Structural Nested Mean Models or History-Adjusted Marginal Structural Models for Time-Varying Effect Modification: An Application to Dental Data

In some epidemiological studies repeated collection of information is very common. Repeated collection of information over time is referred to as longitudinal data analysis. Traditional longitudinal data analysis comprises the use of methods such as random effects/mixed effects models, generalized estimating equations, and correlated data analysis. In these methods the common assumption is that the time-dependent covariate is not influenced by the exposure. However, if the time-dependent covariate at time, t, is influenced by exposure at, t − 1, research has shown that use of traditional methods would lead to biased estimation of the effect. For unbiased estimation, in time-dependent confounding, methods such as G-computation, marginal structural models using inverse probability of treatment weighting (MSM-IPTW) have been developed using the counterfactual data. Counterfactual data are the data that would had been observed if an intervention had been enforced. More recent research in the causal modeling area has shown that the MSM-IPTW would yield biased results in the presence of effect modification by time-varying confounders. To address this problem, methods such as structural nested mean models and history-adjusted marginal structural models have been developed. However, their use has been limited due to lack of availability of software. The aim of this chapter is to discuss, compare, and demonstrate the use of these two models in answering questions relating to oral health. For this demonstration we use data from dental sciences, where the interest is in the estimation of the effect of periodontal treatment on arterial stiffness, measured using pulse wave velocity.