Assessment of Misclassification in a Binary Response: Recovering Information on Clinically Significant Cataract Prevalence from Cataract Surgery Data in Atomic-bomb Survivors

Cataract surgery results when a patient decides to undergo lens surgery following a diagnosis of a clinically significant cataract (CSC). Because the presence of a CSC is generally latent and unobserved, a person might not receive cataract surgery even if the person has a CSC. This misclassification needs to be adjusted in the statistical analysis of CSC so as to reduce the bias in the parameter estimation. Following Magder and Hughes (1997) and using the cataract surgery data on atomic-bomb survivors at the Radiation Effects Research Foundation, we used this method for estimating the prevalence of CSC in a linear logistic dose response model taking account of the sensitivity and/or specificity of the decision for lens surgery. The estimated sensitivity was 0.385 (95% CI: 0.268, 0.517) and the estimated specificity was perfect. The odds ratio estimate for the radiation dose response changed from 1.39 (95% CI: 1.24, 1.55) to 1.58 (95% CI: 1.26, 1.98) when allowing for the imperfect sensitivity. A large sample simulation study with a continuous covariate was conducted, assuming either imperfect sensitivity or imperfect specificity, to investigate the performance of the method. Results indicated that the parameter estimates are almost correct. We calculated the asymptotic relative efficiency (ARE) for a simple logistic regression slope estimate and showed that the ARE depends only on the values of slope and intercept parameters.