Cheng and Wei (2000) proposed a simple inference procedure to estimate regression coefficients of a semiparametric model for repeated measurements observed at irregularly spaced time points. This article provides an inference procedure to estimate baseline mean functions. Based on this procedure, a way to estimate mean functions of a subject with specific covariate information is provided. A way to construct point-wise confidence bands is also proposed. Our proposal is illustrated with a dataset from a clinical trial.

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A varying-coefficient regression model for repeated measurements is considered. It can be applied to variety of data structures including binary and count data. A local linear estimating function is proposed. The resulting estimators of time-varying regression coefficients are consistent and asymptotically normal. Based on these asymptotic results, one can construct pointwise confidence bands of time-varying regression coefficients. For binary data, time-varying covariate effects over time on the risk ratio can be investigated according to our proposal. An illustration is provided with a dataset from a clinical trial and results of a simulation study are presented.

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Inference on gene expression change between two different samples is considered. We develop a mathematical model assuming that there exist two different functional states of a gene: “ON” and “OFF” . Each measured sample-specific gene expression intensity is described by an additive model, which accounts for fluctuations in absolute gene expression intensity and measurement error, to which a two-dimensional mixed normal model with four components considering the joint distribution of the sample “sum” and “difference” is approximated. We can successfully identify genes that are differentially expressed between two samples using posterior probabilities, while avoiding declaring false differences. The proposed methods are applicable to cDNA microarray data with two fluorescent dyes and to oligonucleotide data.

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