Bayesian approach to average power calculations for binary regression models with misclassified outcomes

Abstract

We develop a simulation-based procedure for determining the required sample size in binomial regression risk assessment studies when response data are subject to misclassification. A Bayesian average power criterion is used to determine a sample size that provides high probability, averaged over the distribution of potential future data sets, of correctly establishing the direction of association between predictor variables and the probability of event occurrence. The method is broadly applicable to any parametric binomial regression model including, but not limited to, the popular logistic, probit, and complementary log-log models. We detail a common medical scenario wherein ascertainment of true disease status is impractical or otherwise impeded, and in its place the outcome of a single binary diagnostic test is used as a surrogate. These methods are then extended to the two diagnostic test setting. We illustrate the method with categorical covariates using one example that involves screening for human papillomavirus. This example coupled with results from simulated data highlights the utility of our Bayesian sample size procedure with error prone measurements.

Marginal analysis of longitudinal ordinal data with misclassification in both response and covariates

“…Carroll et al., 2006), error in response has received relatively less attention except for binary misclassification (e.g. Neuhaus, , ; Rosychuk and Thompson, , ; Luan et al., ; Paulino et al., ; Roy and Banerjee, ; Cheng et al., ; Chen et al., ). The misclassification process for the binary or ordinal response is modeled via misclassification probabilities; this is different from the case with a continuous variable for which an additive measurement error model is commonly used.…”

Binomial regression with a misclassified covariate and outcome

“…Moreover, Bayesian average power criterion has recently been used to evaluate the impact of misclassified variables in logistic regression models. 53,54 As a direction of future research, we can use Bayesian average power to investigate whether misclassification of response or misclassification of a covariate has a larger effect on power and bias.…”

Bayesian inference for unidirectional misclassification of a binary response trait

“…The true values of the conditional probabilities are assumed to be 00 = 0.1 and 10 = 0.2. For the limiting posteriors, we specify the prior for p as U(0, 1), beta(2, 2), beta(10, 10), beta (1,3), beta (2,6), and an additional beta (1,9) prior for the case with p 0 = 0.10 to represent an accurate guess. The limiting posterior distributions can then be obtained based on Equation 2.…”

“…We use 7 models, with the first being the naive model ignoring the possibility of unidirectional misclassification and the other 6 being the proposed model in Section 2.2 assuming different beta priors for the misclassification probability. As sensitivity analyses, we assume 6 prior distributions, beta (2,2), beta (1,3), beta (2,6), beta (5,5), beta (1,9), and beta (1,19) for the misclassification probability. We standardize the continuous covariates and code the categorical ones with binary indicators.…”

“…In this paper, we consider Bayesian inference in regression models when the binary response variable is subject to unidirectional misclassification. Bayesian methods have become popular for ameliorating the impact of misclassification in categorical variables, owing to their ability to allow for a guess on the severity of misclassification along with an assessment of uncertainty in this guess incorporated through priors. Unidirectional misclassification is a special case of misclassification when we know the direction of the error in categorical variables.…”