Efficiency Comparison Between Mean and Log-rank Tests with Recurrent Time Data

• Activity Number: 388
• Type: Contributed
• Date/Time: Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section*
• Author(s): Wenbin Lu*+ and Zhiliang Ying and Steven Wang
• Affiliation(s): Columbia University and Columbia University and R.W. Johnson Pharmaceutical Research Institute
• Keywords: proportional mean model ; frailty model ; asymptotic relative efficiency ; recurrence event times ; log-rank test ; robust variance estimation

Abstract

Recurrent event time data are common in biomedical follow-up studies, in which a subject may experience repeated occurrences of an event of interest. Examples include studies of asthmatic attacks, epileptic seizures, and repeated infections. Motivated by protocol development of studies for treatment efficacies of epileptic medicine, we evaluate two popular nonparametric tests for event time data in terms of their relative efficiency. One is the classical log-rank test for survival data and the other a more recently developed nonparametric test based on comparing mean recurrent rates. We show analytically that, somewhat surprisingly, the log-rank test that only makes use of time to the first occurrence could be more efficient than the counting process-based test for mean occurrence rates that makes use of all available recurrence times, provided that subject-to-subject variation of recurrence times is large, which is known to be true for epileptic seizure counts. Explicit formula are derived for asymptotic relative efficiency. The findings are demonstrated via extensive simulations. Applications of the results to protocol design of clinical trials are discussed.