Design and sample size estimation in clinical trials with clustered survival times as the primary endpoint

Many clinical trials involve the collection of data on the time to occurrence of the same type of multiple events within sample units, in which ordering of events is arbitrary and times are usually correlated. To design a clinical trial with this type of clustered survival times as the primary endpoint, estimating the number of subjects (sampling units) required for a given power to detect a specified treatment difference is an important issue. In this paper we derive a sample size formula for clustered survival data via Lee, Wei and Amato's marginal model. It can be easily used to plan a clinical trial in which clustered survival times are of primary interest. Simulation studies demonstrate that the formula works very well. We also discuss and compare cluster survival time design and single survival time design (for example, time to the first event) in different scenarios.

[1]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[2]  S. Lagakos,et al.  Sample size and power determination for stratified clinical trials , 1978 .

[3]  D. Schoenfeld,et al.  Sample-size formula for the proportional-hazards regression model. , 1983, Biometrics.

[4]  M D Hughes,et al.  Power considerations for clinical trials using multivariate time-to-event data. , 1997, Statistics in medicine.

[5]  J. Wittes,et al.  The role of internal pilot studies in increasing the efficiency of clinical trials. , 1990, Statistics in medicine.

[6]  K K Lan,et al.  A comparison of sample size methods for the logrank statistic. , 1992, Statistics in medicine.

[7]  D. Lin,et al.  Cox regression analysis of multivariate failure time data: the marginal approach. , 1994, Statistics in medicine.

[8]  S R Lipsitz,et al.  Sample size for repeated measures studies with binary responses. , 1994, Statistics in medicine.

[9]  E. Lakatos,et al.  Sample sizes based on the log-rank statistic in complex clinical trials. , 1988, Biometrics.

[10]  E. Gumbel.  Bivariate Exponential Distributions , 1960 .

[11]  M H Gail,et al.  Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observation. , 1981, Journal of chronic diseases.

[12]  Neil Klar,et al.  Sample size re‐estimation in cluster randomization trials , 2002, Statistics in medicine.

[13]  Lee-Jen Wei,et al.  Cox-Type Regression Analysis for Large Numbers of Small Groups of Correlated Failure Time Observations , 1992 .

[14]  L. J. Wei,et al.  Regression analysis of multivariate incomplete failure time data by modeling marginal distributions , 1989 .

[15]  L. Freedman.  Tables of the number of patients required in clinical trials using the logrank test. , 1982, Statistics in medicine.

[16]  M M Shoukri,et al.  Estimating the number of clusters for the analysis of correlated binary response variables from unbalanced data. , 1992, Statistics in medicine.

[17]  N Dubin,et al.  Estimation and sample size considerations for clustered binary responses. , 1994, Statistics in medicine.

[18]  A Donner,et al.  Sample size requirements for stratified cluster randomization designs. , 1992, Statistics in medicine.

[19]  Jack Moshman,et al.  A Method for Selecting the Size of the Initial Sample in Stein's Two Sample Procedure , 1958 .

[20]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[21]  R J Cook,et al.  The design and analysis of randomized trials with recurrent events. , 1995, Statistics in medicine.

[22]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .