Research Interests
Peihua Qiu's Research on Survival Analysis and Reliability
Motivated by a clinical trial of Zinc nasal spray for the treatment of
the common cold, I have been involved in the research problem of
comparing two crossing hazard rate functions since 2000. Comparison of
two hazard rates is important in applications related to times to
occurrence of a specific event. Conventional comparison procedures,
such as the logrank, Gehan-Wilcoxon, and Peto-Peto tests, are powerful
only when the two hazard rate functions do not cross each other. But, in
applications, the two hazard rate functions often cross each other,
representing different treatment effects in different time periods.
A number of procedures have been proposed in the literature for comparing
crossing hazard rate functions. Some of them take the modeling
approach; but, the proposed models are usually too restrictive to be used
in various applications. Liu, Qiu and Sheng (2007) tried to overcome
this limitation by proposing a Cox proportional hazards model with
the Box-Cox transformation, which covers a wide range of crossing hazard
patterns.
Some existing methods take the hypothesis testing approach
by proposing several different testing statistics. However, most of these
methods only consider the alternative hypothesis with crossing hazard rates;
many other realistic cases, including those when the two hazard rates run
parallel to each other, are excluded from consideration. In Qiu and Sheng
(2008), we proposed a two-stage procedure that considers all possible
alternatives, including the ones with crossing or running parallel hazard
rate functions. To define its significance level and p-value properly, a
new procedure for handling the crossing hazard rates problem is suggested
in that paper, which has the property that its test statistic is
asymptotically independent of the test statistic of the logrank test.
In Sheng and Qiu (2007), a method for computing the p-value of a multi-stage
additive test was proposed. Generalization of the method by Qiu and Sheng
(2008) for comparing more than two hazard rate functions is discussed in
Chen, Huang and Qiu (2016).
In applications with crossing hazard rate functions involved, the crossing
points are often important to estimate, because they define different time
periods that the treatment effect is different. In Cheng, Qiu, Tan, and
Tu (2009), a confidence interval formula is proposed in cases when the
hazard rate functions are assumed to be continuous and nonparametric.
Right now, my coauthors and I are working on the crossing hazard rate
problem when both survival data and longitudinal data are available.
One paper has been published recently in Park and Qiu (2014).
My coauthor and I also proposed a parametric model family for analyzing
accelerated life testing data which included the three commonly used
models, including the power law model, the Arrhenius model and the
Eyring model, as special cases (Qiu and Tsokos 2000).
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