Skip to main content
SpringerLink
Log in

Group sequential tests for treatment effect on survival and cumulative incidence at a fixed time point

  • Published:
Lifetime Data Analysis Aims and scope Submit manuscript

Abstract

Medical research frequently involves comparing an event time of interest between treatment groups. Rather than comparing the entire survival or cumulative incidence curves, it is sometimes preferable to evaluate these probabilities at a fixed point in time. Performing a covariate adjusted analysis can improve efficiency, even in randomized clinical trials, but no currently available group sequential test for fixed point analysis provides this adjustment. This paper introduces covariate adjusted group sequential pointwise comparisons of survival and cumulative incidence probabilities. Their test statistics have an asymptotic distribution with independent increments, permitting use of common stopping boundary specification methods. These tests are demonstrated through a redesign of BMT CTN 0402, a clinical trial that evaluated a prophylactic treatment for adverse outcomes following blood and marrow transplantation. A simulation study demonstrates that these tests maintain the type I error rate and power at nominal levels under a variety of settings involving influential covariates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Andersen P, Borgan O, Gill R, Keiding N (1993) Statistical models based on counting processes. Springer, Berlin

    Book  Google Scholar 

  • Bilias Y, Gu M, Ying Z (1997) Towards a general asymptotic theory for Cox model with staggered entry. Ann Stat 25(2):662–682

    Article  MathSciNet  Google Scholar 

  • Ciolino JD, Martin R, Zhao W, Jauch EC, Hill MD, Palesch YY (2014) Continuous covariate imbalance and conditional power for clinical trial interim analyses. Contemp Clin Trials 38(1):9–18

    Article  Google Scholar 

  • Ciolino JD, Martin RH, Zhao W, Hill MD, Jauch EC, Palesch YY (2015) Measuring continuous baseline covariate imbalances in clinical trial data. Stat Methods Med Res 24(2):255–272

    Article  MathSciNet  Google Scholar 

  • Cox D (1972) Regression and life tables (with discussion). J R Stat Soc Ser B 34(2):187–220

    MATH  Google Scholar 

  • Cutler C, Logan BR, Nakamura R, Johnston L, Choi SW, Porter DL, Hogan WJ, Pasquini MC, MacMillan ML, Wingard JR, Waller EK, Grupp SA, McCarthy PL, Wu J, Hu Z, Carter SL, Horowitz MM, Antin JH (2012) Tacrolimus/sirolimus vs. tacrolimus/methotrexate for graft-vs.-host disease prophylaxis after HLA-matched, related donor hematopoietic stem cell transplantation: results of Blood and Marrow Transplant Clinical Trials Network Trial 0402. Blood 120(21):739–739

    Article  Google Scholar 

  • Fine JP, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94(446):496–509

    Article  MathSciNet  Google Scholar 

  • Gail MH, Wieand S, Piantadosi S (1984) Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates. Biometrika 71(3):431–444

    Article  MathSciNet  Google Scholar 

  • Gray RJ (1988) A class of k-sample tests for comparing the cumulative incidence of a competing risk. Ann Stat 16(3):1141–1154

    Article  MathSciNet  Google Scholar 

  • Gu MG, Lai TL (1991) Weak convergence of time-sequential censored rank statistics with applications to sequential testing in clinical trials. Ann Stat 19(3):1403–1433

    Article  MathSciNet  Google Scholar 

  • Hauck WW, Anderson S, Marcus SM (1998) Should we adjust for covariates in nonlinear regression analyses of randomized trials? Control Clin Trials 19(3):249–256

    Article  Google Scholar 

  • He P (2014) Bias reduction by using covariate-adjusted censoring weights for survival and competing risks data. Doctoral Dissertation, Medical College of Wisconsin

  • Jennison C, Turnbull BW (1999) Group sequential methods with applications to clinical trials. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Klein JP, Andersen PK (2005) Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61(1):223–229

    Article  MathSciNet  Google Scholar 

  • Kosorok M (2008) Introduction to empirical processes and semiparametric inference. Springer, New York

    Book  Google Scholar 

  • Lin D, Shen L, Ying Z, Breslow N (1996) Group sequential designs for monitoring survival probabilities. Biometrics 52(3):1033–1041

    Article  MathSciNet  Google Scholar 

  • Logan BR, Zhang MJ (2013) The use of group sequential designs with common competing risks tests. Stat Med 32(6):899–913

    Article  MathSciNet  Google Scholar 

  • Logan BR, Zhang M, Klein JP (2011) Marginal models for clustered time-to-event data with competing risks using pseudovalues. Biometrics 67(1):1–7

    Article  MathSciNet  Google Scholar 

  • Martens MJ, Logan BR (2018) A group sequential test for treatment effect based on the Fine-Gray model. Biometrics 74(3):1006–1013

    Article  MathSciNet  Google Scholar 

  • Peto R, Pike M, Armitage P, Breslow N, Cox D, Howard SV, Mantel N, McPherson K, Peto J, Smith P (1976) Design and analysis of randomized clinical trials requiring prolonged observation of each patient. i. Introduction and design. Br J Cancer 34(6):585

    Article  Google Scholar 

  • Pocock SJ, Assmann SE, Enos LE, Kasten LE (2002) Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practice and problems. Stat Med 21(19):2917–2930

    Article  Google Scholar 

  • Pollard D (1990) Empirical processes: theory and applications. In: NSF-CBMS regional conference series in probability and statistics. Institute of Mathematical Statistics, Hayward, California; American Statistical Association, Alexandria, Virginia, pp. 1–86

  • Robinson LD, Jewell NP (1991) Some surprising results about covariate adjustment in logistic regression models. Int Stat Rev 59(2):227–240

    Article  Google Scholar 

  • Scheike TH, Zhang MJ, Gerds TA (2008) Predicting cumulative incidence probability by direct binomial regression. Biometrika 95(1):205–220

    Article  MathSciNet  Google Scholar 

  • Zhang M, Tsiatis AA, Davidian M (2008) Improving efficiency of inferences in randomized clinical trials using auxiliary covariates. Biometrics 64(3):707–715

    Article  MathSciNet  Google Scholar 

  • Zhang X, Loberiza FR, Klein JP, Zhang MJ (2007) A SAS macro for estimation of direct adjusted survival curves based on a stratified Cox regression model. Comput Methods Programs Biomed 88(2):95–101

    Article  Google Scholar 

Download references

Acknowledgements

Support for this study was provided by Grant #F31HL134317 by the National Heart, Lung, and Blood Institute of the National Institutes of Health. Support for the BMT CTN 0402 trial was provided by Grant #U10HL069294 to the Blood and Marrow Transplant Clinical Trials Network from the National Heart, Lung, and Blood Institute and the National Cancer Institute, along with contributions by Wyeth Pharmaceuticals Inc. The authors thank the Blood and Marrow Transplant Clinical Trials Network for permitting use of the 0402 trial data. The content is solely the responsibility of the authors and does not necessarily represent the official views of the above mentioned parties.

Author information

Authors and Affiliations

  1. The Emmes Company, Rockville, MD, 20850, USA

    Michael J. Martens

  2. Division of Biostatistics, Medical College of Wisconsin, Milwaukee, WI, 53226, USA

    Brent R. Logan

Authors
  1. Michael J. Martens
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brent R. Logan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael J. Martens.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 285 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Martens, M.J., Logan, B.R. Group sequential tests for treatment effect on survival and cumulative incidence at a fixed time point. Lifetime Data Anal 26, 603–623 (2020). https://doi.org/10.1007/s10985-019-09491-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10985-019-09491-z

Keywords

Search

Navigation