History-Adjusted Marginal Structural Models: Time-Varying Effect Modification

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment, particularly in the context of longitudinal data structures. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. However, standard MSM cannot incorporate modification of treatment effects by time-varying covariates. In the context of clinical decision- making such time-varying effect modifiers are often of considerable interest, as they are used in practice to guide treatment decisions for an individual. In this article we introduce a generalization of marginal structural models, which we call history-adjusted marginal structural models (HA-MSM). These models allow estimation of adjusted causal effects of treatment, given the observed past, and are therefore more suitable for making treatment decisions at the individual level and for identification of time-dependent effect modifiers. We provide a practical introduction to HA-MSM relying on an example drawn from the treatment of HIV, and discuss parameters estimated, assumptions, and implementation using standard software

Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting

Causal mediation analysis can improve understanding of the mechanisms underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the mediator-outcome relationship that is affected by prior exposure---an assumption frequently violated in practice. We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust semiparametric targeted minimum loss-based estimator for data-dependent stochastic direct and indirect effects. The proposed method treats the intermediate confounder affected by prior exposure as a time-varying confounder and intervenes stochastically on the mediator using a distribution which conditions on baseline covariates and marginalizes over the intermediate confounder. In addition, we assume the stochastic intervention is given, conditional on observed data, which results in a simpler estimator and weaker identification assumptions. We demonstrate the estimator's finite sample and robustness properties in a simple simulation study. We apply the method to an example from the Moving to Opportunity experiment. In this application, randomization to receive a housing voucher is the treatment/instrument that influenced moving to a low-poverty neighborhood, which is the intermediate confounder. We estimate the data-dependent stochastic direct effect of randomization to the voucher group on adolescent marijuana use not mediated by change in school district and the stochastic indirect effect mediated by change in school district. We find no evidence of mediation. Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.Comment: 24 pages, 2 tables, 2 figure

Generalizing the Causal Effect of Fertility on Female Labor Supply

Abstract We study the effect of fertility on labor supply in Argentina and Mexico exploiting a source of exogenous variability in family size first introduced by Angrist and Evans (1998) for the United States. Our results constitute the first external validation of the estimates obtained for the US. External validation of empirical results is central to the making of rigorous science, but there are very few attempts to establish it. We find that the estimates for the US can be generalized both qualitatively and quantitatively to the populations of two developing countries where, compared to the US, fertility is known to be higher, female education levels are much lower and there are fewer facilities for childcare.http://deepblue.lib.umich.edu/bitstream/2027.42/40011/2/wp625.pd

Causal inference for social network data

We describe semiparametric estimation and inference for causal effects using observational data from a single social network. Our asymptotic result is the first to allow for dependence of each observation on a growing number of other units as sample size increases. While previous methods have generally implicitly focused on one of two possible sources of dependence among social network observations, we allow for both dependence due to transmission of information across network ties, and for dependence due to latent similarities among nodes sharing ties. We describe estimation and inference for new causal effects that are specifically of interest in social network settings, such as interventions on network ties and network structure. Using our methods to reanalyze the Framingham Heart Study data used in one of the most influential and controversial causal analyses of social network data, we find that after accounting for network structure there is no evidence for the causal effects claimed in the original paper

Natural direct and indirect effects on the exposed : effect decomposition under weaker assumptions

We define natural direct and indirect effects on the exposed. We show that these allow for effect decomposition under weaker identification conditions than population natural direct and indirect effects. When no confounders of the mediator-outcome association are affected by the exposure, identification is possible under essentially the same conditions as for controlled direct effects. Otherwise, identification is still possible with additional knowledge on a nonidentifiable selection-bias function which measures the dependence of the mediator effect on the observed exposure within confounder levels, and which evaluates to zero in a large class of realistic data-generating mechanisms. We argue that natural direct and indirect effects on the exposed are of intrinsic interest in various applications. We moreover show that they coincide with the corresponding population natural direct and indirect effects when the exposure is randomly assigned. In such settings, our results are thus also of relevance for assessing population natural direct and indirect effects in the presence of exposure-induced mediator-outcome confounding, which existing methodology has not been able to address

Estimation of Causal Effects of Community Based Interventions

Suppose one assigns two interventions to a small number K of different populations or communities, and one measures covariates and outcomes on a random sample of independent individuals from each of the K populations. We investigate the problem of identification and estimation of the causal effect of the choice of intervention assigned at the community level, and, if the intervention is time-dependent, the causal effect of the changes in the intervention at time t, on the outcome. The challenge one is confronted with is that different populations have different environmental factors and that the intervention and environment are assigned to the whole population instead of to the individual. The question we wish to address is if one can still estimate the causal effect of the intervention one would have obtained if one would have combined all units across the multiple populations, each unit having their assigned environment and individual covariates, randomly assign the intervention among the two possible interventions to the unit, and then compare the outcome distributions for the two treatment groups: i.e., if one would have carried out the ideal experiment of randomizing treatment allocation to the units of the combined population, thereby dealing with confounding due to different units having different environments and corresponding individual covariates. We apply the roadmap based on causal modeling with a nonparametric structural equation model, which involves 1) defining the target causal effect as a parameter on the nonparametric structural equation model, 2) addressing the identifiability from the observed data, and, 3) given an identifiability result under the required assumptions, the efficient estimation of the resulting statistical target parameter through targeted maximum likelihood substitution estimators, using cross-validation to fine tune the estimators. The fundamental identifiability assumption we make is that one collects baseline covariates on the individual that block the effect of the environment on the outcome of interest, which is formulated as an exclusion restriction assumption in the nonparametric structural equation model. In addition, we utilize the understanding of the causal identifiability assumptions to evaluate the matched sampling design in which the units of different communities are matched on individual factors. We present efficient weighted targeted maximum likelihood estimators for these matched sampling designs, and we establish the concrete theoretical gain in information for the target parameter relative to independent sampling, by application of general results on case-control biased sampling in van der Laan (2008). Our methods can be reasonably well applied to the case that the intervention causes infectious behavior among individuals, possibly resulting in an enhanced effect, and to the case that interaction between individuals creates dependence between the individuals. However, the methods would not take into account the effect of this dependence among individuals on the assessment of uncertainty in the point estimates. For that purpose we also propose an estimate of standard error of the point estimate that takes into account arbitrary (and unknown to the user) dependence structures that still permit a central limit theorem based normal approximations. Our framework and methods are extended to the case that the communities are followed up over time and exposed to a single time-dependent treatment regimen, while also being subjected to changes in environment over time. In particular, we consider the case of estimation of a causal effect of a change in treatment over time based on observing a single community over time under a certain time-dependent treatment regimen. We also generalize our results to causal effects of combined community based intervention and individually assigned treatment on an outcome of interest. It is shown that G-computation formulas and corresponding estimators developed for causal effects of individually assigned treatments can be fully utilized to estimate these causal effects. Finally, we consider the case in which one is not willing to assume the exclusion restriction assumption, but many communities are sampled. For that purpose we propose statistical inference that naturally adapts to the degree at which the exclusion restriction assumption is approximated and the number of communities that are sampled. This allows for a unified framework for analyzing studies that involve community based interventions