The Impact Of Coarsening The Explanatory Variable Of Interest In Making Causal Inferences: Implicit Assumptions Behind Dichotomizing Variables

It is common in analyses designed to estimate the causal effect of a continuous exposure/treatment to dichotomize the variable of interest. By dichotomizing the variable and assessing the causal effect of the newly fabricated variable practitioners are implicitly making assumptions. However, in most analyses these assumptions are ignored. In this article we formally address what assumptions are made in dichotomizing variables to assess causal effects. We introduce two assumptions, either of which must be met, in order for the estimates of the causal effects to be unbiased estimates of the parameters of interest. We title those assumptions the Mechanism Equivalence and Effect Equivalence assumptions. Furthermore, we quantify the bias induced when these assumptions are violated. Lastly, we present an analysis of a Malaria study that exemplifies the danger of naively dichotomizing a continuous variable to assess a causal effect

A General Implementation of TMLE for Longitudinal Data Applied to Causal Inference in Survival Analysis

In many randomized controlled trials the outcome of interest is a time to event, and one measures on each subject baseline covariates and time-dependent covariates until the subject either drops-out, the time to event is observed, or the end of study is reached. The goal of such a study is to assess the causal effect of the treatment on the survival curve. Standard methods (e.g., Kaplan-Meier estimator, Cox-proportional hazards) ignore the available baseline and time-dependent covariates, and are therefore biased if the drop-out is affected by these covariates, and are always inefficient. We present a targeted maximum likelihood estimator of the causal effect of treatment on survival fully utilizing all the available covariate information, resulting in a double robust locally efficient substitution estimator that will be consistent and asymptotically linear if either the censoring mechanism is consistently estimated, or if the maximum likelihood based estimator is already consistent. In particular, under the independent censoring assumption assumed by current methods, this TMLE is always consistent and asymptotically linear so that it provides valid confidence intervals and tests. Furthermore, we show that when both the censoring mechanism and the initial maximum likelihood based estimator are mis-specified, and thus inconsistent, the TMLE exhibits stability when inverse probability weighted estimators and double robust estimating equation based methods break down The TMLE is used to analyze the Tshepo study, a study designed to evaluate the efficacy, tolerability, and development of drug resistance of six different first-line antiretroviral therapies. Most importantly this paper presents a general algorithm that may be used to create targeted maximum likelihood estimators of a large class of parameters of interest for general longitudinal data structures

Collaborative Targeted Maximum Likelihood For Time To Event Data

Current methods used to analyze time to event data either, rely on highly parametric assumptions which result in biased estimates of parameters which are purely chosen out of convenience, or are highly unstable because they ignore the global constraints of the true model. By using Targeted Maximum Likelihood Estimation one may consistently estimate parameters which directly answer the statistical question of interest. Targeted Maximum Likelihood Estimators are substitution estimators, which rely on estimating the underlying distribution. However, unlike other substitution estimators, the underlying distribution is estimated specifically to reduce bias in the estimate of the parameter of interest. We will present here an extension of Targeted Maximum Likelihood Estimation for observational time to event data, the Collaborative Targeted Maximum Likelihood Estimator for the treatment specific survival curve. Through the use of a simulation study we will show that this method improves on commonly used methods in both robustness and efficiency. In fact, we will show that in certain situations the C-TMLE produces estimates whose mean square error is lower than the semi-parametric efficiency bound. Lastly, we will show that the bootstrap is able to produce valid 95 percent confidence intervals in sparse data situations, while influence curve based inference breaks down

Collaborative Targeted Maximum Likelihood for Time to Event Data

Current methods used to analyze time to event data either rely on highly parametric assumptions which result in biased estimates of parameters which are purely chosen out of convenience, or are highly unstable because they ignore the global constraints of the true model. By using Targeted Maximum Likelihood Estimation (TMLE) one may consistently estimate parameters which directly answer the statistical question of interest. Targeted Maximum Likelihood Estimators are substitution estimators, which rely on estimating the underlying distribution. However, unlike other substitution estimators, the underlying distribution is estimated specifically to reduce bias in the estimate of the parameter of interest. We will present here an extension of TMLE for observational time to event data, the Collaborative Targeted Maximum Likelihood Estimator (C-TMLE) for the treatment specific survival curve. Through the use of a simulation study we will show that this method improves on commonly used methods in both robustness and efficiency. In fact, we will show that in certain situations the C-TMLE produces estimates whose mean square error is lower than the semi-parametric efficiency bound. We will also demonstrate that a semi-parametric efficient substitution estimator (TMLE) outperforms a semi-parametric efficient non-substitution estimator (the Augmented Inverse Probability Weighted estimator) in sparse data situations. Lastly, we will show that the bootstrap is able to produce valid 95 percent confidence intervals in sparse data situations, while influence curve based inference breaks down.

Targeted Maximum Likelihood Estimation of Effect Modification Parameters in Survival Analysis

The Cox proportional hazards model or its discrete time analogue, the logistic failure time model, posit highly restrictive parametric models and attempt to estimate parameters which are specific to the model proposed. These methods are typically implemented when assessing effect modification in survival analyses despite their flaws. The targeted maximum likelihood estimation (TMLE) methodology is more robust than the methods typically implemented and allows practitioners to estimate parameters that directly answer the question of interest. TMLE will be used in this paper to estimate two newly proposed parameters of interest that quantify effect modification in the time to event setting. These methods are then applied to the Tshepo study to assess if either gender or baseline CD4 level modify the effect of two cART therapies of interest, efavirenz (EFV) and nevirapine (NVP), on the progression of HIV. The results show that women tend to have more favorable outcomes using EFV while males tend to have more favorable outcomes with NVP. Furthermore, EFV tends to be favorable compared to NVP for individuals at high CD4 levels