arXiv subjects

Kenneth A. Frank

Publications and source records attributed to Kenneth A. Frank.

3 recordsLinked to original sources

arXiv2025

Sensitivity Analysis of the Consistency Assumption

Sensitivity analysis informs causal inference by assessing the sensitivity of conclusions to departures from assumptions. The consistency assumption states that there are no hidden versions of treatment and that the outcome arising naturally equals the outcome arising from intervention. When reasoning about the possibility of consistency violations, it can be helpful to distinguish between covariates and versions of treatment. In the context of surgery, for example, genomic variables are covariates and the skill of a particular surgeon is a version of treatment. There may be hidden versions of treatment, and this paper addresses that concern with a new kind of sensitivity analysis. Whereas many methods for sensitivity analysis are focused on confounding by unmeasured covariates, the methodology of this paper is focused on confounding by hidden versions of treatment. In this paper, new mathematical notation is introduced to support the novel method, and example applications are described.

stat.ME↗

arXiv2020

The probability of a robust inference for internal validity and its applications in regression models

The internal validity of observational study is often subject to debate. In this study, we define the unobserved sample based on the counterfactuals and formalize its relationship with the null hypothesis statistical testing (NHST) for regression models. The probability of a robust inference for internal validity, i.e., the PIV, is the probability of rejecting the null hypothesis again based on the ideal sample which is defined as the combination of the observed and unobserved samples, provided the same null hypothesis has already been rejected for the observed sample. When the unconfoundedness assumption is dubious, one can bound the PIV of an inference based on bounded belief about the mean counterfactual outcomes, which is often needed in this case. Essentially, the PIV is statistical power of the NHST that is thought to be built on the ideal sample. We summarize the process of evaluating internal validity with the PIV into a six-step procedure and illustrate it with an empirical example (i.e., Hong and Raudenbush (2005)).

stat.ME↗

arXiv2019

On the probability of a causal inference is robust for internal validity

The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a causal inference is robust for internal validity, i.e., the PIV, as a robustness index of causal inference. Formally, the PIV is the probability of rejecting the null hypothesis again based on both the observed sample and the counterfactuals, provided the same null hypothesis has already been rejected based on the observed sample. Under either frequentist or Bayesian framework, one can bound the PIV of an inference based on his bounded belief about the counterfactuals, which is often needed when the unconfoundedness assumption is dubious. The PIV is equivalent to statistical power when the NHST is thought to be based on both the observed sample and the counterfactuals. We summarize the process of evaluating internal validity with the PIV into an eight-step procedure and illustrate it with an empirical example (i.e., Hong and Raudenbush (2005)).

stat.AP↗