Location
Mathematics/Psychology : 103
Date & Time
December 5, 2014, 11:00 am – 12:00 pm
Description
Speaker
Dr. Bo Zhang
Dr. Bo Zhang
Mathematical Statistician
Division of Biostatistics
Center for Devices and Radiological Health
U.S. Food and Drug Administration
Title
On the Analysis of Correlated Data with Informative Cluster Sizes
Abstract
Clustered data commonly arise in biomedical, economic and other social science studies. When cluster sizes are correlated with primary outcomes, the data are then identified as correlated data with “informative cluster sizes", for which the standard data analysis methods do not apply due to induced biases. Joint modeling approach has been proved preferable for informative cluster size data, in that the statistical inference made from using joint modeling approach is (asymptotically) unbiased. However, this is based upon the assumption that the cluster size model in joint models is correctly specified. This presentation unveils the prodigious impact of cluster size model misspecification on the statistical inferences in joint models, and then offer solutions to this misspecification problem. We adopt modified information matrix test and sandwich estimator test, and demonstrate their effectiveness as a diagnostic tool in detecting cluster size model misspecification. Numerical studies show that the two diagnostic tests are highly favorable, except that they may inflate Type I errors when the sample size is small. We consequently recommend, after receiving a rejection in the diagnostic tests, using frequentist model combining if there is strong confidence that the suitable model is indeed included in the pool of candidate cluster size models. This presentation reviews a set of related theorems but complemented with comprehensive numerical studies that together give a methodological solution to the cluster size model misspecification in joint modeling.
Abstract
Clustered data commonly arise in biomedical, economic and other social science studies. When cluster sizes are correlated with primary outcomes, the data are then identified as correlated data with “informative cluster sizes", for which the standard data analysis methods do not apply due to induced biases. Joint modeling approach has been proved preferable for informative cluster size data, in that the statistical inference made from using joint modeling approach is (asymptotically) unbiased. However, this is based upon the assumption that the cluster size model in joint models is correctly specified. This presentation unveils the prodigious impact of cluster size model misspecification on the statistical inferences in joint models, and then offer solutions to this misspecification problem. We adopt modified information matrix test and sandwich estimator test, and demonstrate their effectiveness as a diagnostic tool in detecting cluster size model misspecification. Numerical studies show that the two diagnostic tests are highly favorable, except that they may inflate Type I errors when the sample size is small. We consequently recommend, after receiving a rejection in the diagnostic tests, using frequentist model combining if there is strong confidence that the suitable model is indeed included in the pool of candidate cluster size models. This presentation reviews a set of related theorems but complemented with comprehensive numerical studies that together give a methodological solution to the cluster size model misspecification in joint modeling.
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