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Responder cell frequency estimation and binomial three-level nonlinear mixed effects model in limiting dilution
Misoo C Ellison1, Gary O Zerbe, Myron J Levin
1Division of Biostatistics, National Jewish Medical and Research Center, Denver, Colorado 80206, USA. ellisonm@njc.org
Journal of Biopharmaceutical Statistics
|February 11, 2005
Summary
This study improves estimating vaccine-boosted immune responses by modifying statistical models for limiting dilution assays (LDA). A new negative binomial model and a three-level nonlinear mixed-effects model offer more accurate responder cell frequency (RCF) estimations in herpes zoster (HZ) studies.
Area of Science:
- Immunology
- Biostatistics
- Vaccinology
Background:
- Responder cell frequencies (RCF) are crucial for assessing vaccine-boosted immune responses in herpes zoster (HZ) prevention.
- Current estimation methods using limiting dilution assays (LDA) often violate theoretical assumptions, leading to biased RCF estimates.
- The single-hit Poisson model's linearity assumption between cell concentration and non-responder wells is frequently unmet.
Purpose of the Study:
- To develop a more accurate statistical method for estimating RCF in HZ prevention studies.
- To address the limitations of the Poisson model in LDA by incorporating a more flexible distribution.
- To propose a robust statistical model accounting for correlated responses in longitudinal LDA data.
Main Methods:
- Modified the Poisson assumption in LDA by using a mixture of Poisson and gamma distributions, resulting in a negative binomial model.
- Proposed a binomial three-level nonlinear mixed-effects model to handle correlated binary responses from varying cell concentrations and over time.
- Employed maximum likelihood estimation via adaptive Gaussian quadrature for parameter estimation.
Main Results:
- The negative binomial assumption provides a better fit between the logarithm of non-responding wells and cell concentration compared to the standard Poisson model.
- The proposed three-level nonlinear mixed-effects model effectively accounts for the complex correlations in LDA data.
- An algorithm for implementing this complex model within SAS NLMIXED is provided.
Conclusions:
- The modified statistical approach offers improved accuracy in estimating RCF for HZ vaccine studies.
- The developed mixed-effects model provides a powerful tool for analyzing correlated, non-Gaussian longitudinal data in immunological assays.
- The suggested algorithm facilitates the practical application of advanced statistical methods in biostatistical research.