Maya Petersen - Academia.edu (original) (raw)
Papers by Maya Petersen
New England Journal of Medicine, 2019
BACKGROUND Universal antiretroviral therapy (ART) with annual population testing and a multidisea... more BACKGROUND Universal antiretroviral therapy (ART) with annual population testing and a multidisease, patient-centered strategy could reduce new human immunodeficiency virus (HIV) infections and improve community health. METHODS We randomly assigned 32 rural communities in Uganda and Kenya to baseline HIV and multidisease testing and national guideline-restricted ART (control group) or to baseline testing plus annual testing, eligibility for universal ART, and patient-centered care (intervention group). The primary end point was the cumulative incidence of HIV infection at 3 years. Secondary end points included viral suppression, death, tuberculosis, hypertension control, and the change in the annual incidence of HIV infection (which was evaluated in the intervention group only). RESULTS A total of 150,395 persons were included in the analyses. Population-level viral suppression among 15,399 HIV-infected persons was 42% at baseline and was higher in the intervention group than in the control group at 3 years (79% vs. 68%; relative prevalence, 1.15; 95% confidence interval [CI], 1.11 to 1.20). The annual incidence of HIV infection in the intervention group decreased by 32% over 3 years (from 0.43 to 0.31 cases per 100 personyears; relative rate, 0.68; 95% CI, 0.56 to 0.84). However, the 3-year cumulative incidence (704 incident HIV infections) did not differ significantly between the intervention group and the control group (0.77% and 0.81%, respectively; relative risk, 0.95; 95% CI, 0.77 to 1.17). Among HIV-infected persons, the risk of death by year 3 was 3% in the intervention group and 4% in the control group (0.99 vs. 1.29 deaths per 100 person-years; relative risk, 0.77; 95% CI, 0.64 to 0.93). The risk of HIV-associated tuberculosis or death by year 3 among HIV-infected persons was 4% in the intervention group and 5% in the control group (1.19 vs. 1.50 events per 100 person-years; relative risk, 0.79; 95% CI, 0.67 to 0.94). At 3 years, 47% of adults with hypertension in the intervention group and 37% in the control group had hypertension control (relative prevalence, 1.26; 95% CI, 1.15 to 1.39). CONCLUSIONS Universal HIV treatment did not result in a significantly lower incidence of HIV infection than standard care, probably owing to the availability of comprehensive baseline HIV testing and the rapid expansion of ART eligibility in the control group. (Funded by the National Institutes of Health and others; SEARCH ClinicalTrials.gov number, NCT01864603.
Statistics in medicine, Jan 6, 2017
Binary classification problems are ubiquitous in health and social sciences. In many cases, one w... more Binary classification problems are ubiquitous in health and social sciences. In many cases, one wishes to balance two competing optimality considerations for a binary classifier. For instance, in resource-limited settings, an human immunodeficiency virus prevention program based on offering pre-exposure prophylaxis (PrEP) to select high-risk individuals must balance the sensitivity of the binary classifier in detecting future seroconverters (and hence offering them PrEP regimens) with the total number of PrEP regimens that is financially and logistically feasible for the program. In this article, we consider a general class of constrained binary classification problems wherein the objective function and the constraint are both monotonic with respect to a threshold. These include the minimization of the rate of positive predictions subject to a minimum sensitivity, the maximization of sensitivity subject to a maximum rate of positive predictions, and the Neyman-Pearson paradigm, whic...
JAMA, Jan 6, 2017
Antiretroviral treatment (ART) is now recommended for all HIV-positive persons. UNAIDS has set gl... more Antiretroviral treatment (ART) is now recommended for all HIV-positive persons. UNAIDS has set global targets to diagnose 90% of HIV-positive individuals, treat 90% of diagnosed individuals with ART, and suppress viral replication among 90% of treated individuals, for a population-level target of 73% of all HIV-positive persons with HIV viral suppression. To describe changes in the proportions of HIV-positive individuals with HIV viral suppression, HIV-positive individuals who had received a diagnosis, diagnosed individuals treated with ART, and treated individuals with HIV viral suppression, following implementation of a community-based testing and treatment program in rural East Africa. Observational analysis based on interim data from 16 rural Kenyan (n = 6) and Ugandan (n = 10) intervention communities in the SEARCH Study, an ongoing cluster randomized trial. Community residents who were 15 years or older (N = 77 774) were followed up for 2 years (2013-2014 to 2015-2016). HIV se...
Epidemiologic Methods, 2016
In conducting studies on an exposure of interest, a systematic roadmap should be applied for tran... more In conducting studies on an exposure of interest, a systematic roadmap should be applied for translating causal questions into statistical analyses and interpreting the results. In this paper we describe an application of one such roadmap applied to estimating the joint effect of both time to availability of a nurse-based triage system (low risk express care (LREC)) and individual enrollment in the program among HIV patients in East Africa. Our study population is comprised of 16,513 subjects found eligible for this task-shifting program within 15 clinics in Kenya between 2006 and 2009, with each clinic starting the LREC program between 2007 and 2008. After discretizing follow-up into 90-day time intervals, we targeted the population mean counterfactual outcome (i. e. counterfactual probability of either dying or being lost to follow up) at up to 450 days after initial LREC eligibility under three fixed treatment interventions. These were (i) under no program availability during the...
Statistics in medicine, Jan 18, 2016
In cluster randomized trials, the study units usually are not a simple random sample from some cl... more In cluster randomized trials, the study units usually are not a simple random sample from some clearly defined target population. Instead, the target population tends to be hypothetical or ill-defined, and the selection of study units tends to be systematic, driven by logistical and practical considerations. As a result, the population average treatment effect (PATE) may be neither well defined nor easily interpretable. In contrast, the sample average treatment effect (SATE) is the mean difference in the counterfactual outcomes for the study units. The sample parameter is easily interpretable and arguably the most relevant when the study units are not sampled from some specific super-population of interest. Furthermore, in most settings, the sample parameter will be estimated more efficiently than the population parameter. To the best of our knowledge, this is the first paper to propose using targeted maximum likelihood estimation (TMLE) for estimation and inference of the sample ef...
In randomized trials, pair-matching is an intuitive design strategy to protect study validity and... more 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. Instead, the observed data consist of n dependent units. This paper explores the consequences of adaptive pair-matching in randomized trials for estimation of the average treatment effect, given the baseline covariates of the n study units. We contrast the unadjusted estimator with targeted minimum loss-based estimation (TMLE) and show substantial efficiency gains from matching and further gains with adjustment. This work is motivated by the Sustainable East Africa Research in Community Health (SEARCH) study, a community randomized trial to evaluate the impact of immediate and streamlined antiretroviral therapy on HIV incidence in rural East Africa.
JAIDS Journal of Acquired Immune Deficiency Syndromes, 2015
Author contributions: MP and DB conceived the study, planned and supervised the analysis, interpr... more Author contributions: MP and DB conceived the study, planned and supervised the analysis, interpreted results, and wrote the manuscript. EL, JS, VS, and DE implemented the analysis and contributed to interpretation and writing. MP, MVL, and EL developed, validated, and implemented analytic methods used, and contributed to interpretation and writing.
Fundamentals of Data Mining in Genomics and Proteomics, 2007
This chapter describes a systematic and targeted approach for estimating the impact of each of a ... more This chapter describes a systematic and targeted approach for estimating the impact of each of a large number of baseline covariates on an outcome that is measured repeatedly over time. These variable importance estimates can be adjusted for a user-specified set of confounders and lend themselves in a straightforward way to obtaining confidence intervals and p-values. Hence, they can in particular be used to identify a subset of baseline covariates that are the most important explanatory variables for the time-varying outcome of interest. We illustrate the methodology in a data analysis aimed at finding mutations of the human immunodeficiency virus that predict how well a patient responds to a drug regimen containing the two antiretroviral drugs lamivudine and stavudine. The most significant mutation we identify, 184IV, has previously been characterized as conferring high-level resistance to lamivudine. Our analysis furthermore points to a second mutation, 75AIMTS, that has been linked to moderate resistance to both lamivudine and stavudine.
Statistics in medicine, Jan 15, 2009
Researchers in clinical science and bioinformatics frequently aim to learn which of a set of cand... more 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 th...
Statistics in medicine, Jan 25, 2014
In randomized trials, pair-matching is an intuitive design strategy to protect study validity and... more 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 a consequence, the observed data cannot be considered as n/2 independent, identically distributed pairs of units, as common practice assumes. Instead, the observed data consist of n dependent units. This paper explores the consequences of adaptive pair-matching in randomized trials for estimation of the average treatment effect, conditional the baseline covariates of the n study units. By avoiding estimation of the covariate distribution, estimators of this conditional...
American journal of epidemiology, Jan 15, 2015
The consistency of propensity score (PS) estimators relies on correct specification of the PS mod... more The consistency of propensity score (PS) estimators relies on correct specification of the PS model. The PS is frequently estimated using main-effects logistic regression. However, the underlying model assumptions may not hold. Machine learning methods provide an alternative nonparametric approach to PS estimation. In this simulation study, we evaluated the benefit of using Super Learner (SL) for PS estimation. We created 1,000 simulated data sets (n = 500) under 4 different scenarios characterized by various degrees of deviance from the usual main-term logistic regression model for the true PS. We estimated the average treatment effect using PS matching and inverse probability of treatment weighting. The estimators' performance was evaluated in terms of PS prediction accuracy, covariate balance achieved, bias, standard error, coverage, and mean squared error. All methods exhibited adequate overall balancing properties, but in the case of model misspecification, SL performed bet...
Statistical Methods in Medical Research, 2010
The assumption of positivity or experimental treatment assignment requires that observed treatmen... more The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated and real data. Several approaches for improving the identifiability of parameters in the presence of positivity violations are reviewed. Potential responses to data sparsity include restriction of the covariate adjustment set, use of an alternative projection function to define the target parameter within a marginal structural ...
Statistical Applications in Genetics and Molecular Biology, 2007
Many alternative data-adaptive algorithms can be used to learn a predictor based on observed data... more Many alternative data-adaptive algorithms can be used to learn a predictor based on observed data. Examples of such learners include decision trees, neural networks, support vector regression, least angle regression, logic regression, and the Deletion/Substitution/Addition algorithm. The optimal learner for prediction will vary depending on the underlying data-generating distribution. In this article we introduce the "super learner", a prediction algorithm that applies any set of candidate learners and uses cross-validation to select between them. Theory shows that asymptotically the super learner performs essentially as well as or better than any of the candidate learners. In this article we present the theory behind the super learner, and illustrate its performance using simulations. We further apply the super learner to a data example, in which we predict the phenotypic antiretroviral susceptibility of HIV based on viral genotype. Specifically, we apply the super learne...
Journal of Multivariate Analysis, 2007
Many applications aim to learn a high dimensional parameter of a data generating distribution bas... more Many applications aim to learn a high dimensional parameter of a data generating distribution based on a sample of independent and identically distributed observations. For example, the goal might be to estimate the conditional mean of an outcome given a list of input variables. In this prediction context, bootstrap aggregating (bagging) has been introduced as a method to reduce the variance of a given estimator at little cost to bias. Bagging involves applying an estimator to multiple bootstrap samples and averaging the result across bootstrap samples. In order to address the curse of dimensionality, a common practice has been to apply bagging to estimators which themselves use cross-validation, thereby using cross-validation within a bootstrap sample to select fine-tuning parameters trading off bias and variance of the bootstrap sample-specific candidate estimators. In this article we point out that in order to achieve the correct bias variance trade-off for the parameter of interest, one should apply the cross-validation selector externally to candidate bagged estimators indexed by these fine-tuning parameters. We use three simulations to compare the new cross-validated bagging method with bagging of cross-validated estimators and bagging of noncross-validated estimators.
The International Journal of Biostatistics, 2012
Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the searc... more Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the search for optimized treatment regimes in ongoing treatment settings. Analyzing data for multiple time-point treatments with a view toward optimal treatment regimes is of interest in many types of afflictions: HIV infection, Attention Deficit Hyperactivity Disorder in children, leukemia, prostate cancer, renal failure, and many others. Methods for analyzing data from SRCTs exist but they are either inefficient or suffer from the drawbacks of estimating equation methodology. We describe an estimation procedure, targeted maximum likelihood estimation (TMLE), which has been fully developed and implemented in point treatment settings, including time to event outcomes, binary outcomes and continuous outcomes. Here we develop and implement TMLE in the SRCT setting. As in the former settings, the TMLE procedure is targeted toward a pre-specified parameter of the distribution of the observed data, and thereby achieves important bias reduction in estimation of that parameter. As with the so-called Augmented Inverse Probability of Censoring Weight (A-IPCW) estimator, TMLE is double-robust and locally efficient. We report simulation results corresponding to two data-generating distributions from a longitudinal data structure.
The International Journal of Biostatistics, 2008
The causal effect of a treatment on an outcome is generally mediated by several intermediate vari... more 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.
The International Journal of Biostatistics, 2007
The International Journal of Biostatistics, 2007
Marginal structural models (MSM) are an important class of models in causal inference. Given a lo... more 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 intention-to-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.
The International Journal of Biostatistics, 2005
Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a tr... more 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 treatmentspecific 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 timevarying covariates. Particularly in the context of clinical decision making, such time-varying effect modifiers are often of considerable or even primary interest, as they are used in practice to guide treatment decisions for an individual. In this article we propose a generalization of marginal structural models, which we call history-adjusted marginal structural models (HA-MSM). These models allow estimation of adjusted causal effects of treatment, given the observed past, and are therefore more suitable for making treatment decisions at the individual level and for identification of time-dependent effect modifiers. Specifically, a HA-MSM models the conditional distribution of treatment-specific counterfactual outcomes, conditional on the whole or a subset of the observed past up till a time-point, simultaneously for all time-points. Double robust inverse probability of treatment weighted estimators have been developed and studied in detail for standard MSM. We extend these results by proposing a class of double robust inverse probability of treatment weighted estimators for the unknown parameters of the HA-MSM. In addition, we show that HA-MSM provide a natural approach to identifying the dynamic treatment regimen which follows, at each time-point, the history-adjusted (up till the most recent time point) optimal static treatment regimen. We illustrate our results using an example drawn from the treatment of HIV infection.
Epidemiology, 2014
1. Specify knowledge about the system to be studied using a causal model. Represent background kn... more 1. Specify knowledge about the system to be studied using a causal model. Represent background knowledge about the system to be studied. A causal model describes the set of possible data-generating processes for this system. 2. Specify the observed data and their link to the causal model. Specify what variables have been or will be measured, and how these variables are generated by the system described by the causal model. 3. Specify a target causal quantity. Translate the scientific question into a formal causal quantity (defined as some parameter of the distribution of counterfactual random variables), following the process in Figure 3. 4. Assess identifiability. Assess whether it is possible to represent the target causal quantity as a parameter of the observed data distribution (estimand), and, if not, what further assumptions would allow one to do so. 5. State the statistical estimation problem. Specify the estimand and statistical model. If knowledge is sufficient to identify the causal effect of interest, commit to the corresponding estimand. If not, but one still wishes to proceed, choose an estimand that under minimal additional assumptions would equal or approximate the causal effect of interest. 6. Estimate. Estimate the target parameter of the observed data distribution, respecting the statistical model. 7. Interpret. Select among a hierarchy of interpretations, ranging from purely statistical to approximating a hypothetical randomized trial. FIGURE 1. A general roadmap for approaching causal questions.
New England Journal of Medicine, 2019
BACKGROUND Universal antiretroviral therapy (ART) with annual population testing and a multidisea... more BACKGROUND Universal antiretroviral therapy (ART) with annual population testing and a multidisease, patient-centered strategy could reduce new human immunodeficiency virus (HIV) infections and improve community health. METHODS We randomly assigned 32 rural communities in Uganda and Kenya to baseline HIV and multidisease testing and national guideline-restricted ART (control group) or to baseline testing plus annual testing, eligibility for universal ART, and patient-centered care (intervention group). The primary end point was the cumulative incidence of HIV infection at 3 years. Secondary end points included viral suppression, death, tuberculosis, hypertension control, and the change in the annual incidence of HIV infection (which was evaluated in the intervention group only). RESULTS A total of 150,395 persons were included in the analyses. Population-level viral suppression among 15,399 HIV-infected persons was 42% at baseline and was higher in the intervention group than in the control group at 3 years (79% vs. 68%; relative prevalence, 1.15; 95% confidence interval [CI], 1.11 to 1.20). The annual incidence of HIV infection in the intervention group decreased by 32% over 3 years (from 0.43 to 0.31 cases per 100 personyears; relative rate, 0.68; 95% CI, 0.56 to 0.84). However, the 3-year cumulative incidence (704 incident HIV infections) did not differ significantly between the intervention group and the control group (0.77% and 0.81%, respectively; relative risk, 0.95; 95% CI, 0.77 to 1.17). Among HIV-infected persons, the risk of death by year 3 was 3% in the intervention group and 4% in the control group (0.99 vs. 1.29 deaths per 100 person-years; relative risk, 0.77; 95% CI, 0.64 to 0.93). The risk of HIV-associated tuberculosis or death by year 3 among HIV-infected persons was 4% in the intervention group and 5% in the control group (1.19 vs. 1.50 events per 100 person-years; relative risk, 0.79; 95% CI, 0.67 to 0.94). At 3 years, 47% of adults with hypertension in the intervention group and 37% in the control group had hypertension control (relative prevalence, 1.26; 95% CI, 1.15 to 1.39). CONCLUSIONS Universal HIV treatment did not result in a significantly lower incidence of HIV infection than standard care, probably owing to the availability of comprehensive baseline HIV testing and the rapid expansion of ART eligibility in the control group. (Funded by the National Institutes of Health and others; SEARCH ClinicalTrials.gov number, NCT01864603.
Statistics in medicine, Jan 6, 2017
Binary classification problems are ubiquitous in health and social sciences. In many cases, one w... more Binary classification problems are ubiquitous in health and social sciences. In many cases, one wishes to balance two competing optimality considerations for a binary classifier. For instance, in resource-limited settings, an human immunodeficiency virus prevention program based on offering pre-exposure prophylaxis (PrEP) to select high-risk individuals must balance the sensitivity of the binary classifier in detecting future seroconverters (and hence offering them PrEP regimens) with the total number of PrEP regimens that is financially and logistically feasible for the program. In this article, we consider a general class of constrained binary classification problems wherein the objective function and the constraint are both monotonic with respect to a threshold. These include the minimization of the rate of positive predictions subject to a minimum sensitivity, the maximization of sensitivity subject to a maximum rate of positive predictions, and the Neyman-Pearson paradigm, whic...
JAMA, Jan 6, 2017
Antiretroviral treatment (ART) is now recommended for all HIV-positive persons. UNAIDS has set gl... more Antiretroviral treatment (ART) is now recommended for all HIV-positive persons. UNAIDS has set global targets to diagnose 90% of HIV-positive individuals, treat 90% of diagnosed individuals with ART, and suppress viral replication among 90% of treated individuals, for a population-level target of 73% of all HIV-positive persons with HIV viral suppression. To describe changes in the proportions of HIV-positive individuals with HIV viral suppression, HIV-positive individuals who had received a diagnosis, diagnosed individuals treated with ART, and treated individuals with HIV viral suppression, following implementation of a community-based testing and treatment program in rural East Africa. Observational analysis based on interim data from 16 rural Kenyan (n = 6) and Ugandan (n = 10) intervention communities in the SEARCH Study, an ongoing cluster randomized trial. Community residents who were 15 years or older (N = 77 774) were followed up for 2 years (2013-2014 to 2015-2016). HIV se...
Epidemiologic Methods, 2016
In conducting studies on an exposure of interest, a systematic roadmap should be applied for tran... more In conducting studies on an exposure of interest, a systematic roadmap should be applied for translating causal questions into statistical analyses and interpreting the results. In this paper we describe an application of one such roadmap applied to estimating the joint effect of both time to availability of a nurse-based triage system (low risk express care (LREC)) and individual enrollment in the program among HIV patients in East Africa. Our study population is comprised of 16,513 subjects found eligible for this task-shifting program within 15 clinics in Kenya between 2006 and 2009, with each clinic starting the LREC program between 2007 and 2008. After discretizing follow-up into 90-day time intervals, we targeted the population mean counterfactual outcome (i. e. counterfactual probability of either dying or being lost to follow up) at up to 450 days after initial LREC eligibility under three fixed treatment interventions. These were (i) under no program availability during the...
Statistics in medicine, Jan 18, 2016
In cluster randomized trials, the study units usually are not a simple random sample from some cl... more In cluster randomized trials, the study units usually are not a simple random sample from some clearly defined target population. Instead, the target population tends to be hypothetical or ill-defined, and the selection of study units tends to be systematic, driven by logistical and practical considerations. As a result, the population average treatment effect (PATE) may be neither well defined nor easily interpretable. In contrast, the sample average treatment effect (SATE) is the mean difference in the counterfactual outcomes for the study units. The sample parameter is easily interpretable and arguably the most relevant when the study units are not sampled from some specific super-population of interest. Furthermore, in most settings, the sample parameter will be estimated more efficiently than the population parameter. To the best of our knowledge, this is the first paper to propose using targeted maximum likelihood estimation (TMLE) for estimation and inference of the sample ef...
In randomized trials, pair-matching is an intuitive design strategy to protect study validity and... more 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. Instead, the observed data consist of n dependent units. This paper explores the consequences of adaptive pair-matching in randomized trials for estimation of the average treatment effect, given the baseline covariates of the n study units. We contrast the unadjusted estimator with targeted minimum loss-based estimation (TMLE) and show substantial efficiency gains from matching and further gains with adjustment. This work is motivated by the Sustainable East Africa Research in Community Health (SEARCH) study, a community randomized trial to evaluate the impact of immediate and streamlined antiretroviral therapy on HIV incidence in rural East Africa.
JAIDS Journal of Acquired Immune Deficiency Syndromes, 2015
Author contributions: MP and DB conceived the study, planned and supervised the analysis, interpr... more Author contributions: MP and DB conceived the study, planned and supervised the analysis, interpreted results, and wrote the manuscript. EL, JS, VS, and DE implemented the analysis and contributed to interpretation and writing. MP, MVL, and EL developed, validated, and implemented analytic methods used, and contributed to interpretation and writing.
Fundamentals of Data Mining in Genomics and Proteomics, 2007
This chapter describes a systematic and targeted approach for estimating the impact of each of a ... more This chapter describes a systematic and targeted approach for estimating the impact of each of a large number of baseline covariates on an outcome that is measured repeatedly over time. These variable importance estimates can be adjusted for a user-specified set of confounders and lend themselves in a straightforward way to obtaining confidence intervals and p-values. Hence, they can in particular be used to identify a subset of baseline covariates that are the most important explanatory variables for the time-varying outcome of interest. We illustrate the methodology in a data analysis aimed at finding mutations of the human immunodeficiency virus that predict how well a patient responds to a drug regimen containing the two antiretroviral drugs lamivudine and stavudine. The most significant mutation we identify, 184IV, has previously been characterized as conferring high-level resistance to lamivudine. Our analysis furthermore points to a second mutation, 75AIMTS, that has been linked to moderate resistance to both lamivudine and stavudine.
Statistics in medicine, Jan 15, 2009
Researchers in clinical science and bioinformatics frequently aim to learn which of a set of cand... more 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 th...
Statistics in medicine, Jan 25, 2014
In randomized trials, pair-matching is an intuitive design strategy to protect study validity and... more 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 a consequence, the observed data cannot be considered as n/2 independent, identically distributed pairs of units, as common practice assumes. Instead, the observed data consist of n dependent units. This paper explores the consequences of adaptive pair-matching in randomized trials for estimation of the average treatment effect, conditional the baseline covariates of the n study units. By avoiding estimation of the covariate distribution, estimators of this conditional...
American journal of epidemiology, Jan 15, 2015
The consistency of propensity score (PS) estimators relies on correct specification of the PS mod... more The consistency of propensity score (PS) estimators relies on correct specification of the PS model. The PS is frequently estimated using main-effects logistic regression. However, the underlying model assumptions may not hold. Machine learning methods provide an alternative nonparametric approach to PS estimation. In this simulation study, we evaluated the benefit of using Super Learner (SL) for PS estimation. We created 1,000 simulated data sets (n = 500) under 4 different scenarios characterized by various degrees of deviance from the usual main-term logistic regression model for the true PS. We estimated the average treatment effect using PS matching and inverse probability of treatment weighting. The estimators' performance was evaluated in terms of PS prediction accuracy, covariate balance achieved, bias, standard error, coverage, and mean squared error. All methods exhibited adequate overall balancing properties, but in the case of model misspecification, SL performed bet...
Statistical Methods in Medical Research, 2010
The assumption of positivity or experimental treatment assignment requires that observed treatmen... more The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated and real data. Several approaches for improving the identifiability of parameters in the presence of positivity violations are reviewed. Potential responses to data sparsity include restriction of the covariate adjustment set, use of an alternative projection function to define the target parameter within a marginal structural ...
Statistical Applications in Genetics and Molecular Biology, 2007
Many alternative data-adaptive algorithms can be used to learn a predictor based on observed data... more Many alternative data-adaptive algorithms can be used to learn a predictor based on observed data. Examples of such learners include decision trees, neural networks, support vector regression, least angle regression, logic regression, and the Deletion/Substitution/Addition algorithm. The optimal learner for prediction will vary depending on the underlying data-generating distribution. In this article we introduce the "super learner", a prediction algorithm that applies any set of candidate learners and uses cross-validation to select between them. Theory shows that asymptotically the super learner performs essentially as well as or better than any of the candidate learners. In this article we present the theory behind the super learner, and illustrate its performance using simulations. We further apply the super learner to a data example, in which we predict the phenotypic antiretroviral susceptibility of HIV based on viral genotype. Specifically, we apply the super learne...
Journal of Multivariate Analysis, 2007
Many applications aim to learn a high dimensional parameter of a data generating distribution bas... more Many applications aim to learn a high dimensional parameter of a data generating distribution based on a sample of independent and identically distributed observations. For example, the goal might be to estimate the conditional mean of an outcome given a list of input variables. In this prediction context, bootstrap aggregating (bagging) has been introduced as a method to reduce the variance of a given estimator at little cost to bias. Bagging involves applying an estimator to multiple bootstrap samples and averaging the result across bootstrap samples. In order to address the curse of dimensionality, a common practice has been to apply bagging to estimators which themselves use cross-validation, thereby using cross-validation within a bootstrap sample to select fine-tuning parameters trading off bias and variance of the bootstrap sample-specific candidate estimators. In this article we point out that in order to achieve the correct bias variance trade-off for the parameter of interest, one should apply the cross-validation selector externally to candidate bagged estimators indexed by these fine-tuning parameters. We use three simulations to compare the new cross-validated bagging method with bagging of cross-validated estimators and bagging of noncross-validated estimators.
The International Journal of Biostatistics, 2012
Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the searc... more Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the search for optimized treatment regimes in ongoing treatment settings. Analyzing data for multiple time-point treatments with a view toward optimal treatment regimes is of interest in many types of afflictions: HIV infection, Attention Deficit Hyperactivity Disorder in children, leukemia, prostate cancer, renal failure, and many others. Methods for analyzing data from SRCTs exist but they are either inefficient or suffer from the drawbacks of estimating equation methodology. We describe an estimation procedure, targeted maximum likelihood estimation (TMLE), which has been fully developed and implemented in point treatment settings, including time to event outcomes, binary outcomes and continuous outcomes. Here we develop and implement TMLE in the SRCT setting. As in the former settings, the TMLE procedure is targeted toward a pre-specified parameter of the distribution of the observed data, and thereby achieves important bias reduction in estimation of that parameter. As with the so-called Augmented Inverse Probability of Censoring Weight (A-IPCW) estimator, TMLE is double-robust and locally efficient. We report simulation results corresponding to two data-generating distributions from a longitudinal data structure.
The International Journal of Biostatistics, 2008
The causal effect of a treatment on an outcome is generally mediated by several intermediate vari... more 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.
The International Journal of Biostatistics, 2007
The International Journal of Biostatistics, 2007
Marginal structural models (MSM) are an important class of models in causal inference. Given a lo... more 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 intention-to-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.
The International Journal of Biostatistics, 2005
Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a tr... more 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 treatmentspecific 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 timevarying covariates. Particularly in the context of clinical decision making, such time-varying effect modifiers are often of considerable or even primary interest, as they are used in practice to guide treatment decisions for an individual. In this article we propose a generalization of marginal structural models, which we call history-adjusted marginal structural models (HA-MSM). These models allow estimation of adjusted causal effects of treatment, given the observed past, and are therefore more suitable for making treatment decisions at the individual level and for identification of time-dependent effect modifiers. Specifically, a HA-MSM models the conditional distribution of treatment-specific counterfactual outcomes, conditional on the whole or a subset of the observed past up till a time-point, simultaneously for all time-points. Double robust inverse probability of treatment weighted estimators have been developed and studied in detail for standard MSM. We extend these results by proposing a class of double robust inverse probability of treatment weighted estimators for the unknown parameters of the HA-MSM. In addition, we show that HA-MSM provide a natural approach to identifying the dynamic treatment regimen which follows, at each time-point, the history-adjusted (up till the most recent time point) optimal static treatment regimen. We illustrate our results using an example drawn from the treatment of HIV infection.
Epidemiology, 2014
1. Specify knowledge about the system to be studied using a causal model. Represent background kn... more 1. Specify knowledge about the system to be studied using a causal model. Represent background knowledge about the system to be studied. A causal model describes the set of possible data-generating processes for this system. 2. Specify the observed data and their link to the causal model. Specify what variables have been or will be measured, and how these variables are generated by the system described by the causal model. 3. Specify a target causal quantity. Translate the scientific question into a formal causal quantity (defined as some parameter of the distribution of counterfactual random variables), following the process in Figure 3. 4. Assess identifiability. Assess whether it is possible to represent the target causal quantity as a parameter of the observed data distribution (estimand), and, if not, what further assumptions would allow one to do so. 5. State the statistical estimation problem. Specify the estimand and statistical model. If knowledge is sufficient to identify the causal effect of interest, commit to the corresponding estimand. If not, but one still wishes to proceed, choose an estimand that under minimal additional assumptions would equal or approximate the causal effect of interest. 6. Estimate. Estimate the target parameter of the observed data distribution, respecting the statistical model. 7. Interpret. Select among a hierarchy of interpretations, ranging from purely statistical to approximating a hypothetical randomized trial. FIGURE 1. A general roadmap for approaching causal questions.