Left-censored recurrent event analysis in epidemiological studies: a proposal for when the number of previous episodes is unknown

Background When dealing with recurrent events in observational studies it is common to include subjects who became at risk before follow-up. This phenomenon is known as left censoring, and simply ignoring these prior episodes can lead to biased and inefficient estimates. We aimed to propose a statistical method that performs well in this setting. Methods Our proposal was based on the use of models with specific baseline hazards. In this, the number of prior episodes were imputed when unknown and stratified according to whether the subject had been at risk of presenting the event before t = 0. A frailty term was also used. Two formulations were used for this “Specific Hazard Frailty Model Imputed” based on the “counting process” and “gap time.” Performance was then examined in different scenarios through a comprehensive simulation study. Results The proposed method performed well even when the percentage of subjects at risk before follow-up was very high. Biases were often below 10% and coverages were around 95%, being somewhat conservative. The gap time approach performed better with constant baseline hazards, whereas the counting process performed better with non-constant baseline hazards. Conclusions The use of common baseline methods is not advised when knowledge of prior episodes experienced by a participant is lacking. The approach in this study performed acceptably in most scenarios in which it was evaluated and should be considered an alternative in this context. It has been made freely available to interested researchers as R package miRecSurv.

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.

A Spatial Survival Model for Risk Factors of Under-Five Child Mortality in Kenya

Child mortality is high in Sub-Saharan Africa compared to other regions in the world. In Kenya, the risk of mortality is assumed to vary from county to county due to diversity in socio-economic and even climatic factors. Recently, the country was split into 47 different administrative regions called counties, and health care was delegated to those county governments, further aggravating the spatial differences in health care from county to county. The goal of this study is to evaluate the effects of spatial variation in under-five mortality in Kenya. Data from the Kenya Demographic Health Survey (KDHS-2014) consisting the newly introduced counties was used to analyze this risk. Using a spatial Cox Proportional Hazard model, an Intrinsic Conditional Autoregressive Model (ICAR) was fitted to account for the spatial variation among the counties in the country while the Cox model was used to model the risk factors associated with the time to death of a child. Inference regarding the risk factors and the spatial variation was made in a Bayesian setup based on the Markov Chain Monte Carlo (MCMC) technique to provide posterior estimates. The paper indicate the spatial disparities that exist in the country regarding child mortality in Kenya. The specific counties have mortality rates that are county-specific, although neighboring counties have similar hazards for death of a child. Counties in the central Kenya region were shown to have the highest hazard of death, while those from the western region had the lowest hazard of death. Demographic factors such as the sex of the child and sex of the household head, as well as social economic factors, such as the level of education, accounted for the most variation when spatial differences were factored in. The spatial Cox proportional hazard frailty model performed better compared to the non-spatial non-frailty model. These findings can help the country to plan health care interventions at a subnational level and guide social and health policies by ensuring that counties with a higher risk of Under Five Child Mortality (U5CM) are considered differently from counties experiencing a lower risk of death.

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.

An Introspective Overview of the Dynamics of Recurrent Events Data Analysis

A recurrent event remains the outcome variable of interest in many biometric studies. Recurrent events can be explained as events of defined interest that can occur to same person more than once during the study period. This study presents an overview of different pertinent recurrent models for analyzing recurrent events. Aims: To introduce, compare, evaluate and discuss pros and cons of four models in analyzing recurrent events, so as to validate previous findings in respect of the superiority or appropriateness of these models. Study Design: A comparative studies based on simulation of recurrent event models applied to a tertiary data on cancer studies. Methodology: Codes in R were implemented for simulating four recurrent event models, namely; The Andersen and Gill model; Prentice, Williams and Peterson models; Wei, Lin and Weissferd; and Cox frailty model. Finally, these models were applied to analyze the first forty subjects from a study of Bladder Cancer Tumors. The data set contained the first four repetitions of the tumor for each patient, and each recurrence time was recorded from the entry time of the patient into the study. An isolated risk interval is defined by each time to an event or censoring. Results: The choice and usage of any of the models lead to different conclusions, but the choice depends on: risk intervals; baseline hazard; risk set; and correlation adjustment or simplistically, type of data and research question. The PWP-GT model could be used if the research question is focused on whether treatment was effective for the event since the previous event happened. However, if the research question is designed to find out whether treatment was effective for the event since the start of treatment, then we could use the PWP- TT. The AG model will be adequate if a common baseline hazard could be assumed, but the model lacks the details and versatility of the event-specific models. The WLW model is very suitable for data with diverse events for the same person, which underscores a potentially different baseline hazard for each type. Conclusion: PWP-GT has proven to be the most useful model for analyzing recurrent event data.

Mean Residual Lifetime Frailty Models: A Weighted Perspective

The mean residual life frailty model and a subsequent weighted multiplicative mean residual life model that requires weighted multiplicative mean residual lives are considered. The expression and the shape of a mean residual life for some semiparametric models and also for a multiplicative degradation model are given in separate examples. The frailty model represents the lifetime of the population in which the random parameter combines the effects of the subpopulations. We show that for some regular dependencies of the population lifetime on the random parameter, some aging properties of the subpopulations’ lifetimes are preserved for the population lifetime. We indicate that the weighted multiplicative mean residual life model generates positive dependencies of this type. The copula function associated with the model is also derived. Necessary and sufficient conditions for certain aging properties of population lifetimes in the model are determined. Preservation of stochastic orders of two random parameters for the resulting population lifetimes in the model is acquired.

Analyzing Infant Mortality in Rural Bangladesh: A Frailty Modeling Approach

In practice, it may happen that data may arise from a hierarchical structure i.e., a cluster is nested within another cluster. In this case, nested frailty model is appropriate to analyze survival data to obtain optimal estimates of the parameters of interest. To identify significant determinants of infant mortality in rural Bangladesh, survival data have been extracted from Bangladesh Demographic and Health Survey (BDHS), 2014. Because of the presence of two-level clustering in data, nested frailty model has been employed for the purpose of analysis. Recommendations have been suggested based on the results obtained from the survival model to reduce the infant mortality in rural Bangladesh to a great extent. Dhaka Univ. J. Sci. 69(2): 63-69, 2021 (July)

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.