Predicting power for longitudinal studies with attrition

Power analyses play an integral role in designing biomedical studies and are customary in biomedical research proposals, for example, submitted to federal regulatory and medical research agencies. An underpowered study potentially leads to inconclusive inferences and consequently misspends valuable time and financial resources allocated to the study. The occurrence of attrition or dropout further increases the risk of conducting an underpowered study. In some applications, it is desirable to provide additional assurance against insufficient statistical power by producing conservative power predictions. We propose two new methods for predicting power when expecting attrition, and both methods employ a simple probability model for the number of dropouts. One approach allows conservative power predictions that reduce the chance of underpowering studies. The second procedure gives the minimum mean squared error predictor of conditional power, given dependence on a random number of unobserved values or dropouts. We illustrate our methods for predicting power using a longitudinal study of depression.