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Fixed Size Confidence Regions for the Parameters of the Mixed Effects Logistic Regression Model


Abstract


We develop fixed size confidence regions for estimating the fixed and random effects parameters of the mixed effects logistic regression model. This model applies to, among others, the study of the effects of covariates on a dichotomous response variable when subjects are sampled in clusters. Two sequential procedures are developed to estimate with a prescribed accuracy (confidence level) and fixed precision the set of fixed and random effects parameters and linear transformations of these parameters, respectively. We show that the two procedures are asymptotically consistent (i.e., the coverage probability converges to the nominal confidence level) and asymptotically efficient (i.e., the ratio of the expected random sample size to the unknown best fixed sample size converges to 1) as the width of the confidence region converges to 0. Suggestions to improve the performance of the procedures are provided based on Monte Carlo simulation and illustrated through a longitudinal clinical trial data.

DOI Code: 10.1285/i20705948v12n1p1

Keywords: Mixed effects logistic regression model, sequential estimation, fixed width confidence estimation

References


Brostrom, G. and Holmberg, H. (2011). Generalized linear models with clustered data: Fixed and random effects models. Comput. Statist. Data Anal., 55, 3123-3134.

Chambaz, A., Zhengy, W., and J. van der Laan M. (2014). Targeted Covariate-Adjusted Response-Adaptive LASSO-Based Randomized Controlled Trials. Berkeley Div. of Biostat. Working Paper Series}, Paper 323.

Chang, Y. I. (1999). Strong consistency of maximum quasi-likelihood estimate in generalized linear models via a last time.

Statist. & Probab. Lett.}, 45, 237-246.

Chang, Y. I. (2011). Sequential estimation in generalized linear models when covariates are subject to errors. Metrika, 73, 93-120.

Chang, Y. C. and Martinsek, A. T. (1992). Fixed size confidence regions for parameters of a logistic regression model. Ann. Statist., 20, 1953-1969.

Chang Y. I. and Park E. (2013). Sequential estimation for covariate-adjusted response-adaptive designs. J. Korean Statist. Soc., 42, 105–116.

Chien, C., Chang, Y. I., and Hsueh, H. (2011). Optimal sampling in retrospective logistic regression via two-stage method. Biom. J., 53, 5-18.

Davis C. S. (1991). Semi-parametric and non-parametric methods for the analysis of repeated measurements with applications to clinical trials. Statist. Med., 10, 1959–1980.

De Backer, M., De Vroey, C., Lesaffre, E., Scheys, I., and De Keyser, P. (1998). Twelve weeks of continuous oral therapy for toenail onychomycosis caused by dermatophytes: A double-blind comparative trial of terbinafine 250 mg/day versus itraconazole 200 mg/day. J. Am. Acad. Dermat., 38, 57-63.

Grabovsky, I. and Chang, H. H. (2003). Deriving a stopping rule for sequential adaptive tests. Manuscript, http://www.psych.umn.edu/psylabs/catcentral/pdf%20files/gr01-01.pdf. Accessed on 17-11-2011.

Govindarajulu, Z. (2004). Sequential Statististics. World Scientific Publishing Co., Singapore.

Sinha, S. K. (2004). Robust analysis of generalized linear mixed models. J. Am. Statist. Assoc., 99:466, 451-460.

Spiessens, B., Lesaffre, E., Verbeke, G. and Kim, K. (2002).

Group sequential methods for an ordinal logistic random-effects model under misspecification. Biometrics, 58, 569-575.

Tuerlinckx, F., Rijmen, F., Verbeke, G. and De Boeck, P. (2006). Statistical inference in generalized linear mixed models: A review. Br. J. Math. Statist. Psychol., 59, 225–255.

Zhang, L. X. and Hu, F. F. A. (2009). New family of covariate-adjusted response-adaptive designs and their properties. Appl. Math. J. Chin. Univ. Ser. B, 24(1), 1–13.


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