Background The natural indirect effect (NIE) and mediation proportion (MP) are two measures of primary interest in mediation analysis. The standard approach for mediation analysis is through the product method, which involves a model for the outcome conditional on the mediator and exposure and another model describing the exposure–mediator relationship. The purpose of this article is to comprehensively develop and investigate the finite-sample performance of NIE and MP estimators via the product method. Methods With four common data types with a continuous/binary outcome and a continuous/binary mediator, we propose closed-form interval estimators for NIE and MP via the theory of multivariate delta method, and evaluate its empirical performance relative to the bootstrap approach. In addition, we have observed that the rare outcome assumption is frequently invoked to approximate the NIE and MP with a binary outcome, although this approximation may lead to non-negligible bias when the outcome is common. We therefore introduce the exact expressions for NIE and MP with a binary outcome without the rare outcome assumption and compare its performance with the approximate estimators. Results Simulation studies suggest that the proposed interval estimator provides satisfactory coverage when the sample size ≥500 for the scenarios with a continuous outcome and sample size ≥20,000 and number of cases ≥500 for the scenarios with a binary outcome. In the binary outcome scenarios, the approximate estimators based on the rare outcome assumption worked well when outcome prevalence less than 5% but could lead to substantial bias when the outcome is common; in contrast, the exact estimators always perform well under all outcome prevalences considered. Conclusions Under samples sizes commonly encountered in epidemiology and public health research, the proposed interval estimator is valid for constructing confidence interval. For a binary outcome, the exact estimator without the rare outcome assumption is more robust and stable to estimate NIE and MP. An R package is developed to implement the methods for point and variance estimation discussed in this paper.
A detailed theory is presented for how humans induce mathematical functions to explain observed data. The theory is based on both solution times and verbal protocols. The theory proposes that induction is a heuristically directed generate-and-test process. The order in which hypotheses are generated is mostly independent of the data. Each hypothesis is maintained until it is negated, but a false hypothesis that matches part of the data is frequently retested. A computer simulation program, incorporating these processes, accurately predicted solution times for subjects on different sets of problems without any changes in parameters. In addition, the program's solution protocols were indistinguishable from human protocols.
By combining data across multiple studies, researchers increase sample size, statistical power, and precision for pooled analyses of biomarker–disease associations. However, researchers must adjust for between-study variability in biomarker measurements. Previous research often treats the biomarker measurements from a reference laboratory as a gold standard, even though those measurements are certainly not equal to their true values. This paper addresses measurement error and bias arising from both the reference and study-specific laboratories. We develop two calibration methods, the exact calibration method and approximate calibration method, for pooling biomarker data drawn from nested or matched case–control studies, where the calibration subset is obtained by randomly selecting controls from each contributing study. Simulation studies are conducted to evaluate the empirical performance of the proposed methods. We apply the proposed methods to a pooling project of nested case–control studies to evaluate the association between circulating 25-hydroxyvitamin D (25(OH)D) and colorectal cancer risk.
Mediation analysis is widely used in biomedical research to quantify the extent to which a mediator may explain in exposure-outcome mechanisms. A traditional approach for quantifying mediation is through the difference method. The other popular approach uses a counterfactual framework from which the product method arises. However, there is little prior work to articulate which method is more efficient for estimating two key quantities in mediation analysis, the natural indirect effect (NIE) and mediation proportion (MP). To fill in this gap, we investigated the asymptotic relative efficiency for mediation measure estimators given by the product method and the difference method. We considered four data types characterized by continuous and binary mediatorsand outcomes. Under certain conditions, we show analytically that the product method is equally or more efficient than the difference method. However, our numerical studies demonstrate that the difference method is usually at least 90% efficient as the product method under realistic scenarios in epidemiological research, especially for estimating the MP. We demonstrate the efficiency results by analyzing the MaxART study, 2014–2017, which aims to evaluate the effectiveness of the early access to antiretroviral therapy among HIV-positive patients.
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