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

Introduction

Population-based longitudinal studies are a key tool for epidemiologists to investigate individual and ecological risk factors on disease development and mortality over time. In many countries, including the United Kingdom, Germany and the Nordic countries, nationwide cohort studies have been established by linking information from population registries and secondary data sources (Olsen et al., 2001; Ahrens et al., 2014; Connelly & Platt, 2014). In Switzerland, a nationwide cohort study was established in 2008, based on a probabilistic record linkage of census and mortality information covering the whole Swiss population (Bopp et al., 2009; Spoerri et al., 2010). This cohort study relied on an almost complete census (coverage of 98.6% (Renaud, 2004)) and allowed for almost unbiased mortality analyses (Schmidlin et al., 2013; Moser et al., 2014).

In 2010, Switzerland changed from a full enumeration census—which was conducted every 10 years—to a registry-based and survey-based census system. This new Swiss census system is based on a yearly updated registry-based census—which collects information from harmonised community registries covering the entire resident population of Switzerland (STATPOP)—and a micro census of roughly 3.5% of the resident Swiss population aged 15 years or older, living in a private household. This micro census collects individual and household information, which is not available in the STATPOP population (e.g., attained educational level). The new census system aims to be more cost-efficient and to require less administrative resources compared to the traditional full enumeration census. However, because the micro census is based on only a stratified sampled subpopulation, the sampling design needs to be addressed in descriptive and inferential statistical analyses to get valid population estimates (Korn & Graubard, 1999; Fuller, 2009).

The Swiss Federal Statistical Office (SFSO) planned and performed the sampling of the micro census, and provided calibrated survey (CS) weights for the analysis of the micro census sample. CS weights address the sampling process (i.e., probabilities of selection) and account for sampling biases (e.g., nonresponse adjustments) to get consistent statistical estimates for the whole Swiss population in weighted descriptive analyses (Assoulin, 2012). These analyses are valid for cross-sectional results, but not necessary for longitudinal analyses. For example, if the outcome of interest is time to death and the sampling selection is not independent of the survival time and censoring, given other covariates, the sampling design is called “informative” (Lawless, 2003; Boudreau & Lawless, 2006). When sampling is informative, the outcome of interest is not missing at random and unweighted or CS weighted inferential statistical analyses may be biased. IP weighting models, which account for the probability of survey inclusion and censoring, could correct for such bias and lead to valid survival estimates (Scharfstein & Robins, 2002; Little, 2004; Boudreau & Lawless, 2006).

In the present study, we performed time to death analyses using data from the Swiss micro census. Specifically, we calculated mortality rates (i.e., survival time is an offset variable in a Poisson regression model) and life expectancy (i.e., survival time is directly modelled in a censored skew-normal regression model (Moser, Clough-Gorr & Zwahlen, 2015)). In Switzerland, non-responders of surveys have a higher risk of dying compared to responders (Bopp, Braun & Faeh, 2014). Thus, we hypothesised that bias due to informative sampling may exist in CS weighted analyses, caused by unmeasured predictors (e.g., health status), which are possibly related to the sampling process and mortality. We therefore compared CS weighted results with those from an IP weighting approach, which uses known sampling covariates and survival information, and validated our findings using data from the total Swiss population. Additionally, we performed a simulation study to investigate the bias due to informative sampling under different sampling and nonresponse scenarios.

Methods

Mortality information

Survival status for the years 2011–2014 could be one-to-one linked to the STATPOP and the SE 2010 population by unique anonymous personal identifier. The percentage of non-linked death records is 0.2%. Vital status is ascertained by death certificates. We used information about vital status as binary variable (dead: yes or no) and survival time.

Results

Mortality analysis

Figure 2 shows the estimated 1-year MR for the STATPOP population and the SE of the year 2010, by age categories and gender. STATPOP MR (red coloured lines) serve as the reference MR, because they contain full population information. IP weighted MR (green coloured lines) were comparable to STATPOP MR, especially for ages 40 years or older. Unweighted (blue coloured lines) MR and CS weighted (purple coloured lines) MR underestimated the STATPOP MR. Figure 3 shows the estimated LE at age 30 years. The male population of the STATPOP had an estimated LE of 50.9 years (95% CI [50.8–51.0] years). The IP weighted LE estimates for men were 50.9 years (95% CI [50.2–51.6] years), whereas the CS weighted were 53.4 years (95% CI [52.7–54.0] years). The results for women were comparable, i.e., CS weighted results overestimated LE, compared to IP weighted results. Table S2 describes the distribution of individuals who died in 2011 for the STATPOP and SE population, across months of death. Individuals who died in January and February were underrepresented in the SE, for example, only 4.8% of SE 2010 participants who died in 2011 did so in January, compared to 9.3% in the underlying STATPOP population. This pattern was consistent across all surveys 2010–2013. Figure S1 shows estimated MR for the STATPOP and SE population of 2010, with an increasing follow-up time until end of 2011, 2012, 2013 and 2014. We found that MR differences between the CS and IP weighting approaches diminished with increasing follow-up time.

Discussion

We hypothesised that time to event analyses using data from the Swiss survey-based census system may biased because of informative sampling. We investigated whether an IP weighting approach leads to representative statistical estimates in the analysis of the 2010 SE sample, representing approximately 3.5% of the Swiss population aged 15 years or older at the end of 2010. The SE is a stratified random sample of the underlying population, but unweighted and CS weighted survival analyses may be biased, because the sampling is informative. We constructed IP weights, which accounted for known sampling covariates and survival information, and compared those to CS weighted MR and LE estimates. We found that CS weighted estimates were biased, whereas IP weighted estimates were comparable to those from the total Swiss population.

Unmeasured predictors, which are related to future survival and the sampling process—but which are not part of the sampling design—could cause bias in the CS weighted analysis: for example, individuals with a poor health status were less likely to respond to the SE questionnaire, but had also a higher risk of dying. Such a situation may be caused by possible survey participants nonresponse, which is related to certain population characteristics (e.g., older people), which—on the other hand—are also related to the regression outcome (see Fig. 1). Bias in the regression analysis of survey data and possible strategies to handle this kind of bias have been extensively discussed in the demographical and statistical literature (see e.g., Pfeffermann, 2010 and the references therein). Pizzi et al. (2012) compared results from an internet-based cohort study sample and results from the general population and concluded that differences in estimates between the two analysis populations reflect changes in confounding pattern due to the sampling selection process. Such a change of confounding patterns is likely to influence mortality estimates in our present study using the Swiss population. Confounding patterns in our study are likely to be caused by the underrepresentation of certain subpopulations in the micro census sample. For example, we found that individuals who died in 2011 were less likely to having participated in the micro census of 2010. Specifically, we found that individuals who died in the early months of the year were less likely to participate in the micro census. Delayed information adjustments between the process of sending out questionnaires to individuals, and the alignment between mortality and registry information, could introduce specific nonresponse patterns. Further, our observed lower chance of micro census participation of non-Swiss individuals could be explained by a migrant effect (Nielsen & Knardahl, 2016). In additional analyses, we found that older foreigners tend to have a higher odd of participation in the survey, than younger individuals, which could be partly explained by the health status of these individuals (Nielsen & Knardahl, 2016). Such a migrant effect is likely to confound our current analysis.

When sampling design variables are related to survival time and censoring, unweighted survival estimates may be biased (Lawless, 2003; Boudreau & Lawless, 2006). However, IP weighting approaches, addressing the sampling design and the censoring information, have been shown to provide consistent population survival estimates (Scharfstein & Robins, 2002; Lawless, 2003; Boudreau & Lawless, 2006; Pyy-Martikainen, 2013). Several countries, also Switzerland, reported a higher risk of death among non-responders of surveys, compared to responders (Barchielli & Balzi, 2002; Bopp, Braun & Faeh, 2014). An Australian study investigated attrition patterns over five survey periods, starting in 1996–2008, in a population of older women, and reported that health status was associated with frailty, withdrawal from the study, and lost to follow-up (Brilleman, Pachana & Dobson, 2010). Such unmeasured factors, which are related to mortality and non-response, are likely leading to an informative sampling design in the new Swiss census system, and may cause bias in survival analysis of survey data. In our analyses, we found that IP weighting may adequately address the bias introduced by informative sampling. Our simulation study confirmed that IP weights, using survival information from the full population, leads to comparable MR estimates as those from known CS weights. The design of the present study—with a combination of registry-based, survey and mortality information—allowed the identification of predictors, which are associated with informative sampling, in a large population of 6.7 million individuals. This allowed us to validate our findings for consistency. Because mortality information could be deterministically linked to a registry and survey record—by using anonymous person identifiers—we could avoid uncertainty inherent to probabilistic record linkages (Schmidlin et al., 2013). The Swiss Harmonized Registry Act Revision of the year 2008 legally regulated the electronic exchange between communities and state personal registries, and led to virtually no lost-to-follow-up of individuals.

Our present study has limitations. First, the IP weighting approaches is a design-based approach, i.e., the probability distribution of participation in a random sample is treated as a fixed quantity (Hansen, Madow & Tepping, 1983; Little, 1983; Little, 2004). Design-based approaches have been shown to be only asymptotically unbiased, and potentially inefficient (Little, 2004; Kim & Skinner, 2013). In the present study we did not investigate model-based approaches, where non-participation in a random sample is predicted using regression models (Gelman, 2007; Little, 2007). Further, IP modelling relies on strong statistical assumptions which have to be fulfilled to provide unbiased statistical estimates (Scharfstein & Robins, 2002). In our setting, for example, exchangeability requires that the mortality among censored and uncensored individuals is the same in participating and not-participating individuals, given all predictors which predict mortality and those in the sampling design. However, researchers never know whether all relevant predictors were identified and collected in a real data setting. Second, our approach includes the outcome variable (i.e., survival status) in the IP weight construction. Thus, the validity of our estimates depends on the strength of the participation-outcome association and on the risk factor-outcome association (i.e., age and gender) (Pizzi et al., 2011). Third, our findings are limited to observed and available data within the registries and surveys. We could not investigate in more detail the real nonresponse patterns, i.e., which survey participants could not be contacted from the SFSO and whether sampled persons subsequently proved to have died were handled as non-responders or if they were excluded. Detailed information on those, who were contacted, but refused to participate, would strengthen our findings and could improve our estimates. Further, in the STATPOP population we could not differentiate whether individuals lived in a collective household (i.e., nursing homes) or not. This leads to a potential numerator/denominator bias, because the SE population is restricted to individuals living in a private household.

For many decades, most European countries relied on full enumeration censuses, where information for the whole population was collected at a specific reference date. A full enumeration census approach provides very detailed information on individual level (e.g., civil status, religion, household composition), but requires considerable financial and administrative resources. Registry-based and micro-census approaches are cost-efficient and require fewer resources. Among the countries of the United Nations Economic Commission for Europe (UNECE), there was an increase of registry-based and micro census approaches from 8% of all countries in 2000, to 19% in 2010 (UNECE (2017), accessed (30 November 2017)). However, from a statistical perspective they are prone to the sampling design errors, including informative sampling, and require adequate analysis techniques. In the following we give examples from other studies which analysed (or plan to analyse) mortality in samples of registry or census populations. One of the largest cohort studies worldwide—the Global Burden of Disease Study—depends on a combination of complete and partially-complete (i.e., sampling information) registry and census information from different countries worldwide (Abajobir et al., 2017). To account for sampling and non-response errors, the study authors differentiate between different data sources and adjust for country-specific non-sampling error in their analysis. A study from the United Kingdom analysed mortality patterns from 1991 to 2011 from three different regions and data sources (Katikireddi et al., 2017). The analysis was based on information from the whole population of Northern Ireland, a 5.3% sample of the Scottish population, and a 1% sample of the English and Wales population. The authors calculated mortality rates stratified by sex, by estimating the number of expected deaths for the Scottish and English/Wales samples using a simulation approach. A recent study from Finland investigated migrant mortality for the years 1939–2010 (Haukka et al., 2017). The authors used a 10% sample of the 1950 and 1970 Finish population censuses, and calculated all-cause and cause-specific mortality rates. The authors discuss possible selection and attrition biases in their study limitations, but did not address this kind of bias in sensitivity analyses. The German National Cohort (GNC) is a nationwide cohort study, based on a sample of 200,000 German residents, which are recruited through a network of 18 study centres (Ahrens et al., 2014). The authors estimated the anticipated response rate between 40 and 50%, but did not further specify how sampling bias will be included in their planned analyses. The above-mentioned examples show that a combination of registry-based information and population-sampling information play a crucial role in demographic and epidemiological research, and adequate analysis strategies are necessary to avoid bias due to non-response and non-participation.

In the present study, we concluded that in Switzerland—which uses a combination of registry and survey-based censuses—unweighted or CS weighted analyses lead to biased estimates, if the main outcome is survival time. The observed bias from unweighted and CS weighted survival analysis is of importance for absolute quantities (for example, mortality rates or life expectancy), but the bias may be less pronounced in relative outcomes measures (for example, hazard ratios or odds ratios). We highlight that the IP approach is not only restricted to the described setting of a change from a full enumeration census to a micro census system, but may be generalized to other settings. For example, non-response in a full enumeration census or lost-to-follow-up scenarios can be addressed by this approach to improve longitudinal validity, given the non-response or non-participation is known in the study population. The underrepresentation of population subgroups in survey data and possible selection bias have been extensively discussed in the literature, but survey-based mortality analyses often lack validation using registry data, or external data in general. Keiding & Louis (2016) exemplary discuss the limited generalisability of survey data when external validation is lacking for internet-based surveys with possible self-selection. Obviously, generalisability is more limited if the survey participation is informative.

Conclusion

We conclude from our study that weighted regression analysis of census-linked survey data has to be conducted carefully, and if possible, validated by registry-population information. If a validation or a registry sampling weight construction is missing, estimation results have to be interpreted with caution and might be biased.

Supplemental Information