Sample sizes for long-term medical trial with time-dependent dropout and event rates

A general model is formulated that allows for time-dependent dropout and event rates in the determination of sample sizes for long-term medical trials when a therapy group and a control group are to be compared. The need for time-dependent event (dropout) rate is illustrated by using the Framingham Heart Study Mortality data to estimate sample size for the NHLBI (National Heart, Lung, and Blood Institute) Multiple Risk Factor Intervention Trial (MRFIT). A further generalization of the model allows for participants who drop out of the control group (e.g., because of therapeutic measures prescribed by their own physicians) to return (or not return) to the control group at a later date. The question of unequal sample sizes for the therapy and the control groups is also discussed.