational data. The implications of these difficulties and related methodological issues are discussed. Electronic supplementary material The online version of this article (10.1007/s10198-019-01039-0) contains supplementary material, which is available to authorized users.


A.1 Regional remaining life expectancy
At the national level, we collect data on remaining life expectancy (RLE) by age and gender for 1970-2016. At the regional level, we calculate the same measure using the number of deaths ( ) by region , where = 100 includes everyone a hundred years or older; this mortality rate is applied to all ages above 100. Statistics Sweden provide five-year averages of RLE at birth by gender and region. As a robustness check, we use our method to calculate RLE at birth for the periods 2002-2006, 2007-2011, and 2012-2016. The correlation between this and the Statistic Sweden series is 0.9995. Finally, in order to produce a single aggregate measure of mortality, we derive standardised average remaining life expectancy (ARLE) according to Equation A.3   , = ∑   , , , , , , is the national population in 2016. In this way, we capture regional and temporal variations in mortality that are not confounded by either type of variation in the age and gender structure of the population.

A.2.1 Time series, 1970-2016
Since healthcare expenditure from the OECD is only reported at current prices or constants prices using the GDP deflator, we construct a healthcare price index in order to adjust expenditure by its sector specific price level. The regional council price index (LPI) excluding pharmaceuticals and the pharmaceutical price index are available from 1980. From 2004, the LPI including pharmaceuticals is also available. All indices are plotted in Figure A.1. We note that the LPI followed the general price level quite closely up until the 1990s. We therefore assume that the GDP deflator can be used to describe the price increase of healthcare services for 1970-1979. The adjusted series shows that the increase in real expenditure since 1970 has been slightly lower, which is due to a sharper increase in healthcare prices compared to the GDP deflator since the 1990s.

A.2.2 Panel data, 2003-2016
The regional council price index (LPI) does not capture regional variations in price level. We adjust for this using a healthcare wage index ( ) for 2004, which is part of one of the models in the system of regional redistribution.

A.3 Unit root tests
We determine the order of integration of the variables for the time series analysis using the ADF-test and the KPSS-test. In the former, the null hypothesis is that the series has a unit root. In the latter, the null is that the series is stationary. The test results are reported in Table A.1.  In the ADF-tests, the null cannot be rejected for the series in levels but rejected at 1% significance for the first-difference. The reverse holds true for the KPPS-tests. This strongly suggests that the series are integrated of order one, usually denoted I(1). When including a linear trend in the specification, the tests provide conflicting evidence on whether the series can be regarded as trend stationary in levels, i.e. I(0) when accounting for a linear trend. For the purpose of Granger causality testing, this does not matter; we can confidently regard the maximum order of integration as one. In the case of testing for cointegration, all variables must be I(1). However, since the specification of both a constant and linear trend in a VAR-model is implausible, we include only a constant and regard the variables as I(1). Notes: The zero restriction is imposed on the coefficients of the first ⋆ lags; the additional = 1 lags are added to account for the maximum order of integration. Under the null of no causality, the test statistic is 2 with ⋆ degrees of freedom. '***'/'**'/'*' denotes 1/5/10% significance.

A.5 Population weighted 2SLS
The results from the weighted regression are reported in Table 3.A. We use the average population of each region for 2003-2016 as weights. The standard errors in the weighted regression are of the same type as in the other analyses, but use a different estimator. For this reason, the first two columns of Table 3 illustrate the effect of switching estimators (without weighting). 167 Notes: '***'/'**'/'*' denotes 1/5/10% significance. Robust standard errors within parentheses. a Annual change in the variable from inter-regional migration. 'log()' is the natural logarithm, 'pr()' is the proportion of the population, and 'd()' is a dummy variable. MC is the marginal cost in 2016 SEK. All models are estimated with period fixed effects (i.e. year dummies) using data for 2003-2015 (N = 20, T = 13). Annual change in the variable from inter-regional migration. b Divided by the proportion of the working age (25-69) population age 60-69. 'pr()' is the proportion of the population and 'd()' is a dummy variable. ARLE is average remaining life expectancy. HCE is per capita healthcare expenditure in 2016 SEK. 'p.c.k.' denotes per 1,000 persons.