Sensitivity Analysis for Causal Inference under Unmeasured Confounding and Measurement Error Problems

Díaz, Iván; Laan, Mark J. van der

doi:10.1515/ijb-2013-0004

Cited by 39 publications

(33 citation statements)

References 24 publications

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“…An estimator's robustness can be evaluated by performing hypothesis tests across levels of a sensitivity parameter, which represents an overall degree of violation from statistical assumptions (e.g., unmeasured confounding, misclassification, and lack of overlap between exposed and unexposed patient characteristics). This approach can be applied either parametrically or non-parametrically across a broad range of study designs and effect parameters [16,17]. For matching analyses, a similar approach is to establish Rosenbaum bounds that assess the strength of confounding required to undermine the conclusions about causal effects [18].…”

Section: Alternative Assessment Of Uncertaintymentioning

confidence: 99%

Limitations of empirical calibration of p‐values using observational data

Gruber

Tchetgen

2016

Statistics in Medicine

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Controversy over non-reproducible published research reporting a statistically significant result has produced substantial discussion in the literature. P-value calibration is a recently proposed procedure for adjusting p-values to account for both random and systematic error that addresses one aspect of this problem. The method’s validity rests on the key assumption that bias in an effect estimate is drawn from a normal distribution whose mean and variance can be correctly estimated. We investigated the method’s control of type-I and type-II error rates using simulated and real world data. Under mild violations of underlying assumptions control of the type-I error rate can be conservative, while under more extreme departures it can be anti-conservative. The extent to which the assumption is violated in real world data analyses is unknown. Barriers to testing the plausibility of the assumption using historical data are discussed. Our studies of the type-II error rate using simulated and real-world electronic healthcare data demonstrated that calibrating p-values can substantially increase the type-II error rate. The use of calibrated p-values may reduce the number of false positive results, but there will be a commensurate drop in the ability to detect a true safety or efficacy signal. While p-value calibration can sometimes offer advantages in controlling the type-I error rate, its adoption for routine use in studies of real-world healthcare datasets is premature. Separate characterizations of random and systematic errors provides a richer context for evaluating uncertainty surrounding effect estimates.

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Section: Alternative Assessment Of Uncertaintymentioning

confidence: 99%

Limitations of empirical calibration of p‐values using observational data

Gruber

Tchetgen

2016

Statistics in Medicine

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“…As a next step in the roadmap, we develop targeted estimators of the statistical estimand and develop the theory for statistical inference. To understand the deviation between the estimand and the causal quantity under a variety of violations of these causal assumptions, one may carry out a sensitivity type analysis [16–18, 36], which represents the final step of the roadmap.…”

Section: Introductionmentioning

confidence: 99%

Causal Inference for a Population of Causally Connected Units

Laan

2014

J. Causal Infer.

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Suppose that we observe a population of causally connected units. On each unit at each time-point on a grid we observe a set of other units the unit is potentially connected with, and a unit-specific longitudinal data structure consisting of baseline and time-dependent covariates, a time-dependent treatment, and a final outcome of interest. The target quantity of interest is defined as the mean outcome for this group of units if the exposures of the units would be probabilistically assigned according to a known specified mechanism, where the latter is called a stochastic intervention. Causal effects of interest are defined as contrasts of the mean of the unit-specific outcomes under different stochastic interventions one wishes to evaluate. This covers a large range of estimation problems from independent units, independent clusters of units, and a single cluster of units in which each unit has a limited number of connections to other units. The allowed dependence includes treatment allocation in response to data on multiple units and so called causal interference as special cases. We present a few motivating classes of examples, propose a structural causal model, define the desired causal quantities, address the identification of these quantities from the observed data, and define maximum likelihood based estimators based on cross-validation. In particular, we present maximum likelihood based super-learning for this network data. Nonetheless, such smoothed/regularized maximum likelihood estimators are not targeted and will thereby be overly bias w.r.t. the target parameter, and, as a consequence, generally not result in asymptotically normally distributed estimators of the statistical target parameter. To formally develop estimation theory, we focus on the simpler case in which the longitudinal data structure is a point-treatment data structure. We formulate a novel targeted maximum likelihood estimator of this estimand and show that the double robustness of the efficient influence curve implies that the bias of the targeted minimum loss-based estimation (TMLE) will be a second-order term involving squared differences of two nuisance parameters. In particular, the TMLE will be consistent if either one of these nuisance parameters is consistently estimated. Due to the causal dependencies between units, the data set may correspond with the realization of a single experiment, so that establishing a (e.g. normal) limit distribution for the targeted maximum likelihood estimators, and corresponding statistical inference, is a challenging topic. We prove two formal theorems establishing the asymptotic normality using advances in weak-convergence theory. We conclude with a discussion and refer to an accompanying technical report for extensions to general longitudinal data structures.

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“…However, the simulation also demonstrated that unmeasured confounding can have an impact on estimation, which makes developing relevant sensitivity analyses (e.g., Rotnitzky et al, 2001;Díaz and van der Laan, 2013) an important next step.…”

Section: Discussionmentioning

confidence: 99%

Estimating and Testing Vaccine Sieve Effects Using Machine Learning

Benkeser

Gilbert

Carone

2019

Journal of the American Statistical Association

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When available, vaccines are an effective means of disease prevention. Unfortunately, efficacious vaccines have not yet been developed for several major infectious diseases, including HIV and malaria. Vaccine sieve analysis studies whether and how the efficacy of a vaccine varies with the genetics of the pathogen of interest, which can guide subsequent vaccine development and deployment. In sieve analyses, the effect of the vaccine on the cumulative incidence corresponding to each of several possible genotypes is often assessed within a competing risks framework. In the context of clinical trials, the estimators employed in these analyses generally do not account for covariates, even though the latter may be predictive of the study endpoint or censoring. Motivated by two recent preventive vaccine efficacy trials for HIV and malaria, we develop new methodology for vaccine sieve analysis. Our approach offers improved validity and efficiency relative to existing approaches by allowing covariate adjustment through ensemble machine learning. We derive results that indicate how to perform statistical inference using our estimators. Our analysis of the HIV and malaria trials shows markedly increased precision-up to doubled efficiency in both trials-under more plausible assumptions compared with standard methodology. Our findings provide greater evidence for vaccine sieve effects in both trials.

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Sensitivity Analysis for Causal Inference under Unmeasured Confounding and Measurement Error Problems

Cited by 39 publications

References 24 publications

Limitations of empirical calibration of p‐values using observational data

Limitations of empirical calibration of p‐values using observational data

Causal Inference for a Population of Causally Connected Units

Estimating and Testing Vaccine Sieve Effects Using Machine Learning

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