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.