Estimating the Response Rate when Measurements are Subject to Error
Yongming Qu, Pandurang M. Kulkarni and Todd Sanger
 
In clinical trials, it is often of interest to estimate the proportion of responders or non-responders by giving a clinically meaningful threshold. A subject is classified as a responder if the change of a variable of interest during the study is greater (or smaller) than the threshold value. The response rate is defined as the proportion of responders. In the presence of measurement error, the naïve estimator for the response rate, calculated as the proportion of subjects with observed change above (or below) a threshold, is in general biased. The full non-parametric methods adjusting for the measurement error are complicated and may not be efficient. We propose a method assuming a parametric model for the true change in the response variable based only on the first few moments for the measurement error. The estimator for the true response rate and the variance of the estimator are derived. An innovative method using bootstrap simulation is proposed to check the model assumption. An example from a clinical trial shows that the estimate of response rate in terms of bone mineral density considering the measurement error is improved compared to the naïve estimate.