Maya Petersen

Direct Effect Models

Mark J. van der Laan — Mon, 19 Jan 2009 05:47:25 PST

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 not mediated by an intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Robins, Greenland and Pearl develop counterfactual definitions for two types of direct effects, natural and controlled, and discuss assumptions, beyond those of sequential randomization, required for the identifiability of natural direct effects. Building on their earlier work and that of others, this article provides an alternative counterfactual definition of a natural direct effect, the identifiability of which is based only on the assumption of sequential randomization. In addition, a novel approach to direct effect estimation is presented, based on assuming a model directly on the natural direct effect, possibly conditional on a subset of the baseline covariates. Inverse probability of censoring weighted estimators, double robust inverse probability of censoring weighted estimators, likelihood-based estimators, and targeted maximum likelihood-based estimators are proposed for the unknown parameters of this novel causal model.

Biomarker discovery using targeted maximum-likelihood estimation: Application to the treatment of antiretroviral-resistant HIV infection

Oliver Bembom — Sat, 01 Nov 2008 14:16:28 PDT

Researchers in clinical science and bioinformatics frequently aim to learn which of a set of candidate biomarkers is important in determining a given outcome, and to rank the contributions of the candidates accordingly. This article introduces a new approach to research questions of this type, based on targeted maximum-likelihood estimation of variable importance measures. The methodology is illustrated using an example drawn from the treatment of HIV infection. Specifically, given a list of candidate mutations in the protease enzyme of HIV, we aim to discover mutations that reduce clinical virologic response to antiretroviral regimens containing the protease inhibitor lopinavir. In the context of this data example, the article reviews the motivation for covariate adjustment in the biomarker discovery process. A standard maximum-likelihood approach to this adjustment is compared with the targeted approach introduced here. Implementation of targeted maximum-likelihood estimation in the context of biomarker discovery is discussed, and the advantages of this approach are highlighted. Results of applying targeted maximum-likelihood estimation to identify lopinavir resistance mutations are presented and compared with results based on unadjusted mutation-outcome associations as well as results of a standard maximum-likelihood approach to adjustment. The subset of mutations identified by targeted maximum likelihood as significant contributors to lopinavir resistance is found to be in better agreement with the current understanding of HIV antiretroviral resistance than the corresponding subsets identified by the other two approaches. This finding suggests that targeted estimation of variable importance represents a promising approach to biomarker discovery.

Long-term consequences of the delay between virologic failure of highly active antiretroviral therapy and regimen modification

Maya L. Petersen — Sat, 01 Nov 2008 14:09:54 PDT

Objectives: Current treatment guidelines recommend immediate modification of antiretroviral therapy in HIV-infected individuals with incomplete viral suppression. These recommendations have not been tested in observational studies or large randomized trials. We evaluated the consequences of delayed modification following virologic failure. Design/methods: We used prospective data from two clinical cohorts to estimate the effect of time until regimen modification following first regimen failure on all-cause mortality. The impact of regimen type was also assessed. As the effect of delayed switching can be confounded if patients with a poor prognosis modify therapy earlier than those with a good prognosis, we used a statistical methodology - marginal structural models - to control for time-dependent confounding. Results: A total of 982 patients contributed 3414 person-years of follow-up following first regimen failure. Delay until treatment modification was associated with an elevated hazard of all-cause mortality among patients failing a reverse transcriptase inhibitor-based regimen (hazard ratio per additional 3 months delay: 1.23, 95% confidence interval: 1.08, 1.40), but appeared to have a small protective effect among patients failing a protease inhibitor-based regimen (hazard ratio per additional 3 months delay: 0.93, 95% confidence interval: 0.87, 0.99). Conclusion: Delay in modification after failure of regimens that do not contain a protease inhibitor is associated with increased mortality. Protease inhibitor-based regimens are less dependent on early versus delayed switching strategies. Efforts should be made to minimize delay until treatment modification in resource-poor regions, where the majority of patients are starting reverse transcriptase inhibitor-based regimens and HIV RNA monitoring may not be available.

History-Adjusted Marginal Structural Models to Estimate Time-Varying Effect Modification

Maya Petersen — Tue, 14 Aug 2007 12:00:10 PDT

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 frequently of great practical relevance. For example, clinical researchers are often interested in how the prognostic significance of a biomarker for treatment response can change over time. This article provides a practical introduction to the implementation and interpretation of history-adjusted marginal structural models. The method is illustrated using a clinical question drawn from the treatment of HIV infection. Observational cohort data from San Francisco, California, collected between 2000 and 2004, are used to estimate the effect of time until switching antiretroviral therapy regimen among patients receiving a non-suppressive regimen, and how this effect differs depending on CD4 T cell count.

Virologic Efficacy of Boosted Double vs. Boosted Single Protease Inhibitor Therapy.

Maya Petersen — Tue, 14 Aug 2007 11:55:24 PDT

Objective: Although regimens containing two protease inhibitor (PI) together with ritonavir boosting are used with the aim of improving virologic response to salvage therapy, there is little evidence to support or reject this approach. We compared the probability of attaining an undetectable HIV RNA level after using either boosted double or boosted single PI regimens. Design: Retrospective clinical cohort. Methods: PI-experienced subjects in a Northern California-based database who initiated either a boosted single or boosted double PI salvage therapy regimen were analysed. Traditional multivariable regression and marginal structural model analyses were used to compare the effects of the two regimens on virologic suppression 12-36 weeks after initiation of salvage therapy, controlling for confounding by baseline HIV RNA level, CD4 lymphocyte count, treatment history, drug resistance, and multiple characteristics of the salvage regimen. Results: Fifty-one percent of boosted single PI regimens (n=805) and 51.6% of boosted double PI regimens (n=183) achieved a plasma HIV RNA level of <75 >copies/ml at week 12-36. In models including multiple potentially confounding variables, estimates of the relative odds of suppression on boosted double versus boosted single PI regimens ranged from 1.17 (95% CI, 0.54-2.55) to 1.33 (95% CI, 0.82-2.14). Conclusions: We were not able to reject the null hypothesis that boosted double versus boosted single PI regimens, resulted in equivalent probabilities of virologic success.

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

Maya Petersen — Tue, 14 Aug 2007 11:44:10 PDT

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

Hospital-based surveillance of meningococcal meningitis in Salvador, Brazil

Soraia Cordeiro — Tue, 14 Aug 2007 11:39:45 PDT

This study aimed to describe the clinical, epidemiological and microbiological features of meningococcal meningitis in Salvador, Brazil. Between February 1996 and January 2001, a hospital-based surveillance prospectively identified cases of culture-positive meningococcal meningitis. Demographic and clinical data were collected through interview and medical chart review. Antisera and monoclonal antibodies were used to determine the serogroup and serotype:serosubtype of the isolates, respectively. Surveillance identified a total of 408 cases of meningococcal meningitis, with a case fatality rate of 8% (32/397). The mean annual incidence for the 304 culture-positive cases residing in metropolitan Salvador was 1.71 cases per 100 000 population. Infants <1 year old presented the highest incidence>(14.7 cases per 100 000 population). Of the 377 serogrouped isolates, 82%, 16%, 2% and 0.3% were serogroups B, C, W135 and Y, respectively. A single serotype:serosubtype (4,7:P1.19,15) accounted for 64% of all cases. Continued surveillance is necessary to characterise strains and to define future prevention and control strategies.

Individualized treatment rules: Generating candidate clinical trials

Maya Petersen — Mon, 11 Jun 2007 18:12:39 PDT

Individualized treatment rules, or rules for altering treatments over time in response to changes in individual covariates, are of primary importance in the practice of clinical medicine. Several statistical methods aim to estimate the rule, termed an optimal dynamic treatment regime, which will result in the best expected outcome in a population. In this article, we discuss estimation of an alternative type of dynamic regime--the statically optimal treatment rule. History-adjusted marginal structural models (HA-MSM) estimate individualized treatment rules that assign, at each time point, the first action of the future static treatment plan that optimizes expected outcome given a patient's covariates. However, as we discuss here, HA-MSM-derived rules can depend on the way in which treatment was assigned in the data from which the rules were derived. We discuss the conditions sufficient for treatment rules identified by HA-MSM to be statically optimal, or in other words, to select the optimal future static treatment plan at each time point, regardless of the way in which past treatment was assigned. The resulting treatment rules form appropriate candidates for evaluation using randomized controlled trials. We demonstrate that a history-adjusted individualized treatment rule is statically optimal if it depends on a set of covariates that are sufficient to control for confounding of the effect of past treatment history on outcome. Methods and results are illustrated using an example drawn from the antiretroviral treatment of patients infected with HIV. Specifically, we focus on rules for deciding when to modify the treatment of patients infected with resistant virus.

Statistical Learning of Origin-Specific Statically Optimal Individualized Treatment Rules

Mark J. van der Laan — Tue, 10 Apr 2007 13:34:58 PDT

Consider a longitudinal observational or controlled study in which one collects chronological data over time on a random sample of subjects. The time-dependent process one observes on each subject contains time-dependent covariates, time-dependent treatment actions, and an outcome process or single final outcome of interest. A statically optimal individualized treatment rule (as introduced in van der Laan et. al. (2005), Petersen et. al. (2007)) is a treatment rule which at any point in time conditions on a user-supplied subset of the past, computes the future static treatment regimen that maximizes a (conditional) mean future outcome of interest, and applies the first treatment action of the latter regimen. In particular, Petersen et. al. (2007) clarified that, in order to be statically optimal, an individualized treatment rule should not depend on the observed treatment mechanism. Petersen et. al. (2007) further developed estimators of statically optimal individualized treatment rules based on a past capturing all confounding of past treatment history on outcome. In practice, however, one typically wishes to find individualized treatment rules responding to a user-supplied subset of the complete observed history, which may not be sufficient to capture all confounding. The current article provides an important advance on Petersen et. al. (2007) by developing locally efficient double robust estimators of statically optimal ndividualized treatment rules responding to such a user-supplied subset of the past. However, failure to capture all confounding comes at a price; the static optimality of the resulting rules becomes origin-specific. We explain origin-specific static optimality, and discuss the practical importance of the proposed methodology. We further present the results of a data analysis in which we estimate a statically optimal rule for switching antiretroviral therapy among patients infected with resistant HIV virus.

Causal Effect Models for Realistic Individualized Treatment and Intention to Treat Rules

Mark J. van der Laan — Wed, 07 Mar 2007 08:57:33 PST

Marginal structural models (MSM) are an important class of models in causal inference. Given a longitudinal data structure observed on a sample of n independent and identically distributed experimental units, MSM model the counterfactual outcome distribution corresponding with a static treatment intervention, conditional on user-supplied baseline covariates. Identification of a static treatment regimen-specific outcome distribution based on observational data requires, beyond the standard sequential randomization assumption, the assumption that each experimental unit has positive probability of following the static treatment regimen. The latter assumption is called the experimental treatment assignment (ETA) assumption, and is parameter-specific. In many studies the ETA is violated because some of the static treatment interventions to be compared cannot be followed by all experimental units, due either to baseline characteristics or to the occurrence of certain events over time. For example, the development of adverse effects or contraindications can force a subject to stop an assigned treatment regimen.In this article we propose causal effect models for a user-supplied set of realistic individualized treatment rules. Realistic individualized treatment rules are defined as treatment rules which always map into the set of possible treatment options. Thus, causal effect models for realistic treatment rules do not rely on the ETA assumption and are fully identifiable from the data. Further, these models can be chosen to generalize marginal structural models for static treatment interventions. The estimating function methodology of Robins and Rotnitzky (1992) (analogue to its application in Murphy, et. al. (2001) for a single treatment rule) provides us with the corresponding locally efficient double robust inverse probability of treatment weighted estimator.In addition, we define causal effect models for "intention-to-treat" regimens. The proposed intentionto- treat interventions enforce a static intervention until the time point at which the next treatment does not belong to the set of possible treatment options, at which point the intervention is stopped. We provide locally efficient estimators of such intention-to-treat causal effects.