Beyond the Cox Model: A Comparative Parametric Survival Modelling of Time to First Birth Among Married Women
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.023 | 0.058 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".