Efficient semiparametric mean-association estimation for longitudinal binary responses.

Semiparametric methods for longitudinal data with association within subjects have recently received considerable attention. However, existing methods for semiparametric longitudinal binary regression modeling (i) mainly concern mean structures with association parameters treated as nuisance; (ii) generally require a correct specification of the covariance structure for misspecified covariance structure may lead to inefficient mean parameter estimates; and (iii) usually run into computation and estimation problems when the time points are irregularly and possibly subject specific. In this article, we propose a semiparametric logistic regression model, which simultaneously takes into account both the mean and response-association structures (via conditional log-odds ratio) for multivariate longitudinal binary outcomes. Our main interest lies in efficient estimation of both the marginal and association parameters. The estimators of the parameters are obtained via the profile kernel approach. We evaluate the proposed methodology through simulation studies and apply it to a real dataset. Both theoretical and empirical results demonstrate that the proposed method yields highly efficient estimators and performs satisfactorily.

Maximum likelihood estimates of two-locus recombination fractions under some natural inequality restrictions.

BACKGROUND: The goal of linkage analysis is to determine the chromosomal location of the gene(s) for a trait of interest such as a common disease. Three-locus linkage analysis is an important case of multi-locus problems. Solutions can be found analytically for the case of triple backcross mating. However, in the present study of linkage analysis and gene mapping some natural inequality restrictions on parameters have not been considered sufficiently, when the maximum likelihood estimates (MLEs) of the two-locus recombination fractions are calculated. RESULTS: In this paper, we present a study of estimating the two-locus recombination fractions for the phase-unknown triple backcross with two offspring in each family in the framework of some natural and necessary parameter restrictions. A restricted expectation-maximization (EM) algorithm, called REM is developed. We also consider some extensions in which the proposed REM can be taken as a unified method. CONCLUSION: Our simulation work suggests that the REM performs well in the estimation of recombination fractions and outperforms current method. We apply the proposed method to a published data set of mouse backcross families.

The extraction of LRP via functional data analysis techniques.

A new strategy based on functional data analysis (FDA) techniques is proposed to extract the lateralized readiness potential (LRP), which treats electroencephalographic data as functional data. This FDA-based method combines longitudinal information from each trial (time series data) with cross-sectional information from all trials at a fixed time point (cross-sectional data). The comparison results show that the FDA-based LRP is closer to the assumed true LRP and is more robust against a reduction in the number of trials than the traditional average-based LRP. Furthermore, the results indicate that the onset of an FDA-based LRP is more accurate than that of an average-based LRP under several measuring criteria.

Analyzing Longitudinal Item Response Data via the Pairwise Fitting Method.

Multidimensional item response theory (MIRT) models can be applied to longitudinal educational surveys where a group of individuals are administered different tests over time with some common items. However, computational problems typically arise as the dimension of the latent variables increases. This is especially true when the latent variable distribution cannot be integrated out analytically, as with MIRT models for binary data. In this article, based on the pseudolikelihood theory, we propose a pairwise modeling strategy to estimate item and population parameters in longitudinal studies. Our pairwise method effectively reduces the dimensionality of the problem and hence is applicable to longitudinal IRT data with high-dimensional latent variables, which are challenging for classical methods. And in the low-dimensional case, our simulation study shows that it performs comparably with the classical methods. We further illustrate the implementation of the pairwise method using a development study of mathematics levels of junior high school students in which the response data are collected from 65 classes of 8 schools from 4 different school districts in China.

Sieve Maximum Likelihood Estimation for Doubly Semiparametric Zero-Inflated Poisson Models.

For nonnegative measurements such as income or sick days, zero counts often have special status. Furthermore, the incidence of zero counts is often greater than expected for the Poisson model. This article considers a doubly semiparametric zero-inflated Poisson model to fit data of this type, which assumes two partially linear link functions in both the mean of the Poisson component and the probability of zero. We study a sieve maximum likelihood estimator for both the regression parameters and the nonparametric functions. We show, under routine conditions, that the estimators are strongly consistent. Moreover, the parameter estimators are asymptotically normal and first-order efficient, while the nonparametric components achieve the optimal convergence rates. Simulation studies suggest that the extra flexibility inherent from the doubly semiparametric model is gained with little loss in statistical efficiency. We also illustrate our approach with a dataset from a public health study.

On the use of historical control information for trend test in carcinogenesis.

In this article a new non-model-based significance test for detecting dose-response relationship with the incorporation of historical control data is proposed. This non-model-based test is considered simpler from a regulatory perspective because it does not require validating any modeling assumptions. Moreover, our test is especially appropriate to those studies in which the intravenous doses for the investigational chemical are labeled as, e.g., low, medium and high or the dose labels do not suggest any obvious choices of dose scores. This test can be easily adopted for detecting general dose-response shape, such as an umbrella pattern. Simple adjustments will be proposed for better control of the actual Type I error. Data sets from two carcinogenesis studies will be used to illustrate our method. We also evaluate the performance of the proposed test and the famous model-based Tarone's trend test with respect to size and power.