Parameterization of Beta Distributions for Bias Parameters of Binary Exposure Misclassification in Probabilistic Bias...

To account for misclassification of dichotomous variables using probabilistic bias analysis, beta distributions are often assigned to bias parameters (e.g., positive and negative predictive values) based on data from an internal validation substudy. Due to the small sample size of validation substudies, zero-cell frequencies can occur. In these scenarios, it may be helpful to assign prior distributions or apply continuity corrections to the predictive value estimates.

We simulated cohort studies of varying sizes, with a binary exposure and outcome and a true risk ratio (RR) = 2.0, as well as internal validation substudies, to account for exposure misclassification. We conducted bias adjustment under five approaches assigning prior distributions to the positive and negative predictive value parameters: (1) conventional method (i.e., no prior), (2) uniform prior beta ( α = 1, β = 1), (3) Jeffreys prior beta ( α = 0.5, β = 0.5), (4) using Jeffreys prior as a continuity correction only when zero cells occurred, and (5) using the uniform prior as a continuity correction only when zero cells occurred. We evaluated performance by measuring coverage probability, bias, and mean squared error.

For sparse validation data, methods (2)-(5) all had better coverage and lower mean squared error than the conventional method, with the uniform prior (2) yielding the best performance. However, little difference between methods was observed when the validation substudy did not contain zero cells.

If sparse data are expected in a validation substudy, using a uniform prior for the beta distribution of bias parameters can improve the validity of bias-adjusted measures.