arXiv subjects

Stephen R. Cole

Publications and source records attributed to Stephen R. Cole.

11 recordsLinked to original sources

arXiv2026

A Law of Iterated Expectation Primer for Causal Inference

The g-formula is a foundational tool for identifying causal effects in observational data. This tool is based on the law of iterated expectation, a key mathematical identity in statistics. However, the notation with which the law of iterated expectation and the g-formula is expressed can be opaque to those with little background in statistics. We provide a primer introducing the law of iterated expectation, the integration notation used to express it, and its role for causal effect identification via the g-formula. Under the assumptions of causal consistency, positivity, and conditional exchangeability, the law of iterated expectation can be rewritten as a causal standardization formula (the g-formula) in two nonparametrically equivalent forms: a non-iterative conditional expectation (NICE) form involving a single weighted average of conditional outcome means, and an iterative conditional expectation (ICE) form involving nested expectations. We illustrate both forms using three progressively complex numerical examples: a time-fixed example with a single binary confounder, a time-fixed example with discrete and continuous confounders, and a time-varying example with two timepoints. We provide clarity on what the law of iterated expectation is, how it is related to the g-formula, and how to gain intuition of its mathematical formulations in actual data examples that can be generalized to a range of settings.

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arXiv2026

Investigating symptom duration using current status data: a case study of post-acute COVID-19 syndrome

For infectious diseases, characterizing symptom duration is of clinical and public health importance. Symptom duration may be assessed by surveying infected individuals and querying symptom status at the time of survey response. For example, in a SARS-CoV-2 testing program at the University of Washington, participants were surveyed at least $28$ days after testing positive and asked to report current symptom status. This study design yielded current status data: outcome measurements for each respondent consisted only of the time of survey response and a binary indicator of whether symptoms had resolved by that time. Such study design benefits from limited risk of recall bias, but analyzing the resulting data necessitates tailored statistical tools. Here, we review methods for current status data and describe a novel application of modern nonparametric techniques to this setting. The proposed approach is valid under weaker assumptions compared to existing methods, allows use of flexible machine learning tools, and handles potential survey nonresponse. From the university study, under an assumption that the survey response time is conditionally independent of symptom resolution time within strata of measured covariates, we estimate that 19% of participants experienced ongoing symptoms 30 days after testing positive, decreasing to 7% at 90 days. We assess the sensitivity of these results to deviations from conditional independence, finding the estimates to be more sensitive to assumption violations at 30 days compared to 90 days. Female sex, fatigue during acute infection, and higher viral load were associated with slower symptom resolution.

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arXiv2024

Double Robust Variance Estimation with Parametric Working Models

Doubly robust estimators have gained popularity in the field of causal inference due to their ability to provide consistent point estimates when either an outcome or exposure model is correctly specified. However, for nonrandomized exposures the influence function based variance estimator frequently used with doubly robust estimators of the average causal effect is only consistent when both working models (i.e., outcome and exposure models) are correctly specified. Here, the empirical sandwich variance estimator and the nonparametric bootstrap are demonstrated to be doubly robust variance estimators. That is, they are expected to provide valid estimates of the variance leading to nominal confidence interval coverage when only one working model is correctly specified. Simulation studies illustrate the properties of the influence function based, empirical sandwich, and nonparametric bootstrap variance estimators in the setting where parametric working models are assumed. Estimators are applied to data from the Improving Pregnancy Outcomes with Progesterone (IPOP) study to estimate the effect of maternal anemia on birth weight among women with HIV.

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arXiv2024

Finite sample performance of optimal treatment rule estimators with right-censored outcomes

Patient care may be improved by recommending treatments based on patient characteristics when there is treatment effect heterogeneity. Recently, there has been a great deal of attention focused on the estimation of optimal treatment rules that maximize expected outcomes. However, there has been comparatively less attention given to settings where the outcome is right-censored, especially with regard to the practical use of estimators. In this study, simulations were undertaken to assess the finite-sample performance of estimators for optimal treatment rules and estimators for the expected outcome under treatment rules. The simulations were motivated by the common setting in biomedical and public health research where the data is observational, survival times may be right-censored, and there is interest in estimating baseline treatment decisions to maximize survival probability. A variety of outcome regression and direct search estimation methods were compared for optimal treatment rule estimation across a range of simulation scenarios. Methods that flexibly model the outcome performed comparatively well, including in settings where the treatment rule was non-linear. R code to reproduce this study's results are available on Github.

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arXiv2023

Exposure Effects on Count Outcomes with Observational Data, with Application to Incarcerated Women

Causal inference methods can be applied to estimate the effect of a point exposure or treatment on an outcome of interest using data from observational studies. For example, in the Women's Interagency HIV Study, it is of interest to understand the effects of incarceration on the number of sexual partners and the number of cigarettes smoked after incarceration. In settings like this where the outcome is a count, the estimand is often the causal mean ratio, i.e., the ratio of the counterfactual mean count under exposure to the counterfactual mean count under no exposure. This paper considers estimators of the causal mean ratio based on inverse probability of treatment weights, the parametric g-formula, and doubly robust estimation, each of which can account for overdispersion, zero-inflation, and heaping in the measured outcome. Methods are compared in simulations and are applied to data from the Women's Interagency HIV Study.

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arXiv2023

Fusing Trial Data for Treatment Comparisons: Single versus Multi-Span Bridging

While randomized controlled trials (RCTs) are critical for establishing the efficacy of new therapies, there are limitations regarding what comparisons can be made directly from trial data. RCTs are limited to a small number of comparator arms and often compare a new therapeutic to a standard of care which has already proven efficacious. It is sometimes of interest to estimate the efficacy of the new therapy relative to a treatment that was not evaluated in the same trial, such as a placebo or an alternative therapy that was evaluated in a different trial. Such multi-study comparisons are challenging because of potential differences between trial populations that can affect the outcome. In this paper, two bridging estimators are considered that allow for comparisons of treatments evaluated in different trials using data fusion methods to account for measured differences in trial populations. A "multi-span'' estimator leverages a shared arm between two trials, while a "single-span'' estimator does not require a shared arm. A diagnostic statistic that compares the outcome in the standardized shared arms is provided. The two estimators are compared in simulations, where both estimators demonstrate minimal empirical bias and nominal confidence interval coverage when the identification assumptions are met. The estimators are applied to data from the AIDS Clinical Trials Group 320 and 388 to compare the efficacy of two-drug versus four-drug antiretroviral therapy on CD4 cell counts among persons with advanced HIV. The single-span approach requires fewer identification assumptions and was more efficient in simulations and the application.

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arXiv2022

Estimating SARS-CoV-2 Seroprevalence

Governments and public health authorities use seroprevalence studies to guide responses to the COVID-19 pandemic. Seroprevalence surveys estimate the proportion of individuals who have detectable SARS-CoV-2 antibodies. However, serologic assays are prone to misclassification error, and non-probability sampling may induce selection bias. In this paper, nonparametric and parametric seroprevalence estimators are considered that address both challenges by leveraging validation data and assuming equal probabilities of sample inclusion within covariate-defined strata. Both estimators are shown to be consistent and asymptotically normal, and consistent variance estimators are derived. Simulation studies are presented comparing the estimators over a range of scenarios. The methods are used to estimate SARS-CoV-2 seroprevalence in New York City, Belgium, and North Carolina.

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arXiv2022

Generalizing trial evidence to target populations in non-nested designs: Applications to AIDS clinical trials

Comparative effectiveness evidence from randomized trials may not be directly generalizable to a target population of substantive interest when, as in most cases, trial participants are not randomly sampled from the target population. Motivated by the need to generalize evidence from two trials conducted in the AIDS Clinical Trials Group (ACTG), we consider weighting, regression and doubly robust estimators to estimate the causal effects of HIV interventions in a specified population of people living with HIV in the USA. We focus on a non-nested trial design and discuss strategies for both point and variance estimation of the target population average treatment effect. Specifically in the generalizability context, we demonstrate both analytically and empirically that estimating the known propensity score in trials does not increase the variance for each of the weighting, regression and doubly robust estimators. We apply these methods to generalize the average treatment effects from two ACTG trials to specified target populations and operationalize key practical considerations. Finally, we report on a simulation study that investigates the finite-sample operating characteristics of the generalizability estimators and their sandwich variance estimators.

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arXiv2020

Tutorial: Introduction to computational causal inference using reproducible Stata, R and Python code

The purpose of many health studies is to estimate the effect of an exposure on an outcome. It is not always ethical to assign an exposure to individuals in randomised controlled trials, instead observational data and appropriate study design must be used. There are major challenges with observational studies, one of which is confounding that can lead to biased estimates of the causal effects. Controlling for confounding is commonly performed by simple adjustment for measured confounders; although, often this is not enough. Recent advances in the field of causal inference have dealt with confounding by building on classical standardisation methods. However, these recent advances have progressed quickly with a relative paucity of computational-oriented applied tutorials contributing to some confusion in the use of these methods among applied researchers. In this tutorial, we show the computational implementation of different causal inference estimators from a historical perspective where different estimators were developed to overcome the limitations of the previous one. Furthermore, we also briefly introduce the potential outcomes framework, illustrate the use of different methods using an illustration from the health care setting, and most importantly, we provide reproducible and commented code in Stata, R and Python for researchers to apply in their own observational study. The code can be accessed at https://github.com/migariane/TutorialCausalInferenceEstimators

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arXiv2020

Sensitivity analyses for effect modifiers not observed in the target population when generalizing treatment effects from a randomized controlled trial: Assumptions, models, effect scales, data scenarios, and implementation details

Background: Randomized controlled trials are often used to inform policy and practice for broad populations. The average treatment effect (ATE) for a target population, however, may be different from the ATE observed in a trial if there are effect modifiers whose distribution in the target population is different that from that in the trial. Methods exist to use trial data to estimate the target population ATE, provided the distributions of treatment effect modifiers are observed in both the trial and target population -- an assumption that may not hold in practice. Methods: The proposed sensitivity analyses address the situation where a treatment effect modifier is observed in the trial but not the target population. These methods are based on an outcome model or the combination of such a model and weighting adjustment for observed differences between the trial sample and target population. They accommodate several types of outcome models: linear models (including single time outcome and pre- and post-treatment outcomes) for additive effects, and models with log or logit link for multiplicative effects. We clarify the methods' assumptions and provide detailed implementation instructions. Illustration: We illustrate the methods using an example generalizing the effects of an HIV treatment regimen from a randomized trial to a relevant target population. Conclusion: These methods allow researchers and decision-makers to have more appropriate confidence when drawing conclusions about target population effects.

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arXiv2016

Sensitivity analysis for an unobserved moderator in RCT-to-target-population generalization of treatment effects

In the presence of treatment effect heterogeneity, the average treatment effect (ATE) in a randomized controlled trial (RCT) may differ from the average effect of the same treatment if applied to a target population of interest. If all treatment effect moderators are observed in the RCT and in a dataset representing the target population, we can obtain an estimate for the target population ATE by adjusting for the difference in the distribution of the moderators between the two samples. This paper considers sensitivity analyses for two situations: (1) where we cannot adjust for a specific moderator $V$ observed in the RCT because we do not observe it in the target population; and (2) where we are concerned that the treatment effect may be moderated by factors not observed even in the RCT, which we represent as a composite moderator $U$. In both situations, the outcome is not observed in the target population. For situation (1), we offer three sensitivity analysis methods based on (i) an outcome model, (ii) full weighting adjustment, and (iii) partial weighting combined with an outcome model. For situation (2), we offer two sensitivity analyses based on (iv) a bias formula and (v) partial weighting combined with a bias formula. We apply methods (i) and (iii) to an example where the interest is to generalize from a smoking cessation RCT conducted with participants of alcohol/illicit drug use treatment programs to the target population of people who seek treatment for alcohol/illicit drug use in the US who are also cigarette smokers. In this case a treatment effect moderator is observed in the RCT but not in the target population dataset.

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