Multivariate-t linear mixed models with censored responses, intermittent missing values and heavy tails
Tsung-I Lin1,2, Wan-Lun Wang3
1Institute of Statistics, National Chung Hsing University, Taichung, Taiwan.
Statistical Methods in Medical Research
|June 28, 2019
Summary
This study introduces a robust statistical model for complex medical data, addressing censored and missing values. The new method enhances accuracy in analyzing longitudinal health information, particularly for HIV-AIDS research.
Area of Science:
- Biostatistics
- Longitudinal Data Analysis
- Medical Statistics
Background:
- Medical studies generate complex multivariate longitudinal data with challenges like censored responses, missing values, and outliers.
- The multivariate-t linear mixed model (MtLMM) offers robust modeling for such data, handling outliers and fat-tailed distributions.
Purpose of the Study:
- To present a generalized multivariate-t linear mixed model (MtLMM-CM) that accounts for censorship due to detection limits and missingness in longitudinal data.
- To develop an Expectation Conditional Maximization Either (ECME) algorithm for parameter estimation via Maximum Likelihood (ML).
- To investigate methods for estimating random effects and imputing missing responses.
Main Methods:
- Developed the MtLMM-CM, a generalization of MtLMM, to handle censored and missing data in multivariate longitudinal settings.
- Employed an ECME algorithm for ML parameter estimation.
- Utilized Louis' method for calculating asymptotic standard errors via the empirical information matrix.
Main Results:
- The proposed MtLMM-CM effectively adjusts for censorship and missingness in longitudinal data.
- The ECME algorithm provides reliable parameter estimates and standard errors.
- The methodology demonstrated utility in real-world HIV-AIDS data and simulation studies.
Conclusions:
- The MtLMM-CM is a powerful and flexible tool for robustly analyzing complex multivariate longitudinal data from medical studies.
- The developed methods offer improved statistical approaches for handling data with censored and missing observations.
- The approach is validated through practical applications and simulations, showing its effectiveness.
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