Did the health of the Dutch population improve between 2001 and 2008? Investigating age- and gender-specific trends in quality of life

Abstract

Although many countries’ populations have experienced increasing life expectancy in recent decades, quality of life (QoL) trends in the general population have yet to be investigated. This paper investigates whether QoL changed for the general Dutch population over the period 2001–2008. A beta regression model was employed to address specific features of the QoL distribution (i.e., boundedness, skewness, and heteroskedasticity), as well non-linear age and time trends. Quality-adjusted life expectancy (QALE) was calculated by combining model estimates of mean QoL with mortality rates provided by Statistics Netherlands. Changes in QALE were decomposed into those changes caused by QoL changes and those caused by mortality-rate changes. The results revealed a significant increase in QoL over 2001–2008 for both genders and most ages. For example, QALE for a man/woman aged 20 was found to have increased by 2.3/1.9 healthy years, of which 0.6/0.8 was due to QoL improvements.

Appendix

Multiple imputation model

We used a fully conditional specification (FCS), also known as multivariate imputation by chained equations (MICE), proposed by various authors [24–26] for each SF-12 item with missing values, conditional on all other variables in an imputation model. We developed the imputation model based on variables from the POLS face-to-face interview, in particular: year, age, educational level, marital status, self-rated health, general practitioner (GP) visits, smoking status, number of sport activities per week, happiness, number of working hours per week, number of church visits per month. The number of imputations used was established following pre-defined guidelines [56]. Given the percentage of missing data (around 20–25 % of the SF-12 items) and the computer power necessary, ten imputations were used to impute the SF-12 missing values.

Analyzing multiple imputed data involves two steps: first a standard method is applied to each simulated data set, then the estimates of interest from each data are combined to obtain a final result using the rules defined in [28] and adapted from [42].

Delta method

The delta method estimates the variance of a non-linear function of one or more variables by using the Taylor expansion around the mean of the variables. Therefore, if $x_{0}$ and $y_{0}$ are the mean values of $\mu$ and $\nu$, respectively, the first order Taylor expansion of $f(\mu ,\nu ) = \frac{\mu + \nu }{1 + \nu }$ about the values $(x_{0} ,y_{0} )$ is:

$$\begin{gathered} f(\mu ,\nu ) \approx f(x_{0} ,y_{0} ) + \frac{\partial f(\mu ,\nu )}{\partial \mu }\left| {_{{(x_{0} ,y_{0} )}} } \right.(\mu - x_{0} ) + \frac{\partial f(\mu ,\nu )}{\partial \nu }\left| {_{{(x_{0} ,y_{0} )}} } \right.(\nu - y_{0} ) \hfill \\ = f(x_{0} ,y_{0} ) + \frac{1}{{1 + y_{0} }}(\mu - x_{0} ) + \frac{{1 - x_{0} }}{{(1 + y_{0} )^{2} }}(\nu - y_{0} ) \hfill \\ \end{gathered}$$

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Then,

$$\begin{gathered} {\text{Var[}}f(\mu ,\nu )] = \frac{1}{{(1 + y_{0} )^{2} }}{\text{Var[}}\mu ] + \frac{{(1 - x_{0} )^{2} }}{{(1 + y_{0} )^{4} }}{\text{Var[}}\nu ] + 2\frac{{1 - x_{0} }}{{(1 + y_{0} )^{3} }}\text{cov} (\mu ,\nu ) \hfill \\ = \frac{1}{{(1 + y_{0} )^{2} }}{\text{Var[}}\mu ] + \frac{{(1 - x_{0} )^{2} }}{{(1 + y_{0} )^{4} }}{\text{Var[}}\nu ] + 2\frac{{1 - x_{0} }}{{(1 + y_{0} )^{3} }}\rho (\mu ,\nu )\sigma_{\mu } \sigma_{\nu } \hfill \\ \end{gathered}$$

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where $\rho$ is the product moment correlation between $\mu$ and $\nu$. If we assume $\rho = 0$, the estimated variance of the $f(\mu ,\nu )$ is:

$${\text{Var[}}f(\mu ,\nu )] = \frac{1}{{(1 + y_{0} )^{2} }}{\text{Var[}}\mu ] + \frac{{(1 - x_{0} )^{2} }}{{(1 + y_{0} )^{4} }}{\text{Var[}}\nu ]$$

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