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Abstract:
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In many clinical trials, immuno-oncologic agents showed a delayed effect, thus leading to a violation of the proportional hazard assumption when comparing with the other drugs. Fleming-Harrington test is categorized in the weighted log-rank statistics, and which has two parameters, i.e. the parameter p and q. When setting p>0 and q=0, it weights the early events heavily. In the delayed effect situation, it is reasonable to weight the later events by setting p=0 and q>0. However, it is difficult to choose an appropriate value of parameter q, for example, by discussing with clinicians, because parameter q is not directly clinically interpretable. As Zucker and Lakatos (1990) and Ting (2018) discussed the several prototypical lag model (i.e. ‘linear’, ‘threshold’ and generalized linear lag models), where a delayed effect is expected. These lag model includes clinically interpretable parameter. Especially, generalized linear lag model can be very useful to explain the variety of delayed effect. We further investigate a practical procedure to determine parameter q in Fleming-Harrington test in relation to these lag models, using the Pitman’s asymptotic relative efficiency.
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