Calibration adjustments to address bias in mortality analyses due to informative sampling—a census-linked survey analysis in Switzerland

Background Sampling bias, like survey participants' nonresponse, needs to be adequately addressed in the analysis of sampling designs. Often survey weights will be calibrated on specific covariates related to the probability of selection and nonresponse to get representative population estimates. However, such calibrated survey (CS) weights are usually constructed for cross-sectional results, but not for longitudinal analyses. For example, when the outcome of interest is time to death, and sampling selection is related to time to death and censoring, sampling is informative. Then, unweighted or CS weighted inferential statistical analyses may be biased. In 2010, Switzerland changed from a decennial full enumeration census to a yearly registry-based (i.e., data from harmonised community registries) and a survey-based census system. In the present study, we investigated the potential bias due to informative sampling when time to death is the outcome of interest, using data from the new Swiss census system. Methods We analysed more than 6.5 million individuals aged 15 years or older from registry-based census data from years 2010 to 2013, linked with mortality records up to end of 2014. Out of this population, a target sample of 3.5% was sampled from the Swiss Federal Statistical Office (SFSO) in a stratified yearly micro census. The SFSO calculated CS weights to enable representative population estimates from the micro census. We additionally constructed inverse probability (IP) weights, where we used survival information in addition to known sampling covariates. We compared CS and IP weighted mortality rates (MR) and life expectancy (LE) with estimates from the underlying population. Additionally, we performed a simulation study under different sampling and nonresponse scenarios. Results We found that individuals who died in 2011, had a 0.67 (95% CI [0.64-0.70]) times lower odds of participating in the 2010 micro census, using a multivariable logistic regression model with covariates age, gender, nationality, civil status, region and survival information. IP weighted MR were comparable to estimates from the total population, whereas CS weighted MR underestimated the population MR in general. The IP weighted LE estimates at age 30 years for men were 50.9 years (95% CI [50.2-51.6] years), whereas the CS weighted overestimated LE by 2.5 years. Our results from the simulation study confirmed that IP weighted models are comparable to population estimates. Conclusion Mortality analyses based on the new Swiss survey-based census system may be biased, because of informative sampling. We conclude that mortality analyses based on census-linked survey data have to be carefully conducted, and if possible, validated by registry information to allow for unbiased interpretation and generalisation.