Causal inference for continuous-time processes when covariates are observed only at discrete times

Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumptions that guarantee the consistency of discrete-time g-estimation. In more general cases, when those assumptions are violated, we propose a controlling-the-future method that performs at least as well as g-estimation in most scenarios and which provides consistent estimation in some cases where g-estimation is severely inconsistent. We apply the methods discussed in this paper to simulated data, as well as to a data set collected following a massive flood in Bangladesh, estimating the effect of diarrhea on children's height. Results from different methods are compared in both simulation and the real application.Comment: Published in at http://dx.doi.org/10.1214/10-AOS830 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Defining and Estimating Intervention Effects for Groups that will Develop an Auxiliary Outcome

It has recently become popular to define treatment effects for subsets of the target population characterized by variables not observable at the time a treatment decision is made. Characterizing and estimating such treatment effects is tricky; the most popular but naive approach inappropriately adjusts for variables affected by treatment and so is biased. We consider several appropriate ways to formalize the effects: principal stratification, stratification on a single potential auxiliary variable, stratification on an observed auxiliary variable and stratification on expected levels of auxiliary variables. We then outline identifying assumptions for each type of estimand. We evaluate the utility of these estimands and estimation procedures for decision making and understanding causal processes, contrasting them with the concepts of direct and indirect effects. We motivate our development with examples from nephrology and cancer screening, and use simulated data and real data on cancer screening to illustrate the estimation methods.Comment: Published at http://dx.doi.org/10.1214/088342306000000655 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal Restricted Estimation for More Efficient Longitudinal Causal Inference

Efficient semiparametric estimation of longitudinal causal effects is often analytically or computationally intractable. We propose a novel restricted estimation approach for increasing efficiency, which can be used with other techniques, is straightforward to implement, and requires no additional modeling assumptions

Random Effects Logistic Models for Analyzing Efficacy of a Longitudinal Randomized Treatment With Non-Adherence

We present a random effects logistic approach for estimating the efficacy of treatment for compliers in a randomized trial with treatment non-adherence and longitudinal binary outcomes. We use our approach to analyse a primary care depression intervention trial. The use of a random effects model to estimate efficacy supplements intent-to-treat longitudinal analyses based on random effects logistic models that are commonly used in primary care depression research. Our estimation approach is an extension of Nagelkerke et al.\u27s instrumental variables approximation for cross-sectional binary outcomes. Our approach is easily implementable with standard random effects logistic regression software. We show through a simulation study that our approach provides reasonably accurate inferences for the setting of the depression trial under model assumptions. We also evaluate the sensitivity of our approach to model assumptions for the depression trial

Macrolide Resistance in Adults with Bacteremic Pneumococcal Pneumonia

We conducted a case-control study of adults with bacteremic pneumococcal pneumonia to identify factors associated with macrolide resistance. Study participants were identified through population-based surveillance in a 5-county region surrounding Philadelphia. Forty-three hospitals contributed 444 patients, who were interviewed by telephone regarding potential risk factors. In multivariable analyses, prior exposure to a macrolide antimicrobial agent (odds ratio [OR] 2.8), prior flu vaccination (OR 2.0), and Hispanic ethnicity (OR 4.1) were independently associated with an increased probability of macrolide resistance, and a history of stroke was independently associated with a decreased probability of macrolide resistance (OR 0.2). Fifty-five percent of patients with macrolide-resistant infections reported no antimicrobial drug exposure in the preceding 6 months. Among patients who reported taking antimicrobial agents in the 6 months preceding infection, failure to complete the course of prescribed drugs was associated with an increased probability of macrolide resistance (OR 3.4)

Mediation Analysis With Principal Stratification

In assessing the mechanism of treatment efficacy in randomized clinical trials, investigators often perform mediation analyses by analyzing if the significant intent-to-treat treatment effect on outcome occurs through or around a third intermediate or mediating variable: indirect and direct effects, respectively. Standard mediation analyses assume sequential ignorability, i.e. conditional on covariates the intermediate or mediating factor is randomly assigned, as is the treatment in a randomized clinical trial. This research focuses on the application of the principal stratification (PS) approach for estimating the direct effect of a randomized treatment but without the standard sequential ignorability assumption. This approach is used to estimate the direct effect of treatment as a difference between expectations of potential outcomes within latent subgroups of participants for whom the intermediate variable behavior would be constant, regardless of the randomized treatment assignment. Using a Bayesian estimation procedure, we also assess the sensitivity of results based on the PS approach to heterogeneity of the variances among these principal strata. We assess this approach with simulations and apply it to two psychiatric examples. Both examples and the simulations indicated robustness of our findings to the homogeneous variance assumption. However, simulations showed that the magnitude of treatment effects derived under the PS approach were sensitive to model mis-specification

Surrogate Markers for Time-Varying Treatments and Outcomes

BACKGROUND: A surrogate marker is a variable commonly used in clinical trials to guide treatment decisions when the outcome of ultimate interest is not available. A good surrogate marker is one where the treatment effect on the surrogate is a strong predictor of the effect of treatment on the outcome. We review the situation when there is one treatment delivered at baseline, one surrogate measured at one later time point, and one ultimate outcome of interest and discuss new issues arising when variables are time-varying. METHODS: Most of the literature on surrogate markers has only considered simple settings with one treatment, one surrogate, and one outcome of interest at a fixed time point. However, more complicated time-varying settings are common in practice. In this article, we describe the unique challenges in two settings, time-varying treatments and time-varying surrogates, while relating the ideas back to the causal-effects and causal-association paradigms. CONCLUSION: In addition to discussing and extending popular notions of surrogacy to time-varying settings, we give examples illustrating that one can be misled by not taking into account time-varying information about the surrogate or treatment. We hope this article has provided some motivation for future work on estimation and inference in such settings