Combining multiple survival endpoints within a single statistical analysis


  • Zakiyah Zain
  • John Whitehead



Survival analysis, Global test, Score statistics, Recurrent events, Multivariate, Interval-censored,


Multiple endpoints are common in survival data and this scenario complicates the analysis. For example, sets of responses concerned with survival times in a single clinical trial include: time to first cardiac event and time to death from any cause; time to loss of vision in the left eye and time to loss of vision in the right eye; and times from entry to a trial until the first, the second and the third asthma exacerbations. In a clinical trial evaluating the treatment effect of a new drug, often a single statistic is required to measure its overall performance. The cumulative treatment advantage is often measured by the score statistic for each endpoint. The aim of this paper is to develop methodology for combining multiple endpoints within a single statistical analysis that compares the responses of patients treated with a novel treatment with those of control patients treated conventionally. The focus is on interval-censored bivariate survival data, and a real dataset from previous study concerning multiple responses are used for illustration. In this paper we take a direct approach to combining the univariate score statistics for comparing treatments with respect to each survival endpoint. Recurrent events are considered in this investigation and the accuracy of the estimator is evaluated. The combined methodology is accurate, consistent and comparable to the established method of Wei, Lin and Weissfeld.


R. Peto, and J. Peto, Journal of the Royal Statistical Society Series A-General, 135 (1972) 185-207.

D. R. Cox, Journal of the Royal Statistical Society Series B-Statistical Methodology, 74 (1972) 187-220.

P. O'Brien, Biometrics, 40 (1984) 1079-1087. [4] S. J.Pocock, N. L.Geller, and A. A. Tsiatis, Biometrics, 43 (1987) 487-498. [5] B. C. Tilley, J.Marler, N. L. Geller, et al., Stroke, 27 (1996) 2136-2142.

A. Davalos, J.Alvarez-Sabín, J.Castillo, et al.,, Published online June 11, 2012 DOI:10.1016/S0140-6736(12)60813-7

K.Bolland, J. Whitehead, E.Cobo, and J. J. Secades, Pharmaceutical Statistics, 8 (2009) 136-149.

J. Whitehead, M.Branson, and S. Todd, Statistics in Medicine (2010)521-532.

L.J.Wei,D.Y. Lin, and L. Weissfeld, Journal of the American Statistical Association, 84 (1989) 1065-73.

J. Sun, The statistical analysis of interval-censored failure time data, Springer, USA,2006.

P. Hougaard, Analysis of multivariate survival data, Springer,New York,2000.

L. J.Wei, and W. E. Johnson, Biometrika, 72 (1985) 359-364. [13] P. J. Kelly, and L. L.Y. Lim, Statistics in Medicine, 19 (2000) 13–33.

W. B. Nelson, Recurrent Events Analysis for Product Repairs, Disease Recurrences, and Other Applications, ASA, Philadelphia, 2003.

B.Genser, and K. D. Wernecke, Biometrical Journal, 47 (2005) 388-401.

G. E. Bijwaard, P. H.Franses, and R. Paap, Journal of Business & Economic Statistics, 24 (2006) 487-502.

E.Gutierrez, S.Lozano, and J. R. Gonzalez, IMA Journal of Management Mathematics, 22 (2011) 115-128.

J. M.Box-Steffensmeier, and C. Zorn, Journal of Politics, 64 (2002) 1069-