Mark J. van der Laan

Coarsening at Random: Characterizations, Conjectures, Counter-Examples

The notion of coarsening at random (CAR) was introduced by Heitjan and Rubin (1991) to describe the most general form of randomly grouped, censored, or missing data, for which the coarsening mechanism can be ignored when making likelihood-based inference about the parameters of the distribution of the variable of interest. The CAR assumption is popular, and applications abound. However the full implications of the assumption have not been realized. Moreover a satisfactory theory of CAR for continuously distributed data—which is needed in many applications, particularly in survival analysis—hardly exists as yet. This paper gives a detailed study of CAR. We show that grouped data from a finite sample space always fit a CAR model: a nonparametric model for the variable of interest together with the assumption of an arbitrary CAR mechanism puts no restriction at all on the distribution of the observed data. In a slogan, CAR is everything. We describe what would seem to be the most general way CAR data could occur in practice, a sequential procedure called randomized monotone coarsening. We show that CAR mechanisms exist which are not of this type. Such a coarsening mechanism uses information about the underlying data which is not revealed to the observer, without this affecting the observer’s conclusions. In a second slogan, CAR is more than it seems. This implies that if the analyst can argue from subject-matter considerations that coarsened data is CAR, he or she has knowledge about the structure of the coarsening mechanism which can be put to good use in non-likelihood-based inference procedures. We argue that this is a valuable option in multivariate survival analysis. We give a new definition of CAR in general sample spaces, criticising earlier proposals, and we establish parallel results to the discrete case. The new definition focusses on the distribution rather than the density of the data. It allows us to generalise the theory of CAR to the important situation where coarsening variables (e.g., censoring times) are partially observed as well as the variables of interest.

Pillbox Organizers are Associated with Improved Adherence to HIV Antiretroviral Therapy and Viral Suppression: a Marginal Structural Model Analysis

BACKGROUND Pillbox organizers are inexpensive and easily used; however, their effect on adherence to antiretroviral medications is unknown. METHODS Data were obtained from an observational cohort of 245 human immunodeficiency virus (HIV)-infected subjects who were observed from 1996 through 2000 in San Francisco, California. Adherence was the primary outcome and was measured using unannounced monthly pill counts. Plasma HIV RNA level was considered as a secondary outcome. Marginal structural models were used to estimate the effect of pillbox organizer use on adherence and viral suppression, adjusting for confounding by CD4+ T cell count, viral load, prior adherence, recreational drug use, demographic characteristics, and current and past treatment. RESULTS Pillbox organizer use was estimated to improve adherence by 4.1%-4.5% and was associated with a decrease in viral load of 0.34-0.37 log10 copies/mL and a 14.2%-15.7% higher probability of achieving a viral load < or = 400 copies/mL (odds ratio, 1.8-1.9). All effect estimates were statistically significant. CONCLUSION Pillbox organizers appear to significantly improve adherence to antiretroviral therapy and to improve virologic suppression. We estimate that pillbox organizers may be associated with a cost of approximately

Statistical inference for simultaneous clustering of gene expression data.

19,000 per quality-adjusted life-year. Pillbox organizers should be a standard intervention to improve adherence to antiretroviral therapy.

Generalizations of Current Status Data With Applications

Current methods for analysis of gene expression data are mostly based on clustering and classification of either genes or samples. We offer support for the idea that more complex patterns can be identified in the data if genes and samples are considered simultaneously. We formalize the approach and propose a statistical framework for two-way clustering. A simultaneous clustering parameter is defined as a function theta=Phi(P) of the true data generating distribution P, and an estimate is obtained by applying this function to the empirical distribution P(n). We illustrate that a wide range of clustering procedures, including generalized hierarchical methods, can be defined as parameters which are compositions of individual mappings for clustering patients and genes. This framework allows one to assess classical properties of clustering methods, such as consistency, and to formally study statistical inference regarding the clustering parameter. We present results of simulations designed to assess the asymptotic validity of different bootstrap methods for estimating the distribution of Phi(P(n)). The method is illustrated on a publicly available data set.

Nonparametric locally efficient estimation of the Treatment Specific Survival distribution with right Censored Data and Covariates in Observational Studies

In estimation of a survival function, current status data arises when the only information available on individuals is their survival status at a single monitoring time. Here, we briefly review extensions of this form of data structure in two directions: (i) doubly censored current status data, where there is incomplete information on the origin of the failure time random variable, and (ii) current status information on more complicated stochastic processes. Simple examples of these data forms are presented for motivation.

Robust estimation of encouragement design intervention effects transported across sites

In many observational studies one is concerned with comparing treatment specific survival distributions in the presence of confounding factors and censoring. In this paper we develop locally efficient point and interval estimators of these survival distributions which adjust for confounding by using an estimate of the propensity score and concurrently allow for dependent censoring. The proposed methodology is an application of a general methodology for construction of locally efficient estimators as presented in Robins (1993) and Robins and Rotnitzky (1992). The practical performance of the methods are tested with a simulation study.

The Kaplan-Meier Integral in the Presence of Covariates: A Review

We develop robust targeted maximum likelihood estimators (TMLE) for transporting intervention effects from one population to another. Specifically, we develop TMLE estimators for three transported estimands: intent-to-treat average treatment effect (ATE) and complier ATE, which are relevant for encouragement-design interventions and instrumental variable analyses, and the ATE of the exposure on the outcome, which is applicable to any randomized or observational study. We demonstrate finite sample performance of these TMLE estimators using simulation, including in the presence of practical violations of the positivity assumption. We then apply these methods to the Moving to Opportunity trial, a multi-site, encouragement-design intervention in which families in public housing were randomized to receive housing vouchers and logistical support to move to low-poverty neighborhoods. This application sheds light on whether effect differences across sites can be explained by differences in population composition.

Identifying important explanatory variables for time-varying outcomes.

In a series of papers, Winfried Stute introduced and studied the Kaplan-Meier integral as an estimator of parameters of the joint distribution of survival times and covariates based on right censored survival times. We present a review of this work and show that his estimator has an inverse probability of censoring weighting (IPCW) representation. We further investigate large sample bias and efficiency. As a central application in a biostatistical context, Kaplan-Meier integrals are used to estimate transition probabilities in a non-Markov illness-death model. We extend already existing approaches by introducing a novel estimator that also works in the presence of additional left truncation. This application illustrates that Winfried Stute’s work can successfully be used to develop inferential statistical methods in complex survival models.

CV-TMLE for Nonpathwise Differentiable Target Parameters

Many applications in modern biology measure a large number of genomic or proteomic covariates and are interested in assessing the impact of each of these covariates on a particular outcome of interest. In a study which follows a cohort of HIV-positive patients over time, for example, a researcher may genotype the virus infecting each patient to ascertain the presence or absence of a large number of mutations, in the hope of identifying mutations that affect how a patient’s plasma HIV RNA level (viral load) responds to a new drug regimen. Along with an estimate of the impact of each mutation on the time course of viral load, the researcher would generally like to have a measure of the statistical significance of these estimates in order to identify those mutations that are most likely to be genuinely related to the outcome. Such information could then be used to inform the decision of which drugs should be included in the regimen of a patient with a particular pattern of mutations.

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

TMLE has been developed for the construction of efficient substitution estimators of pathwise differentiable target parameters. Many parameters are nonpathwise differentiable such as a density or regression curves at a single point in a nonparametric model. In these cases one often uses a specific estimator under a specific smoothness assumptions for which it is possible to establish a limit distribution and thereby provide statistical inference. However, such estimators do not adapt to the true unknown smoothness of the data density and, as a consequence, can be easily outperformed by an adaptive estimator that is able to adapt to the underlying true smoothness.