Fitting The First Birth Interval in Indonesia Using Weibull Proportional Hazards Model

Alfensi Faruk, Endro Setyo Cahyono, Ning Eliyati


The first birth interval is one of the indicators of women’s fertility rate. Because in most cases the first birth interval contains censored observations, the only appropriate statistical method to handle such data is survival analysis. The main objective of this study is to analyze several socioeconomic and demographic factors that affect the first birth interval in Indonesia using the univariate and multivariate survival analysis, that is Kaplan-Meier method and Cox regression model, respectively. The sample is obtained from 2012 Indonesian Demographic and Health Survey (IDHS) and consists of 28242 ever married women aged 15-49 at the time of interview. The results show that age at the first birth, women's educational level, husband’s educational level, contraceptive knowledge, wealth index, and employment status are the significant factors affecting the first birth interval in Indonesia.


first birth interval; fertility rate; survival analysis; Cox regression model

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Statistics Indonesia, Statistik Indonesia 2016 statistical yearbook of Indonesia 2016, Jakarta: Statistics Indonesia, 2016.

M. D. Islam, "Differential determinants of birth spacing since marriage to first live birth in rural Bangladesh," Pertanika Journal of Social Science & Humanities, vol. 17, no. 1, pp. 1-6, 2009.

R. Hidayat, H. Sumarno and E. H. Nugrahani, "Survival analysis in modeling the birth interval of the first child in Indonesia," Open Journal of Statistics, vol. 4, pp. 198-206, 2014.

E. Hailu, "Survival analysis of time to first birth after marriage," Department of Statistics, School of Graduate Studies, Addis Ababa University, Addis Ababa, 2015.

A. Gebeyehu, "Survival analysis of time-to-first birth after marriage among women in Ethiopia: application of parametric shared frailty model," Department of Statistics, College of Natural Sciences, Jimma University, Jimma, 2015.

I. Gijbels, "Censored data," WIREs Computational Statistics, vol. 2, p. 178–188, 2010 .

E. T. Lee and W. J. Wang, Statistical methods for survival data analysis, 3rd ed., Hoboken: John Wiley & Sons, Inc., 2003.

E. L. Kaplan and P. Meier, "Nonparametric estimation from incomplete observations," Journal of the American Statistical Association, vol. 53, no. 282, pp. 457-481, 1958.

A. Faruk, A. Amran and N. Nasir, "Aplikasi model proportional hazard Cox pada waktu tunggu kerja lulusan jurusan matematika fakultas MIPA Universitas Sriwijaya," Jurnal Penelitian Sains, vol. 17, no. 1, pp. 5-8, 2014.

A. Amran and A. Faruk, "Model survival nonparametrik pada data rawat inap pasien diare di puskesmas Indralaya," Jurnal Matematika, vol. 5, no. 2, pp. 105-116, 2015.

D. R. Cox, "Regression models and life-tables," Journal of the Royal Statistical Society. Series B (Methodological), vol. 34, no. 2, pp. 187-220, 1972.

A. Faruk, "Estimasi parameter data tersensor tipe I berdistribusi loglogistik menggunakan maximum likelihood estimate dan iterasi Newton-Rhapson," in Seminar Nasional MIPA, Palembang, 2014.

R. Peto and J. Peto, "Asymptotically efficient rank invariant test procedures," Journal of the Royal Statistical Society. Series A (General), vol. 135, no. 2, pp. 185-207, 1972.

D. G. Kleinbaum and M. Klein, Survival analysis a self-learning text, 3rd ed., New York: Springer, 2012.

A. Kamal and M. K. Pervaiz, "Determinants of marriage to first birth interval in Pakistan," Journal of Statistics, vol. 20, pp. 44-68, 2013.



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