Student Seminar Series - June 26, 2006
University of Minnesota
School of Statistics
College of Liberal Arts

Methods for Comparing Two Crossing Hazard Functions


Jun Sheng


Monday, June 26, 2006
1:00 PM, 231 Smith Hall
Minneapolis, East Bank Campus

Refreshments at 12:30 PM
300 Ford Hall


Abstract


Motivated by a clinical trial in which zinc nasal spray is the primary treatment for viral respiratory illness, we consider the problem of comparing two crossing hazard functions. First, a new method is proposed based on characterizing the hazard ratio under the framework of the Cox proportional hazard modeling. Monte Carlo simulations and reallife examples show that the proposed method outperforms its peers in various cases. Second, we develop a two-stage testing procedure for comparing two hazard functions. To ensure that the overall significance level and p-value of the two-stage procedure are properly defined, we construct a new test statistic for the crossing hazards problem, which is proved to be asymptotically independent of the statistic of the routinely used log-rank test. Then, it is shown that the two-stage procedure would perform well in applications to detect any difference of two hazard functions. Finally, joint modeling approaches of longitudinal and time-to-event data are under investigation. We suggest a new approach for including some binary time-dependent covariates in analyzing the zinc nasal spray data. A latent symptom intensity trajectory is assumed for each individual, and it is applied to submodels for describing longitudinal observations and event times, respectively. It is shown that the joint analysis, compared to the so-called naive survival model, not only reduces the bias of the regression parameter estimates, but also increases the power in detecting the crossing of two hazard functions.