Non-proportional hazards in clinical trials with failure-time endpoints
Abstract/Contents
- Abstract
- In clinical trials, enrolled patients are randomized into treatment and control groups to test if the new treatment has advantages over the control. Data have been collected from both groups to form test statistics. For life-threatening diseases, such as cancer and heart attacks, the primary endpoint of a confirmatory trial for a new treatment is time to failure. This endpoint often involves censored data because some subjects may not fail by the end of the study or may have been lost to follow-up. To handle survival data in the problem of explanatory variables, Cox (1972) introduced a semi-parametric model based on the assumption of proportional hazards. In this model, the log ratio of the hazard function of the treatment group to that of the control group is a constant that does not vary over time. Earlier Mantel (1966) introduced the logrank test that is asymptotically efficient for proportional hazards alternative. Both logrank test and proportional hazards regression model have become standard procedures in clinical trials with survival endpoints. Since clinical trials can run for years, interim analyses by a Data and Safety Monitoring Board (DSMB) are typically included in the trial protocol. This led to the development of ``time-sequential'' methods for early stopping during interim analyses. Lan and DeMets (1988) have noted that there are two time scales in time-sequential trials. One is the calendar time t at which interim analysis is carried out, and the other is the information time V(t), which can be measured by the variance of the test statistic (under the null hypothesis) based on all the data collected up to time t and is unknown before time t. Therefore, to determine the sample size and study duration, assumptions have to be made on the accrual rate, the survival distribution of both treatment and control groups, and the censoring distribution. These assumptions are commonly based on the literature concerning related studies and on educated guesses. In particular, since logrank tests and time-invariant hazard ratios are typically used to summarize the results of the studies, it is convenient to assume proportional hazards as the working model at the design stage. During interim analyses, marked discrepancies for the assumptions at the design stage may be observed. Herein we propose a group sequential design that addresses theses discrepancies and thereby makes the trial more efficient in terms of power, study duration and expected sample size. The design allows one to combine the logrank statistic with the more powerful test statistics in case of non-proportional hazards at the terminal stage. A new approach to futility stopping is developed as well as a piecewise constant hazard ratio model replacing the proportional hazards model.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | He, Pei |
|---|---|
| Associated with | Stanford University, Department of Statistics |
| Primary advisor | Lai, T. L |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Lavori, Philip W, 1949- |
| Thesis advisor | Shih, Mei-Chiung |
| Advisor | Lavori, Philip W, 1949- |
| Advisor | Shih, Mei-Chiung |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Pei He. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Ph.D. Stanford University 2012 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Pei He
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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