Sequential analysis methodology for a Poisson GLMM with applications to multicenter randomized clinical trials. (English) Zbl 1349.62369
Summary: Sequential analyses in clinical trials have ethical and economic advantages over fixed sample size methods. The sequential probability ratio test (SPRT) is a hypothesis testing procedure which evaluates data as it is collected. The original SPRT was developed by Wald for one-parameter families of distributions and later extended by Bartlett to handle the case of nuisance parameters. However, Bartlett’s SPRT requires independent and identically distributed observations. In this paper we show that Bartlett’s SPRT can be applied to generalized linear model (GLM) contexts. Then we propose an SPRT analysis methodology for a Poisson generalized linear mixed model (GLMM) that is suitable for our application to the design of a multicenter randomized clinical trial that compares two preventive treatments for surgical site infections. We validate the methodology with a simulation study that includes a comparison to Neyman-Pearson and Bayesian fixed sample size test designs and the Wald SPRT.
MSC:
| 62L10 | Sequential statistical analysis |
| 62J12 | Generalized linear models (logistic models) |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
References:
| [1] | Baksh, F. M.; Todd, S.; Whitehead, J.; Lucini, M. M., Design consideration in the sequential analysis of matched case-control data, Statistics in Medicine, 24, 853-867 (2005) |
| [2] | Bartlett, M. S., The large sample theory of sequential tests, Proceedings of the Cambridge Philosophical Society, 42, 239-244 (1946) · Zbl 0063.00231 |
| [3] | Coad, S. D.; Ivanova, A., The use of the triangular test with response-adaptive treatment allocation, Statistics in Medicine, 24, 1483-1493 (2005) |
| [4] | Cox, D. R., Sequential tests for composite hypotheses, Proceedings of the Cambridge Philosophical Society, 48, 5-12 (1952) · Zbl 0129.31902 |
| [5] | Cox, D. R., Large sample sequential tests for composite hypotheses, Sankhya, 25, 5-12 (1963) · Zbl 0129.31902 |
| [6] | Eisenberg, B.; Ghosh, B. K., The Sequential Probability Ratio Test, (Ghosh, B. K.; Sen, P. K., Handbook of Sequential Analysis (1991), Marcel Dekker) · Zbl 0403.62006 |
| [7] | Ghosh, B. K., Sequential Tests of Statistical Hypotheses (1970), Addison-Wesley · Zbl 0223.62097 |
| [8] | Jennison, C.; Turnbull, D. W., Group Sequential Methods (2000), Chapman and Hall · Zbl 0934.62078 |
| [9] | Lee, J. W.; DeMets, D. L., Sequential comparison of changes with repeated measurements data, Journal of the American Statistical Association, 86, 757-762 (1991) |
| [10] | Paulsen, K. B.; Bremmelgaard, A.; Sorensen, A. I.; Raahave, D.; Petersen, J. V., Estimated costs of postoperative wound infections: a case-control study of marginal hospital and social security costs, Epidemiology and Infection, 113, 283-295 (1994) |
| [11] | Reyes, E. M.; Ghosh, S. K., Bayesian Average Error Based Approach to Sample Size Calculations for Hypothesis Testing, Journal of Biopharmaceutical Statistics, 21, 920-937 (2012) |
| [12] | Scharfstein, D. O.; Tsiatis, A. A.; Robins, J. M., Semiparametric efficiency and its implication on the design and analysis of group-sequential studies, Journal of the American Statistical Association, 92, 1342-1350 (1997) · Zbl 0913.62075 |
| [13] | Spiessens, B.; Lesaffre, E.; Verbeke, G.; Kim, K.; DeMets, D. L., An overview of group sequential methods in longitudinal clinical trials, Statistical Methods in Medical Research, 9, 497-515 (2000) · Zbl 1121.62666 |
| [14] | Spiessens, B.; Lesaffre, E.; Verbeke, G.; Kim, K., Group sequential methods for an ordinal logistic random-effects model under misspecification, Biometrics, 58, 569-575 (2002) · Zbl 1210.62206 |
| [15] | Spiessens, B.; Lesaffre, E.; Verbeke, G., A comparison of group sequential methods for binary longitudinal data, Statistics in Medicine, 22, 501-515 (2003) |
| [16] | Wald, A., Sequential Analysis (1947), Dover Publications · Zbl 0041.26303 |
| [17] | Wu, M. C.; Lan, K. K., Sequential monitoring for comparison of changes in a response variable in clinical studies, Biometrics, 48, 765-779 (1992) · Zbl 0825.62841 |
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