Comparing the performance of statistical and machine learning survival models in predicting timing and determinants of postnatal care in Rwanda

Abstract

Background

Postnatal care (PNC) remains the least utilized component of the maternal care continuum despite its critical role in preventing maternal and neonatal deaths. Conventional survival models estimate associations and identify determinants of time to postnatal care, whereas machine-learning survival models aim to improve prediction by capturing complex nonlinear relationships in the data.

Methods

This was a cross-sectional study based on a secondary analysis of the 2019–2020 Rwanda Demographic and Health Survey (RDHS) data for 3,135 women who had a live birth within two years preceding the survey. Data pre-processing addressed missingness through model-based and group-wise imputation. Feature selection was performed using the Least Absolute Shrinkage and Selection Operator (LASSO–L1), which identified ten predictors. For conventional modelling, time to first PNC was analyzed using Cox proportional hazards and accelerated failure time (AFT) models to estimate associations with PNC timing. For machine-learning (ML) modelling, Random Survival Forests (RSF), Gradient Boosted Survival Trees (GBST), and Deep Survival Analysis (DeepSurv) were applied to predict time to PNC by capturing nonlinear relationships among predictors. Model performance was evaluated using the concordance index (C-index) and integrated Brier score (IBS), while model fit for likelihood-based models was assessed using Akaike (AIC) and Bayesian (BIC) information criteria.

Results

The median time to first PNC was 24 h. Within 24 h, 54.9% (95% CI: 53.2–56.7) of women received first PNC; 70.4% (95% CI: 69.8–73.0) received PNC within 48 h, while 25.8% did not receive PNC by 42 days (censored at 1,008 h). Higher hazards (earlier PNC uptake) were observed for cesarean compared to vaginal delivery (AHR = 1.80; 95% CI: 1.58–2.05; p < 0.001), health center compared to home delivery (AHR = 1.41; 95% CI: 1.19–1.68; p < 0.001), at least four ANC visits compared to women with no ANC (AHR = 1.64; 95% CI: 1.05–2.57; p = 0.030), insured compared to uninsured women (AHR = 1.13; 95% CI: 1.00–1.28; p = 0.045), and regular media exposure (AHR = 1.30; 95% CI: 1.16–1.45; p < 0.001). Machine learning models showed better predictive performance than classical models. The GBST performed best overall (C-index = 0.78; IBS = 0.142), followed by RSF (C-index = 0.76; IBS = 0.153). Among classical models, the log–logistic AFT model provided the best fit (C-index = 0.72; IBS = 0.168).

Conclusion

Machine learning survival models showed improved predictive performance for predicting time to first PNC compared with classical survival models. These findings suggest that ML may complement conventional approaches for risk stratification and prediction of postnatal care timing in Rwanda.

Introduction

The postnatal period, particularly the first 24–48 h after delivery, is a critical window for both maternal and newborn survival [1]. Globally, approximately 295,000 women die each year from pregnancy-related complications, with 94% of these deaths occurring in low- and middle-income countries [2]. Newborn mortality is also alarmingly high during this period, with nearly 2.3 million newborn deaths occurring annually, many of which could be prevented through timely and quality postnatal care [3]. Recognizing the importance of early intervention, the World Health Organization (WHO) recommends that all mothers and newborns receive their first postnatal check-up within 24 to 48 h of birth [1].

Uptake of timely postnatal care remains low in many sub-Saharan African countries. The studies in sub-Saharan Africa indicated that only 42% of women in sub-Saharan Africa receive a postnatal check-up within the first two days after delivery [4, 5]. Limiting factors include limited health infrastructure, insufficient awareness, socio-cultural barriers, and inequities in healthcare access. These barriers are particularly pronounced among women who reside in rural and underserved regions [6].

Without timely postnatal care, conditions such as postpartum hemorrhage, infections, and high blood pressure can lead to maternal deaths, with hemorrhage alone accounting for about 27% [7, 8]. For newborns, early care helps prevent deaths from infections, birth asphyxia, and complications of prematurity. Most of these deaths are preventable with prompt and quality postnatal care [9].

Rwanda has made considerable strides in maternal and child health over the past decades, with notable improvements in health facility delivery rates and skilled birth attendance [10]. According to the 2019–2020 Rwanda Demographic and Health Survey (RDHS), 91% of births occurred in health facilities, and 93% were attended by skilled personnel [11]. However, ensuring that women receive timely postnatal care remains a challenge. The RDHS reports that, PNC is the least utilized maternal care service with only 70% of mothers received postnatal check-up, despite the high rate of facility-based births [12].

Previous research on postnatal care in Rwanda and sub-Saharan Africa has primarily examined whether women receive PNC or whether they receive adequate PNC content, rather than when the first PNC check occurs. For example, a study by Kawuki used multivariable logistic regression to analyze determinants of adequate PNC content in Rwanda but did not assess the timing of the first PNC visit [13]. Similarly, Rwabufigiri applied chi-square tests and logistic regression to identify factors associated with PNC utilization within seven days after delivery, offering no insight into variations in early (0–48 h) uptake [14]. Multi-country analysis by Mekonen also relied on logistic regression, focusing on prevalence and predictors of PNC use, but not on time-to-PNC or survival patterns [5]. The classical regression techniques assume linear relationships and may not capture non-linear interactions between sociodemographic, behavioral, and health-service factors interactions that machine learning (ML) methods are designed to identify [15]. ML has been applied in maternal health for prediction tasks such as postpartum hemorrhage risk [16] and hospital readmission using survival forests [17].

This study extends existing work by comparing classical survival analysis and machine-learning survival models for time-to-first PNC in Rwanda. By focusing on time-to-event, rather than binary PNC use, and by comparing ML and statistical models, this study provides more actionable evidence to guide targeted strategies for improving early PNC uptake.

Materials and methods

Study design

This was a cross-sectional analytical study based on data from the Rwanda Demographic and Health Survey (RDHS) conducted in 2019–2020, using retrospectively reported time-to-event information on the first postnatal care visit. Two datasets were merged on household identification, namely the RDHS Women’s Individual Recode (IR) dataset and the Child Recode (KR) dataset. Although DHS data are cross-sectional, retrospective reporting of time to first PNC allows reconstruction of time-to-event outcomes, making survival analysis appropriate for modeling timing and censoring patterns in postnatal care utilization.

Study setting

This study was conducted in Rwanda, a landlocked country located in the Great Lakes region of East Africa, bordered by Uganda to the north, Tanzania to the east, Burundi to the south, and the Democratic Republic of the Congo to the west. The country is administratively divided into four provinces (Northern, Southern, Eastern, and Western) and the Capital city of Kigali, comprising 30 districts, 416 sectors, and over 14,000 villages. According to the 2022 National Census, Rwanda’s population was estimated at 13,246,394 individuals, of whom 51.5% were female. Notably, 28% of the total population consisted of women of reproductive age (15–49 years) [18].

Target population

The target population for this study consisted of 3,135 women aged 15–49 years who had given birth within the two years preceding the 2019–2020 Rwanda Demographic and Health Survey (RDHS) [11]. This group was selected to ensure that the analysis focused on recent maternal experiences relevant to current health service provision. By restricting inclusion to women with recent births, the study aimed to minimize recall bias and maximize the validity of reported postnatal care timing.

Sample size and sampling procedures

The sample size was determined by the 2019–2020 Rwanda Demographic and Health Survey (RDHS), which employed a two-stage stratified cluster sampling design to ensure national representativeness. In the first stage, enumeration areas were selected using probability proportional to size. In the second stage, households within each cluster were systematically sampled. All eligible women aged 15–49 years who had given birth within the two years preceding the survey and who completed the maternal health questions were included in this analysis.

Variables included in the study

The variables were grouped into three categories: sociodemographic characteristics, reproductive and maternity-care factors, and health system and access-related factors. Sociodemographic variables included maternal age, place of residence, wealth index, working status, and media exposure. Reproductive and maternity-care variables included the number of antenatal care (ANC) visits, place of delivery, and mode of delivery (caesarean section). Health system and access-related factors included health insurance coverage and perceived distance to a health facility.

These variables were selected based on theoretical relevance and evidence from previous studies examining determinants of postnatal care utilization [19, 20]. Variables such as maternal education and partner education were excluced due to correlation with wealth status and media exposure, consequently these variables were exluded to reduce redudancy and improve model stability. The outcome variable was time to first postnatal care visit, defined as the number of hours between childbirth and the first PNC contact (visit), with women who did not receive PNC within 42 days considered right-censored.

Outcome definition

Reported times exhibited heaping at clinically meaningful intervals (particularly 24 h), reflecting recall patterns typical of DHS data. These values were retained without smoothing to preserve interpretability, while right-censoring was applied at 42 days (1008 h) in accordance with WHO recommendations.

Data preprocessing

As shown in (Fig. 1), the preprocessing workflow involved sequential data cleaning, elimination of variables with complete missingness, and restriction of the sample to women with a recent live birth. Missing data were handled using a combination of model-based imputation for continuous variables and group-wise mode imputation for categorical variables [21]. To prevent data leakage, imputation procedures were performed after train–test partitioning, with parameters estimated exclusively on the training set and then applied to the test set.

Fig. 1.

Data preprocessing workflow, including sample restriction, imputation, quality checks, and feature selection

Feature selection was conducted using Least Absolute Shrinkage and Selection Operator (LASSO) regularization to identify the final set of predictors [22]. Survey weights were incorporated in descriptive and classical survival analyses; ML models did not fully accommodate complex survey design. To analyze the timing of first postnatal care (PNC) and its predictors, both survival analysis models and modern machine learning–based time-to-event models were applied, allowing a comprehensive assessment of both interpretable associations and complex nonlinear relationships. All analyses were conducted in Python (3.11), using key libraries including pandas, NumPy, scikit-learn, and scikit-survival. Multicollinearity was assessed using variance inflation factors, and no problematic collinearity was detected (all Variance Inflation Factor (VIF) < 5).

Statistical survival models

Conventional survival models [23] were used to estimate the effects of predictors on the timing of first postnatal care (PNC) while accounting for censored observations. The Cox proportional hazards (Cox PH) model served as the primary analytical framework due to its flexibility and interpretability in modeling time-to-event data [20]. The model assumes that the hazard for an individual at time t, given covariates X, is expressed as:

1

The proportional hazards assumption was evaluated using Schoenfeld residuals and log–log survival plots. No major violations were detected.

Parametric Accelerated Failure Time (AFT) models

Parametric accelerated failure time (AFT) models, including the Weibull, log-normal, and log-logistic, were applied to directly model the effect of covariates on survival time [24, 25]. These models express the logarithm of time to event as a linear function of covariates:

2

where α is the intercept, β are regression coefficients, and ε denotes the error term following an extreme value, normal, or logistic distribution for the Weibull, log-normal, and log-logistic models, respectively. These models yield time ratios (TRs) that describe the acceleration or deceleration of event timing associated with each covariate.

Machine learning models

Machine learning survival models were applied to capture nonlinear and high-dimensional relationships that conventional models may overlook [26]. Three algorithms were implemented: Random Survival Forests (RSF), Gradient Boosted Survival Trees (GBST), and a deep learning–based survival model (DeepSurv) [27].

The dataset was randomly partitioned into an 80% training set and 20% testing set. Hyperparameters were selected based on prior literature and empirical performance, and further optimized using 5-fold cross-validation within the training dataset to balance bias–variance trade-offs and minimize overfitting. For RSF, 500 trees were grown with log-rank splitting and tuned values for the number of variables randomly selected at each node. GBST models were trained with a learning rate of 0.01, maximum tree depth of 3, and 500 boosting iterations. DeepSurv extends the Cox proportional hazards framework using neural networks and was trained using the Adam optimizer with early stopping based on validation loss.

Models’ performance evaluation

Model performance was evaluated using the concordance index (C-index) for discrimination and the Akaike (AIC) and Bayesian (BIC) information criteria for model fit [28]. The C-index quantifies the proportion of all comparable pairs of individuals whose predicted survival times are correctly ordered:

3

The AIC and BIC were computed to compare the relative goodness of fit across models, penalizing model complexity [29]:

4

where k is the number of parameters, n is the number of observations, and is the maximized likelihood. Lower AIC and BIC values indicate better-fitting models, while higher C-index values denote greater discriminative accuracy. Time-dependent ROC/AUC methods appropriate for censored survival data were used to estimate AUC at 24 and 48 h. All performance metrics (C-index, IBS, and time-dependent AUC) were calculated on the held-out test dataset, with 95% confidence intervals estimated using bootstrap resampling.

Error measurement and model validation

To quantify prediction error of the survival models, the time-dependent Brier score and the integrated Brier score (IBS) were used. Let denote the event time for individual  i, the censoring time, the observed time, and the event indicator [30]. For a given prediction time  t, the true status is defined as

5

and the model-based predicted survival probability is , where is the covariate vector for individual  i. Because of right censoring, we used inverse probability of censoring weighting (IPCW). Let be the Kaplan–Meier estimator of the censoring distribution [31]. The IPCW weight for individual  iat time  tis

6

The time-dependent Brier score at time  t is then defined as

7

To summarize prediction error over the follow-up period , the integrated Brier score (IBS) was computed:

8

with chosen as the maximum follow-up time used for model comparison. Lower BS and IBS values indicate better overall predictive accuracy (combining calibration and discrimination) across time. These prediction error measures were used alongside discrimination metrics (concordance index) and information criteria (AIC and BIC) to evaluate and compare the performance of the statistical and machine-learning survival models.

Results

Descriptive characteristics of the study population

The socio-demographic characteristics of 3,135 reproductive women aged 15–49 years who had a live birth within two years prior to the 2019–2020 RDHS were analyzed and the results are presented in Table 1.

Table 1.

Sociodemographic characteristics of the time to first PNC (N = 3,135)

Variables	Frequency	Status		Median Time (Hours)	Log-rank Test	P-value
		Censored	Event
Age group (years)					5.19	0.405
15–19	96	24	72	24
20–24	616	151	465	24
25–29	730	186	544	24
30–34	760	198	562	24
35–39	618	153	465	24
40–44	266	83	183	24
45–49	49	14	35	12
Residence					1.14	0.26
Urban	793	150	643	24
Rural	2342	659	1683	24
Wealth category					26.67	< 0.001
Poor	1404	419	985	24
Middle	581	144	437	24
Rich	1150	246	904	24
ANC Visits					73.52	< 0.001
None	72	45	27	1008
4 and less	1575	455	1120	24
More than 4	1488	309	1179	24
Place of delivery					2226.21	< 0.001
Home	204	46	158	24
Health Center	838	112	726	24
District Hospital	1809	477	1332	24
Referral hospital	284	174	110	1008
Caesarian delivery					143.69	< 0.001
No	2590	767	1823	24
Yes	545	42	503	24
Distance to health facility is a problem					3.94	0.033
No	2390	597	1793	24
Yes	745	212	533	24
Insurance coverage					33.02	< 0.001
No	535	190	345	26
Yes	2600	619	1981	24
Working status					0.82	0.66
Not working	874	234	640	24
Working	2261	575	1686	24
Media exposure					39.58	< 0.001
No	677	236	441	28
Yes	2458	573	1885	24

Source: RDHS 2019–2020

The median time to first postnatal care (PNC) was consistently 24 h across most subgroups, indicating that many women received care shortly after delivery. However, the interquartile ranges (IQRs) often extended to 1008 h (42 days), reflecting a substantial proportion of women whose PNC was delayed or censored at six weeks. Age group showed no significant association with PNC timing (p = 0.405). Although the medians were similar (24 h), wide IQRs extending to 1008 h among older women suggest that some did not receive timely care within the recommended period. By residence, urban women had narrower IQRs (358 h) compared to rural women (1006 h), suggesting earlier uptake in urban settings, though the difference was not statistically significant (p = 0.260).

Wealth status was strongly associated with PNC timing (p < 0.001). Poorer women had IQRs reaching the censoring limit (1006 h), while richer women had a markedly narrower IQR (34 h), indicating more consistent and timely access. Antenatal care (ANC) attendance was also influential (p < 0.001). Women with more than four ANC visits had a very narrow IQR (34 h), while those with none (978 h) or four or fewer visits (1006 h) frequently reached the censoring boundary, reflecting much later or unobserved PNC.

Health system factors showed the clearest disparities. Place of delivery (p < 0.001) was highly predictive: women delivering at referral hospitals had median times censored at 1008 h (indicating late or unrecorded PNC), while those delivering at health centers had the narrowest IQR (10 h). Mode of delivery was equally decisive (p < 0.001): cesarean deliveries were followed by prompt PNC (IQR = 10 h), whereas vaginal deliveries often stretched to 1006 h, showing much later follow-up.

Access-related barriers were evident in problem distance to facility (p = 0.033). Women reporting difficulties were more likely to hit the 1008-hour censoring point compared to those with no distance problem (IQR = 358). Similarly, insurance coverage (p < 0.001) facilitated earlier PNC, with insured women showing narrower IQRs (358 h) than uninsured women (1006 h).

Media exposure was one of the strongest predictors (p < 0.001). Women exposed to radio or television at least once a week had narrow IQRs (10–36 h), while those without exposure reached the censoring limit (1006 h), highlighting the role of information in promoting early care-seeking. Working status was not significantly associated with PNC timing (p = 0.660); both employed and unemployed women showed wide IQRs extending to censoring. The wide interquartile ranges approaching 1008 h largely reflect right-censoring rather than true variability in timing, indicating that a substantial proportion of women did not receive PNC within the follow-up period. Although interquartile ranges (IQRs) are discussed in the text to describe variability in time to first PNC, they are not presented in the table to maintain simplicity of presentation.

Time to first postnatal care: Kaplan-Meier estimates

The timing of first postnatal care (PNC) uptake was assessed using the Kaplan-Meier survival estimator. Figure 2 presents the overall survival curve, illustrating the probability of not having received first PNC as a function of time after delivery. The shaded area represents the 95% confidence interval.

Fig. 2.

Kaplan–Meier curve for time to first postnatal care after delivery. Source: RDHS (2019–2020)

The Kaplan-Meier curve demonstrates that the probability of not receiving postnatal care declines rapidly within the first 24 to 48 h after delivery, with the survival probability dropping from approximately 0.7 to below 0.3 during this period. Beyond 48 h, the curve plateaus, indicating that the majority of women who receive postnatal care do so early (54.9%) experienced the event within 24 h (CI: 53.18–56.66), while a smaller proportion continue to delay or miss care entirely throughout the postpartum period. By the end of follow-up, about 25% of women had not received any postnatal care.

Determinants of time to first PNC using statistical approach

To examine determinants of the timing of first postnatal care (PNC), we employed the Cox proportional hazards model and accelerated failure time models with Time ratio (TR) indicating the time to event between groups while hazard ratios (HR) were estimated to capture the effects of sociodemographic, reproductive, and health service factors on early PNC uptake (Table 2).

Table 2.

Predictors of Time to First Postnatal Care: Cox PH and AFT Models

Variables	Cox PH	P-value	Weibull	P-value	Log-Normal	P-value	Log-Logistic	P-value
	HR (95%CI)		TR (95%CI)		TR (95%CI)		TR (95%CI)
Age group (years)
15–19	Ref	-	Ref	-	Ref	-	Ref	-
20–24	1.01 (0.78–1.30)	0.949	0.93 (0.60–1.45)	0.761	0.91 (0.44–1.95)	0.812	0.93 (0.40–2.16)	0.846
25–29	0.98 (0.76–1.26)	0.887	1.09 (0.73–1.55)	0.68	1.03 (0.47–2.29)	0.935	1.03 (0.46–2.28)	0.946
30–34	0.95 (0.74–1.23)	0.715	1.22 (0.80–1.87)	0.359	1.06 (0.51–2.29)	0.871	1.09 (0.53–2.29)	0.821
35–39	1.11 (0.86–1.43)	0.441	0.73 (0.47–1.14)	0.163	0.73 (0.35–1.56)	0.406	0.74 (0.36–1.54)	0.426
40–44	1.03 (0.78–1.36)	0.853	1.03 (0.59–1.79)	0.926	0.90 (0.40–2.01)	0.799	0.89 (0.41–1.96)	0.77
45–49	0.98 (0.64–1.50)	0.932	1.16 (0.38–3.28)	0.801	0.99 (0.29–3.41)	0.986	1.00 (0.30–3.43)	0.997
Residence
Urban	Ref	-	Ref	-	Ref	-	Ref	-
Rural	1.05 (0.94–1.18)	0.377	0.75 (0.53–1.01)	0.098	0.97 (0.63–1.50)	0.884	0.98 (0.66–1.45)	0.92
Wealth category
Poor	Ref	-	Ref	-	Ref	-	Ref	-
Middle	1.01 (0.89–1.13)	0.91	0.94 (0.68–1.29)	0.717	0.99 (0.66–1.49)	0.968	0.99 (0.65–1.48)	0.964
Rich	1.03 (0.92–1.15)	0.586	0.85 (0.63–1.16)	0.315	0.85 (0.61–1.17)	0.31	0.87 (0.62–1.17)	0.388
ANC Visits
None	Ref	-	Ref	-	Ref	-	Ref	-
4 and less	1.39 (0.89–2.18)	0.144	1.08 (0.67–1.73)	0.753	0.24 (0.09–0.61)	0.006**	0.27 (0.10–0.65)	0.015*
More than 4	1.64 (1.05–2.57)	0.030 *	0.57 (0.36–0.93)	0.023*	0.14 (0.05–0.34)	< 0.001***	0.16 (0.08–0.31)	< 0.001***
Place of delivery
Home	Ref	-	Ref	-	Ref	-	Ref	-
Health Center	1.41 (1.19–1.68)	< 0.001 ***	0.31 (0.21–0.46)	< 0.001***	0.34 (0.18–0.61)	< 0.001***	0.40 (0.24–0.71)	< 0.001***
District Hospital	1.38 (1.15–1.67)	0.001 **	0.52 (0.35–0.79)	0.002**	0.36 (0.21–0.65)	< 0.001***	0.38 (0.22–0.71)	< 0.001***
Referral hospital	0.37 (0.28–0.50)	< 0.001 ***	26.87 (14.12–51.3)	< 0.001***	20.71 (10.3–41.6)	< 0.001***	50.14 (23.8–105.6)	< 0.001***
Caesarian delivery
No	Ref	-	Ref	-	Ref	-	Ref	-
Yes	1.80 (1.58–2.05)	< 0.001 ***	0.12 (0.08–0.17)	< 0.001***	0.17 (0.09–0.30)	< 0.001***	0.22 (0.12–0.32)	< 0.001***
Distance to health facility is a problem
No	Ref	-	Ref	-	Ref	-	Ref	-
Yes	1.02 (0.92–1.13)	0.672	0.96 (0.71–1.27)	0.819	0.92 (0.62–1.36)	0.581	0.91 (0.68–1.31)	0.525
Insurance coverage
No	Ref	-	Ref	-	Ref	-	Ref	-
Yes	1.44 (1.28–1.63)	0.003*	0.61 (0.42–0.88)	0.008**	0.68 (0.52–0.96)	0.029*	0.69 (0.50–0.97)	0.038*
Working status
Not working	Ref	-	Ref	-	Ref	-	Ref	-
Working	1.08 (0.98–1.19)	0.115	0.78 (0.58–1.04)	0.089	0.79 (0.49–1.58)	0.087	0.78 (0.53–1.02)	0.069
Media exposure
No	Ref	-	Ref	-	Ref	-	Ref	-
Yes	1.30 (1.16–1.45)	< 0.001 ***	0.41 (0.29–0.61)	< 0.001***	0.44 (0.28–0.70)	< 0.001***	0.44 (0.29–0.71)	< 0.001***

HR >1 indicates earlier uptake of first PNC

HR Hazard Ratio, TR Time Ratio, CI Confidence Interval, Ref reference category

*p< 0.05, **p< 0.01, ***p< 0.001

Source: RDHS (2019–2020)

The multivariable Cox proportional hazards model identified several factors significantly associated with the timing of the first postnatal care (PNC) visit. Mode of delivery was a strong predictor: women who delivered by caesarean section had a higher likelihood of receiving PNC earlier than those with vaginal births (AHR = 1.80; 95% CI: 1.58–2.05, p < 0.001). Place of delivery also showed a clear pattern. Compared with home deliveries, giving birth in a health center (AHR = 1.41; 95% CI: 1.19–1.68, p < 0.001) or a district hospital (AHR = 1.38; 95% CI: 1.15–1.67, p = 0.001) increased the likelihood of early PNC. In contrast, births in referral hospitals were associated with a substantially lower hazard of early PNC (AHR = 0.37; 95% CI: 0.28–0.50, p < 0.001), indicating delayed PNC uptake in this group.

Antenatal care (ANC) was another important determinant. Women with more than four ANC visits were significantly more likely to obtain early PNC compared with those with no ANC (AHR = 1.64; 95% CI: 1.05–2.57, p = 0.030). Health insurance coverage had a positive association with timely PNC (AHR = 1.44; 95% CI: 1.28–1.63, p = 0.003), as did media exposure (AHR = 1.30; 95% CI: 1.16–1.45, p < 0.001). Age, residence, wealth index, working status, and reporting distance to a health facility were not statistically significant predictors in the Cox model.

Consistent with the Cox findings, the Accelerated Failure Time (AFT) models (Weibull, Log-normal, and Log-logistic) also highlighted caesarean delivery, place of delivery, ANC attendance, insurance coverage, and media exposure as key predictors of time to first PNC. Caesarean delivery consistently accelerated time to PNC across all distributions (TR = 0.12–0.22, p < 0.001), indicating substantially earlier PNC compared with vaginal delivery. Deliveries in health centers and district hospitals significantly shortened the time to first PNC relative to home births (TR ≈ 0.31–0.52, p < 0.01).

However, referral hospital births were associated with marked delays (TR = 20–50, p < 0.001), reflecting very late PNC among this subgroup. These extremely large TRs should be interpreted with caution, as they may reflect instability due to small subgroup sizes, case-mix differences, and sensitivity to parametric model assumptions.

Women with more than four ANC visits experienced notably shorter times to PNC across all AFT distributions (TR = 0.14–0.57, p < 0.05). Insurance coverage (TR = 0.61–0.69, p < 0.05) and media exposure (TR = 0.41–0.44, p < 0.001) were also associated with faster PNC uptake. In contrast, age, residence, wealth category, working status, and perceived distance barriers were not statistically significant predictors in the adjusted AFT models.

Machine learning-based survival analysis

To evaluate the predictive potential of flexible approaches, we applied machine learning survival models, including Random Survival Forests (RSF), Gradient Boosted Survival Trees (GBST), and the neural network–based DeepSurv. Model performance was compared using concordance index (C-index) and integrated Brier score (IBS) to assess discrimination and calibration (Fig. 3).

Fig. 3.

Illustrative predicted survival curves for a single individual under RSF, GBST, and DeepSurv. Note: This figure is presented to demonstrate model output and is not used for model performance evaluation. Source: RDHS (2019–2020)

The predicted survival curves illustrate how each model estimates the probability that this individual has not yet attended postnatal care over time. For this case, RSF predicts the earliest PNC attendance (lowest curve), DeepSurv predicts a moderate delay, and GBST predicts a longer time to PNC (highest curve). These curves show differences in how each model shapes risk for this one woman, but they do not reflect overall model performance. GBST showed a higher survival curve for this individual, the global validation metrics (C-index, IBS, AUC) confirm that GBST performs best overall across the full dataset.

The Fig. 3 presents an illustrative example of individual predicted survival curves under RSF, GBST, and DeepSurv. This figure is included to demonstrate model output for a single covariate profile and is not used for model performance evaluation or comparative inference.

Predictors of time to first PNC using machine learning survival model

The Random Survival Forest model identified mode of delivery, place of delivery, number of ANC visits, health insurance coverage, and media exposure as the strongest contributors to predicting earlier initiation of postnatal care. These predictors demonstrated the largest marginal decrease in the concordance index when permuted, confirming their substantive importance. Other factors including residence, employment status, distance to facility, wealth index, and age showed comparatively smaller effects, indicating limited predictive influence in the RSF model. RSF was used for permutation importance because, unlike GBST and DeepSurv, it provides a stable, well-established, and model-agnostic importance framework specifically designed for survival data (Fig. 4).

Fig. 4.

Permutation importance of predictors from the Random Survival Forest model

Comparison of model performance

Machine-learning survival models showed slightly higher predictive discrimination than classical statistical models. The Gradient Boosted Survival Trees (GBST) achieved the highest performance (C-index = 0.78, 95% CI: 0.76–0.80) with the lowest Integrated Brier Score (IBS = 0.142), followed by Random Survival Forest (C-index = 0.76, 95% CI: 0.74–0.78) and DeepSurv (C-index = 0.74, 95% CI: 0.72–0.76). Among classical survival models, the log-logistic accelerated failure time (AFT) model showed the best discrimination (C-index = 0.72, 95% CI: 0.70–0.74), slightly outperforming the Cox proportional hazards model (C-index = 0.70, 95% CI: 0.68–0.72), the log-normal AFT model (C-index = 0.71, 95% CI: 0.69–0.73), and the Weibull AFT model (C-index = 0.69, 95% CI: 0.67–0.71) (Table 3).

Table 3.

Comparative performance of survival models for predicting time to first postnatal care (PNC)

Model	C-index (95% CI)	IBS (95% CI)	AUC_24h (95% CI)	AUC_48h (95% CI)	AIC	BIC
Gradient Boosted Survival Trees (GBST)	0.78 (0.76–0.80)	0.142 (0.138–0.147)	0.86 (0.84–0.88)	0.83 (0.81–0.85)	–	–
Random Survival Forest (RSF)	0.76 (0.74–0.78)	0.153 (0.149–0.158)	0.84 (0.82–0.86)	0.81 (0.79–0.83)	–	–
DeepSurv	0.74 (0.72–0.76)	0.161 (0.157–0.166)	0.82 (0.80–0.84)	0.80 (0.78–0.82)	–	–
Cox Proportional Hazards	0.70 (0.68–0.72)	0.176 (0.171–0.181)	0.79 (0.77–0.81)	0.77 (0.75–0.79)	25,314	25,438
Log–Logistic AFT	0.72 (0.70–0.74)	0.168 (0.164–0.173)	0.80 (0.78–0.82)	0.78 (0.76–0.80)	−1384.6	−1412.7
Log–Normal AFT	0.71 (0.69–0.73)	0.170 (0.165–0.175)	0.79 (0.77–0.81)	0.77 (0.75–0.79)	−1370.4	−1398.1
Weibull AFT	0.69 (0.67–0.71)	0.182 (0.177–0.187)	0.77 (0.75–0.79)	0.75 (0.73–0.77)	−1225.3	−1252.8

Higher C-index indicates better discrimination, while lower AIC and BIC indicate better parsimony among likelihood-based models. AIC and BIC are reported only for likelihood-based survival models and are not defined for machine-learning models (RSF, GBST, DeepSurv); therefore, these values are denoted as “--”

Source: RDHS (2019–2020)

Model fit statistics further indicated that the log-logistic and log-normal distributions provided better parametric fit compared with the Weibull model, as reflected by lower AIC and BIC values. The log-logistic distribution allows a non-monotonic hazard function that increases shortly after delivery and then declines over time, which is consistent with the expected pattern of postnatal care utilization. While machine-learning models demonstrated modest improvements in predictive accuracy, classical survival models remain valuable due to their interpretability and ability to quantify associations between predictors and time to postnatal care.

Discussion

This study compared prediction of the timing and determinants of the first postnatal care (PNC) contact in Rwanda using statistical and machine learning survival models. Using nationally representative RDHS 2019–2020 data, the study found that a median time to first PNC of 24 h, with 54.9% receiving PNC within 24 h and 70.4% of women receiving PNC within 48 h postpartum. Earlier PNC was associated with caesarean delivery (Earlier PNC among caesarean deliveries likely reflects inpatient monitoring protocols rather than maternal care-seeking behavior), facility-based birth, particularly at health centers, at least 4 ANC visits, health insurance coverage, and regular media exposure. Gradient Boosted Survival Trees achieved the strongest predictive performance, outperforming Cox PH and other models, underscoring the utility of flexible machine learning for risk stratification. DeepSurv underperformed in this study. This is likely because the DHS dataset is moderately sized, dominated by categorical predictors, and highly censored conditions under which tree-based survival models are more stable and data-efficient.

Placing these findings in context, our estimate of very early uptake (54.9% within 24 h) compares favorably with regional evidence that typically benchmarks “timely” PNC within 48 h. In northwest Ethiopia, only 13.3% of women received PNC within 48 h in a 2020 community-based study [32]. A national EDHS 2019 analysis likewise reported 34% PNC within two days, with substantial spatial clustering [33]. Uganda’s DHS-based analysis documented 50% within two days [34], and Bangladesh’s BDHS 2017–18 reported 52.8% within two days [35]. Beyond 48 h, Afghanistan’s recent MICS 2022–23 analysis found 16% within one week [36], while a pooled 36-country Sub-Saharan Africa (SSA) meta- and multilevel analysis estimated overall PNC utilization at 52.5% (any PNC within 42 days) with wide subregional variation [37]. A district study in Malawi reported high overall PNC use (84.8%), but without a strict early-timing definition [38]. Differences in operational definitions (24 h vs. 48 h vs. one week), study designs, and service environments likely explain much of the observed heterogeneity. Rwanda’s comparatively earlier uptake plausibly reflects high health facility delivery coverage, strong community health worker (CHW) engagement, and widespread health insurance, which may facilitate rapid post-delivery checks.

Determinants identified in this study align closely with prior work across low- and middle-income settings. Consistent with our findings, facility delivery and mode of delivery (caesarean) repeatedly predict earlier or higher PNC use in Ethiopia [33, 39], Uganda [34], Tanzania [40], Afghanistan [36], and pooled SSA analyses [20]. Socioeconomic gradients education, wealth, and employment feature prominently in Bangladesh, Nigeria, Tanzania, and SSA-wide studies [20, 35, 41] and are concordant with our wealth and employment effects. ANC utilization and media exposure, a proxy for information access, were significant in our models and in studies from Ethiopia, Bangladesh, and Afghanistan, mirroring our result that at least four ANC visits accelerates PNC timing [33, 35, 36]. Notably, health insurance emerged as a distinct facilitator in Rwanda less commonly measured elsewhere suggesting financial protection may shorten delays from delivery to first check.

The methodological contribution of this study is the comparison of classical and machine-learning survival models for predicting time to first PNC in Rwanda. In this dataset, GBST showed modestly better discrimination than classical approaches. Our findings align with broader evidence: [42] showed that Gradient Boosted Survival Trees outperformed conventional methods across large colorectal cancer datasets, confirming the superior predictive capacity of gradient-boosting in time-to-event settings. Similar advantages have been reported in maternal and population-level datasets, including improved prediction of postpartum hemorrhage using boosting and forests [16] and superior COVID-19 risk prediction using gradient boosting in Ontario’s health databases [43]. However, consistent with [17], ML gains may be modest in highly structured clinical environments. Together, these findings indicate that ML models yield the greatest benefits in complex, nonlinear, population-based data such as the RDHS where relationships are not well captured by conventional survival models.

This study found that among statistical models, the Log-Logistic AFT achieved better discrimination and fit than the Cox model, reflecting its flexibility in handling non-monotonic hazards typical of postnatal care timing. Similarly, in the Nigerian study on diabetes and hypertension survival, the Weibull AFT model with random effects outperformed both the standard AFT and CPH models, capturing unobserved heterogeneity and improving predictive accuracy [44].

This study has strengths, including use of nationally representative data, clear time-to-event framing with right-censoring at 42 days per WHO, and side-by-side evaluation of statistical and ML survival methods. The determinants across multiple countries and designs support the generalizability of key levers facility-based delivery, ANC intensity, financial protection, and information access to improve timely PNC.

Rwanda exhibits comparatively earlier PNC uptake than many settings in sub-Saharan Africa, yet disparities persist by service access and socioeconomic resources. Reinforcing universal facility delivery and immediate post-delivery checks, expanding insurance coverage, ensuring adequate ANC contact, and leveraging media and community platforms may further compress delays. The superior predictive performance of GBST suggests that machine learning can complement public health programs by identifying women at risk of delayed PNC for proactive, equity-focused follow-up.

Study limitations

This study has some limitations to consider. First, the cross-sectional DHS design limits causal inference and restricts interpretation to associations rather than causal effects. Second, time to first PNC was self-reported and may be affected by recall bias and heaping at commonly reported time points, particularly 24 h. Right-censoring at 1,008 h (42 days) may also have influenced estimates in the tail of the survival distribution. Third, residual confounding from unmeasured factors such as women’s knowledge of PNC, clinical severity, cultural practices, and health facility readiness may persist. Fourth, model validation relied on a single train–test split with internal cross-validation, and external validation using independent datasets was not performed. Finally, the machine-learning models did not fully account for the complex survey design of the RDHS in the same way as the classical survival models, which may affect the population-level generalizability of ML-based predictions.

Conclusion

This study addressed important methodological and public health gaps in maternal health research. It examined the timing and predictors of postnatal care (PNC) in Rwanda using both classical and machine-learning survival models. Machine-learning survival models demonstrated improvements in predictive performance compared with classical survival models, suggesting their potential usefulness for identifying women at risk of delaying PNC. Early PNC uptake was predicted by factors including facility delivery, cesarean section, adequate ANC attendance, insurance coverage, and media exposure, highlighting persistent disparities in access and healthcare utilization. These findings suggest that combining machine-learning approaches with statistical survival analysis may support improved prediction, risk stratification, and more targeted maternal health interventions in Rwanda.

Abbreviations

AFT

Accelerated Failure Time

ANC

Antenatal Care

AHR

Adjusted Hazard Ratio

AIC

Akaike Information Criterion

BIC

Bayesian Information Criterion

BS

Brier Score

C-index

Concordance Index

Cox PH

Cox Proportional Hazards

DHS

Demographic and Health Survey

GBST

Gradient Boosted Survival Trees

IBS

Integrated Brier Score

LASSO

Least Absolute Shrinkage and Selection Operator

ML

Machine Learning

PNC

Postnatal Care

RDHS

Rwanda Demographic and Health Survey

RSF

Random Survival Forest

TR

Time Ratio

WHO

World Health Organization

Authors' contributions

TK conceptualized the study, developed the methodology, conducted formal analyses, and drafted the original manuscript. IK and FN contributed to conceptualization of the study, provided methodological guidance, supervised the study and mentored TK and critically reviewed and edited the manuscript. All authors made significant contributions to the work reported, participated in revising the manuscript, and approved the final version for publication.

Funding

This study did not receive any funding.

Data availability

The data used in this study are publicly available from the Demographic and Health Surveys (DHS) Program. Access to the dataset can be obtained upon reasonable request through the DHS Program website (https://dhsprogram.com/data/), after registration and approval of a brief research proposal outlining the intended use of the data.

Declarations

Ethics approval and consent to participate

Permission to access and use the RDHS dataset was obtained from the DHS Program. The RDHS data are publicly available, fully anonymized, and contain no personal identifiers. This study complied with all ethical requirements for secondary data analysis, as outlined in the DHS guidelines and relevant institutional standards. The original RDHS protocol received ethical approval from the Rwanda National Ethics Committee and the International Coaching Federation (ICF) Independent Review Board. As this study involved analysis of de-identified secondary data, no additional ethical approval was required. The study was conducted in full accordance with the ethical principles outlined in the Declaration of Helsinki.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.