Determining the effect of change in income on self - rated health using regression models – ordered , linear , fixed or random ?

Many observational studies have shown an association between income and health. However, much less research has assessed how changes in income influence health over time. This could help illuminate the issue of whether income is causally related to health, if longitudinal survey data were analysed with methods to account for bias from both measured and unmeasured time-invariant confounders. The aims of this paper are to discuss econometric and biostatistical regression approaches to such analyses using panel data (i.e., fixed and random effects, and ordinal versus continuous specification of the five-level self-rated health (outcome) variable). We used data from 16,365 adults from the first four waves (2002-2005) of the New Zealand fixed household panel Survey of Family, Income and Employment (SoFIE). The outcome was annual self-rated health (SRH; five responses: excellent, very good, good, fair, poor),and the main exposure variable was annual household equivalised income. Potential confounding variables included age, sex, ethnicity, education, employment status, marital status, family structure and area deprivation level. Random and fixed effects linear and proportional odds models were fitted using SAS 8.2. Theoretically, we argue that the best analytical approach is to treat the self-rated heath outcome as ordinal (not continuous), and with a fixed effects methodology. A fixed effects proportional odds logistic regression model in SAS is possible using the NLMIXED procedure to compute a hybrid model. This model produces fixed effects estimates for time-varying covariates. The NLMIXED procedure can also be used to estimate the random effects proportional odds model, allowing the inclusion of timeinvariant covariates. Empirically, the random effects proportional odds models found a very small but significant positive effect of increasing income on the odds of a higher/better level of SRH. This diminished and became non-significant in the (theoretically preferred) fixed effects/hybrid proportional odds models. Qualitatively similar results were found in the linear random and fixed effects models. Working Paper Draft 2 Substantively, changes in income in our study have at most a small effect on SRH over the short-term at least. Econometric and biostatistical approaches can be brought together and usefully applied to panel data to answer questions of interest to both the health and economic fields.