### Keynote Speakers

**Dr. Niels Keiding**, University of Copenhagen, Denmark

“Survival Analysis Around a Cross-Section and Unobserved Heterogeneity”**Dr. Lee-Jen Wei**, Harvard University

“The Myth of Design and Analysis of Cancer Clinical Studies with PFS or OS as the Endpoint”

### “Survival Analysis Around a Cross-Section and Unobserved Heterogeneity”

**Dr. Niels Keidings**, University of Copenhagen, Denmark

Consider lifetimes originating at a series of calendar times t_{12},… At a certain time t_{0} a cross-sectional sample is taken, generating a sample of current durations (backward recurrence times) of survivors until t_{0} and a prevalent cohort study consisting of survival times left-truncated at the current durations. A Lexis diagram is helpful in visualizing this situation. Survival analysis based on current durations and prevalent cohort studies is now well-established as long as all covariates are observed.

The general problems with unobserved covariates have been well understood for ordinary prospective follow-up studies, with the good help of hazard rate models incorporating frailties: as for ordinary regression models, the added noise generates attenuation in the regression parameter estimates. For current durations and prevalent cohort studies this attenuation remains, but in addition one needs to take account of the differential selection of the survivors from initiation t_{i} to cross-sectional sampling at t_{0}.

This talk intends to survey the recent development of these matters and the consequences for routine use of hazard rate models or accelerated failure time models in the many cases where unobserved heterogeneity may be an issue.

#### Dr. Niels Keiding, University of Copenhagen, Denmark

Dr. Keiding is now an Emeritus Professor of Biostatistics, University of Copenhagen. His research interests include methods for analysis of survival and event history data, particularly under non-standard observational plans, causal analysis and epidemiological methods, history of statistics and demography. Main applications of his research are reproductive epidemiology, particularly time-to pregnancy studies.

### “The Myth of Design and Analysis of Cancer Clinical Studies with PFS or OS as the Endpoint”

**Dr. Lee-Jen Wei**, Harvard University

In a longitudinal clinical cancer study to compare a new treatment with a control, the primary end point is generally either the overall survival or progress-free survival time. The hazard ratio (HR) is routinely utilized to quantify a desirable treatment effect for sizing the study. The estimated total number of events needed to achieve a specific statistical power for the study can be obtained easily via a back-of-the-envelope calculation. However, since it is not clear how to interpret HR clinically, the specific HR value (e.g., 0.75) quantifying the desirable treatment effect is often justified via a certain degree of improvement from the treatment with respect to the median survival time (e.g., from 10 to 12 months). The median survival time is a clinically meaningful summary measure, however, it does not capture the long term survival profile well. Therefore, using the difference of two median survival times may not help us much to interpret a HR value at the design stage.

At the end of the study, the PFS/OS data are routinely analyzed via the HR estimation procedure and logrank test. This practice is more problematic at the analysis stage. The concerns and issues of using this summary measure have been discussed extensively in the literature. The validity of using HR depends on the proportional hazards assumption, that is, the hazard ratio for two groups is constant over the entire study period. This assumption is rarely valid in practice and the resulting HR estimate is difficult to interpret. In fact, in an interview article, being an extremely modest giant in our profession, Professor Cox stated that “Of course, another issue is the physical or substantive basis for the proportional hazards model. I think that’s one of its weaknesses…” To ease the difficulty of interpreting the estimated HR, the individual median survival time estimates for two groups are usually reported descriptively without formal comparisons in the study publications. However, since the median survival estimate is insensitivity to outliers and is unstable with respect to estimation precision, often the estimate for the difference of two medians results in an inconsistent conclusion regarding the treatment effect to that based on the HR estimate. It seems that the partnership between the HR and median survival is not working well for most conventional survival studies.

An alternative to the median survival is to use the restricted mean survival time (RMST) to summarize the survival profile. This measure has an intuitive, clinically meaningful interpretation. The procedure for estimating the difference of two RMSTs is always valid without any model assumption and is much stable than its median counterpart.

There is no single summary measure which can capture the entire survival profile of a group of patients. On the other hand, for the design and analysis of a study, a primary summary measure for the between-group-difference is needed. Moreover, the pre-specified analysis procedure for this measure should be robust, not heavily model-dependent, and will result in clinically interpretable conclusions about the treatment effect.

#### Dr. Lee-Jen Wei, Harvard University

L.J. Wei’s research is in the area of developing statistical methods for the design and analysis of clinical trials. Dr. Wei has developed numerous methods for analyzing data with multiple outcome or repeated measurements obtained from study subjects. Currently, Wei and his colleagues are developing graphical and numerical methods for checking the adequacy of the Cox proportional hazards model, other semi-parametric survival models, parametric models, and random effects models for repeated measurements. Presently, Wei and his colleagues are working on various resampling methods for quantile regression, rank regression, and regression models for censored data. Dr. Wei is also a senior statistician at the Statistical and Data Analysis Center. He works closely with the medical investigators in Pediatrics AIDS clinical trials for evaluating new treatments for HIV patients.