A practical illustration of the importance of realistic individualized treatment rules in causal inference

The effect of vigorous physical activity on mortality in the elderly is difficult to estimate using conventional approaches to causal inference that define this effect by comparing the mortality risks corresponding to hypothetical scenarios in which all subjects in the target population engage in a given level of vigorous physical activity. A causal effect defined on the basis of such a static treatment intervention can only be identified from observed data if all subjects in the target population have a positive probability of selecting each of the candidate treatment options, an assumption that is highly unrealistic in this case since subjects with serious health problems will not be able to engage in higher levels of vigorous physical activity. This problem can be addressed by focusing instead on causal effects that are defined on the basis of realistic individualized treatment rules and intention-to-treat rules that explicitly take into account the set of treatment options that are available to each subject. We present a data analysis to illustrate that estimators of static causal effects in fact tend to overestimate the beneficial impact of high levels of vigorous physical activity while corresponding estimators based on realistic individualized treatment rules and intention-to-treat rules can yield unbiased estimates. We emphasize that the problems encountered in estimating static causal effects are not restricted to the IPTW estimator, but are also observed with the $G$-computation estimator, the DR-IPTW estimator, and the targeted MLE. Our analyses based on realistic individualized treatment rules and intention-to-treat rules suggest that high levels of vigorous physical activity may confer reductions in mortality risk on the order of 15-30%, although in most cases the evidence for such an effect does not quite reach the 0.05 level of significance.Comment: Published in at http://dx.doi.org/10.1214/07-EJS105 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimating the Effect of Vigorous Physical Activity on Mortality in the Elderly Based on Realistic Individualized Treatment and Intention-to-Treat Rules

The effect of vigorous physical activity on mortality in the elderly is difficult to estimate using conventional approaches to causal inference that define this effect by comparing the mortality risks corresponding to hypothetical scenarios in which all subjects in the target population engage in a given level of vigorous physical activity. A causal effect defined on the basis of such a static treatment intervention can only be identified from observed data if all subjects in the target population have a positive probability of selecting each of the candidate treatment options, an assumption that is highly unrealistic in this case since subjects with serious health problems will not be able to engage in higher levels of vigorous physical activity. This problem can be addressed by focusing instead on causal effects that are defined on the basis of realistic individualized treatment rules and intention-to-treat rules that explicitly take into account the set of treatment options that are available to each subject. We present a data analysis to illustrate that estimators of static causal effects in fact tend to overestimate the beneficial impact of high levels of vigorous physical activity while corresponding estimators based on realistic individualized treatment rules and intention-to-treat rules can yield unbiased estimates. We emphasize that the problems encountered in estimating static causal effects are not restricted to the IPTW estimator, but are also observed with the G-computation estimator, the DR-IPTW estimator, and the targeted MLE. Our analyses based on realistic individualized treatment rules and intention-to-treat rules suggest that high levels of vigorous physical activity may confer reductions in mortality risk on the order of 15-30%, although in most cases the evidence for such an effect does not quite reach the 0.05 level of significance

Analyzing Sequentially Randomized Trials Based on Causal Effect Models for Realistic Individualized Treatment Rules

In this paper, we argue that causal effect models for realistic individualized treatment rules represent an attractive tool for analyzing sequentially randomized trials. Unlike a number of methods proposed previously, this approach does not rely on the assumption that intermediate outcomes are discrete or that models for the distributions of these intermediate outcomes given the observed past are correctly specified. In addition, it generalizes the methodology for performing pairwise comparisons between individualized treatment rules by allowing the user to posit a marginal structural model for all candidate treatment rules simultaneously. If only a small number of candidate treatment rules are under consideration, a non-parametric marginal structural can be used to conveniently carry out all of the pairwise comparisons of interest in a single step. An appropriately chosen marginal structural model becomes particularly useful, however, as the number of candidate treatment rules increases, in which case an approach based on individual pairwise comparisons would be likely to suffer from too much sampling variability to provide an informative answer. In addition, such causal effect models represent an interesting alternative to methods previously proposed for selecting an optimal individualized treatment rule in that they give the user a sense of how the optimal outcome is estimated to change in the neighborhood of the identified optimum. We discuss an inverse-probability-of-treatment-weighted (IPTW) estimator for these causal effect models that is straightforward to implement using standard statistical software and develop an approach for constructing valid asymptotic confidence intervals based on the influence curve of this estimator. The methodology is illustrated in two simulation studies that are intended to mimic an HIV/AIDS trial

Supervised Detection of Conserved Motifs in DNA Sequences with cosmo

A number of computational methods have been proposed for identifying transcription factor binding sites from a set of unaligned sequences that are thought to share the motif in question. We here introduce an algorithm, called cosmo, that allows this search to be supervised by specifying a set of constraints that the position weight matrix of the unknown motif must satisfy. Such constraints may be formulated, for example, on the basis of prior knowledge about the structure of the transcription factor in question. The algorithm is based on the same two-component multinomial mixture model used by MEME, with stronger reliance, however, on the likelihood principle instead of more ad-hoc criteria like the E-value. The intensity parameter in the ZOOPS and TCM models, for instance, is estimated based on a profile-likelihood approach, and the width of the unknown motif is selected based on BIC. These changes allow cosmo to outperform MEME even in the absence of any constraints, as evidenced by 2- to 3-fold greater sensitivity in some simulation studies. Additional improvements in performance can be achieved by selecting the model type (OOPS, ZOOPS, or TCM) data-adaptively or by supplying correctly specified constraints, especially if the motif appears only as a weak signal in the data. The algorithm can data-adaptively choose between working in a given constrained model or in the completely unconstrained model, guarding against the risk of supplying mis-specified constraints. Simulation studies suggest that this approach can offer 3 to 3.5 times greater sensitivity than MEME. The algorithm has been implemented in the form of a stand-alone C program as well as a web application that can be accessed at http://cosmoweb.berkeley.edu. An R package is available through Bioconductor (http://bioconductor.org)

The Causal Effect of Recent Leisure-Time Physical Activity on All-Cause Mortality Among the Elderly

We analyze data collected as part of a prospective cohort study of elderly people living in and around Sonoma, CA, in order to estimate, for each round of interviews, the causal effect of leisure-time physical activity (LTPA) over the past year on the risk of mortality in the following two years. For each round of interviews, this effect is estimated separately for subpopulations defined based on past exercise habits, age, and whether subjects have had cardiac events in the past. This decomposition of the original longitudinal data structure into a series of point-treatment data structures corresponds to an application of history-adjusted marginal structural models as introduced by van der Laan et al. (2005). We propose five different estimators of the parameter of interest, based on various combinations of the usual G-computation, inverse-weighting, and double robust approaches for the two layers of missingness corresponding to the treatment mechanism and right-censoring by drop-out. The models for all nuisance parameters required by these different estimators are selected data-adaptively. For most subpopulations, our analyses suggest that high leisure-time physical activity reduces the subsequent two-year mortality risk by about 50%. Among populations of elderly people aged 75 years or older, these effect estimates are generally significant at the 0.05 level. Notably, our analyses also identify one subpopulation that is estimated to experience an increase in mortality risk when exercising at a higher level, namely subjects aged 75 years or older with previous cardiac events and no history of habitual exercise (RR: 2.33, 95% CI: 0.76-4.35)