Mediation analysis with case-control sampling: Identification and estimation in the presence of a binary mediator.

With reference to a stratified case-control (CC) procedure based on a binary variable of primary interest, we derive the expression of the distortion induced by the sampling design on the parameters of the logistic model of a secondary variable. This is particularly relevant when performing mediation analysis (possibly in a causal framework) with stratified case-control (SCC) data in settings where both the outcome and the mediator are binary. Despite being designed for parametric identification, our strategy is general and can be used also in a nonparametric context. With reference to parametric estimation, we derive the maximum likelihood (ML) estimator and the M-estimator of the joint outcome-mediator parameter vector. We then conduct a simulation study focusing on the main causal mediation quantities (i.e., natural effects) and comparing M- and ML estimation to existing methods, based on weighting. As an illustrative example, we reanalyze a German CC data set in order to investigate whether the effect of reduced immunocompetency on listeriosis onset is mediated by the intake of gastric acid suppressors.

Causal inference accounting for unobserved confounding after outcome regression and doubly robust estimation.

Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We therefore develop uncertainty intervals for average causal effects based on outcome regression estimators and doubly robust estimators, which provide inference taking into account both sampling variability and uncertainty due to unobserved confounders. In contrast with sampling variation, uncertainty due to unobserved confounding does not decrease with increasing sample size. The intervals introduced are obtained by modeling the treatment assignment mechanism and its correlation with the outcome given the observed confounders, allowing us to derive the bias of the estimators due to unobserved confounders. We are thus also able to contrast the size of the bias due to violation of the unconfoundedness assumption, with bias due to misspecification of the models used to explain potential outcomes. This is illustrated through numerical experiments where bias due to moderate unobserved confounding dominates misspecification bias for typical situations in terms of sample size and modeling assumptions. We also study the empirical coverage of the uncertainty intervals introduced and apply the results to a study of the effect of regular food intake on health. An R-package implementing the inference proposed is available.

Predictors of decline in self-reported health: addressing non-ignorable dropout in longitudinal studies of aging.

Predictors of decline in health in older populations have been investigated in multiple studies before. Most longitudinal studies of aging, however, assume that dropout at follow-up is ignorable (missing at random) given a set of observed characteristics at baseline. The objective of this study was to address non-ignorable dropout in investigating predictors of declining self-reported health (SRH) in older populations (50 years or older) in Sweden, the Netherlands, and Italy. We used the SHARE panel survey, and since only 2895 out of the original 5657 participants in the survey 2004 were followed up in 2013, we studied whether the results were sensitive to the expectation that those dropping out have a higher proportion of decliners in SRH. We found that older age and a greater number of chronic diseases were positively associated with a decline in self-reported health in the three countries studies here. Maximum grip strength was associated with decline in self-reported health in Sweden and Italy, and self-reported limitations in normal activities due to health problems were associated with decline in self-reported health in Sweden. These results were not sensitive to non-ignorable dropout. On the other hand, although obesity was associated with decline in a complete case analysis, this result was not confirmed when performing a sensitivity analysis to non-ignorable dropout. The findings, thereby, contribute to the literature in understanding the robustness of longitudinal study results to non-ignorable dropout while considering three different population samples in Europe.