arXiv subjects

Paul N. Zivich

Publications and source records attributed to Paul N. Zivich.

5 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. Combined with the assumptions of causal consistency, positivity, and conditional exchangeability, the law of iterated expectation yields 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.

stat.OT↗

arXiv2026

Transporting summary measures of relative effects from randomised trials to the treated patient population: an application to breast cancer endocrine therapy

Randomised trials often report relative treatment effects, such as risk ratios and hazard ratios, for trial populations. Clinical decision-making, however, often benefits from estimates of absolute treatment effects in the population eligible for treatment. Trial participants may not represent this target population well, and restrictions on access to individual participant trial data can further complicate absolute effect estimation. Routine care data are often representative of the target population but may be subject to uncontrolled confounding. We consider estimation of the average treatment effect on the treated (ATT), an absolute measure, by combining a representative sample of treated routine care patients with summary measures (i.e., estimated risk or hazard ratios) from either a randomised trial or a meta-analysis of trials. Under marginal or conditional transportability assumptions, the ATT is shown to be identifiable. The implications of collapsibility of the effect measure on transportability are discussed, and plug-in estimators of the ATT are presented. Simulation studies are used to assess finite sample performance of the estimators in a range of settings. The proposed methods are applied to estimate the ATT of endocrine therapy on 15-year breast cancer mortality using results from a meta-analysis of randomised trials and England's National Disease Registration Service.

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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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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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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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