The Metropolis algorithm: A useful tool for epidemiologists

TL;DR

This paper explains the Metropolis algorithm's mechanics and demonstrates its application in epidemiology for estimating risk measures, highlighting its versatility in Bayesian and frequentist inference.

Contribution

It provides a clear explanation, pseudocode, and R implementation of the Metropolis algorithm, illustrating its use in epidemiological risk estimation.

Findings

Successfully estimated odds ratio and risk difference for childhood leukemia

Demonstrated advantages of MCMC in small sample scenarios

Provided accessible resources for epidemiologists to implement the algorithm

Abstract

The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies classical and modern MCMC methods and facilitates simple analysis of complex statistical models. Beyond Bayesian analysis, MCMC is useful for generating uncertainty intervals, even under the common scenario in causal inference in which the target parameter is not directly estimated by a single, fitted statistical model. We demonstrate, with a worked example, pseudo-code, and R code, the basic mechanics of the Metropolis algorithm. We use the Metropolis algorithm to estimate the odds ratio and risk difference contrasting the risk of childhood leukemia among those exposed to high versus low level magnetic fields. This approach can be used for inference from Bayesian and frequentist paradigms and, in small samples, offers advantages over large-sample methods like the bootstrap.