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A Frailty Mixture Model for Estimating Vaccine Efficacy

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  • Ira M. Longini
  • M. Elizabeth Halloran

Abstract

Vaccines can have heterogeneous effects on the host's immune response. Some vaccinated people may have a strong response and be highly protected against infectious challenge, but others may only derive varying levels of partial protection. We derive a statistical model for estimating vaccine efficacy that expresses the often unmeasured heterogeneous host response and other vaccine effects in terms of estimable parameters. In addition, the model incorporates the infection process into the base‐line hazard rate. The model falls into the general category of frailty models (with point mass at 0) employed in survival analysis. As an example, we estimate the efficacy of a measles vaccine from a measles outbreak in Burundi.

Suggested Citation

  • Ira M. Longini & M. Elizabeth Halloran, 1996. "A Frailty Mixture Model for Estimating Vaccine Efficacy," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(2), pages 165-173, June.
    • Handle: RePEc:bla:jorssc:v:45:y:1996:i:2:p:165-173
    DOI: 10.2307/2986152
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    Cited by:

    1. Kimberly M. Thompson, 2016. "Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis," Risk Analysis, John Wiley & Sons, vol. 36(7), pages 1383-1403, July.
    2. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    3. Anastasios A. Tsiatis & Marie Davidian, 2022. "Estimating vaccine efficacy over time after a randomized study is unblinded," Biometrics, The International Biometric Society, vol. 78(3), pages 825-838, September.
    4. Andreas Wienke & Paul Lichtenstein & Anatoli I. Yashin, 2003. "Unobserved heterogeneity in a model with cure fraction applied to breast cancer," MPIDR Working Papers WP-2003-010, Max Planck Institute for Demographic Research, Rostock, Germany.
    5. Amy Ming-Fang Yen & Tony Hsiu-Hsi Chen, 2007. "Mixture Multi-state Markov Regression Model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 11-21.
    6. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    7. Yen, Amy Ming-Fang & Chen, Hsiu-Hsi, 2013. "Stochastic models for multiple pathways of temporal natural history on co-morbidity of chronic disease," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 570-588.
    8. M Gabriela M Gomes & Marc Lipsitch & Andrew R Wargo & Gael Kurath & Carlota Rebelo & Graham F Medley & Antonio Coutinho, 2014. "A Missing Dimension in Measures of Vaccination Impacts," PLOS Pathogens, Public Library of Science, vol. 10(3), pages 1-3, March.
    9. Susmita Datta & M. Elizabeth Halloran & Ira M. Longini Jr, 1999. "Efficiency of Estimating Vaccine Efficacy for Susceptibility and Infectiousness: Randomization by Individual Versus Household," Biometrics, The International Biometric Society, vol. 55(3), pages 792-798, September.
    10. Yang, Yang & Longini Jr., Ira M. & Elizabeth Halloran, M., 2007. "A data-augmentation method for infectious disease incidence data from close contact groups," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6582-6595, August.
    11. Delphine Pessoa & Caetano Souto-Maior & Erida Gjini & Joao S Lopes & Bruno Ceña & Cláudia T Codeço & M Gabriela M Gomes, 2014. "Unveiling Time in Dose-Response Models to Infer Host Susceptibility to Pathogens," PLOS Computational Biology, Public Library of Science, vol. 10(8), pages 1-9, August.

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