Introducing Survival and Event History Analysis

A previous paper (Hutchison, 1988) in this journal has provided an introduction to the basic concepts of survival and event history analysis, originally developed in medical research, econometrics and engineering, and argued the case for their wider application in the social sciences. This paper introduces some further complications that the researcher is likely to meet, and offers some guidelines for handling problems that arise in applying such methods to the highly complex social situations involved.

BackgroundGlobally, the estimated recurrent childbirth of one forth of women happens every two years or fewer. Next to Nigeria, Ethiopia is the second populist country in Africa and the first populist country in sub-Saharan Africa which consists of over 114 million population. There are prevalent short successive birth intervals problems in underdeveloped nations such as Ethiopia that contributes to adverse effects on mother and child health. However, studies that explore recurrent birth events and associated factors are very limited. Thus, this study aimed to explore and model the recurrent birth event by considering its subsequent within a mother and identifying its important determinants. As a result, the research findings of this study will be one of the preliminary research papers on the recurrent birth events that take into account the subsequent event and enable to be input for the policymakers, health institutions, and future researchers.MethodsA total of 4676 mothers with their 16833 corresponding children were involved in this study. The data was obtained from the 2019 Ethiopian Mini Demographic and Health Survey (EMDHS). In this study, extended cox regression models such as Andersen-Gill (AG), Prentice, Williams, and Peterson total time (PWP-TT) model, PWP-gap time (PWP-GT) model, and Frailty model were employed. These all models are used to consider recurrent events within mothers and determine the potential determinants. AG, PWP-TT, and PWP-GT estimate the effect of covariates by considering the correlation between event times for a person can be explained by past events given the covariates, kth event since the entry time, kth event since the time from the previous event, respectively.ResultsAmong mothers who have first and ninth recurrent birth events, 75.5% and 80.1% of them respectively were rural residents while 57.6% and 70.6% of them respectively were a place of delivery in the health sector. The highest prevalence of first recurrent births (44.3%) was obtained from Muslim mothers. Mothers' education level (HR: 1.210; 95%CI: 1.010, 1.460), mothers' age at first birth (HR: 0.713; 95% CI: 0.614, 0.828), household wealth index (HR: 0.776; 95% CI: 0.625, 0.965), child mortality (HR: 0.673; 95%CI: 0.514, 0.881), household size (HR: 1.914; 95%CI:1.539,2.381) and sex of child (HR:0.836; 95%CI = 0.755,0.926) were important determinants of recurrent birth event. This indicates mothers’ education level and household size were positively associated with recurrent birth events. Whereas mothers’ age at first birth, household wealth index, child mortality, and sex of the child was negatively associated with recurrent birth events.ConclusionThe WHO recommends a minimum of 33 months between two consecutive births, which is longer than the Ethiopian recurrent birth intervals observed in this study. The highest recurrent birth occurred during the age of fewer than twenty years old of mothers at first birth as compared to mothers whose age was older at first birth. Mothers, children, and household characteristics had significant effects on recurrent birth events. We authors would like to recommend communities, governmental and non-governmental stakeholders consider the associated factors of frequent recurrence of birth noticed in this study. Besides, we would also like to recommend women start birth while they got mature in age to reduce frequent recurrent birth and its corresponding adverse effects.

Introduction: Recurrent event data are common in many longitudinal studies. Often, a terminating event such as death can be correlated with the recurrent event process. A shared frailty model applied to account for the association between recurrent and terminal events. In some situations, a fraction of subjects experience neither recurrent events nor death; these subjects are cured.
 Methods: In this paper, we discussed the Bayesian approach of a joint frailty model for recurrent and terminal events in the presence of cure fraction. We compared estimates of parameters in the Frequentist and Bayesian approaches via simulation studies in various sample sizes; we applied the joint frailty model in the presence of cure fraction with Frequentist and Bayesian approaches for breast cancer.
 Results: In small sample size Bayesian approach compared to Frequentist approach had a smaller standard error and mean square error, and the coverage probabilities close to nominal level of 95%. Also, in Bayesian approach, the sampling means of the estimated standard errors were close to the empirical standard error.
 Conclusion: The simulation results suggested that when sample size was small, the use of Bayesian joint frailty model in the presence of cure fraction led to more efficiency in parameter estimation and statistical inference.

BackgroundUse of survival models for the analysis of sports injury data has grown rapidly potentially enabling better understanding of time to sports injury events. Choosing an appropriate model is a...

The frailty model is increasingly popular for analyzing multivariate time-to-event data. The most common model is the shared frailty model. Although study design consideration is as important as analysis strategies, sample size determination methodology in studies with multivariate time-to-event data is greatly lacking in the literature. In this article, we develop a sample size determination method for the shared frailty model to investigate the treatment effect on multivariate event times. We analyzed the data using both a parametric model and a piecewise model with unknown baseline hazard, and compare the empirical power with the calculated power. Last, we discuss the formula for testing the treatment effect on recurrent events.

Panel count data is common in cancer screening. In the context of colorectal cancer screening, our work focuses on the prediction of the probability of advanced adenoma conditional on patient-level risk factors and/or event history. We implement the joint frailty model proposed by Huang et al. which involves a non-stationary Poisson process for recurrent adenoma events and informative screening time using semi-parametric Cox models correlated by a latent frailty variable, where coefficients and baseline intensity functions are estimated by estimating equations. Subject-specific frailty value is estimated by the borrow-strength method. In addition, marginal models for the adenoma and screening events are also applicable when average covariate effects on the population level are of interest. Predictions based on the marginal model and predictions based on the frailty models for patients with or without a screening history are compared. When a patient's screening history is available and sufficient adenoma events are observed, the predictions based on the frailty model with estimated subject-specific frailty are superior. However, in the cases of early censoring when adenoma events are not observed for most patients and screening history is not available, the prediction based on the marginal model has better performance. Furthermore, for patients' future screening, the individualized screening intervals derived from the dynamic predictions of advanced adenoma risks will detect adenoma events earlier with shorter lag time between the adenoma state transition and the screening compared to the current practice of regular screening intervals.

In patients with aplastic anemia (AA), infection-related complications are the leading cause of mortality. However, limited knowledge about the predictive factors for infection in these patients exists. Thus, this study aimed to evaluate risk factors for infection and develop a risk prediction model for the occurrence of infection in patients with AA. Between January 2004 and December 2020, 206 patients with AA ≥15 years of age were included in this study. Survival analysis using recurrent event methodologies was conducted to identify predictive factors associated with infection, including the Anderson and Gill model; Prentice, Williams, and Peterson (PWP) Total Time model; PWP Gap Time model; marginal model; and frailty models. The best model was determined using backward stepwise regression, and internal validation was performed using the bootstrapping method with 500 re-samplings. With a median follow-up of 2.95 years, the incidence rate of infection among patients with AA was 32.8 events per 100 person-years. The PWP Total Time model revealed that cirrhosis comorbidity, lymphocytes ≥80%, and previous infection increased the risk of infection, while bone marrow cellularity ≥20% offered protection. The bone marrow cellularity, lymphocyte percentage, previous infection, cirrhosis, and hematocrit (BLICH) model was generated to predict the risk of infection. The internal validation showed a good calibration of this model. Cirrhosis, lymphocytes ≥80%, previous infection, and bone marrow cellularity <20% are risk factors for infection in patients with AA. The BLICH model can predict the risk of infection in these patients.

A survival analysis model leads one to analyze main factors which impact a patient’s therapy process. In practice a survival analysis is capable of affecting therapeutic protocols. Different methods have been approached to analyze the survival of a breast cancer patient by researchers. The objective of this research is to lead specialists analyzing the breast cancer patients effectively. This research by analyzing 2010 breast cancer patients 1) attempts to propose six different statistical models using parametric and semi-parametric approaches for survival analysis of breast cancer patients, 2) compares the performance capabilities of the proposed statistical models analytically, and 3) addresses the most superior approach for a survival analysis of a breast cancer. To analyze the capability of the six proposed models Akaike term is used. This comprehensive research also indicates that the hazard factors commonly proposed in literature are not capable of leading a specialist to analyze the survival completely. Although it is possible to model the breast cancer survival using different approaches, this research reveals the proposed semi parametric model is capable of providing the most superior condition. The capability of the best parametric model among the five proposed parametric models of this comprehensive research is also addressed. Kaplan-Meier diagram is used to analyze the importance of two new hazard factors proposed in this paper.

ABSTRACTThe unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared gamma frailty model and the inverse Gaussian frailty model with the reversed hazard rate. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin data set and a better model is suggested.

Frailty Models in Public Health

SUMMARY Bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima. No natural parametric family exists for the dependence between the marginal distributions, but there are considerable restrictions on the dependence structure. We consider modelling the dependence function with parametric models, for which two new models are presented. Tests for independence, and discriminating between models, are also given. The estimation procedure, and the flexibility of the new models, are illustrated with an application to sea level data. Extreme value theory has recently been an area of much theoretical and practical work. Univariate theory is a well documented area, whereas bivariate/multivariate extreme value theory has, until recently, received surprisingly little attention. In the multivariate case, no natural parametric family exists for the dependence structure, so this must be modelled in some way. In the analysis of environmental extreme value data, there is a need for models of dependence between extremes from different sources: for example at various sea ports, or at various -points of a river. In this paper we consider bivariate extreme value distributions. We assume, without loss of generality, that we have exponential marginal distributions with unit means. The class of bivariate exponential distributions in which we are interested, satisfy a strong stability relation. Exponential variables (X, Y) satisfy the stability relation if and only if W = min (aX, bY) is also exponentially distributed for all a, b > 0 (Pickands, 1981). Therefore, the models we will consider have particular application in reliability and survival analysis. One approach to modelling the dependence structure is via parametric models. This requires a flexible family of models which satisfy certain constraints. Models are of two kinds: either differentiable, or nondifferentiable. All nondifferentiable models give distri- butions which are singular, with nonzero probability concentrated on a certain subspace. The differentiable models have densities, but the existing models are symmetric which leads to the variables being exchangeable. Here, we present two new asymmetric differenti- able models, which have increased flexibility. Properties of the differentiable models are examined. Estimation of the parametric models has previously been by ad hoc methods, because there is a nonregular estimation problem when the margins are independent. For the

Many diseases and clinical outcomes may recur to the same patient. These events are termed as recurrent events. Several statistical models have been proposed in the literature to analyze recurrent events. In this study, we identify the clinical and the genetic risk factors for recurring tumors among prostate cancer patients from The Cancer Genome Atlas (TCGA). Five statistical approaches for modeling recurrent time-to-event are implemented to identify and to determine the effects of the clinical and the genetic risk factors of tumor recurrence. In particular, we consider Andersen-Gill (A-G), Wei-Lin-Weissfeld (WLW), Prentice-Williams-Peterson Total Time (PWP-TT), Prentice-Williams-Peterson Gap Time (PWPGT) and Frailty models. We present and discuss the risk factors influencing the recurrence of tumors and their impacts in prostate cancer patients obtained from five commonly used models in this paper.

This paper proposes a method that uses mean square error (MSE) and model confidence set (MCS) as the loss function of back‐propagation neural network (BPNN), aiming to train and find a generalized autoregressive conditional heteroskedastic (GARCH) model that has the best forecasting performance of a time series. Combining MSE and the p‐value of MCS can not only estimate better parameters for the GARCH models but also find the best GARCH model to forecast the volatility of a time series. Meanwhile, we divide a time series into several parts and use each part as the input of the BPNN. Through the BPNN, each part of the time series will be turned into several forecasting values. These values will be used to calculate the MSE and the p‐value of MCS, which will then be used to update the parameters of the BPNN. In the end, we use MCS to choose the best GARCH model among the trained GARCH models and compare this method with maximum likelihood estimation (MLE) and the generalized least squares estimation (GLS). The result shows that the p‐value of MCS of the best model estimated by this method is higher than the p‐value of MCS of the best model estimated by MLE and GLS. According to the theory of MCS, a model that has a larger p‐value does have a better forecasting performance. The method proposed by this paper can provide a potential application of neural network in GARCH model forecasting and estimation.

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyse the bivariate data on related survival times (e.g., matched pairs experiments, twin or family data), the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this paper, we introduce the gamma correlated frailty models based on reversed hazard rate (RHR) with three different baseline distributions namely, the generalised log-logistic type I, the generalised log-logistic type II and the modified inverse Weibull. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin dataset and a better model is suggested.

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