Maternal education and lifetime fertility in Bangladesh: a mean-parameterized Conway-Maxwell-Poisson regression approach

Children ever born (CEB) is the standard cumulative measure of realised fertility and the quantity on which Bangladesh’s long-standing small-family policy target is defined. CEB in contemporary Bangladeshi survey data is markedly underdispersed, a feature that conventional count regression models cannot represent. We analysed 3,839 ever-married women aged 15–49 years who reported a live birth in the three years preceding the 2022 Bangladesh Demographic and Health Survey (BDHS). A mean-parameterized Conway-Maxwell-Poisson (COM-Poisson) regression model incorporating sampling weights and a cluster-level random intercept was fitted using a pre-specified three-stage sequential strategy: maternal education alone (Model I), plus reproductive timing and sociodemographic and economic covariates (Model II), and plus information-related covariates (Model III). Underdispersion was evaluated using the estimated dispersion parameter, a likelihood ratio test against the Poisson model, the model-implied variance-to-mean ratio, comparison of observed with model-predicted count distributions, and simulation-based residual diagnostics. Poisson and generalized Poisson specifications were fitted for comparison. CEB was strongly underdispersed (mean 1.993; variance 1.078; variance-to-mean ratio 0.541). The COM-Poisson dispersion parameter was 0.231 (95% CI 0.220 to 0.242) and the likelihood ratio test against the Poisson model gave a test statistic of 2135.21 on 1 degree of freedom ( p < 0.001). The COM-Poisson model achieved the lowest AIC (8748.45), the lowest BIC (8867.26) and the highest log-likelihood (-4355.23) and was the only specification whose simulated residuals were consistent with uniformity (Kolmogorov-Smirnov p = 0.185). Maternal education showed a graded inverse association with CEB in the fully adjusted model: relative to women with no formal education, the adjusted incidence rate ratio (IRR) was 0.937 (95% CI 0.891 to 0.985) for primary, 0.828 (95% CI 0.787 to 0.871) for secondary and 0.640 (95% CI 0.601 to 0.683) for higher education. Later age at last birth (IRR 1.937 and 2.964 for ages 20–35 and above 35 years relative to below 20 years), current employment (IRR 1.088) and rural residence were associated with higher CEB, whereas husband’s education and knowledge of family planning were associated with lower CEB. Household wealth was not significantly associated with CEB when the poor group was used as the reference. Between-cluster variation was modest (intraclass correlation 2.31%; median rate ratio 1.077; design effect 1.11). Maternal education is the strongest modifiable correlate of cumulative fertility in this nationally representative sample, and the association is robust to adjustment for household and information-related characteristics. Explicit modelling of underdispersion materially changes the estimated education-fertility gradient relative to equidispersed and overdispersion-oriented alternatives, which supports the use of the COM-Poisson framework for this outcome. Because the design is cross-sectional, all associations should be interpreted as associational rather than causal.