On a Shape-Invariant Hazard Regression Model with application to an HIV Prevention Study of Mother-to-Child Transmission
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On a Shape-Invariant Hazard Regression Model with application to an HIV Prevention Study of Mother-to-Child Transmission Cheng Zheng1
· Ying Qing Chen2
Received: 16 October 2018 / Revised: 28 July 2019 / Accepted: 9 October 2019 © International Chinese Statistical Association 2019
Abstract In survival analysis, Cox model is widely used for most clinical trial data. Alternatives include the additive hazard model, the accelerated failure time (AFT) model and a more general transformation model. All these models assume that the effects for all covariates are on the same scale. However, it is possible that for different covariates, the effects are on different scales. In this paper, we propose a shape-invariant hazard regression model that allows us to estimate the multiplicative treatment effect with adjustment of covariates that have non-multiplicative effects. We propose momentbased inference procedures for the regression parameters. We also discuss the risk prediction and the goodness of fit test for our proposed model. Numerical studies show good finite sample performance of our proposed estimator. We applied our method to the HIVNET 012 study, a milestone trial of single-dose nevirapine in prevention of mother-to-child transmission of HIV. From the HIVNET 012 data analysis, singledose nevirapine treatment is shown to improve 18-month infant survival significantly with appropriate adjustment of the maternal CD4 counts and the virus load. Keywords Censoring · Counting processes · Semiparametric methods · Time-to-event analysis Mathematics Subject Classification 62N01 · 62N02 · 62P10
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s12561019-09260-4) contains supplementary material, which is available to authorized users.
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Cheng Zheng [email protected]
1
Zilber School of Public Health, University of Wisconsin-Milwaukee, 1240 N. 10th St, Room 378, Milwaukee, USA
2
Program in Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N. Arnorld Building M2-C200, Seattle, USA
123
Statistics in Biosciences
1 Introduction An important HIV/AIDS randomized prevention trial was conducted between November 1997 and January 2001 ([7]). This trial was named as HIVNET 012, and the goal was to evaluate the efficacy and the safety of a short-course nevirapine (NVP) treatment compared to a short-course zidovudine (AZT) treatment for pregnant mothers during labor and delivery. The primary clinical endpoint is the mother-to-child transmission (MTCT) of human immunodeficiency virus type-1 (HIV-1), and the secondary endpoint is the 18 months’ infant survival. In [4], the NVP is shown to improve the infant survival over time when looking at the Kaplan–Meier curve. Cox regression analysis also suggests that the NVP would reduce hazard by 26.0%, but this improvement is not statistically significant ( p > 0.20). It is natural to ask whether there are alternative models to detect the treatment effect. For these data, we consider two important covariate
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