Balance Index to Determine the Follow-Up Duration of Oncology Trials

Several indices were suggested to determine the follow up duration in oncology trials from either maturity or stability perspective, by maximizing time $t$ such that the index was either greater or less than a pre-defined cutoff value. However, the selection of cutoff value was subjective and usually no commonly agreed cutoff value existed; sometimes one had to resort to simulations. To solve this problem, a new balance index was proposed, which integrated both data stability and data maturity. Its theoretical properties and relationships with other indices were investigated; then its performance was demonstrated through a case study. The highlights of the index are: (1) easy to calculate; (2) free of cutoff value selection; (3) generally consistent with the other indices while sometimes able to shorten the follow-up duration thus more flexible. For the cases where the new balance index cannot be calculated, a modified balance index was also proposed and discussed. For either single arm trial or randomized clinical trial, the two new balance indices can be implemented to widespread situations such as designing a new trial from scratch, or using aggregated trial information to inform the decision-making in the middle of trial conduct.