Abstract
When the number of independent units is not adequate to invoke large sample approximations in clustered data analysis, a situation that often arises in group randomized trials (GRTs), valid and efficient small sample inference becomes important. We review the current methods for analyzing data from small numbers of clusters, namely methods based on full distribution assumptions (mixed effect models), semi-parametric methods based on Generalized Estimating Equations (GEE), and non-parametric methods based on permutation tests.
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References
Barlett MS (1937) Properties of sufficiency and statistical tests. Proceedings of the Royal Society, A, 160:268–282.
Braun T and Feng Z (2001) Optimal permutation tests for the analysis of group randomized trials. Journal of the American Statistical Association, 96:1424–1432.
Breslow NE, Clayton DG (1993) Approximate Inference in Generalized Linear Mixed Models. Journal of the American Statistical Association, 88:9–25.
Chandra T and Ghosh J (1979) Valid asymptotic expansions for the likelihood ratio statistic and other perturbed chi-square variables. Sankhya A, 41:22–47.
Cox DR and Reid N (1987) Parameter orthogonality and approximate conditional inference 9 with discussion) Journal of the Royal Statistical Society Series B, 49:1–39.
Donner A, Eliasziw M, Klar N (1994) A comparison of methods for testing homogeneity of proportions for teratologic studies. Statistics in Medicine, 13:479–93.
Donner A, Klar N (2000) Design and Analysis of Cluster Randomization Trials In Health Research. New York, Oxford University Press.
Edgington ES (1987) Randomization Tests Marcel Decker, New York.
Emrich L, Piedmonte M (1992) On some small sample properties of generalized estimating equation Estimates for multivariate dichotomous outcomes. Journal of Statistical Computation and Simulationa, 41:19–29.
Evans B, Feng Z, Peterson AV (2001) A comparison of generalized linear mixed model procedures with Estimating equations for variance and covariance parameter Estimation in longitudinal studies and group randomized trials. Statistics in Medicine, 20:3353–3373.
Fay M, Graubard B (2001) Small-sample adjustment for Wald-type tests using sandwich Estimators. Biometrics, 57:1198–1206.
Feng Z, McLerran D, Grizzle J (1996) A comparison of statistical methods for clustered data analysis with Gaussian error. Statistics in Medicine, 15:1793–806.
Feng Z, Diehr P, Peterson A, McLerran D (2001) Selected statistical issues in group randomized trials. Annual Review of Public Health, 22:167–87.
Frydenberg M and Jensen J (1989) Is the ‘improved likelihood ratio statistic’ really improved in the discrete case? Biometrika, 76:655–662.
Gail MH, Tan WY, and Piantadosi S (1988) Tests for no treatment effect in randomized clinical trials, Biometrika, 75:57–64.
Gail MH, Byar DP, Pechacek TF, Corle DK (1992) Aspects of statistical design for the Community Intervention Trial for Smoking Cessation (COMMIT). Controlled Clinical Trials, 123:6–21.
Gail MH, Mark SD, Carroll R, Greeen S, Pee D (1996) On design considerations and randomization-based inference for community intervention trials. Statistics in Medicine, 15:1069–92.
Good P Permutation Tests (1994) Springer-Verlag, New York.
Harville D (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association, 72:320–340.
Jennrich Rand Schluchter M (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42:805–820.
Kackar A and Harville D (1984) Approximations for standard errors of Estimators of fixed and random effects in mixed linear models. Journal of the American Statistical Association, 79:853–862.
Kauermann G, Carroll R (2001) A note on the efficiency of sandwich covariance matrix Estimation. Journal of the American Statistical Association, 96:1387–1396.
Kenward M and Roger J (1997) Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 53:983–997.
Laird N and Ware J (1982). Random-effects models for longitudinal data. Biometrics, 38:963–974.
Lehmann EL and Stein C (1949) On the theory of some non-parametric hypotheses. The Annals of Mathematical Statistics, 20:28–45.
Liang KY, Zeger SL (1986) Longitudinal Data Analysis Using Generalized Linear Models. Biometrika, 73:13–22.
Lyons B, Peters D (2000) Applying Skovgaard’s modified directed likelihood statistic to mixed linear models. Journal of Statistical Computation and Simulations, 65:225–242.
MacKinnon JG, White H (1985) Some heteroscedasticity-consistent covariance matrix Estimators with improved finite sample properties. Journal of Econometrics, 29:305–325.
Mancl L and DeRouren T (2001) A covariance Estimator for GEE with improved small-sample properties. Biometrics, 57:126–134.
Maritz J, Jarrett R (1983) The use of statistics to examine the association between fluoride in drinking water and cancer death rates. Applied Statistics, 32:97–101.
McCulloch CE (1994) Maximum likelihood variance components Estimation for binary data. Journal of the American Statistical Association, 89:330–35.
McCulloch CE (1997) Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association, 92:162–70.
McCulloch CE and Searle SR (2001) Generalized, Linear, and Mixed Models. New York, Wiley.
McGilchrist CA. (1994) Estimation in Generalized Mixed Models. Journal of the Royal Statistical Society Series B, 56:61–69
Murray DM (1998) Design and Analysis of Group-Randomized Trials. New York, Oxford University Press.
Neyman J, Iwaskiewicz K, and Kolodziejczyk T (1935) Statistical problems in agricultural experimentation. Journal of the Royal Statistical Society, 2:107–180.
Pan W and Wall M (2002) Small-sample adjustments in using the sandwich variance Estimator in generalized Estimating equations. Statistics in Medicine, 21:1429–1441.
Park T (1993) A Comparison of the Generalized Estimating Equation Approach with the Maximum Likelihood Approach for Repeat ed measurements. Statistics in Medicine, 12:1723–1732.
Rao CR (1971) Minimum variance quadratic unbiased Estimation of variance components. Journal of Multivariate Analysis, 1:445–56.
Romano J (1990) On the behavior of randomization tests without a group invariance assumption, Journal of the American Statistical Association, 85:686–692.
Satterthwaite F (1941) Synthesis of variance. Psychometrika, 6:309–316.
Schall R (1991) Estimation in Generalized Linear Models with Random Effects. Biometrika, 40:917–927.
Sharples K, Breslow N (1992) Regression analysis of correlated binary data: some small sample results for the Estimating equation approach. Journal of Statistical Computation and Simulations, 42:1–20.
Sorensen G, Thompson B, Glanz K, Feng Z, Kinne S, Diclemente C, Emmons K, Heimendinger J, Probart C, Lichtenstein E, for Working Well Trial (1996) Work site-based cancer prevention: primary results form the Working Well Trial. American Journal of Public Health, 86:939–947.
Thornquist M, Anderson G (1992) Small sample properties of generalized Estimating equations in group-randomized designs with gaussian response. Technical Report, Fred Hutchinson Cancer Research Center.
Zucker D, Lieberman O, and Manor O (2000) Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society Series B, 62:827–838.
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Feng, Z., Braun, T., McCulloch, C. (2004). Small Sample Inference for Clustered Data. In: Lin, D.Y., Heagerty, P.J. (eds) Proceedings of the Second Seattle Symposium in Biostatistics. Lecture Notes in Statistics, vol 179. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9076-1_5
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DOI: https://doi.org/10.1007/978-1-4419-9076-1_5
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