Study setting, study population, and data source

The study was conducted in East African nations and employed a community-based cross-sectional survey design. The study incorporates DHS data from 2012–2022 from 12 countries. The specific East African countries included in this study were Burundi, Ethiopia, Kenya, Comoros, Madagascar, Malawi, Mozambique, Rwanda, Tanzania, Uganda, Zambia, and Zimbabwe. The most recent standard DHS reports available for these countries were obtained and used as the primary data source for the study. All reproductive-aged women (15–49 years) in these countries were the source populations, whereas all reproductive-aged women (15–49 years) in the selected enumeration area (EAs) were the study population.

The DHS program was collaborated with various national institutions to ensure that all surveys adhere to the ethical standards and guidelines set by the country’s legislation. Stringent protocols were followed in DHS to protect the rights and privacy of participants. These protocols were included obtaining informed consent, maintaining confidentiality, and ensuring the anonymity of collected data. The surveys were designed to uphold high ethical standards and prioritize the well-being and safety of participants. The DHS program is expected to gain wide recognition and endorsement from international organizations, including the United Nations and the World Health Organization, as a valuable source of data for evidence-based policies and programs. No additional microdata beyond those utilized in this study was manipulated or applied. There was no involvement of patients or the general public in the study.

Inclusion and exclusion criteria

The study targeted all pregnant women aged 15–49 years, including those with recorded gestational age, either at their initial ANC visit or for those who did not attend ANC at the time of delivery or pregnancy termination. This inclusion ensured the comprehensive coverage of women with known gestational ages, regardless of ANC attendance. However, women whose gestational age was unrecorded or undetermined at their initial ANC visit were excluded to maintain data accuracy and reliability.

Data extraction, quality control and Sampling methods

Following an online request explaining the study’s purpose and obtaining authorization, data for the specified countries was extracted using STATA (version 17) from the official DHS program database (https://dhsprogram.com). The analysis focused on the individual’s record (IR file) dataset, extracting dependent and independent variables. This program has been a crucial source of data on reproductive health issues in low and middle-income countries, providing information on topics such as marriage, fertility, fertility preferences, and contraception [36].

The DHS dataset was collected using structured and pre-tested comprehensive standard questionnaires. Data quality was ensured through the implementation of training for data collectors, supervisors, and field editors; conducting ongoing supervision; employing standardized and translated questionnaires in international, national, and country-specific local languages; and engaging data processing specialists for data entry and management. Throughout the process, measures were taken to address systematic bias. More detailed guidance on the data collection process can be found in DHS documentation [37].

The DHS program employed two-stage stratified sampling techniques to select households for the survey. EAs were randomly selected in the first stage, while households were randomly selected in the second stage. All women between the ages of 15 and 49, who were either permanent residents or overnight visitors in the selected households, were eligible to participate in the study. A total of 243,157 women aged 15–49 years were interviewed for the survey with a response rate of 95%. A total of 93,213 weighted reproductive-age women (15–49 years) from 12 East African countries were included in this study (Fig 1).

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Fig 1. Illustration of sampling procedure from 12 East African Countries using their recent DHS.

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Study variables

In this study, the time of the initial ANC contact, measured in months, was the dependent variable. The aim was to investigate the factors that influence the time of initiation of ANC contact. Several factors were considered in the analysis to identify determinants of time to ANC contact. Clusters, Enumeration areas, or clusters were used as clustering variables in all frailty models. This approach accounts for the potential correlation or similarities within communities.

The independent factors included in the analysis are residence, maternal age, marital status, maternal and husband education level, parity (number of previous pregnancies), wealth index, sex of the household head, health insurance coverage, media exposure (specifically, listening to radio, watching television, and reading magazines or newspapers), distance to the health facility, husband’s education level, work status, pregnancy intention, and the number of children.

Definitions for some operational terms

In the context of this study, the following definitions and statistical models were utilized

Ethical consideration

This study used a publicly available secondary survey dataset from the Measure DHS Program. Therefore, ethical approval and participant consent were not required. Written permission letters were secured from the DHS program data archivists to download and use data for this study. The DHS data were kept confidential, and any identifying information was removed. The data were only used for this authorized research project and would not be shared with researchers.

Data management and analysis

Before conducting any statistical analysis, appropriate data management procedures, including missing data management, data weighting, and recoding, were implemented using R software. Missing data were initially examined utilizing graphical methods or visual plots to identify patterns. For missing patterns value <5%, Little’s MCAR test was employed to assess whether the data were missing completely at random, which indicated that they were missing at random (MAR) (p < 0.05). Consequently, Multivariate Imputation by Chained Equations (MICE) with logistic regression was utilized to generate 10 imputed datasets using R software. To ensure the robustness of the findings, a sensitivity analysis was conducted to compare results from the imputed datasets with those from a complete case analysis. The data were weighted using sampling weights to ensure representativeness and obtain reliable estimates before conducting any statistical analysis. The weighted results of the analysis were reported in this study.

Statistical analysis was then conducted using R statistical software version 4.4.2 for the imputed dataset. Descriptive metrics such as percentages, graphs, and frequency tables were used to summarize the data and characterize the study population. To estimate the time to the first ANC contact, the nonparametric Kaplan-Meier (K-M) test was utilized. This non-parametric method allows for the estimation of survival probabilities over time. The log-rank test was applied to assess differences in survival times across categorical variables and the desired outcome. For fitting survival data and incorporating factors, both the Cox Proportional Hazard Model and the Accelerated Failure Time (AFT) model were considered. Additionally, shared frailty models, which account for unobserved random effects affecting the survival function, were employed. In the analysis, variables found to be significant (with a p-value of less than 0.25) in the uni-variable analysis were included in the multivariable analysis. The selection of the optimal model was based on criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and log-likelihood.

The Cox proportional hazard model

Cox regression model or the Cox proportional hazards model is a semi-parametric mode1, in which no assumptions are made about the actual form of the baseline hazard function , introduced by Cox in 1972 [38].

The general proportional hazards model is given by:

, or in matrix form, it can be written as:

, where is the vector of coefficients of the explanatory variables in the model, the vector of values of the explanatory variables for the individual, whose components are , ,..., , and =baseline hazard function.

When the Cox regression model is used in the analysis of survival data, there is no need to assume a particular form of probability distribution for the survival times. As a result, the hazard function is not restricted to a specific functional form, and the model has flexibility and widespread applicability [39,40].

The general accelerated failure time model

When the proportional hazards assumption doesn’t hold, the accelerated failure time model becomes a valuable alternative for studying time-to-event data. This model assumes that individual characteristics affect the time scale multiplicatively, influencing how quickly someone moves along the time axis. Essentially, it allows one to interpret the model in terms of disease progression speed, providing an intuitively appealing way to understand how different factors impact the rate at which an individual experiences events related to the condition [39,41].

As in the proportional hazards model, the baseline hazard function, , is the hazard of the outcome of interest at the time for an individual for whom the values of the explanatory variables are all equal to zero. According to the general accelerated failure time model, the hazard function of the individual at time, is then such that:

Where, is the linear component of the model, in which is the value of the explanatory variable, , for the individual,

The acceleration factor (ϕ) and the corresponding survivor function for the individual is given by the following equations [39], respectively.

, where, is the baseline survivor function

Multivariable Shared frailty models

Frailty models are the survival data analog to regression models, which account for heterogeneity and random effects. A frailty is a latent multiplicative effect on the hazard function and is assumed to have unit mean and variance θ, which is estimated along with the other model parameters [42]. A frailty model is a heterogeneity model where the frailties are assumed to be individual or cluster-specific. In general, it is a random effects model where the frailties are common (or shared) among groups of individuals or spells and are randomly distributed across groups [43–45].

Frailty serves as a useful tool to incorporate random effects within a model, enabling the consideration of associations and unobserved differences among individuals or groups. At its core, frailty represents an unseen or unmeasured random element that alters the hazard function of either an individual or a cluster of individuals in a way that multiplies or modifies it. This latent factor essentially accounts for variations among individuals or groups that might affect how likely they are to experience an event of interest, such as survival or failure, even when these differences aren’t directly measured or observed in the data [46].

To formulate a shared frailty model for survival data, suppose that there are g groups of individuals with individuals in the group. For the proportional hazards model, the hazard of death at time t for the individual, , in the group is then given by:

where s a vector of values of p explanatory variables for the individual in the group; β is the vector of their coefficients; is the baseline hazard function; and the are frailty effects or random effects that are common for all individuals within the group [39].

The hazard function in the Equation can also be written in the form:

Where,

, and are assumed to be realizations of g random variables , …, . The distribution assumed for is taken to have zero mean, and the normal distribution is a common choice.

When the frailty or random effect (Z) is greater than one (Z > 1), it indicates an increased risk and when frailty is below one ((Z < 1) it shows a decreased risk of hazard for the cluster. But, if the proportional hazards assumption is not satisfied, the accelerated failure time frailty model can be used [43].

Accelerated failure time frailty model

The concept of “accelerated failure time-shared frailty models” refers to a statistical methodology used in survival analysis to model the time until an event occurs while considering unobserved heterogeneity among individuals. These models combine the principles of AFT models and shared frailty models. The model that incorporates this unobserved heterogeneity takes the form of an AFT model with shared frailty is given by [43,47]:

With the event time for the subject from cluster, the intercept, the vector of covariates for the subject from cluster, the vector containing the covariate effects, the scale parameter, the random error term for the subject from cluster, and finally the’s are the cluster-specific random effects that are assumed to be identically and independently distributed random variables with density function. The random error term is assumed to have a fully specified distribution. Different assumptions have been proposed leading to event time distributions other than the Weibull (e.g., gamma, inverse Gaussian, lognormal, and log-logistic) [47].

In frailty models for survival analysis, three fundamental assumptions govern the behavior of the frailty term. First, frailty independence posits that the frailty term () is independent of the covariates () and follows a cumulative distribution function , characterized by an unknown parameter () [48]. Second, to ensure identifiability, the frailty distribution () is selected such that the model remains identifiable, typically by employing a distribution with a fixed expectation (mean), often set to . This ensures that the effects of frailty can be distinguished from other model components. Third, the assumption of noninformative censoring stipulates that, given the covariates () and frailty (), censoring is independent and noninformative with respect to the frailty, regression parameters (), and baseline hazard () [49].

In addition to the widely used Cox proportional hazards model [38], AFT models offer two main advantages. First, AFT models provide a simple interpretation of regression parameters, as the log-linear formulation allows the regression coefficients to represent the rate at which failure times are “accelerated” or “decelerated” by covariates, making the relationship between covariates and time-to-event outcomes easier to understand [50]. Second, AFT models are robust to omitted covariates. When relevant covariates are missing, the estimates of regression parameters for the AFT model are less biased compared to the Cox model, which is more sensitive to omitted variables [51].

For this study, the frailty parameter in a shared frailty model represents unobserved heterogeneity at the country level, accounting for the correlation between individuals within the same country who may share common, unmeasured risk factors that influence the time to ANC initiation. It introduces a random effect that captures country-specific variability, addressing the dependency structure among individuals within each country. By modeling this shared risk, the frailty parameter ensures that the analysis reflects both individual- and country-level influences on the time to ANC initiation [52].

In empirical applications, the frailty parameter adjusts for clustering effects, ensuring that the estimates of individual-level covariate effects on the time to ANC initiation are not biased by the unmeasured characteristics of countries. It facilitates more precise estimation by isolating the influence of country-specific factors, such as healthcare access, cultural practices, and policy differences, which could affect the time to ANC initiation but are not directly measured [53].

Socio-demographic, economic, and obstetrical characteristics of respondents

The distribution of pregnant women in this study showed variation across East African countries. Most participants, 13,448 (14.50%), were from Malawi. Conversely, Comoros had the lowest number of participants, 2,016 (2.21%). Tanzania and Rwanda followed with 5,837 (6.26%) women and 6,302 (6.76%) women, respectively (Table 1).

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Table 1. Description of surveys and sample size characteristics of East African Countries.

https://doi.org/10.1371/journal.pone.0325002.t001

A total of 93,213 women who became pregnant in East African countries during the five-year survey period were included. Among them, 86,736 (93.05%) received their first ANC visit, representing the events in the study, whereas 6,477 (6.95%) did not receive their first ANC visit and were considered right-censored. A significant proportion of 20,657 (22.16%) included in the study had no formal education. Among these women, 17,058 (18.30%) initiated ANC contact (events) during their pregnancies. Regarding the educational status of the husbands, 19,107 (20.50%) had no formal education. A large proportion, 52,809 (44.44%), had attended primary education (Table 2).

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Table 2. Socio-demographic and obstetric characteristics of pregnant women in East African Countries, from their recent DHS (n = 93,213 (weighted).

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Among those who had problems with media access, 4,098 (4.40%) did not have ANC visits and were right-censored. Similarly, among those who reported that media exposure was not a problem, 2,378 (2.55%) individuals did not have ANC visits and were also right-censored. Regarding the wealth index of pregnant women, the largest proportion, comprising 39,842 (42.74%) individuals, fell into the poor category. Additionally, approximately 35,373 (37.95%) women were classified as rich. Within the poor category, 3,916 (4.20%) individuals did not have ANC visits and were considered right-censored. Similarly, among the rich category, 1,339 (1.44%) individuals did not have ANC visits and were right-censored (Table 2).

The pooled prevalence of ANC utilization in pregnant women was estimated based on women’s adherence to the World Health Organization’s recommendation of attending a minimum of four ANC contacts during pregnancy. Among 93,213 women included in the study, approximately 52,444 met or exceeded this crucial threshold. The pooled prevalence of women with a minimum of 4 ANC contacts in East African countries was 57.7% (95% CI: (49.9–65.1%). The variability in ANC utilization across countries is estimated at 0.2032 (95% CI: 0.1111–0.6611). Furthermore, the results indicated high inter-country variability, as reflected by the inconsistency index () of 99.7% (p < 0.01). This substantial heterogeneity suggests that nearly all observed differences in ANC utilization are due to true variability between countries rather than random chance. Zimbabwe recorded the highest ANC utilization at 76%, followed by Kenya at 67.4%. Ethiopia reported the lowest ANC utilization, (32%) (Fig 2).

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Fig 2. Pooled prevalence of ANC contact in East Africa using the recent DHS 2012 to 2022.

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Time to first antenatal care booking among pregnant women in East Africa

The Kaplan-Meier estimate, a non-parametric survival analysis technique, examined the time-to-first ANC contact among pregnant women in East African countries, considering various factors. The probability of starting ANC visits was delayed during the early gestational age. However, as gestational age increases, the probability sharply increases and then gradually declines later. This indicates that pregnant women in East Africa are more likely to initiate ANC contact at the delayed stages of pregnancy. Additionally, the overall median time to the first antenatal care contact was 4 months. This means that, on average, half of the pregnant women in the study population initiated their ANC contacts by the fourth month (Fig 3).

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Fig 3. The K-M plots of Survival functions of time to the first ANC contact among pregnant women in East Africa.

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Comparisons of the different factors in terms of survival time to the first ANC contact

Kaplan-Meier graphs and the log-rank test were conducted to compare differences in survival experiences across categorical variables. In the Kaplan–Meier survival plot, curves positioned below others indicate that the groups represented by the lower curves have a lower survival status compared to those represented by the upper curves (Fig 4).

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Fig 4. Survival estimate of time to first ANC visit among pregnant women using different factors.

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The log-rank test was also used to assess the statistical significance of these differences. The log-rank test revealed a statistically significant (p < 0.001) disparity in survival outcomes for the place of residence, maternal education, maternal age, wealth index, husband’s education, maternal occupation, marital status, parity, media exposure, and pregnancy intention (Table 3).

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Table 3. Comparison of survival time, for the first antenatal care visit (in months) among pregnant women in East Africa.

https://doi.org/10.1371/journal.pone.0325002.t003

Model adequacy or selection

To evaluate the proportional hazard assumption of the Cox proportional hazards model, diagnostic tests were conducted, including the rho statistic and examination of the scaled Schoenfeld residuals. The rho statistic quantifies the extent of correlation between the model’s residuals and time, with a larger value indicating a stronger association. The proportional hazards assumption was violated, as indicated by significant rho and global tests (p < 0.05) linked to time to first ANC contact, leading to the adoption of AFT models with diverse baseline and frailty distributions (Table 4).

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Table 4. Assumption of the proportional hazard model.

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The best model was selected based on the lowest AIC and BIC values, and the highest log-likelihood value. Among the models considered, the log-logistic gamma shared frailty model showed the best performance with the lowest AIC (111,172.1), BIC (111,398.7), and highest log-likelihood (−55,562.07), making it the most suitable for describing factors affecting the time to initiate ANC contacts (Table 5).

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Table 5. AFT Model comparisons with and without frailty for different baseline distribution.

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The rationale for using a shared frailty model is to capture the correlation of outcomes within clusters (countries), as individuals within the same country may experience similar risks due to shared environmental, socio-economic, or healthcare-related factors. By incorporating frailty, the model accounts for this intra-country dependence and provides more accurate estimates of the effects of covariates. It allows for the assumption that individuals within the same cluster may not be independent, thereby improving the robustness of the survival analysis and adjusting for the potential confounding effects that may arise from such clustering.This model offers a flexible parametric approach to survival analysis, enabling the hazard function to exhibit increasing, decreasing, or unimodal patterns over time, which correspond to the observed data. Model diagnostics, including AIC and BIC, confirmed the superior fit of the log-logistic shared frailty model in comparison to alternative models (Table 5). Furthermore, the Cox model’s proportional hazards assumption was potentially violated in preliminary analyses, further substantiating the selection of the log-logistic model for robust and reliable estimates.

Finally, the goodness of fit was assessed using Cox-Snell residual plots to examine the alignment between the residual and cumulative hazard functions. When considering exponential, Weibull, and log-normal distributions, the Cox-Snell residuals deviated significantly from the cumulative hazard function. In contrast, the Cox-Snell residuals for the log-logistic baseline distribution exhibited closer proximity to the cumulative hazard function curve (Fig 5). Therefore, this observation substantiates that the log-logistic frailty baseline distribution offers a more favorable fit to the dataset compared to the other distributions examined. Using the AFT model, the univariable analysis identified all variables as significant at a 25% threshold (p < 0.25), and these were subsequently included in the multivariable analysis.

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Fig 5. Cox-Snell residual plots against cumulative hazard for exponential, Weibull, log-normal, and log-logistic AFT models.

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Log-logistic gamma shared frailty model result

The test problem for the null hypothesis of no unobserved heterogeneity is given by versuswhere denotes the frailty variance (unobserved heterogeneity). The frailty in this model is assumed to follow a gamma distribution with mean 1 and variance equal to theta (). The frailty variance () = 0. 099 (95% CI: 0. 045, 0. 217) indicates that there is heterogeneity between countries. A likelihood ratio test for the hypothesis θ = 0 indicates a chi-square value of 7606.17 with one degree of freedom resulting in a highly significant p-value of less than 0.001. This implied that the frailty component had a significant contribution to the model.

Predictors of time to first antenatal care booking

The outcome of the multivariable AFT model using log-logistic distribution as a frailty factor revealed that factors, including residence, marital status, education levels of both the mother and husband, wealth index, media exposure, parity, maternal age, distance to healthcare, possession of health insurance, and current work status, are statistically significant at the 5% level of significance. On the other hand, factors such as the sex of the household head, the total number of children, and whether the pregnancy was desired or not were insignificant to the time it takes for pregnant mothers in East African countries to make their first ANC visit (Table 6).

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Table 6. Log-logistic gamma shared frailty model results.

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The acceleration factor for time to first ANC visits among mothers who live in rural areas was 1.014 ( = 1.014, 95% CI: 1.006, 1.021) compared to urban dwellers. This means that, after adjusting for other factors and frailty term constant, women residing in rural areas delay ANC contact initiation by a factor of 1.014 compared to urban dwellers. This indicates that the time it takes for rural women to initiate their first ANC visit is longer than that for their urban counterparts.

Women aged 25–34 had an acceleration factor of 0.978 ( = 0.978, 95% CI: 0.970, 0.980), and those over 35 had an acceleration factor of 0.964 ( = 0.964, 95% CI: 0.952, 0.971), using the 15–24 age group as the reference. This indicates that, after adjusting for other factors and maintaining a constant frailty term, women in the 25–34 and 35–45 age groups initiated their first ANC contact 2.2% and 3.6% earlier, respectively, than those in the 15–24 age group. This indicates that both older age groups initiate their first ANC visit significantly earlier than the 15–24 age group.

The acceleration factor for time to first ANC visits among mothers who had secondary or above education levels was 0.962 ( = 0.962, 95% CI: 0.952, 0.971) compared with uneducated mothers. Additionally, the acceleration factor for time to first ANC visits in mothers with primary education was 0.969 ( = 0.969, 95% CI: 0.961, 0.975) compared with the reference group (no education). This means that, after controlling for other variables and maintaining a constant frailty term, mothers with primary education and those with secondary or higher education initiated their first ANC contact 2.2% and 3.6% earlier, respectively, compared to mothers without formal education. This shows that educated women initiate their first ANC visit earlier than uneducated mothers.

Women from the middle and rich wealth index had an acceleration factor of 0.990 (95% CI: 0.982, 0.997) and 0.975 (95% CI: 0.969, 0.983) respectively, compared to the poor groups. This means that, after controlling for other variables and maintaining a constant frailty term, mothers from middle and rich socioeconomic status initiated their first ANC contact 2.7% and 2.5% earlier, respectively, compared to mothers from economically disadvantaged families. This indicates that women who are from rich families initiate their first ANC earlier than the reference category.

Women with multiple parities had an acceleration factor of 1.053 (95% CI: 1.045, 1.062), and women with grand multipara had a higher acceleration factor of 1.111 (95% CI: 1.093, 1.129), compared with nulliparous women as the reference. This implies that, after accounting for other covariates and frailty constant, women with multiple and grand parity take a significantly extended period before initiating their initial ANC visit.

Women with media exposure had an acceleration factor of 0.976 (95% CI: 0.970, 0.982), indicating that, after adjusting for other covariates and accounting for frailty term, they initiated the first ANC visit 2.4% earlier compared to those without regular media exposure. In addition, married women had an acceleration factor of 0.970 (95% CI: 0.963, 0.978), indicating that, after adjusting for other covariates and accounting for frailty term, they initiated the first ANC visit 3% earlier as compared to unmarried women.

The calculated coefficient for the healthcare distance parameter was estimated to be −0. 025, suggesting that proximity to healthcare facilities is a substantial hindrance to access to ANC. The negative sign of the coefficient indicates a decrease in the logarithm of the survival time. In practical terms, this implies a reduction in the expected duration of the time taken to make the first ANC visit when compared to women for whom the distance to healthcare poses a significant obstacle, as denoted by the reference group.

Strengths and limitations of the study

The research utilized nationally representative DHS data, providing a comprehensive perspective on ANC across multiple nations. This extensive coverage enhances the study’s validity and generalizability. Furthermore, the implementation of a frailty model facilitates the examination of time to ANC contact variations, effectively accounting for both observable and unobservable factors.

The limitations of our analysis stem predominantly from the use of secondary data. Surveys were conducted between 2012 and 2022, and all indicators of ANC use and content rely on women’s self-report of events during the pregnancy preceding their most recent live birth, relying on participants’ ability to accurately remember past events. This may introduce maternal recall bias. Finally, the model did not incorporate all possible variables influencing ANC contacts, potentially limiting the comprehensiveness of the analysis and our understanding of ANC contact.