Beyond the Cox Model: A Comparative Parametric Survival Modelling of Time to First Birth Among Married Women
DOI:
https://doi.org/10.6000/1929-6029.2025.14.72Keywords:
Marriage-to-first birth, First birth interval, Survival analysis, Cox model, Parametric model, BangladeshAbstract
Background: Data on time-to-first birth typically involves censoring, as not all individuals in the survey experience their first birth by the survey date. Traditional analyses often rely on the semi-parametric Cox proportional hazards model; however, violations of the proportional hazards (PH) assumption necessitate more flexible modelling approaches.
Objectives: This study aimed to compare the performance of multiple parametric survival models against the Cox model in estimating time-to-first birth among currently married women in Bangladesh and to identify key predictors of time-to-first birth.
Methods: Data were drawn from the 2022 Bangladesh Demographic and Health Survey (BDHS), encompassing 17,146 currently married women aged 15–49 years. Survival analyses were conducted using the Kaplan–Meier estimator, log-rank tests, Cox regression, and five parametric models: Exponential, Weibull, Log-normal, Gompertz, and Generalised Gamma. Model fit was assessed using AIC and BIC, and log-likelihood statistics.
Results: The mean time-to-first birth after marriage was 40.12 ± 0.50 months, with a median of 26 months, indicating a right-skewed distribution caused by some women experiencing notably delayed first births. The Cox model failed PH assumption tests, highlighting its inadequacy. Among parametric models, the Generalized Gamma model provided the best fit, effectively capturing complex hazard structures. Key predictors of the time-to-first birth included age at first marriage, women's and husbands' education, contraceptive use, administrative division, living arrangement with spouse, and media exposure.
Conclusion: This study underscores the importance of using flexible parametric models—such as the Generalised Gamma model—when dealing with time-to-event data where the proportional hazards assumption is violated. This approach provides more reliable effect estimates and improves the interpretability of covariate influences on fertility timing. Findings underscore the importance of the identified predictors in designing reproductive health policies and interventions aimed at delaying early childbearing.
References
Goldstein JR. How late can first births be postponed? Some illustrative population-level calculations. Vienna Yearbook of Population Research 2006; 153-165. DOI: https://doi.org/10.1553/populationyearbook2006s153
Fagbamigbe AF, Idemudia ES. Survival analysis and prognostic factors of timing of first childbirth among women in Nigeria. BMC Pregnancy and Childbirth 2016; 16(1): 102. DOI: https://doi.org/10.1186/s12884-016-0895-y
Safdari-Dehcheshmeh F, Noroozi M, Taleghani F, Memar S. Factors influencing the delay in childbearing: A narrative review. Iranian Journal of Nursing and Midwifery Research 2023; 28(1): 10-19. DOI: https://doi.org/10.4103/ijnmr.ijnmr_65_22
Nagdeve DA, Pradhan MR. Determinants of the First Birth Interval Among Women in India. Journal of Family Reproductive Health 2023; 17(4): 229-39. DOI: https://doi.org/10.18502/jfrh.v17i4.14595
Candia D, Musoke E, Namugenyi C. Female’s preferred birth interval in Uganda: What are the associated factors? Al-Sihah: The Public Health Science Journal 2023; 15(1): 1-11. DOI: https://doi.org/10.24252/al-sihah.v15i1.37913
Alam MM. Marriage to first birth interval and its associated factors in Bangladesh. Asian Journal of Social Sciences & Humanities 2015; 4(4): 36-47.
TurksonAJ, Ayiah-Mensah F, Nimoh V. Handling Censoring and Censored Data in Survival Analysis: A Standalone Systematic Literature Review. International Journal of Mathematics and Mathematical Sciences 2021; 2021: 1-16 DOI: https://doi.org/10.1155/2021/9307475
Cox DR. Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 1972; 34(2): 187-220. DOI: https://doi.org/10.1111/j.2517-6161.1972.tb00899.x
Lee ET, Wang JW. Statistical methods for survival data analysis (3rd ed.). John Wiley and Sons, Hoboken, New Jersey. Wiley 2003. DOI: https://doi.org/10.1002/0471458546
Shayan Z, Ayatollahi SM, Zare N, Moradi F. Prognostic factors of first birth interval using the parametric survival models. Iranian Journal of Reproductive Medicine 2014; 12(2): 125-130.
Moala FA, Dey S. Objective and subjective prior distributions for the Gompertz distribution. Anais Da Academia Brasileira de Ciências 2017; 90(3): 2643-2661. DOI: https://doi.org/10.1590/0001-3765201820171040
Therneau TM, Grambsch PM. Modelling survival data: Extending the Cox model. New York: Springer 2000. DOI: https://doi.org/10.1007/978-1-4757-3294-8
Hiller L, Marshall A, Dunn J. Assessing violations of the proportional hazards assumption in Cox regression: does the chosen method matter? Trials 2015; 16(Suppl 2): p. 134. DOI: https://doi.org/10.1186/1745-6215-16-S2-P134
De Pascoa MAR, Ortega EMM, Cordeiro GM. The Kumaraswamy generalized gamma distribution with application in survival analysis. Statistical Methodology 2011; 8(5): 411-433. DOI: https://doi.org/10.1016/j.stamet.2011.04.001
National Institute of Population Research and Training (NIPORT), ICF. Bangladesh Demographic and Health Survey 2022. Dhaka, Bangladesh, and Rockville (MD): NIPORT and ICF 2024.
Pascual ZN, Langaker MD. Physiology, Pregnancy. In StatPearls. StatPearls Publishing,Treasure Island (FL) 2023. http://www.ncbi.nlm.nih.gov/books/NBK559304/
Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 1958; 53(282): 457-481. DOI: https://doi.org/10.1080/01621459.1958.10501452
Collett D. Modelling survival data in medical research (3rd ed.). Chapman and Hall/CRC, Taylor and Francis Group, Boca Raton 2014.
Liu X. Survival analysis: Models and applications. John Wiley & Sons and Higher Education Press, Hoboken, New Jersey.
Stacy EW. A Generalization of the Gamma Distribution. The Annals of Mathematical Statistics 1962; 33(3): 1187-1192. DOI: https://doi.org/10.1214/aoms/1177704481
Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life 89 contingencies. in a letter to francis baily, esq. frs &c. Philosophical Transactions of the Royal Society of London 1829; (115): 513583.
Setu SP, Kabir R, Islam MA, Alauddin S, Nahar MT. Factors associated with time to first birth interval among ever married Bangladeshi women: A comparative analysis on Cox-PH model and parametric models. PLOS Global Public Health 2024; 4(12): e0004062. DOI: https://doi.org/10.1371/journal.pgph.0004062
Ahammed B, Kabir MR, Abedin MM, Ali M, Islam MA. Determinants of different birth intervals of ever married women: Evidence from Bangladesh. Clinical Epidemiology and Global Health 2019; 7: 450-456. DOI: https://doi.org/10.1016/j.cegh.2019.01.011
Logubayom IA, Luguterah A. Survival analysis of time to first birth after marriage. Research on Humanities and Social Sciences 2013; 3(12): 117-126.
Chernet AG, Shebeshi DS, Banbeta A. Determinant of time-to-first birth interval after marriage among Ethiopian women. BMC Women’s Health 2019; 19: 157. DOI: https://doi.org/10.1186/s12905-019-0858-3
Obite CP, Bartholomew DC, Nwosu UI, Anyiam KE, Aminu SA. Marriage to first birth interval in Nigeria: Analysis of the roles of social-demographic and cultural factors. SN Social Sciences 2021; 1: 120. DOI: https://doi.org/10.1007/s43545-021-00112-x
Fentaw KD, Fenta SM, Biresaw HB, Agegn SB, Muluneh MW. Bayesian shared frailty models for time to first birth of married women in Ethiopia: Using EDHS 2016. Computational and Mathematical Methods in Medicine 2022; 5760662. DOI: https://doi.org/10.1155/2022/5760662
Alazbih NM, Kaya AH, Mengistu MY, Gelaye KA. Determinants of time to first marriage and birth intervals among women of childbearing age in Dabat Health and Demographic Surveillance System site, Northwest Ethiopia. PLoS One 2023; 18(2): e0281997. DOI: https://doi.org/10.1371/journal.pone.0281997
Bongaarts J, Potter RG. Fertility, biology, and behaviour: An analysis of the proximate determinants. Academic Press 1983, New York, USA. DOI: https://doi.org/10.2307/1973328
Marphatia AA, Ambale GS, Reid AM. Women’s marriage age matters for public health: A review of the broader health and social implications in South Asia. Frontiers in Public Health 2017; 5: 269. DOI: https://doi.org/10.3389/fpubh.2017.00269
Sarkar P. Determinants of age at first birth in Bangladesh. Journal of Modern Mathematics and Statistics 2010; 4: 1-6. DOI: https://doi.org/10.3923/jmmstat.2010.1.6
Al-Shanfari NSS, Islam MM. Survival analysis and predictors of time to first birth after marriage in Jordan. International Journal of Statistics and Applications 2021; 11(3): 51-60.
Haque MA, Sayem AM. Socioeconomic Determinants of Age at First Birth in Rural Areas of Bangladesh. Asia Pacific Journal of Public Health 2009; 21(1): 104-111. DOI: https://doi.org/10.1177/1010539508329207
Chowdhury AH, Karim A. Patterns and differentials of birth intervals in Bangladesh. Global Journal of Science Frontier Research: Interdisciplinary 2013; 13(2): 11-24.
Islam MM, Rob U, Chakroborty N. Regional variations in fertility in Bangladesh. Genus 2003; 59(3/4): 103-145
Nie W. The effect of spousal separation and reunification on fertility: Chinese internal and international migration. Demographic Research 2020; 43: 851-888. https://creativecommons.org/licenses/by/3.0/de/legalcode DOI: https://doi.org/10.4054/DemRes.2020.43.29
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