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A hybrid approach for the stratified mark‐specific proportional hazards model with missing covariates and missing marks, with application to vaccine efficacy trials

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  • Yanqing Sun
  • Li Qi
  • Fei Heng
  • Peter B. Gilbert

Abstract

Deployment of the recently licensed tetravalent dengue vaccine based on a chimeric yellow fever virus, CYD‐TDV, requires understanding of how the risk of dengue disease in vaccine recipients depends jointly on a host biomarker measured after vaccination (neutralization titre—neutralizing antibodies) and on a ‘mark’ feature of the dengue disease failure event (the amino acid sequence distance of the dengue virus to the dengue sequence represented in the vaccine). The CYD14 phase 3 trial of CYD‐TDV measured neutralizing antibodies via case–cohort sampling and the mark in dengue disease failure events, with about a third missing marks. We addressed the question of interest by developing inferential procedures for the stratified mark‐specific proportional hazards model with missing covariates and missing marks. Two hybrid approaches are investigated that leverage both augmented inverse probability weighting and nearest neighbourhood hot deck multiple imputation. The two approaches differ in how the imputed marks are pooled in estimation. Our investigation shows that nearest neighbourhood hot deck imputation can lead to biased estimation without properly selected neighbourhoods. Simulations show that the hybrid methods developed perform well with unbiased nearest neighbourhood hot deck imputations from proper neighbourhood selection. The new methods applied to CYD14 show that neutralizing antibody level is strongly inversely associated with the risk of dengue disease in vaccine recipients, more strongly against dengue viruses with shorter distances.

Suggested Citation

  • Yanqing Sun & Li Qi & Fei Heng & Peter B. Gilbert, 2020. "A hybrid approach for the stratified mark‐specific proportional hazards model with missing covariates and missing marks, with application to vaccine efficacy trials," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 791-814, August.
    • Handle: RePEc:bla:jorssc:v:69:y:2020:i:4:p:791-814
    DOI: 10.1111/rssc.12417
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    References listed on IDEAS

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    1. Yanqing Sun & Peter B. Gilbert, 2012. "Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 34-52, March.
    2. Michal Kulich & D.Y. Lin, 2004. "Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 832-844, January.
    3. Guangren Yang & Yanqing Sun & Li Qi & Peter B. Gilbert, 2017. "Estimation of Stratified Mark-Specific Proportional Hazards Models Under Two-Phase Sampling with Application to HIV Vaccine Efficacy Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 259-283, June.
    4. Little, Roderick J A, 1988. "Missing-Data Adjustments in Large Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 287-296, July.
    5. Peter Gilbert & Ian McKeague & Yanqing Sun, 2004. "Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions," UW Biostatistics Working Paper Series 1032, Berkeley Electronic Press.
    6. Guozhi Gao & Anastasios A. Tsiatis, 2005. "Semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure," Biometrika, Biometrika Trust, vol. 92(4), pages 875-891, December.
    7. Michal Juraska & Peter B. Gilbert, 2016. "Mark-specific hazard ratio model with missing multivariate marks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 606-625, October.
    8. Sun, Yanqing & Li, Mei & Gilbert, Peter B., 2016. "Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 348-358.
    9. Little, Roderick J A, 1988. "Missing-Data Adjustments in Large Surveys: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 300-301, July.
    10. M. Juraska & P. B. Gilbert, 2013. "Mark-Specific Hazard Ratio Model with Multivariate Continuous Marks: An Application to Vaccine Efficacy," Biometrics, The International Biometric Society, vol. 69(2), pages 328-337, June.
    11. Peter B. Gilbert & Yanqing Sun, 2015. "Inferences on relative failure rates in stratified mark-specific proportional hazards models with missing marks, with application to human immunodeficiency virus vaccine efficacy trials," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(1), pages 49-73, January.
    12. Rebecca R. Andridge & Roderick J. A. Little, 2010. "A Review of Hot Deck Imputation for Survey Non‐response," International Statistical Review, International Statistical Institute, vol. 78(1), pages 40-64, April.
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