arXiv subjects

Kalyan Das

Publications and source records attributed to Kalyan Das.

4 recordsLinked to original sources

arXiv2023

Likelihood-based Missing Data Analysis in Crossover Trials

A multivariate mixed-effects model seems to be the most appropriate for gene expression data collected in a crossover trial. It is, however, difficult to obtain reliable results using standard statistical inference when some responses are missing. Particularly for crossover studies, missingness is a serious concern as the trial requires a small number of participants. A Monte Carlo EM (MCEM)-based technique was adopted to deal with this situation. In addition to estimation, MCEM likelihood ratio tests (LRTs) are developed to test fixed effects in crossover models with missing data. Intensive simulation studies were conducted prior to analyzing gene expression data.

stat.ME↗

arXiv2023

Likelihood-based Inference for Skewed Responses in a Crossover Trial Setup

This work proposes a statistical model for crossover trials with multiple skewed responses measured in each period. A 3 $\times$ 3 crossover trial data where different drug doses were administered to subjects with a history of seasonal asthma rhinitis to grass pollen is used for motivation. In each period, gene expression values for ten genes were measured from each subject. It considers a linear mixed effect model with skew normally distributed random effect or random error term to model the asymmetric responses in the crossover trials. The paper examines cases (i) when a random effect follows a skew-normal distribution, as well as (ii) when a random error follows a skew-normal distribution. The EM algorithm is used in both cases to compute maximum likelihood estimates of parameters. Simulations and crossover data from the gene expression study illustrate the proposed approach. Keywords: Crossover design, Mixed effect models, Skew-normal distribution, EM algorithm.

stat.ME↗

arXiv2017

A Skew-Normal Copula-Driven GLMM

This paper presents a method for fitting a copula-driven generalized linear mixed models. For added flexibility, the skew-normal copula is adopted for fitting. The correlation matrix of the skew-normal copula is used to capture the dependence structure within units, while the fixed and random effects coefficients are estimated through the mean of the copula. For estimation, a Monte Carlo expectation-maximization algorithm is developed. Simulations are shown alongside a real data example from the Framingham Heart Study.

stat.ME↗

arXiv2004

Mean squared error of empirical predictor

The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases.

math.ST↗