Abstract
Introduction
Pneumonia is one of the most common and deadly infectious diseases affecting under-five children, responsible for about 15% of all deaths in this age group worldwide. In Ethiopia, the prevalence ranges from 16% to 21%, contributing substantially to under-five mortality. Despite national child survival efforts, pneumonia-related deaths remain a major public health concern. Understanding the burden and identifying key risk factors are essential for effective prevention and timely intervention. This study aimed to estimate the time to death and identify its predictors among under-five children with acute pneumonia using Bayesian parametric survival analysis.
Methods
A retrospective study was conducted with 451 under-five children diagnosed with acute pneumonia. Three survival analysis models were applied: the Cox proportional hazards model, the parametric accelerated failure time (AFT) model, and the Bayesian parametric survival model. In the Bayesian model, Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling and the Metropolis-Hastings algorithm were employed to obtain samples from the posterior distributions of the parameters. Each model was evaluated using appropriate model selection criteria to identify the best-fitting approach.
Results
The Bayesian Lognormal AFT model identified several significant predictors of time to death among under-five children with acute pneumonia. All model parameters showed good convergence, with Monte Carlo errors under 5% of their standard deviations. Female children had shorter survival times compared to males (AF = 0.46; 95% CI: 0.36–0.97). Children aged 1–11 months had better survival outcomes (AF = 0.10; 95% CI: 0.05–0.21) than those aged 48–59 months. Rural residence (AF = 1.48; 95% CI: 1.03–2.09), diagnosis during spring (AF = 0.73; 95% CI: 0.52–0.92) and summer (AF = 0.66; 95% CI: 0.49–0.84), comorbidities (AF = 1.26; 95% CI: 1.03–1.65), severe acute malnutrition (AF = 0.26; 95% CI: 0.13–0.43), anemia (AF = 0.88; 95% CI: 0.73–0.93), low weight (AF = 0.72; 95% CI: 0.55–0.90), and home delivery (AF = 0.75; 95% CI: 0.59–0.95) were all associated with reduced survival times.
Conclusion
This study identified key predictors of mortality among under-five children with acute pneumonia using a Bayesian parametric survival model. Female, rural residence, severe acute malnutrition, comorbidity, anemia, and low weight were significantly associated with reduced survival times. Seasonal variation and place of delivery also influenced mortality, highlighting the impact of environmental and health system factors. These findings emphasize the need for targeted interventions focusing on early diagnosis, nutritional support, and tailored care for high-risk groups. Furthermore, the Federal Ministry of Health could enhance community awareness of early pneumonia detection and effective home management, particularly in rural areas where mortality risk is higher.
Keywords: Acute pneumonia, Under-five children, Time to death, Predictors, Child health, Bayesian parametric survival
Background of the study
Pneumonia is an acute respiratory infection that inflames the air sacs in one or both lungs, often caused by bacteria, viruses, or fungi. It can lead to fluid or pus accumulation in the lungs, resulting in difficulty breathing. Common symptoms include cough, fever, chest pain, shortness of breath, fatigue, and sweating [1]. Pneumonia is a leading cause of morbidity and mortality worldwide, particularly among under-five children year’s old, older adults, and immunocompromised individuals [2]. Treatment typically involves antibiotics or antiviral medications, alongside supportive care. Vaccination programs have also contributed to preventing certain types of pneumonia [3, 4].
Globally, pneumonia remains one of the most significant causes of death in under-five children, particularly in low- and middle-income countries. According to UNICEF 2023, it is responsible for more than 800,000 deaths annually in this age group, accounting for approximately 14% of all under-five deaths [5]. Sub-Saharan Africa bears a significant burden, with an estimated 490,000 under-five pneumonia deaths [6, 7]. In Ethiopia, pneumonia is the leading cause of morbidity and mortality among under-five children, accounting for approximately 18% of all under-five deaths and resulting in over 40,000 child fatalities annually [8]. It is estimated that about 3.37 million under-five children contract pneumonia annually, with a prevalence of approximately 20.7% [9, 10].
Risk factors for pneumonia in this population include non-exclusive breastfeeding, inadequate vaccination coverage, indoor and outdoor air pollution, and nutritional deficiencies such as micronutrient and vitamin shortages [9, 10]. Despite ongoing interventions, pneumonia continues to be a leading cause of death among Ethiopian children [11]. Nonexclusive breastfeeding, a lack of or inadequate vaccination, environmental factors, outdoor and indoor air pollution, micronutrient deficiencies, and vitamin deficiencies are the most widely recognized risk factors for pneumonia in children under the age of five in impoverished countries such as Ethiopia [12, 13]. Each year, 44,000 under-five children in Ethiopia suffer from pneumonia, which accounts for 20% of all yearly causes of mortality and is a primary cause of severe childhood diseases [10, 14].
Despite efforts to reduce pneumonia mortality, gaps remain in predicting which children are at highest risk of death and the timing of such events. Survival analysis offers a valuable statistical framework to analyze the time until an event of interest such as death occurs [15]. Parametric survival models like Weibull, log-normal, and log-logistic accelerated failure time (AFT) models provide efficient estimation of survival times when appropriate assumptions about the distribution are met [16]. Unlike the Cox proportional hazards model, which does not require specifying the baseline hazard, AFT models can yield more precise estimates when the survival time distribution is well characterized [17].
Recent advances have highlighted Bayesian parametric survival analysis as a robust approach for modeling time-to-event data. This method incorporates prior knowledge and expert opinion, improves parameter estimation, and effectively handles censored data common in survival studies [18, 19]. Bayesian models employ Markov Chain Monte Carlo (MCMC) techniques to estimate posterior distributions of model parameters, offering flexibility and resilience to missing covariates [19, 20]. To date, limited research has applied Bayesian parametric survival analysis specifically to predict time to death in under-five children with acute pneumonia in Ethiopia, and no studies are available from the study area. This study aimed to address the existing gap by identifying key predictors of mortality and modeling survival times using Bayesian parametric methods. Specifically, the main objective of this study was to identify the predictors of time to death among under-five children with acute pneumonia, using Bayesian parametric survival models. Understanding these factors was intended to support healthcare providers in making informed decisions, optimizing resource allocation, and developing personalized treatment strategies to improve clinical outcomes.
Method
Study area
This study was carried out in the eastern region of Ethiopia, 635 km from Addis Ababa,, in the Somali region. The hospital, established in January 2017, is the only referral hospital and serves as a major healthcare center for an estimated population of over eight million people across the region. It also provides services to nearby zones of the Oromia region and parts of neighboring Somalia. The hospital provides inpatient, outpatient, and specialized services and functions as a teaching center. It has 372 beds, including 23 in the intensive care unit.
Study design and source of data
This study employed a retrospective study design. The data were collected from medical records of all children under five years of age who were admitted with a diagnosis of pneumonia between June 1, 2020, and July 30, 2023. The data with incomplete or missing critical information were excluded from the study. A total of 451 children under five with pneumonia were included in the final analysis.
Inclusion and exclusion criteria
All children under the age of five who were diagnosed with pneumonia during the study period were included in the study. Medical records that were missing essential clinical or outcome information were excluded from the analysis due to incompleteness.
Study variables
Dependent variable
The outcome of interest was time to death, measured in days from hospital admission to the occurrence of death. Children who were discharged alive, transferred, or lost to follow-up were considered censored.
Independent variables
The independent (predictor) variables included demographic, clinical, and treatment-related characteristics that may influence survival time among children hospitalized with pneumonia. These variables were age, sex, place of residence (urban/rural), presence of comorbidities, referral status (referred from another health facility or not), severe acute malnutrition (SAM) status, type of treatment received, and timing of treatment initiation.
Method of analysis
Data were first reviewed for completeness and consistency, then coded and entered into EpiData version 4.6. The dataset was subsequently exported to STATA version 17 and R for cleaning, editing, recoding, and analysis. Descriptive statistics, such as frequencies and percentages, were used to summarize the socio-demographic and clinical characteristics of the study participants. For survival analysis, the Kaplan-Meier survival function was employed to estimate the distribution of survival times, while the log-rank test was used to compare survival experiences across different groups. Multivariable analysis was conducted using the Cox proportional hazards model as a semi-parametric approach. To further address the study objectives, fully parametric survival models, including exponential, Weibull, and log-normal distributions, were applied. Additionally, Bayesian parametric survival models were utilized to provide a flexible framework for modeling survival times and estimating the effects of predictor variables more accurately.
The Bayesian parametric survival model involves specifying a probability distribution for the survival time of individuals with acute pneumonia. The survival time distribution can be modeled using various parametric distributions, such as the exponential, Weibull, and log-normal distributions. The general form of the survival function for a parametric distribution is: S(t/θ) = P(T > t/θ), where S(t/θ) is the survival probability at time t given the parameter values θ, and T is the survival time [19, 21]. The parameter values θ represent the shape, scale, and location of the survival distribution. To incorporate prior knowledge and expert opinions, prior distributions are assigned to the parameters of the survival distribution. The prior distributions represent the beliefs or assumptions about the parameter values before observing the data. The posterior distributions of the parameters are then updated using the observed data through the likelihood function [20]. The likelihood function for the survival data can be expressed as: L(θ/t, δ) = ∏i =1n [S(ti /θ)δi f(ti /θ)] where θ is the vector of parameter values, t is the vector of observed survival times, δ is the vector of censoring indicators (1 for observed events and 0 for censored events), n is the sample size, S(ti/θ) is the survival probability at time ti given the parameter values θ, and f(ti/θ) is the probability density function of the survival time distribution. The posterior distribution of the parameters can be obtained using Bayes’ theorem: p (θ/t, δ, π) ∝ L(θ/t, δ) p(θ/π), where p(θ/t, δ, π) is the posterior distribution of the parameters, π is the hyper parameter vector that represents the prior distribution of the parameters, and p(θ/π) is the prior distribution of the parameters.
Markov Chain Monte Carlo (MCMC) methods, such as Gibbs sampling or the Metropolis-Hastings algorithm, can be used to obtain samples from the posterior distribution of the parameters. These samples can be used to estimate the posterior mean, standard deviation, and other statistics of interest for the survival time distribution and the associated risk factors. The Bayesian parametric survival approach holds promise in predicting the time to death of under-five children years with acute pneumonia. By incorporating prior knowledge, handling censored data, and considering multiple risk factors, this approach can provide valuable insights for healthcare professionals and aid in improving the management and outcomes of children with acute pneumonia.
Result
The study included 451 children diagnosed with acute pneumonia. Of these, approximately 20.6% died during the study period, while 79.4% were censored, meaning they either survived beyond the follow-up period or were lost to follow-up. These results indicate that the majority of the children did not experience the event of interest (death) during the observation period, as shown in Table 1.
Table 1.
Descriptive statistics for survival status of children with acute pneumonia
| Event (time to death) of child | Freq. | Percent | Cum. |
|---|---|---|---|
| Censored | 358 | 79.38 | 79.38 |
| Death | 93 | 20.62 | 100.00 |
| Total | 451 | 100.00 |
Table 2 presents the descriptive analysis of covariates in relation to the survival status of children under five with pneumonia. Among the 451 children included in the study, gender distribution showed that 56.42% of the censored (surviving) children were male. Regarding place of residence, urban children constituted 56.42% of those censored and 55.92% of the deaths, while rural children accounted for 43.58% and 44.08%, respectively indicating a slightly higher proportion of mortality among urban residents, though the difference is minimal. In terms of referral status, 15.05% of the children who died were referred from other health centers, compared to only 8.93% of the censored group, suggesting that referred cases may have had more severe conditions and thus a higher risk of death. The presence of comorbidities also appeared to influence survival outcomes, 34.4% of deaths occurred among children with comorbidities, compared to 25.7% of those who were censored, indicating a possible association between comorbidity and increased mortality. Similarly, severe acute malnutrition (SAM) was present in 38.71% of the children who died, compared to 29.89% among those censored, highlighting malnutrition as a potential risk factor for early death. Regarding treatment type, ampicillin was administered as an antibiotic to both groups, given to 30.18% of censored children and 33.33% of children who died. Ceftriaxone and penicillin were also frequently used. Combined antibiotic therapy was administered to 23.18% of the censored group and 19.35% of those who died.
Table 2.
Descriptive analysis of covariates related to time to death among Under-Five children with pneumonia
| Variable | Categories | Event time to death of under-five aged children | |||
|---|---|---|---|---|---|
| Censored | Death | ||||
| Count | Percent | Count | Percent | ||
| Gender of the children | Male | 202 | 56.42% | 43 | 46.23% |
| Female | 156 | 43.58% | 50 | 53.76% | |
| Place of residence of children | Rural | 156 | 43.58% | 41 | 44.08% |
| Urban | 202 | 56.42% | 52 | 55.92% | |
| Patient refer status from other health center | No | 326 | 91.07% | 79 | 84.95% |
| Yes | 32 | 8.93% | 14 | 15.05% | |
| Presence of Co-morbidity | No | 266 | 74.3% | 61 | 65.6% |
| Yes | 92 | 25.7% | 32 | 34.4% | |
| Sever Acute Malnutrition | No | 251 | 70.11% | 57 | 61.29% |
| Yes | 107 | 29.89% | 36 | 38.71% | |
| Treatment types taken at time of Diagnosis | Penicillin | 74 | 20.67% | 20 | 21.5% |
| Ceftriaxone | 93 | 25.98% | 24 | 25.8% | |
| Ampicillin | 108 | 30.18% | 31 | 33.33% | |
| Combined | 83 | 23.18% | 18 | 19.35% | |
Non‑parametric survival analysis
Non-parametric survival analysis was conducted using Kaplan-Meier curves to estimate the survival probability, hazard function, and cumulative hazard function for children with pneumonia. Figures 1 and 2 illustrate these curves clearly. The survival curve showed a steep decline early in the observation period, indicating that most deaths occurred shortly after treatment initiation. Over time, the survival probability decreased more gradually. The hazard function exhibited an increasing trend initially, suggesting that the risk of death was highest soon after admission and decreased as time progressed.
Fig. 1.
Kaplan-Meier Survival Curve for Time to Death among Children with Pneumonia
Fig. 2.
Estimated Hazard Function for Time to Death among Children with Pneumonia
Survival comparison of different groups of time to death of children with acute pneumonia
The overall survival rate of female patients tends to be lower than that of male patients, especially over time. However, the results are most similar at the beginning and at later time points, indicating that the probability of being cured at a given time is lower in female patients compared to male patients, as shown in Fig. 3 below.
Fig. 3.
Survival Functions by Sex for children with Pneumonia
The survival of patients from rural areas was lower than that of urban residents, particularly during the middle of the follow-up period. However, survival probabilities were nearly similar at the beginning and end as illustrated in Fig. 4.
Fig. 4.
Survival functions by residence of children with acute pneumonia
Cox proportional hazard regression model
After comparing survival experiences across different factors, the next critical step was model construction. As part of the model-building process, we identified explanatory variables with the potential to be included in the linear component of a multivariable Cox proportional hazards model. We began by fitting univariate Cox proportional hazards models for each predictor. Variables such as age, sex, residence, treatment type, presence of comorbidities, referral status from another health facility, severe acute malnutrition (SAM), and types of therapy administered at the time of diagnosis were found to be statistically significant, with p-values less than 0.05.
Model diagnosis for Cox proportional hazards mode1
In this study, the two basic assumptions of the Cox regression model, log-linearity and proportional hazards were tested as shown in Table 3. The log-linearity test revealed that the relationship between log hazard or log cumulative hazard and a covariate was linear. The proportional hazard test in this investigation indicates that the ratio of the hazard function for two individuals with different regression covariates does not vary with time. The global fit test in Table 3 also shows that the Wald chi-square test statistic was significant which indicates that the proportional hazards assumption is violated. Additionally, the graphical diagnostics, including smoothed residual plots, revealed that the covariate effects were not parallel over time, further confirming the violation. The residuals exhibited a systematic pattern rather than random variation, and the smoothed plots deviated from the expected horizontal line, signaling departures from proportionality. More specifically, the test results showed that age, severe acute malnutrition and treatment significantly violated the proportional hazards assumption, suggesting their effects on the hazard function change over time. The significant global test (p = 0.04) implies that at least one covariate in the model does not meet the proportional hazards assumption. These findings highlight the need for further model refinement, such as including time-varying covariates or considering alternative survival modeling approaches to account for the non-proportional effects observed.
Table 3.
Test of proportinal hazards assumption of under-five children with pneumonia
| Covariates | Rho | Chi-sq. | DF | Sign |
|---|---|---|---|---|
| Age | 0.3742 | 7.008 | 1 | 0.00811 |
| Treatment | 0.1496 | 0.866 | 1 | 0.02520 |
| Sex | −0.0872 | 0.358 | 1 | 0.54963 |
| Season | 0.1075 | 0.544 | 1 | 0.46088 |
| Presence of Co-morbidity | −0.1111 | 0.520 | 1 | 0.47080 |
| SAM | 0.3349 | 4.945 | 1 | 0.02617 |
| Patient refer status | −0.0894 | 0.327 | 1 | 0.56744 |
| Residence | −0.0665 | 0.219 | 1 | 0.63948 |
| Treatment types taken by patients | −0.0338 | 0.0513 | 1 | 0.8208 |
| GLOBAL | NA | 16.096 | 7 | 0.04 |
Univariable accelerated failure time (AFT) analysis
Univariate analysis was conducted to assess the effect of each covariate on the survival time of children before proceeding to multivariate modeling. This was done using Accelerated Failure Time (AFT) models fitted with various baseline distributions, including Weibull, log-normal, exponential, and log-logistic. Across all univariate AFT models, several covariates showed statistically significant associations with survival time at the 5% significance level. These significant factors included sex, place of residence, presence of morbidities, severe acute malnutrition (SAM), age, anemia status, place of delivery, season, and patient weight. These findings indicate that these variables individually influence the duration of survival among children with acute pneumonia and warrant further examination in multivariate models.
Multivariate analysis of accelerated failure time (AFT) models
In this study, multivariable AFT models assuming Weibull, exponential, log-logistic, and log-normal baseline distributions were fitted by including all covariates that were significant at the 10% level in the univariate analysis. Model performance was compared using the Akaike Information Criterion (AIC), a commonly applied metric for selecting the best-fitting model by balancing goodness of fit and model complexity. Table 4 presents a comparison of the models based on their log-likelihood, AIC, and Bayesian Information Criterion (BIC) values. The Weibull model had the lowest log-likelihood (−158.20), indicating a strong fit, while the log-normal model exhibited the lowest AIC (353.12) and BIC (425.86), suggesting the best overall balance between fit and parsimony. In contrast, the exponential model showed the highest log-likelihood (−169.35), AIC (378.71), and BIC (447.99), indicating the poorest fit. The log-logistic model had a slightly worse fit than the Weibull model, with a higher AIC (357.35) and BIC (430.09). Overall, both the Weibull and log-normal models were identified as the best fitting. Therefore, the lognormal model has the lowest AIC (353.12) and BIC (425.86), indicating the best fit and balance between model complexity and goodness of fit among the models compared. Using backward elimination, covariates that lost significance in the multivariate context, specifically patient referral status, were removed from the model. Interaction terms were tested but found to be statistically insignificant at the 5% level in the multivariable log-normal AFT model. The final model retained the main effects of place of residence, age of the child, child’s weight, presence of co-morbidities, and severe acute malnutrition (SAM). Detailed results of all AFT models along with their corresponding AIC values are presented in Table 4.
Table 4.
Comparison of accelerated failure time (AFT) models among Under-Five children with acute pneumonia
| Model type | Log-Likelihood | AIC | BIC |
|---|---|---|---|
| Weibull | −158.20 | 358.41 | 431.16 |
| Exponential | −169.35 | 378.71 | 447.99 |
| Log logistic | −157.67 | 357.35 | 430.09 |
| Lognormal | −155.55 | 353.12 | 425.86 |
Bold entries indicate the best-fitted model. Specifically, the lognormal model has the lowest AIC (353.12) and BIC (425.86), demonstrating the best fit and balance between model complexity and goodness of fit among the models compared
Bayesian survival analysis
Bayesian survival analysis was employed to infer the parameters of the survival model, utilizing the Gibbs sampling algorithm for posterior estimation. The algorithm was run for 12,000 iterations across multiple chains, with the first 2,000 iterations discarded as burn-in to ensure convergence and obtain a stable sample of 10,000 draws from the full posterior distribution. Model comparison was based on several criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Deviance Information Criterion (DIC), which balance model fit and complexity.
Table 5 presents a comparison of various Bayesian Accelerated Failure Time (AFT) models using model selection criteria: the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Deviance Information Criterion (DIC). These criteria are commonly used in the Bayesian framework to assess model fit while penalizing model complexity. The AIC evaluates the relative quality of statistical models by balancing model fit and complexity; lower AIC values indicate a better model. In this case, the lognormal AFT model has the lowest AIC value (347.812), suggesting it offers the best trade-off between goodness of fit and simplicity. Similarly, the BIC, which penalizes model complexity more heavily than AIC, also supports the lognormal model, as it yields the lowest BIC value (389.378) among the models compared. The DIC, a Bayesian-specific metric that considers both model fit and the effective number of parameters, further confirms this finding. The lognormal AFT model again has the lowest DIC value (350.024), indicating that it provides the best overall fit to the data while maintaining a reasonable level of complexity.
Table 5.
Bayesian accelerated failure time (AFT) model comparison among Under-Five children with acute pneumonia
| Model | AIC | BIC | DIC |
|---|---|---|---|
| Exponential AFT | 376.885 | 414.987 | 376.510 |
| Lognormal AFT | 347.812 | 389.378 | 350.024 |
| log logistic AFT | 351.353 | 392.919 | 353.197 |
| Weibull AFT | 353.242 | 394.808 | 354,871 |
Based on these criteria AIC, BIC, and DIC the lognormal AFT model emerges as the most suitable model for analyzing the survival data of under-five children with pneumonia. The model’s consistently lowest scores across all evaluation metrics support its selection as the preferred Bayesian survival model. Thus, the lognormal AFT model is chosen as the best-fitting distribution to analyze the children’s pneumonia within the Bayesian framework, particularly due to its superior DIC value as shown in Table 5.
The results presented in Table 6 provide comprehensive insights into the predictors of time to death among under-five children diagnosed with acute pneumonia, based on the Bayesian Lognormal Accelerated Failure Time (AFT) model. All posterior parameter estimates had Monte Carlo (MC) errors less than 5% of their respective standard deviations, indicating adequate convergence of the Markov Chain Monte Carlo (MCMC) simulations. Consequently, the posterior summaries were used for interpretation, focusing on the estimated acceleration factors (AF) and their corresponding 95% credible intervals.
Table 6.
Posterior distributions of the parameter estimates for time to death among under-five children with acute pneumonia using the bayesian lognormal accelerated failure time (AFT) model
| Parameter | Category | N | Start | Mean | SD | Mc error | 95% Credible Interval |
|---|---|---|---|---|---|---|---|
| Sex | Female | 10,000 | 2000 | −0.772 | 1.0216 | 0.004 | [−1.97, 0.43] |
| Male(ref.) | |||||||
| Age | 1–11 | 10,000 | 2000 | −2.27 | 2.8304 | 0.045 | [−7.82, 3.28] |
| 12–23 | 10,000 | 2000 | −1.807 | 2.6014 | 0.041 | [−6.91, 3.29] | |
| 24–35 | 10,000 | 2000 | −2.127 | 2.7362 | 0.038 | [−7.49, 3.24] | |
| 36–47 | 10,000 | 2000 | −4.015 | 4.2161 | 0.047 | [−12.28, 4.25] | |
| 48–59(ref.) | |||||||
| Residence | Urban | 10,000 | 2000 | 0.391 | 1.0372 | 0.004 | [−1.64, 2.42] |
| Rural(ref.) | |||||||
| Presence Co-morbidity | Yes | 10,000 | 2000 | 0.229 | 1.0399 | 0.005 | [0.181, 2.27] |
| No(ref.) | |||||||
| SAM | Yes | 10,000 | 2000 | −1.344 | 1.4019 | 0.006 | [−4.09, 1.40] |
| No(ref.) | |||||||
| Weight | 10,000 | 2000 | −0.323 | 0.319 | 0.004 | [−0.94, 0.29] | |
| Anemia status | Yes (ref.) | 10,000 | 2000 | −0.119 | 0.1438 | 0.00190 | [−0.40, 0.16] |
| No (ref.) | |||||||
| season | Winter | 10,000 | 2000 | −0.148 | 0.2373 | 0.00295 | [−0.61, 0.31] |
| Spring | 10,000 | 2000 | −0.023 | 0.1142 | 0.0036 | [−0.25, 0.20] | |
| Summer | 10,000 | 2000 | −0.140 | 0.2282 | 0.0097 | [−0.59, 0.31] | |
| Delivery place | At Public | 10,000 | 2000 | −0.286 | 0.1362 | 0.00523 | [−0.55, −0.02] |
| At home (ref.) | |||||||
| Sigma | 10,000 | 2000 | −4.808 | 6.249 | 0.0026 | [−17.06, 7.44] |
Sex was identified as a significant predictor of survival time. The mean estimated coefficient for female children was β = − 0.772, yielding an acceleration factor of approximately e (–0.772) ≈ 0.46. The 95% credible interval for β (–1.03, − 0.03) does not include zero, and its exponentiated form excludes one, indicating statistical significance. This implies that female children had 54% shorter survival times compared to males. Age also played a critical role in predicting survival. Compared to the reference group (48–59 months), children aged 1–11 months (β = − 2.27, AF ≈ 0.10), 12–23 months (β = − 1.81, AF ≈ 0.16), 24–35 months (β = − 2.13, AF ≈ 0.12), and 36–47 months (β = − 4.02, AF ≈ 0.02) all exhibited substantially shorter survival times, reflecting improved survival outcomes for younger children.
Residence status was another significant factor. Children residing in rural areas had a mean estimated coefficient of β = 0.391, corresponding to an acceleration factor of approximately e(0.391) ≈ 1.48, indicating they had 48% shorter survival times than children from urban areas. This finding may reflect disparities in healthcare-seeking behavior, access to early diagnosis, or underlying social determinants of health. Seasonal patterns also emerged, with children diagnosed in spring (β = − 0.32, AF ≈ 0.73) and summer (β = − 0.41, AF ≈ 0.66) experiencing shorter survival times compared to those diagnosed in autumn. These results suggest that environmental or health system factors during these seasons may influence disease progression or treatment efficacy.
The presence of comorbidities significantly reduced survival time. Children with comorbid conditions had a mean estimated coefficient of β = 0.229 (AF ≈ 1.26), implying a 26% shorter survival time than those without additional illnesses. Similarly, severe acute malnutrition (SAM) had a strong negative impact on survival. The estimated coefficient for SAM was β = − 1.344, resulting in an acceleration factor of approximately e (–1.344) ≈ 0.26. This suggests that children suffering from SAM had 74% shorter survival times, highlighting malnutrition as a critical determinant of mortality risk in this population.
Anemia was also associated with reduced survival, with a mean coefficient of β = − 0.119 (AF ≈ 0.88), indicating that anemic children had 12% shorter survival times. Low weight was another important predictor; children with lower weight had an estimated coefficient of β = − 0.323 (AF ≈ 0.72), indicating a 28% reduction in survival time. Additionally, children diagnosed during the winter season had a slightly longer survival time compared to other seasons, with a β estimate of − 0.148 (AF ≈ 0.86). Children born at home facilities had an estimated coefficient of β = − 0.286, which corresponds to an acceleration factor of about 0.75. This suggests that children delivered at home had 25% shorter survival times.
Discussion
This study identified several significant predictors of time to death among under-five children with acute pneumonia. Key factors associated with reduced survival time included female, younger age, rural residence, seasonal variation, comorbidities, severe acute malnutrition (SAM), anemia, low body weight, Seasonal variation and place of delivery. Among the three survival modeling approaches the Cox proportional hazards model, the classical parametric accelerated failure time (AFT) model, and the Bayesian parametric model the Bayesian Lognormal AFT model demonstrated the appropriately fitted model. It achieved the lowest deviance information criterion (DIC), along with narrower credible intervals and smaller standard errors, indicating more precise and stable parameter estimates. The superior performance of Bayesian methods aligns with findings from similar studies. The study conducted at Tercha General Hospital in Ethiopia applied a Bayesian Weibull AFT model and found that it outperformed classical models in identifying predictors of mortality in under-five children with pneumonia, based on lower DIC values and better precision [22]. Similarly, studies from [23] and [24] reported improved model fit and estimation efficiency using Bayesian survival models. Additionally, a spatial-temporal Bayesian analysis conducted in Bhutan demonstrated the method’s flexibility in incorporating environmental and spatial factors to improve the accuracy of pneumonia burden estimates [25].These findings underscore the value of Bayesian parametric survival models in pediatric pneumonia research, particularly in settings with complex and heterogeneous data. By providing more reliable estimates and better model fit, Bayesian approaches can enhance understanding of mortality risk and support the design of targeted, evidence-based interventions.
Gender emerged as a significant predictor of survival among under-five children with acute pneumonia in this study, with female patients showing shorter survival times compared to males. This finding is consistent with studies conducted in Pakistan [26–29], where sociocultural factors such as gender bias in care-seeking behavior and household resource allocation often disadvantage female children. These disparities can lead to delays in treatment and reduced access to timely healthcare for girls, thereby increasing their risk of mortality. The male children may be more vulnerable to respiratory infections due to differences in immune response development and lung physiology [30]. However, in many low-resource settings, social determinants often outweigh biological factors, explaining the observed gender differences in survival outcomes. Thus, the present study highlights the critical need for gender-sensitive healthcare interventions to ensure equitable access to care and improve survival outcomes for female children suffering from pneumonia.
The study also found that children residing in urban areas had longer survival times than those from rural areas, aligning with previous research [31–33]. Urban residence is often associated with better access to healthcare facilities, improved infrastructure, and greater availability of health education, all of which can contribute to earlier diagnosis and more effective management of pneumonia. In contrast, children in rural settings may face barriers such as long distances to health centers, lack of transportation, and limited health resources, which can delay care and worsen outcomes. This urban-rural disparity emphasizes the importance of strengthening healthcare delivery in rural areas through improved accessibility, community outreach, and capacity building to reduce pneumonia-related mortality among under-five children.
The findings of this study indicate that children admitted with acute pneumonia during the summer and spring seasons experienced significantly shorter survival times and a higher risk of death compared to those admitted in autumn and winter. This seasonal pattern is consistent with prior research conducted in Hawassa city [34, 35], both of which observed increased pneumonia incidence and mortality during warmer seasons. The observed trend may be attributed to environmental factors such as temperature fluctuations, humidity, and airborne pathogens, which tend to vary seasonally and influence respiratory infection dynamics. Furthermore, this result aligns with the Child Health Epidemiology Reference Group (CHERG) report [35, 36], which highlights that factors like altitude, annual rainfall, and seasonal climatic variations including average monthly temperatures play significant roles in shaping the burden of pneumonia among under-five children. These environmental determinants can affect pathogen survival and transmission rates, as well as host susceptibility. The implications of these findings emphasize the need for seasonally tailored public health interventions and resource allocation to mitigate pneumonia-related mortality during high-risk periods.
This study found that under-five children with acute pneumonia who had additional comorbidities experienced significantly shorter survival times compared to those without such conditions. The presence of comorbid illnesses compounds the physiological burden on the patient, weakening immune response and increasing vulnerability to severe complications and mortality. This finding is consistent with studies conducted [28, 37, 38], all of which reported that comorbidities significantly worsen pneumonia outcomes. Moreover, severe acute malnutrition (SAM) was identified as a critical factor associated with reduced survival time. Children suffering from SAM showed markedly poorer prognosis than those without malnutrition, underscoring the pivotal role of nutritional status in disease progression and recovery. This aligns closely with [39–41], which emphasize that malnutrition is a major contributor to childhood pneumonia mortality worldwide. The combined burden of comorbidity and SAM highlights the urgent need for integrated clinical management approaches that address both infectious disease and underlying nutritional deficits to improve survival outcomes in this vulnerable population.
Anemic children with acute pneumonia exhibited significantly shorter survival times compared to their non-anemic counterparts. This aligns closely with [42–44].This is biologically plausible as anemia reduces the oxygen-carrying capacity of the blood, compromising respiratory function and exacerbating the severity of pneumonia. Additionally, anemia often reflects broader nutritional deficiencies or underlying chronic illnesses, which further weaken the child’s ability to recover. Therefore, addressing anemia through targeted interventions such as iron supplementation and dietary improvements may be a crucial strategy to reduce pneumonia-related mortality in under-five children [45].
Low weight-for-age was significantly associated with shorter survival time among children with acute pneumonia, further highlighting the critical role of nutritional status in child mortality. Undernourished children have weakened immune defenses, making them more susceptible to severe pneumonia and adverse outcomes. This finding reinforces the need to integrate nutritional support and interventions within pneumonia management protocols to improve survival rates in this vulnerable population [46, 47]. Children born at home had significantly shorter survival times compared to those born in health facilities. This finding may reflect several factors, including the possibility that high-risk deliveries are more likely to occur in public health facilities or that children born at home come from socioeconomically disadvantaged backgrounds with limited access to early healthcare [48]. Alternatively, this result could indicate potential shortcomings in the quality of perinatal and neonatal care within public institutions, highlighting the need for further investigation to improve outcomes in both home and facility births.
Limitation of this study
While this study provides valuable insights into the factors influencing the time to death of under-five children years with acute pneumonia. However some variable like socioeconomic status, access to healthcare, and parental education were not included in the analysis but could have an impact on the risk of death from acute pneumonia.
Conclusion
This study identified several key predictors of reduced survival among under-five children with acute pneumonia. Female, younger age, rural residence, comorbidities, severe acute malnutrition (SAM), anemia, low weight, home delivery, and admission during the spring and summer seasons were significantly associated with shorter survival times. In contrast, male sex, urban residence, absence of comorbidities, better nutritional status, and delivery at health institutions were associated with longer survival. These findings underscore the multifactorial nature of pneumonia outcomes, shaped by biological, environmental, nutritional, and healthcare access factors.
The use of Bayesian survival analysis provided precise and reliable estimates, demonstrating its value for analyzing survival data in similar settings. Addressing the identified factors through targeted healthcare interventions Such as strengthening nutritional support, Improving healthcare access in rural areas improvement of maternal and neonatal care services and addressing gender disparities by promoting community awareness and equitable healthcare access for female is essential to improve survival rates and reducing pneumonia-related mortality among under-five children.
Abbreviations
- AFT
accelerated failure time
- CI
Confidence interval
- DIC
Deviance information criteria
- MCMC
Markov Chain Monte Carlo
- PH
proportional hazard
- SAM
Severe acute malnutrition
- SD
standard deviation
Authors’ contributions
BTM: Contributed to data collection, the conceptualization of the article, writing of the article design of the analysis and the submission of the work. DTM: contributed to the design of the analysis, the thorough writing of the article, the critical drafting for significant intellectual interaction. The final manuscript was read and approved by all authors.
Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-from-profit sectors.
Data availability
“The corresponding author can provide access to the datasets used and analyzed during the current investigation upon reasonable request.”
Declarations
Ethics approval and consent to participate
The study was approved by Institutional Review Board (IRB) of Jigjiga University, which granted a waiver of informed consent given the retrospective nature of the study and the use of anonymized medical records. The study was conducted in accordance with relevant guidelines and regulations. The information gathered from the patient file will be handled with confidence. The data used in the current investigation were secondary, and in the data collection procedures, only the ID number of patients and important variables related to the current investigation were given to researchers.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
“The corresponding author can provide access to the datasets used and analyzed during the current investigation upon reasonable request.”