Independent increments in group sequential test: a review

• Autores: Kyung Mann Kim, Anastasios A. Tsiatis
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 44, Nº. 2, 2020, págs. 223-264
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In order to apply group sequential methods for interim analysis for early stopping in clinical trials, the joint distribution of test statistics over time has to be known. Often the distribution is multivariate normal or asymptotically so, and an application of group sequential methods requires multivariate integration to determine the group sequential boundaries. However, if the increments between successive test statistics are independent, the multivariate integration reduces to a univariate integration involving simple recursion based on convolution. This allows application of standard group sequential methods. In this paper we review group sequential methods and the development that established independent increments in test statistics for the primary outcomes of longitudinal or failure time data.

• Referencias bibliográficas
  • Aalen, O. O. (1978). Nonparametric inference for a family of counting processes. Annals of Statistics, 6, 701–726.
  • Anderson, P. K., Borgan, O., Gill, R., and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer-Verlag, New York.
  • Anscombe, F. J. (1954). Fixed-sample-size analysis of sequential observations. Biometrics, 10, 89–100.
  • Armitage, P. (1954). Sequential tests in prophylactic and therapeutic trials. Quarterly Journal of Medicine, 23(91), 255–274.
  • Armitage, P. (1957). Restricted sequential procedures. Biometrika, 44, 9–26.
  • Armitage, P. (1975). Sequential Medical Trials, 2nd ed. Wiley, New York.
  • Armitage, P. (1990). Sequential methods. In Hinkley, D. V., Reid, N., and Snell, E. J. (eds), Statistical Theory and Modeling: In Honor of...
  • Armitage, P., McPherson, C. K., and Rowe, B. C. (1969). Repeated significance tests on accumulating data. Journal of the Royal Statistical...
  • Armitage, P., Stratton, I. M., and Worthington, H. V. (1985). Repeated significance tests for clinical trials with a fixed number of patients...
  • Bross, I. (1952). Sequential medical plans. Biometrics, 8, 188–205.
  • Cox, D. R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B, 34, 187–220.
  • Cox, D. R. (1975). Partial likelihood. Biometrika, 62, 269–276.
  • Cox, D. R. and Hinkley, D. V. (1974). Theoretical Statistics. Chapman and Hall, London.
  • Crowder, M. (1995). On the use of a working correlation matrix in using generalized linear models for repeated measures. Biometrika, 82, 407–410.
  • DeMets, D. L. and Lan, K. K. G. (1994). Interim analysis: the alpha spending function approach. Statistics in Medicine, 13, 1341–1352.
  • Dodge, H. F. and Romig, H. G. (1929). A method of sampling inspection. Bell System Technical Journal, 8, 613–631.
  • Elfring, G. L. and Schultz, J. R. (1973). Group sequential designs for clinical trials. Biometrics, 29(3), 471–477.
  • Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley, New York.
  • Gail, M. H., DeMets, D. L., and Slud, E. V. (1982). Simulation studies on increments of the two sample logrank score test for survival time...
  • Gange, S. J. and DeMets, D. L. (1996). Sequential monitoring of clinical trials with correlated responses. Biometrika, 83, 157–167.
  • Geary, D. N. (1988). Sequential testing in clinical trials with repeated measurements. Biometrika, 75, 311– 318.
  • Gehan, E. A. (1961). The determination of the number of patients required in a preliminary and a follow-up trial of a new chemotherapeutic...
  • Gehan, E. A. (1965). A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika, 52, 203–223.
  • Gu, M. G. and Lai, T. L. (1991). Weak convergence of time-sequential censored rank statistics with applications to sequential testing in clinical...
  • Gu, M. and Ying, Z. (1995). Group sequential methods for survival data using partial score processes with covariate adjustment. Statistica...
  • Hodges, J. L. and Lehmann, E. L. (1963). Estimates of location based on rank tests. Annals of Mathematical Statistics, 34, 598–611.
  • Jennison, C. and Turnbull, B. W. (1990). Statistical approaches to interim monitoring of medical trials: a review and commentary. Statistical...
  • Jennison, C. and Turnbull, B. W. (1991). Exact calculations for sequential t, χ2 and F tests. Biometrika, 78, 133–141.
  • Jennison, C. and Turnbull, B. W. (1997). Group-sequential analysis incorporating covariate information. Journal of the American Statistical...
  • Kim, K., Boucher, H., and Tsiatis, A. A. (1995). Design and analysis of group sequential logrank tests in maximum duration versus information...
  • Kim, K. and DeMets, D. L. (1987). Design and analysis of group sequential tests based on the type I error spending rate function. Biometrika,...
  • Laird, N. M. and Ware, J. H. (1982). Random effects models for longitudinal data. Biometrics, 38, 963–974.
  • Lan, K. K. G. and DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika, 70, 659–663.
  • Lee, J. W. (1994). Group sequential testing in clinical trials with multivariate observations: a review. Statistics in Medicine, 13, 101–111.
  • Lee, J. W. and DeMets, D. L. (1991). Sequential comparison of changes with repeated measurements data. Journal of the American Statistical...
  • Lee, J. W. and DeMets, D. L. (1992). Sequential rank tests with repeated measurements in clinical trials. Journal of the American Statistical...
  • Lee, J. W. and Sather, H. N. (1995). Group sequential methods for comparison of cure rates in clinical trials. Biometrics, 51, 756–763.
  • Lee, S. J., Kim, K., and Tsiatis, A. A. (1996). Repeated significance testing in longitudinal clinical trials. Biometrika, 83, 779–789.
  • Lee, Y. J., Staquet, M., Simon, R., Catane, R., and Muggia, F. (1979). Two-stage plans for patient accrual in phase II cancer clinical trials....
  • Liang, K. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22.
  • Liang, K., Zeger, S. L., and Qaqish, B. (1992). Multivariate regression analyses for categorial data (with discussion). Journal of the Royal...
  • Lin, D. (1992). Sequential log rank tests adjusting for covariates with the accelerated life model. Biometrika, 79, 523–529.
  • Lin, D. Y., Wei, L. J., and Ying, Z. (1998). Accelerated failure time models for counting processes. Biometrika, 85, 605–618.
  • Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Reports,...
  • McCullagh, C. K. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.
  • McPherson, C. K. and Armitage, P. (1971). Repeated significance tests on accumulating data when the null hypothesis is not true. Journal of...
  • Neyman, J. and Pearson, E. S. (1933). IX. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions...
  • O’Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics, 35, 549–556.
  • Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika, 64, 191–199.
  • Prentice, R. L. andMarek, P. (1979). A qualitative discrepancy between censored data rank tests.Biometrics, 35, 861–867.
  • Reboussin, D. M., DeMets, D. L., Kim, K., and Lan, K. K. G. (2000). Programs for computing group sequential bounds using the Lan-DeMets method....
  • Reboussin, D. M., Lan K. K. G., and DeMets, D. L. (1992). Group sequential testing of longitudinal data. Technical Report 72. Department of...
  • Ritov, Y. (1990). Estimation in a linear regression model with censored data. Annals of Statistics, 18, 303– 328.
  • Rotnitzky, A. and Jewell, N. P. (1990). Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster...
  • Scharfstein, D. O., Tsiatis, A. A., and Robins, J. M. (1997). Semiparametric efficiency and its implication on the design and analysis of...
  • Schervish, M. J. (1984). Multivariate normal probabilities with error bound (with corrections in 1985). Applied Statistics, 33, 81–94.
  • Schoenfield, L. J., Lachin, J. M., the Steering Committee, and the NCGS Group (1981). Chenodiol for dissolution of gallstones: The National...
  • Sellke, T. and Siegmund, D. (1983). Sequential analysis of the proportional hazards model. Biometriak, 70, 315–326.
  • Simon, R. (1989). Optimal two-stage designs for phase II clinical trials. Controlled Clinical Trials, 10, 1–10.
  • Slud, E. V. (1984). Sequential linear rank tests for two-sample censored survival data. Annals of Statistics, 12(2), 551–571.
  • Slud, E. V. and Wei, L. J. (1982). Two-sample repeated significance tests based on the modified Wilcoxon statistic. Journal of the American...
  • Sobel, M. and Wald, A. (1949). A sequential decision procedure for choosing one of three hypotheses concerning the unknown mean of a normal...
  • Spiessens, B., Lesaffre, E., Verbeke, G., Kim, K., and DeMets, D.L. (2000). An overview of group sequential methods in longitudinal clinical...
  • Spiessens, B., Lesaffre, E., Verbeke, G., and Kim, K. (2002). Group sequential methods for an ordinal logistic random-effects model under...
  • Stein, C. (1945). A two-sample test for a linear hypothesis whose power is independent of the variance. Annals of Mathematical Statistics,...
  • Su, J. Q. and Lachin, J. M. (1992). Group sequential distribution-free methods for the analysis of multivariate observations. Biometrics,...
  • Tarone, R. E. and Ware, J. H. (1977). On distribution-free tests for equality of survival distributions. Biometrika, 64, 156–160.
  • Tsiatis, A. A. (1981). The asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time....
  • Tsiatis, A. A. (1982). Repeated significance testing for a general class of statistics used in censored survival analysis. Journal of the...
  • Tsiatis, A. A. (1990). Estimating regression parameters using linear rank tests for censored data. Annals of Statistics, 18, 354–372.
  • Tsiatis, A. A., Boucher, H., and Kim, K. (1995). Sequential methods for parametric survival models. Biometrika, 82, 165–173.
  • Tsiatis, A. A., Rosner, G. L., and Tritchler D. L. (1985). Group sequential tests with censored survival data adjusting for covariates. Biometrika,...
  • Wald, A. (1947). Sequential Analysis. Wiley, New York.
  • Wald, A. and Wolfowitz, J. (1948). Optimum character of the sequential probability ratio test. Annals of Mathematical Statistics, 19, 326–339.
  • Wei, L. J., Su, J. Q., and Lachin, J. M. (1990a). Interim analyses with repeated measurements in sequential clinical trial. Biometrika, 77,...
  • Wei, L. J., Ying, Z., and Lin, D. Y. (1990b). Linear regression analysis of censored survival data based on rank tests. Biometrika, 77, 845–851.
  • Wu, M. C. and Bailey, K. R. (1989). Estimation and comparison of changes in the presence of informative right censoring: conditional linear...
  • Wu, M. C. and Lan, K. K. G. (1992). Sequential monitoring for comparison of changes in a response variable in clinical studies. Biometrics,...