Medicine and Health Sciences Commons^™

Evaluation Of Progress Towards The Unaids 90-90-90 Hiv Care Cascade: A Description Of Statistical Methods Used In An Interim Analysis Of The Intervention Communities In The Search Study, Laura Balzer, Joshua Schwab, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

WHO guidelines call for universal antiretroviral treatment, and UNAIDS has set a global target to virally suppress most HIV-positive individuals. Accurate estimates of population-level coverage at each step of the HIV care cascade (testing, treatment, and viral suppression) are needed to assess the effectiveness of "test and treat" strategies implemented to achieve this goal. The data available to inform such estimates, however, are susceptible to informative missingness: the number of HIV-positive individuals in a population is unknown; individuals tested for HIV may not be representative of those whom a testing intervention fails to reach, and HIV-positive individuals with a viral …

The Statistics Of Sensitivity Analyses, Alexander R. Luedtke, Ivan Diaz, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose one wishes to estimate a causal parameter given a sample of observations. This requires making unidentifiable assumptions about an underlying causal mechanism. Sensitivity analyses help investigators understand what impact violations of these assumptions could have on the causal conclusions drawn from a study, though themselves rely on untestable (but hopefully more interpretable) assumptions. Díaz and van der Laan (2013) advocate the use of a sequence (or continuum) of interpretable untestable assumptions of increasing plausibility for the sensitivity analysis so that experts can have informed opinions about which are true. In this work, we argue that using appropriate statistical procedures …

Adaptive Pair-Matching In The Search Trial And Estimation Of The Intervention Effect, Laura Balzer, Maya L. Petersen, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In randomized trials, pair-matching is an intuitive design strategy to protect study validity and to potentially increase study power. In a common design, candidate units are identified, and their baseline characteristics used to create the best n/2 matched pairs. Within the resulting pairs, the intervention is randomized, and the outcomes measured at the end of follow-up. We consider this design to be adaptive, because the construction of the matched pairs depends on the baseline covariates of all candidate units. As consequence, the observed data cannot be considered as n/2 independent, identically distributed (i.i.d.) pairs of units, as current practice assumes. …

Estimating Effects On Rare Outcomes: Knowledge Is Power, Laura B. Balzer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Many of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect of an exposure or treatment on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional risk of the outcome, given the exposure and covariates. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides …

Variable Importance Analysis With The Multipim R Package, Stephan J. Ritter, Nicholas P. Jewell, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

We describe the R package multiPIM, including statistical background, functionality and user options. The package is for variable importance analysis, and is meant primarily for analyzing data from exploratory epidemiological studies, though it could certainly be applied in other areas as well. The approach taken to variable importance comes from the causal inference field, and is different from approaches taken in other R packages. By default, multiPIM uses a double robust targeted maximum likelihood estimator (TMLE) of a parameter akin to the attributable risk. Several regression methods/machine learning algorithms are available for estimating the nuisance parameters of the models, including …

Threshold Regression Models Adapted To Case-Control Studies, And The Risk Of Lung Cancer Due To Occupational Exposure To Asbestos In France, Antoine Chambaz, Dominique Choudat, Catherine Huber, Jean-Claude Pairon, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Asbestos has been known for many years as a powerful carcinogen. Our purpose is quantify the relationship between an occupational exposure to asbestos and an increase of the risk of lung cancer. Furthermore, we wish to tackle the very delicate question of the evaluation, in subjects suffering from a lung cancer, of how much the amount of exposure to asbestos explains the occurrence of the cancer. For this purpose, we rely on a recent French case-control study. We build a large collection of threshold regression models, data-adaptively select a better model in it by multi-fold likelihood-based cross-validation, then fit the …

The Impact Of Coarsening The Explanatory Variable Of Interest In Making Causal Inferences: Implicit Assumptions Behind Dichotomizing Variables, Ori M. Stitelman, Alan E. Hubbard, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

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 …

Causal Inference In Epidemiological Studies With Strong Confounding, Kelly L. Moore, Romain S. Neugebauer, Mark J. Van Der Laan, Ira B. Tager

U.C. Berkeley Division of Biostatistics Working Paper Series

One of the identifiabilty assumptions of causal effects defined by marginal structural model (MSM) parameters is the experimental treatment assignment (ETA) assumption. Practical violations of this assumption frequently occur in data analysis, when certain exposures are rarely observed within some strata of the population. The inverse probability of treatment weighted (IPTW) estimator is particularly sensitive to violations of this assumption, however, we demonstrate that this is a problem for all estimators of causal effects. This is due to the fact that the ETA assumption is about information (or lack thereof) in the data. A new class of causal models, causal …

Causal Inference For Nested Case-Control Studies Using Targeted Maximum Likelihood Estimation, Sherri Rose, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

A nested case-control study is conducted within a well-defined cohort arising out of a population of interest. This design is often used in epidemiology to reduce the costs associated with collecting data on the full cohort; however, the case control sample within the cohort is a biased sample. Methods for analyzing case-control studies have largely focused on logistic regression models that provide conditional and not marginal causal estimates of the odds ratio. We previously developed a Case-Control Weighted Targeted Maximum Likelihood Estimation (TMLE) procedure for case-control study designs, which relies on the prevalence probability q0. We propose the use of …

A Machine-Learning Algorithm For Estimating And Ranking The Impact Of Environmental Risk Factors In Exploratory Epidemiological Studies, Jessica G. Young, Alan E. Hubbard, B Eskenazi, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

No abstract provided.

A Small Sample Correction For Estimating Attributable Risk In Case-Control Studies, Daniel B. Rubin

U.C. Berkeley Division of Biostatistics Working Paper Series

The attributable risk, often called the population attributable risk, is in many epidemiological contexts a more relevant measure of exposure-disease association than the excess risk, relative risk, or odds ratio. When estimating attributable risk with case-control data and a rare disease, we present a simple correction to the standard approach making it essentially unbiased, and also less noisy. As with analogous corrections given in Jewell (1986) for other measures of association, the adjustment often won't make a substantial difference unless the sample size is very small or point estimates are desired within fine strata, but we discuss the possible utility …

Doubly Robust Ecological Inference, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The ecological inference problem is a famous longstanding puzzle that arises in many disciplines. The usual formulation in epidemiology is that we would like to quantify an exposure-disease association by obtaining disease rates among the exposed and unexposed, but only have access to exposure rates and disease rates for several regions. The problem is generally intractable, but can be attacked under the assumptions of King's (1997) extended technique if we can correctly specify a model for a certain conditional distribution. We introduce a procedure that it is a valid approach if either this original model is correct or if we …

Targeted Methods For Biomarker Discovery, The Search For A Standard, Catherine Tuglus, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

More often than not biomarker studies analyze large quantities of variables with complicated and generally unknown correlation structure. There are numerous statistical methods which attempt to unravel these variables and determine the underlying mechanism through identification of causally related biomarkers. Results from these methods are generally difficult to interpret and nearly impossible to compare across studies. The FDA has currently called for a standardization of methods and protocol for biomarker detection. In response, we propose targeted variable importance (tVIM) as a standardized method for biomarker discovery. Through the use of targeted Maximum Likelihood, tVIM provides double robust estimates of variable …

Empirical Efficiency Maximization, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

It has long been recognized that covariate adjustment can increase precision, even when it is not strictly necessary. The phenomenon is particularly emphasized in clinical trials, whether using continuous, categorical, or censored time-to-event outcomes. Adjustment is often straightforward when a discrete covariate partitions the sample into a handful of strata, but becomes more involved when modern studies collect copious amounts of baseline information on each subject.

The dilemma helped motivate locally efficient estimation for coarsened data structures, as surveyed in the books of van der Laan and Robins (2003) and Tsiatis (2006). Here one fits a relatively small working model …

The Causal Effect Of Recent Leisure-Time Physical Activity On All-Cause Mortality Among The Elderly, Oliver Bembom, Mark J. Van Der Laan, Ira B. Tager

U.C. Berkeley Division of Biostatistics Working Paper Series

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 …

Extending Marginal Structural Models Through Local, Penalized, And Additive Learning, Daniel Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal structural models (MSMs) allow one to form causal inferences from data, by specifying a relationship between a treatment and the marginal distribution of a corresponding counterfactual outcome. Following their introduction in Robins (1997), MSMs have typically been fit after assuming a semiparametric model, and then estimating a finite dimensional parameter. van der Laan and Dudoit (2003) proposed to instead view MSM fitting not as a task of semiparametric parameter estimation, but of nonparametric function approximation. They introduced a class of causal effect estimators based on mapping loss functions suitable for the unavailable counterfactual data to those suitable for the …

History-Adjusted Marginal Structural Models To Estimate Time-Varying Effect Modification , Maya L. Petersen, Steven G. Deeks, Jeffrey N. Martin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Much of epidemiology and clinical medicine is focused on the estimation of treatments or interventions administered over time. In such settings of longitudinal treatment, time-dependent confounding is often an important source of bias. Marginal structural models are a powerful tool for estimating the causal effect of a treatment using observational data, particularly when time-dependent confounding is present. Recent statistical work presented a generalization of marginal structural models, called history-adjusted marginal structural models. Unlike standard marginal structural models, history-adjusted marginal structural models can be used to estimate modification of treatment effects by time-varying covariates. Estimation of time-dependent causal effect modification is …

Population Intervention Models In Causal Inference, Alan E. Hubbard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a] treatment variable or risk variable on the distribution of a disease in a population. These models, as originally introduced by Robins (e.g., Robins (2000a), Robins (2000b), van der Laan and Robins (2002)), model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates, and its dependence on treatment. Marginal structural models are particularly useful in the context of longitudinal data structures, in which each subject's treatment and covariate history are measured over time, and an outcome is recorded at …

Estimation Of Direct Causal Effects, Maya L. Petersen, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Many common problems in epidemiologic and clinical research involve estimating the effect of an exposure on an outcome while blocking the exposure's effect on an intermediate variable. Effects of this kind are termed direct effects. Estimation of direct effects arises frequently in research aimed at understanding mechanistic pathways by which an exposure acts to cause or prevent disease, as well as in many other settings. Although multivariable regression is commonly used to estimate direct effects, this approach requires assumptions beyond those required for the estimation of total causal effects. In addition, multivariable regression estimates a particular type of direct effect, …

Direct Effect Models, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

The causal effect of a treatment on an outcome is generally mediated by several intermediate variables. Estimation of the component of the causal effect of a treatment that is mediated by a given intermediate variable (the indirect effect of the treatment), and the component that is not mediated by that intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Under the assumption of no-unmeasured confounders for treatment and the intermediate variable, Robins & Greenland (1992) define an individual direct effect as the counterfactual effect of …

Causal Inference In Longitudinal Studies With History-Restricted Marginal Structural Models, Romain Neugebauer, Mark J. Van Der Laan, Ira B. Tager

U.C. Berkeley Division of Biostatistics Working Paper Series

Causal Inference based on Marginal Structural Models (MSMs) is particularly attractive to subject-matter investigators because MSM parameters provide explicit representations of causal effects. We introduce History-Restricted Marginal Structural Models (HRMSMs) for longitudinal data for the purpose of defining causal parameters which may often be better suited for Public Health research. This new class of MSMs allows investigators to analyze the causal effect of a treatment on an outcome based on a fixed, shorter and user-specified history of exposure compared to MSMs. By default, the latter represents the treatment causal effect of interest based on a treatment history defined by the …

History-Adjusted Marginal Structural Models: Time-Varying Effect Modification, Maya L. Petersen, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment, particularly in the context of longitudinal data structures. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. However, standard MSM cannot incorporate modification of treatment effects by time-varying covariates. In the context of clinical decision- making such time-varying effect modifiers are often of considerable interest, as they are used in practice to guide treatment decisions for an individual. In this article we introduce a generalization of marginal structural models, which we …

History-Adjusted Marginal Structural Models: Optimal Treatment Strategies, Maya L. Petersen, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Much of clinical medicine involves choosing a future treatment plan that is expected to optimize a patient's long-term outcome, and modifying this treatment plan over time in response to changes in patient characteristics. However, dynamic treatment regimens, or decision rules for altering treatment in response to time-varying covariates, are rarely estimated based on observational data. In a companion paper, we introduced a generalization of Marginal Structural Models, named History-Adjusted Marginal Structural Models, that estimate modification of causal effects by time-varying covariates. Here, we illustrate how History-Adjusted Marginal Structural Models can be used to identify a specific type of optimal dynamic …

Data Adaptive Estimation Of The Treatment Specific Mean, Yue Wang, Oliver Bembom, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

An important problem in epidemiology and medical research is the estimation of the causal effect of a treatment action at a single point in time on the mean of an outcome, possibly within strata of the target population defined by a subset of the baseline covariates. Current approaches to this problem are based on marginal structural models, i.e., parametric models for the marginal distribution of counterfactural outcomes as a function of treatment and effect modifiers. The various estimators developed in this context furthermore each depend on a high-dimensional nuisance parameter whose estimation currently also relies on parametric models. Since misspecification …

History-Adjusted Marginal Structural Models And Statically-Optimal Dynamic Treatment Regimes, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. Marginal structural models are particularly useful in the context of longitudinal data structures, in which each subject's treatment and covariate history are measured over time, and an outcome is recorded at a final time point. However, the utility of these models for some applications has been limited by their inability to incorporate modification of the causal effect of treatment by time-varying covariates. …

Estimation Of Treatment Effects In Randomized Trials With Noncompliance And A Dichotomous Outcome , Mark J. Van Der Laan, Alan E. Hubbard, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a class of estimators of the treatment effect on a dichotomous outcome among the treated subjects within covariate and treatment arm strata in randomized trials with non-compliance. Recent articles by Vansteelandt and Goethebeur (2003) and Robins and Rotnitzky (2004) have presented consistent and asymptotically linear estimators of a causal odds ratio, which rely, beyond correct specification of a model for the causal odds ratio, on a correctly specified model for a potentially high dimensional nuisance parameter. In this article we propose consistent, asymptotically linear and locally efficient estimators of a causal relative risk and a new parameter -- …

Estimation Of Direct And Indirect Causal Effects In Longitudinal Studies, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

The causal effect of a treatment on an outcome is generally mediated by several intermediate variables. Estimation of the component of the causal effect of a treatment that is mediated by a given intermediate variable (the indirect effect of the treatment), and the component that is not mediated by that intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Under the assumption of no-unmeasured confounders, Robins & Greenland (1992) and Pearl (2000), develop two identifiability results for direct and indirect causal effects. They define an …

Multiple Testing Methods For Chip-Chip High Density Oligonucleotide Array Data, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit, Simon E. Cawley

U.C. Berkeley Division of Biostatistics Working Paper Series

Cawley et al. (2004) have recently mapped the locations of binding sites for three transcription factors along human chromosomes 21 and 22 using ChIP-Chip experiments. ChIP-Chip experiments are a new approach to the genome-wide identification of transcription factor binding sites and consist of chromatin (Ch) immunoprecipitation (IP) of transcription factor-bound genomic DNA followed by high density oligonucleotide hybridization (Chip) of the IP-enriched DNA. We investigate the ChIP-Chip data structure and propose methods for inferring the location of transcription factor binding sites from these data. The proposed methods involve testing for each probe whether it is part of a bound sequence …

Temporal Stability And Geographic Variation In Cumulative Case Fatality Rates And Average Doubling Times Of Sars Epidemics, Alison P. Galvani, Xiudong Lei, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

We analyze temporal stability and geographic trends in cumulative case fatality rates and average doubling times of severe acute respiratory syndrome (SARS). In part, we account for correlations between case fatality rates and doubling times through differences in control measures. We discuss factors that may alter future estimates of case fatality rates. We also discuss reasons for heterogeneity in doubling times among countries and the implications for the control of SARS in different countries and parameterization of epidemic models.

Analysis Of Longitudinal Marginal Structural Models , Jennifer F. Bryan, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator is used as an initial estimator and the corresponding treatment-orthogonalized, one-step estimator is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. A simulation study demonstrates that the the treatment-orthogonalized, one-step estimator is superior to the IPTW estimator in terms …