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 death and its determinants among under-five children in Sub-Saharan Africa using the recent (2010–2018) demographic and health survey data: country-based shared frailty analyses

Background Substantial global progress has been made in reducing under-five mortality since 1990, yet progress is insufficient to meet the sustainable development goal of 2030 which calls for ending preventable child deaths. There are disproportional survivals among children in the world. Therefore, the study aimed to assess the Survival status of under-five mortality and determinants in Sub-Saharan African Countries using the recent DHS data. Methods The data was retrieved from the birth record file from the standard Demographic and Health Survey dataset of Sub-Saharan Africa countries. Countries that have at least one survey between 2010 and 2018 were retrieved. Parametric shared frailty survival analysis was employed. Results A total of 27,221 (7.35%) children were died before celebrating their fifth birthday. Children at an early age were at higher risk of dying and then decrease proportionally with increased age. The risk of death among rich and middle family were lowered by 18 and 8% (AHR =0.82, 95% CI: 0.77-0.87) and (AHR = 0.92, 95% CI: 0.87-0.97) respectively, the hazard of death were 11, 19, 17, 90 and 55% (AHR = 1.06, 95% CI: 1.00-1.12), (AHR = 1.11,95%CI:1.04-1.19), (AHR = 1.17, 95% CI:1.12-1.23), (AHR = 1.90, 95%CI: 1.78-2.04) and (AHR = 1.55, 95% CI:1.47-1.63) higher than among children in rural, use unimproved water, delivered at home, born less than 18 months and between 18 and 23 months birth intervals respectively. The hazard of death was 7% among females and low birth weights (AHR = 0.93, 95%CI: 0.90 – 0.97) and (AHR = 0.93 95%CI: 0.89-0.97) respectively. There was also a significant association between multiple births and birth orders (AHR = 2.11, 95%CI: 2.51 – 2.90), (AHR = 3.01, 95%CI: 2.85-3.19) respectively. Conclusions Death rate among under-five children was higher at an early age then decreases as age advanced. Wealth status, residence, water source, place of delivery, sex of the child, plurality, birth size, preceding birth interval, and birth order were the most predictor variables. The health care program should be designed to encourage a healthy family structure. The health care providers should intervene in the community to inspire maternal health services.

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.

Time to death and its associated factors among infants in sub-Saharan Africa using the recent demographic and health surveys: shared frailty survival analysis

Background Globally, approximately 4.1 million infants died, accounting for 75% of all under-five deaths. In sub-Saharan Africa (SSA), infant mortality was 52.7/1000 live births in 2018 This study aimed to assess the pooled estimate of infant mortality rate (IMR), time to death, and its associated factors in SSA using the recent demographic and health survey dataset between 2010 and 2018. Methods Data were retrieved from the standard demographic and health survey datasets among 33 SSA countries. A total of 93,765 samples were included. The data were cleaned using Microsoft Excel and STATA software. Data analysis was done using R and STATA software. Parametric shared frailty survival analysis was employed. Statistical significance was declared as a two-side P-value < 0.05. Results The pooled estimate of IMR in SSA was 51 per 1000 live births (95% Confidence Interval (CI): 46.65–55.21). The pooled estimate of the IMR was 53 in Central, 44 in Eastern, 44 in Southern, and 57 in Western Africa per 1000 live births. The cumulative survival probability at the end of 1 year was 56%. Multiple births (Adjusted Hazard ratio (AHR) = 2.68, 95% CI: 2.54–2.82), low birth weight infants (AHR = 1.28, 95% CI: 1.22–1.34), teenage pregnancy (AHR = 1.19, 95 CI: 1.10–1.29), preceding birth interval < 18 months (AHR = 3.27, 95% CI: 3.10–3.45), birth order ≥ four (AHR = 1.14, 95% CI:1.10–1.19), home delivery (AHR = 1.08, 95% CI: 1.04–1.13), and unimproved water source (AHR = 1.07, 95% CI: 1.01–1.13), female sex (AHR = 0.86, 95% CI: 0.83–0.89), immediately breastfeed (AHR = 0.24, 95% CI: 0.23–0.25), and educated mother (AHR = 0.88, 95% CI: 0.82–0. 95) and educated father (AHR = 0.90, 95% CI: 0.85–0.96) were statistically significant factors for infant mortality. Conclusion Significant number of infants died in SSA. The most common cause of infant death is a preventable bio-demographic factor. To reduce infant mortality in the region, policymakers and other stakeholders should pay attention to preventable bio-demographic risk factors, enhance women education and improved water sources.

Continued Adherence to Community-Based Health Insurance Scheme in Two Districts of Northeast Ethiopia: Application of Accelerated Failure Time Shared Frailty Models

Background: The sustainability of a voluntary community-based health insurance scheme depends to a greater extent on its ability to retain members. In low- and middle-income countries, high rate of member dropout has been a great concern for such schemes. Although few studies had investigated the factors influencing dropout decisions, none of these looked into how long and why members adhere to the scheme. The purpose of this study was to determine the factors affecting time to drop out while accounting for the influence of cluster-level variables. Methods: A community-based cross-sectional study was conducted among 1232 rural households who have ever been enrolled in two community-based health insurance schemes. A household survey was conducted using a mobile data collection platform. The Kaplan-Meier estimates were used to compare the time to drop out among subgroups. To identify predictors of time to drop out, a multivariable analysis was done using the accelerated failure time shared frailty models. The degree of association was assessed using the acceleration factor (δ) and statistical significance was determined at 95% confidence interval. Results: Results of the multivariable analysis revealed that marital status of the respondents (δ=1.614; 95% CI: 1.221–2.134), household size (δ=1.167; 95% CI: 1.012–1.344), presence of chronic illness (δ=1.421; 95% CI: 1.163–1.736), hospitalization history (δ=1.308; 95% CI: 1.120–1.529), higher perceived quality of care (δ=1.323; 95% CI: 1.101–1.589), perceived risk protection (δ=1.220; 95% CI: 1.029–1.446), and higher trust in the scheme (δ=1.729; 95% CI: 1.428–2.095) were significant predictors of time to drop out at p-value < 0.05. Conclusions: The study identified evidence suggestive of adverse selection in the schemes. The fact that larger households remain in the scheme indicates the need to reconsider the premium level in line with household size to attract small size households. Issues that are under the control of the scheme and the healthcare system can be adjusted to increase membership adherence. Resolving problems related to the quality of health care can be a cross-cutting area of ​​intervention to retain members by building trust in the scheme and enhancing the risk protection ability of the schemes.

Generalized Lindley Shared Frailty Based on Reversed Hazard Rate

Due to the unavailability of complete data in various circumstances in biological, epidemiological, and medical studies, the analysis of censored data is very common among practitioners. But the analysis of bivariate censored data is not a regular mechanism because it is not necessary to always have independent data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in the data. Ignoring observed and unobserved covariates may have objectionable consequences. But it is not easy to find that whether there is any effect of the unobserved covariate or not. Shared frailty models are the viable choice to counter such scenarios. However, due to certain restrictions such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty distribution generalized Lindley (GL) for reversed hazard rate (RHR) setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under the RHR setup. By assuming exponential Gumbel (EG) and generalized inverted exponential (GIE) baseline distributions, we propose a new class of shared frailty models based on RHR. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been performed for the comparison of models. We analyze Australian twin data and suggest a better model.

A retrospective clinical study on the resin infiltration of proximal caries lesions: the operator’s effect

Purpose This retrospective university-based study investigated the effect of operators’ training and previous experience on the success of resin infiltration (RI) in arresting proximal non-cavitated caries lesions in primary and permanent teeth. Methods Information was collected regarding RI of proximal non-cavitated caries lesions in primary and permanent teeth with a follow-up period up to 32 months. Factors investigated were: operators’ clinical experience and training, patient’s age, tooth, arch, mouth-side, surface treated, tooth separation, and baseline lesion depth. Kaplan–Meier survival and Cox regression analysis with shared frailty were used (α = 5%). Results A total of 130 proximal surfaces treated on 115 teeth of 43 children (11 ± 4.4 years) were evaluated. Survival of RI was 46% up to 32 months. Lesions treated by non-trained dentists were more likely-to-present progression than those performed by non-trained dental students under supervision (HR 2.41, 95% CI: 1.00–5.80); conversely, no difference was found between non-trained dental students under supervision and trained dentists (HR 0.52, 95% CI: 0.16–1.70). Additionally, dentin lesions were 59% more-likely-to-present progression than enamel lesions (HR 0.41, 95% CI: 0.17–0.99). Conclusion The operator’s experience and training could influence the success of RI on proximal non-cavitated caries lesions and it should be taken into consideration when choosing this treatment modality.

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.