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.

A multilevel latent Markov model for the evaluation of nursing homes' performance.

The periodic evaluation of health care services is a primary concern for many institutions. We consider services provided by nursing homes with the aim of ranking a set of these structures with respect to their effect on resident health status. Since the overall health status is not directly observable, and given the longitudinal and multilevel structure of the available data, we rely on latent variable models and, in particular, on a multilevel latent Markov model where residents and nursing homes are the first and the second level units, respectively. The model includes individual covariates to account for resident characteristics. The impact of nursing home membership is modelled through a pair of random effects affecting the initial distribution and the transition probabilities between different levels of health status. Through the prediction of these random effects we obtain a ranking of the nursing homes. Furthermore, the proposed model accounts for nonignorable dropout due to resident death, which typically occurs in these contexts. The motivating dataset is gathered from the Long Term Care Facilities programme, a health care protocol implemented in Umbria (Italy). Our results show that differences in performance between nursing homes are statistically significant.