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Application of a Frailty Modeling Approach to Correlated Breastfeeding Duration Data

Zhao, Jian; Zhao, Yun; Khanal, Vishnu; Lee, Andy H.; Binns, Colin W.

doi: 10.1097/NNR.0000000000000311

Background Correlated breastfeeding duration data are very common in infant feeding research using cohort designs. Intracluster correlation within the same clustering group is expected and needs to be taken into account in statistical analysis; otherwise, the corresponding statistical inferences may be subject to an increased Type I error.

Objectives The aims of this study were to illustrate the necessity of adjusting for the intracluster correlation in correlated breastfeeding duration data analysis and to demonstrate different frailty modeling approaches.

Methods An introduction to shared frailty models was presented under the assumption of proportional hazards (PH). Then, two different approaches—the Cox frailty model (semiparametric approach) and the parametric frailty model (parametric approach)—were used to fit the data from a maternal cohort in Nepal as an illustrative example.

Results For the semiparametric approach, random effects denoting the variations in the hazard of breastfeeding cessation shared by mothers living in the 27 distinct communities were estimated and graphically presented. Compared with the conventional Cox model, Cox frailty model reduced the chance of Type I error occurring, providing a better model fit in the presence of correlated survival data. Among candidate parametric approaches, a Weibull PH model with a gamma frailty term was selected as an appropriate model fitting the breastfeeding data.

Discussion Shared frailty models can be used in other research areas in the presence of correlated time-to-event data. Model selection depends on the assumption of PH, the specification of the baseline hazard function, and also the study purpose.

Jian Zhao, MMed, is PhD candidate, and Yun Zhao, PhD, is Senior Lecturer, School of Public Health, Curtin University, Perth, Western Australia, Australia.

Vishnu Khanal, PhD, Nepal Development Society, Chitwan, Nepal.

Andy H. Lee, PhD, is Professor, School of Public Health, Curtin University, Perth, Western Australia, Australia.

Colin W. Binns, PhD, is John Curtin Distinguished Emeritus Professor, School of Public Health, Curtin University, Perth, Western Australia, Australia.

Accepted for publication May 16, 2018.

This study was partially funded by the China Scholarship Council (Grant 201406240008).

The original study was approved by the Human Research Ethics Committee of Curtin University, Australia (HR 184/2013), and the Nepal Health Research Council, Nepal (773/2014). This study utilized only deidentified data of the original study.

The authors have no conflicts of interest to report.

Corresponding author: Yun Zhao, PhD, School of Public Health, Curtin University, GPO Box U 1987, Perth, WA 6845, Australia (e-mail:

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