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Causal Estimation with Functional Confounders.

ABSTRACT: Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions on a part of the treatment called functional interventions and a sufficient condition for effect estimation of these interventions called functional positivity. Second, we develop conditions for nonparametric effect estimation based on the gradient fields of the functional confounder and the true outcome function. To estimate effects under these conditions, we develop Level-set Orthogonal Descent Estimation (LODE). Further, we prove error bounds on LODE's effect estimates, evaluate our methods on simulated and real data, and empirically demonstrate the value of EFC.

SUBMITTER: Puli A

PROVIDER: S-EPMC8096536 | biostudies-literature | 2020 Dec

REPOSITORIES: biostudies-literature

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Publications

Causal Estimation with Functional Confounders.

Puli Aahlad A Perotte Adler J AJ Ranganath Rajesh R

Advances in neural information processing systems 20201201

Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interven ...[more]

PMID: 33953524

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Project description:BackgroundCausal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received much attention, a key requirement for valid causal inference is that conclusions are drawn based on the true data-generating model.MethodsIt remains widely unknown how large the probability is to reject the true structural causal model when observational data from it is sampled. The latter probability - the causal false-positive risk - is crucial, as rejection of the true causal model can induce bias in the estimation of causal effects. In this paper, the widely used causal models of confounders and colliders are studied regarding their causal false-positive risk in linear Markovian models. A simulation study is carried out which investigates the causal false-positive risk in Gaussian linear Markovian models. Therefore, the testable implications of the DAG corresponding to confounders and colliders are analyzed from a Bayesian perspective. Furthermore, the induced bias in estimating the structural coefficients and causal effects is studied.ResultsResults show that the false-positive risk of rejecting a true SCM of even simple building blocks like confounders and colliders is substantial. Importantly, estimation of average, direct and indirect causal effects can become strongly biased if a true model is rejected. The causal false-positive risk may thus serve as an indicator or proxy for the induced bias.ConclusionWhile the identification of structural coefficients and testable implications of causal models have been studied rigorously in the literature, this paper shows that causal inference also must develop new concepts for controlling the causal false-positive risk. Although a high risk cannot be equated with a substantial bias, it is indicative of the induced bias. The latter fact calls for the development of more advanced risk measures for committing a causal type I error in causal inference.

Project description:BackgroundIn causal analyses, some third factor may distort the relationship between the exposure and the outcome variables under study, which gives spurious results. In this case, treatment groups and control groups that receive and do not receive the exposure are different from one another in some other essential variables, called confounders.MethodPlace of birth was used as exposure variable and age-specific childhood vaccination status was used as outcome variables. Three approaches of confounder selection techniques such as all pre-treatment covariates, outcome cause covariates, and common cause covariates were proposed. Multiple logistic regression was used to estimate the propensity score for inverse probability treatment weighting (IPTW) confounder adjustment techniques. The proportional odds model was used to estimate the causal effect of place of birth on age-specific childhood vaccination. To validate the result obtained from observed data, we used a plasmode simulation of resampling 1000 samples from actual data 500 times.ResultOutcome cause and common cause confounder identification techniques gave comparable results in terms of treatment effect in the plasmode data. However, outcome causes that contain common causes and predictors of the outcome confounder identification gave relatively better treatment effect results. The treatment effect result in the IPTW confounder adjustment method was better than that of the regression adjustment method. The effect of place of birth on log odds of cumulative probability of age-specific childhood vaccination was 0.36 with odds ratio of 1.43 for higher level vaccination status.ConclusionIt is essential to use plasmode simulation data to validate the reproducibility of the proposed methods on the observed data. It is important to use outcome-cause covariates to adjust their confounding effect on the outcome. Using inverse probability treatment weighting gives unbiased treatment effect results as compared to the regression method of confounder adjustment. Institutional delivery increases the likelihood of childhood vaccination at the recommended schedule.

Dataset Information

Causal Estimation with Functional Confounders.

Publications

Causal Estimation with Functional Confounders.

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