K-means for shared frailty models

Background The purpose of this research was to see how the k-means algorithm can be applied to survival analysis with single events per subject for defining groups, which can then be modeled in a shared frailty model to further allow the capturing the unmeasured confounding not already explained by the covariates in the model. Methods For this purpose we developed our own k-means survival grouping algorithm to handle this approach. We compared a regular shared frailty model with a regular grouping variable and a shared frailty model with a k-means grouping variable in simulations as well as analysis on a real dataset. Results We found that in both simulations as well as real data showed that our k-means clustering is no different than the typical frailty clustering even under different situations of varied case rates and censoring. It appeared our k-means algorithm could be a trustworthy mechanism of creating groups from data when no grouping term exists for including in a frailty term in a survival model or comparing to an existing grouping variable available in the current data to use in a frailty model.

Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model

Bayesian paradigm takes advantage of well-fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this chapter, we aim to display the latest tendency in Bayesian computing, in the sense of automating the posterior sampling, through a Bayesian analysis of survival modeling for multivariate survival outcomes with the complicated data structure. Motivated by relaxing the strong assumption of proportionality and the restriction of a common baseline population, we propose a generalized shared frailty model which includes both parametric and nonparametric frailty random effects to incorporate both treatment-wise and temporal variation for multiple events. We develop a survival-function version of the ANOVA dependent Dirichlet process to model the dependency among the baseline survival functions. The posterior sampling is implemented by the No-U-Turn sampler in Stan, a contemporary Bayesian computing tool, automatically. The proposed model is validated by analysis of the bladder cancer recurrences data. The estimation is consistent with existing results. Our model and Bayesian inference provide evidence that the Bayesian paradigm fosters complex modeling and feasible computing in survival analysis, and Stan relaxes the posterior inference.

Time to first antenatal care visit among pregnant women in Ethiopia: secondary analysis of EDHS 2016; application of AFT shared frailty models

Background The survival of pregnant women is one of great interest of the world and especially to a developing country like Ethiopia which had the highest maternal mortality ratios in the world due to low utilization of maternal health services including antenatal care (ANC). Survival analysis is a statistical method for data analysis where the outcome variable of interest is the time to occurrence of an event. This study demonstrates the applications of the Accelerated Failure Time (AFT) model with gamma and inverse Gaussian frailty distributions to estimate the effect of different factors on time to first ANC visit of pregnant women in Ethiopia. Methods This study was conducted by using 2016 EDHS data about factors associated with the time to first ANC visit of pregnant women in Ethiopia. A total of 4328 women from nine regions and two city administrations whose age group between 15 and 49 years were included in the study AFT models with gamma and inverse Gaussian frailty distributions have been compared using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to select the best model. Results The factors residence, media exposure, wealth index, education level of women, education level of husband and husband occupation are found to be statistically significant (P-value < 0.05) for the survival time of time to first ANC visit of pregnant women in Ethiopia. Inverse Gaussian shared frailty model with Weibull as baseline distribution is found to be the best model for the time to first ANC visit of pregnant women in Ethiopia. The model also reflected there is strong evidence of the high degree of heterogeneity between regions of pregnant women for the time to first ANC visit. Conclusion The median time of the first ANC visit for pregnant women was 5 months. From different candidate models, Inverse Gaussian shared frailty model with Weibull baseline is an appropriate approach for analyzing time to first ANC visit of pregnant women data than without frailty model. It is essential that maternal and child health policies and strategies better target women’s development and design and implement interventions aimed at increasing the timely activation of prenatal care by pregnant women. The researchers also recommend using more powerful designs (such as cohorts) for the research to establish timeliness and reduce death.

Determinants of Time-to-recovery from Hypertension using a Comparison of Various Parametric Shared Frailty Models: In Case of Felege Hiwot Refral Hospital.

Background: Hypertension is a major public health problem that is responsible for morbidity and mortality. In Ethiopia hypertension is becoming a double burden due to urbanization. The study aimed to identify factors that affect time-to-recovery from hypertension at Felege Hiwot Referral Hospital. Retrospective study design was used at FHRH. Methods: The data was collected in patient’s chart from September 2016 to January 2018. Kaplan-Meier survival estimate and Log-Rank test were used to compare the survival time. The AFT and parametric shared frailty models were employed to identify factors associated with the recovery time of hypertension patients. All the fitted models were compared by using AIC and BIC. Results: Eighty one percent of sampled patients were recovered to normal condition and nineteen percent of patients were censored observations. The median survival time of hypertensive patients to attain normal condition was 13 months. Weibull- inverse Gaussian shared frailty model was found to be the best model for predicting recovery time of hypertension patients. The unobserved heterogeneity in residences as estimated by the Weibull-Inverse Gaussian shared frailty model was θ=0.385 (p-value=0.00). Conclusion: The final model showed that age, systolic blood pressure, related disease, creantine, blood urea nitrogen and the interaction between blood urea nitrogen and age were the determinants factors of recovery status of patients at 5% level of significance. The result showed that patients creantine >1.5 Mg/dl compared to creantine ≤1.5 Mg/dl and SBP were prolonged the recovery time of patients whereas patients having kidney disease, other disease and had no any disease compared to diabetic patients and the interaction BUN and age were shorten recovery status of hypertension patients.

Time to early initiation of postnatal care service utilization and its predictors among women who gave births in the last 2 years in Ethiopia: a shared frailty model

Background Most maternal and infant deaths occurred within the first month after birth. Nearly half of the maternal deaths and more than a million newborn deaths occurred within the first day of life but these were preventable through early initiation of postnatal care (PNC) services. However, the available evidence on the level of early initiation of PNC service utilization was not adequate to inform policy decisions. Therefore, this study aimed to assess time to early initiation of postnatal care and its predictors using the 2016 Ethiopian Demography and Health Survey (EDHS) datasets. Methods Two-stage stratified cluster sampling technique by separating each region into urban and rural areas. A total weighted sample of 6364 women of the 2016 EDHS datasets who gave birth within 2 years preceding the survey was used. Time to early initiation of the PNC visit was estimated using the Kaplan-Meier (K-M) method. Shared frailty model with baseline distributions (Weibull, Gompertz, exponential, log-logistic, and lognormal) and frailty distributions (gamma and inverse Gaussian) were used by taking enumeration areas/clusters as a random effect for predictors of time to early initiation of PNC visit. The adjusted hazard ratio (AHR) with a 95% confidence interval (CI) and p-value less than 0.05 were used to declare the significant predictor variables for time to early initiation of the PNC service utilization. Results The prevalence of women who utilized PNC services within 42 days was 13.27% (95% CI, 12.46, 14.13). Among these women, only 1.73% of them had got within the first 24 h of birth; 4.66% of them received within 48–72 h and 1.74% of them also had got within 7–14 days. Variables, such as parity (AHR = 1.61, 95% CI: 1.21, 2.15), media exposure (AHR = 1.42, 95% CI: 1.21, 1.68), place of delivery (AHR = 14.36, 95% CI: 11.76, 17.53), caesarean delivery (AHR = 2.17, 95% CI: 1.60, 2.95) and antenatal care visit (AHR = 2.07, 95% CI: 1.63, 2.63) had the higher hazard for PNC services utilization. On the other hand, women who faced with healthcare access problems (AHR = 0.74, 95% CI: 0.60, 0.87) had a lower hazard of PNC service utilization. Conclusion The overall postnatal care service utilization among women in the survey was low, particularly within the first 24 h of delivery. Policy-makers and implementers should promote the utilization of antenatal care and institutional delivery using mass media to increase the continuum of maternity care. The government should also design a new approach to enhance the uptake of postnatal care services for poor households and to scale up the PNC services, including the different possibilities for women who give births at the health facilities and homes. Future researchers had better assess the capacity and accessibility of the local health systems, the level of decentralized decision making, common cultural practices, knowledge, attitude, and perception of mothers towards PNC service utilization.

Time to first birth and its predictors among reproductive-age women in Ethiopia: inverse Weibull gamma shared frailty model

Background High maternal and child death with high fertility rate have been reported in Ethiopia. Extreme age at first birth is linked with both maternal and child morbidity and mortality. However, literatures showed there were limited studies on the timing of the first birth and its predictors in the area so far. Therefore, determining the time to first birth and its predictors will help to design strategies to improve maternal and child survival. Methods A community-based cross-sectional study was conducted among reproductive-age women in Ethiopia using the Ethiopian demographic health survey, 2016 data. Stratified two-stage cluster sampling technique was used for sampling. The Kaplan–Meier method was used to estimate time to first birth. Inverse Weibull gamma shared frailty model applied to model the data at 95% confidence interval (CI), adjusted hazard ratio (AHR) and median hazard ratio (MHR) were reported as effect size. Proportional hazard assumption checked using Schoenfeld residual test. Information Criteria were applied to select a parsimonious model. Stratified analysis performed for the interaction terms and statistical significance was declared at p value < 0.05. Results The overall median age at first birth was found to be 20 years (IQR, 16–24 years). The independent predictors of time to first birth were: married 15–17 years (AHR = 2.33, 95% CI 2.08–2.63), secondary education level (AHR = 0.84, 95% CI 0.78–0.96), higher education level (AHR = 0.75, 95% CI 0.65–0.85), intercourse before 15 years in the married stratum (AHR = 23.81, 95% CI 22.22–25.64), intercourse 15–17 years in married stratum (AHR = 5.56, 95% CI 5.26–5.88), spousal age difference (AHR = 1.11, 95% CI 1.05–1.16),and use of contraceptives (AHR = 0.91, 95% CI 0.86–0.97). The median increase in the hazard of early childbirth in a cluster with higher early childbirth is 16% (MHR = 1.16, 95% CI 1.13–1.20) than low risk clusters adjusting for other factors. Conclusion In this study, first birth was found to be at an early age. Early age at first marriage, at first sexual intercourse and their interaction, high spousal age difference, being Muslim were found to increase early motherhood. Conversely, living in the most urban region, secondary and higher women education were identified to delay the first birth. Investing on women education and protecting them from early marriage is required to optimize time to first birth. The contextual differences in time to first birth are an important finding which requires more study and interventions.

Modeling the Determinants of Time-to-Premarital Cohabitation among Women of Ethiopia: A Comparison of Various Parametric Shared Frailty Models

Background: Premarital cohabitation is defined as the state of living together and having a sexual relationship without being married. It has become more prevalent globally in recent decades. The main objective of this study was modeling the potential risk factors of time-to-premarital cohabitation among women of Ethiopia by using parametric shared frailty models where regional states of the women were used as a clustering effect in the models.Methods: The data source for the analysis was the 2016 EDHS data. The Gamma and Inverse-Gaussian shared frailty distributions with Exponential, Weibull, Log-logistic and Lognormal baseline models were employed to analyze risk factors associated with age at premarital cohabitation. All the fitted models were compared by using AIC values.Results: The median age of women at premarital cohabitation was 18 years. Based on AIC values, Log-logistic-Gamma shared frailty model has smallest AIC value among the models compared. The clustering effect was significant for modeling the determinants of time-to-premarital cohabitation dataset. The results showed that women’s education status, occupation, pregnancy and place of residence were found to be the most significant determinants of age at premarital cohabitation whereas wealth status and religion were not significant at 5% level.Conclusions: The Log-logistic-Gamma shared frailty model described the premarital cohabitation dataset better than other distributions used in this study. There is heterogeneity between the regions of women. Further studies should be conducted to identify other factors of age at premarital cohabitation of women in Ethiopia that were not included in this study.