Data-adaptive longitudinal model selection in causal inference with collaborative targeted minimum loss-based estimation

R code disponible : https://www.mireilleschnitzer.com/collaborative-longitudinal-tmle.htmlCausal inference methods have been developed for longitudinal observationalstudy designs where confounding is thought to occur over time. In particular,one may estimate and contrast the population mean counterfactual outcomeunder specific exposure patterns. In such contexts, confounders of thelongitudinal treatment‐outcome association are generally identified usingdomain‐specific knowledge. However, this may leave an analyst with a largeset of potential confounders that may hinder estimation. Previous approaches todata‐adaptive model selection for this type of causal parameter were limited tothe single time‐point setting. We develop a longitudinal extension of acollaborative targeted minimum loss‐based estimation (C‐TMLE) algorithmthat can be applied to perform variable selection in the models for theprobability of treatment with the goal of improving the estimation of thepopulation mean counterfactual outcome under a fixed exposure pattern. Weinvestigate the properties of this method through a simulation study, comparingit to G‐Computation and inverse probability of treatment weighting. We thenapply the method in a real‐data example to evaluate the safety of trimester‐specific exposure to inhaled corticosteroids during pregnancy in women withmild asthma. The data for this study were obtained from the linkage ofelectronic health databases in the province of Quebec, Canada. The C‐TMLEcovariate selection approach allowed for a reduction of the set of potentialconfounders, which included baseline and longitudinal variables

Nonparametric estimation of a covariate-adjusted counterfactual treatment regimen response curve

Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which we refer to as a stratum based value function. We focus on semiparametric class of decision rules and propose a sieve based nonparametric covariate adjusted regimen-response curve estimator within that class. Our work contributes in several ways. First, we propose an inverse probability weighted nonparametrically efficient estimator of the smoothed regimen-response curve function. We show that asymptotic linearity is achieved when the nuisance functions are undersmoothed sufficiently. Asymptotic and finite sample criteria for undersmoothing are proposed. Second, using Gaussian process theory, we propose simultaneous confidence intervals for the smoothed regimen-response curve function. Third, we provide consistency and convergence rate for the optimizer of the regimen-response curve estimator; this enables us to estimate an optimal semiparametric rule. The latter is important as the optimizer corresponds with the optimal dynamic treatment regimen. Some finite-sample properties are explored with simulations

Comparing Approaches to Causal Inference for Longitudinal Data: Inverse Probability Weighting versus Propensity Scores

In observational studies for causal effects, treatments are assigned to experimental units without the benefits of randomization. As a result, there is the potential for bias in the estimation of the treatment effect. Two methods for estimating the causal effect consistently are Inverse Probability of Treatment Weighting (IPTW) and the Propensity Score (PS). We demonstrate that in many simple cases, the PS method routinely produces estimators with lower Mean-Square Error (MSE). In the longitudinal setting, estimation of the causal effect of a time-dependent exposure in the presence of time-dependent covariates that are themselves affected by previous treatment also requires adjustment approaches. We describe an alternative approach to the classical binary treatment propensity score termed the Generalized Propensity Score (GPS). Previously, the GPS has mainly been applied in a single interval setting; we use an extension of the GPS approach to the longitudinal setting. We compare the strengths and weaknesses of IPTW and GPS for causal inference in three simulation studies and two real data sets. Again, in simulation, the GPS appears to produce estimators with lower MSE.

Variable Selection in Causal Inference using a Simultaneous Penalization Method

In the causal adjustment setting, variable selection techniques based only on the outcome or only on the treatment allocation model can result in the omission of confounders and hence may lead to bias, or the inclusion of spurious variables and hence cause variance inflation, in estimation of the treatment effect. We propose a variable selection method using a penalized objective function that is based on both the outcome and treatment assignment models. The proposed method facilitates confounder selection in high-dimensional settings. We show that under some mild conditions our method attains the oracle property. The selected variables are used to form a doubly robust regression estimator of the treatment effect. Using the proposed method we analyze a set of data on economic growth and study the effect of life expectancy as a measure of population health on the average growth rate of gross domestic product per capita

Instrumental variable analysis with censored data in the presence of many weak instruments: Application to the effect of being sentenced to prison on time to employment

This article discusses an instrumental variable approach for analyzing censored data that includes many instruments that are weakly associated with the endogenous variable. We study the effect of imprisonment on time to employment using an administrative data on all individuals sentenced for felony in Michigan in the years 2003–2006. Despite the large body of research on the effect of prison on employment, this is still a controversial topic, especially since some of the studies could have been affected by unmeasured confounding. We take advantage of a natural experiment based on the random assignment of judges to felony cases and construct a vector of instruments based on judges’ ID that can avoid the confounding bias. However, some of the constructed instruments are weakly associated with the sentence type, that is, the endogenous variable, which can potentially lead to misleading results. Using a dimension reduction technique, we propose a novel semiparametric estimation procedure in a survival context that is robust to the presence of many weak instruments. Specifically, we construct a test statistic based on the structural failure time model and provide inference by inverting the testing procedure. Under some assumptions, the optimal choice of the test statistic has also been derived. Analyses show a significant negative impact of imprisonment on time to employment which is consistent with some of the previous results. Our simulation studies highlight the importance of accounting for weak instruments in the analyses in terms of both bias and inflated type-I error rates

Improved Doubly Robust Estimation in Marginal Mean Models for Dynamic Regimes

Doubly robust (DR) estimators are an important class of statistics derived from a theory of semiparametric efficiency. They have become a popular tool in causal inference, including applications to dynamic treatment regimes. The doubly robust estimators for the mean response to a dynamic treatment regime may be conceived through the augmented inverse probability weighted (AIPW) estimating function, defined as the sum of the inverse probability weighted (IPW) estimating function and an augmentation term. The IPW estimating function of the causal estimand via marginal structural model is defined as the complete-case score function for those subjects whose treatment sequence is consistent with the dynamic regime in question divided by the probability of observing the treatment sequence given the subject's treatment and covariate histories. The augmentation term is derived by projecting the IPW estimating function onto the nuisance tangent space and has mean-zero under the truth. The IPW estimator of the causal estimand is consistent if (i) the treatment assignment mechanism is correctly modeled and the AIPW estimator is consistent if either (i) is true or (ii) nested functions of intermediate and final outcomes are correctly modeled