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Editor's Choice : Modeling of the Deaths Due to Ebola Virus Disease Outbreak in Western Africa
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Abstract: Problem: The recent 2014 Ebola virus outbreak in Western Africa is the worst in history. It is imperative that appropriate statistical and mathematical models are used to identify risk factors and to monitor the development and spread of the disease. Method: Deaths data due to Ebola virus disease (EVD) in Guinea, Liberia, and Sierra Leone from October 10, 2014 to March 24, 2015 were collected via Situation Reports published by the World Health Organization [1]. Conditional autoregressive (CAR) models were applied to account for the spatial dependency in the countries along with the temporal dimension of the disease. Bayesian change-point models were used to identify key changes in growth and drop time points in the spatial distribution of deaths due to EVD within each country. Country-specific Poisson and negative binomial mixed models of covariate effects were applied to understand the between-country variability in deaths due to EVD. Results: Both CAR models and generalized linear mixed models identified statistically significant covariate effects; however, the CAR models depended on the interval of data analyzed, whereas the mixed models depended on the underlying distribution assumed. Bayesian change-point models identified one significant change-point in the distribution of deaths due to EVD within each country. Practical Application: CAR models, Bayesian change-point models, and generalized linear mixed models demonstrate useful techniques in modeling the incidence of deaths due to EVD. Keywords: Ebola Virus Disease, Conditional Autoregressive Model, Bayesian Analysis, Change-Point Model.Download Full Article |
Editor's Choice : On the Relationship between the Reliability and Accuracy of Bio-Behavioral Diagnoses: Simple Math to the Rescue
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Abstract: An equivalence between the J statistic (Jack Youden, 1950) and the Kappa statistic (K), Cohen (1960), was discovered by Helena Kraemer (1982). J is defined as: [Sensitivity (Se) + Specificity (Sp)] – 1. The author (2011) added the remaining two validity components to the J Index, namely, Predicted Positive Accuracy (PPA) and Predicted Negative Accuracy (PNA). The resulting D Index or D = [(Se + Sp) + (PPA + PNA) – 1] / 2. The purpose of this research is to compare J and D as estimates of K, using both actual and simulated data sets. The actual data consisted of ratings of clinical depression and self-reports of gonorrhea. The simulated data sets represented binary diagnoses when the percentages of Negative and Positive cases were: (Identical; Slightly varying; Mildly varying; Moderately varying; or Markedly varying diagnostic patterns, For both the diagnosis of clinical depression, and the self-reports of gonorrhea, D produced closer approximations to Kappa. For the simulated data, under both identical and slightly different patterns of assigning Negative and Positive binary diagnoses, K, D and J produced identical results. While J produced acceptably close values to K under the condition of Mild discrepancies in the proportions of Negative and Positive cases, D continued to more closely approximate K. While D more closely estimated K under Markedly varying diagnostic patterns, D produced values under this extreme condition that were closer than would have been predicted. The significance of these findings for future research is discussed. Keywords: Binary Diagnoses, Diagnostic Reliability, Diagnostic Accuracy. Download Full Article |
Editor's Choice : Specification of Variance-Covariance Structure in Bivariate Mixed Model for Unequally Time-Spaced Longitudinal Data
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Abstract: In medical studies, the longitudinal data sets obtained from more than one response variables and covariates are mostly analyzed to investigate the change in repeated measurements of each subject at different time points. In this study, the usability of multivariate models in the analysis of these kind of data sets is investigated, because it provides the joint analysis of multiple response variables over time and enables researchers to examine both the correlations of response variables and autocorrelation between measurements from each response variable over time. It has been shown that different parameter estimation methods affect the results in the analysis of multivariate unbalanced longitudinal data. We investigated that autocorrelation structure over time between measurements from same response variable should be truly specified. We also illustrated and compared the simpler, more standard models for fixed effects with multivariate models provided by SAS on a real-life data set in the joint analysis of two response variables. Results show that misspecification of autocorrelation structures has a negative impact on the parameter estimates and parameter estimation method should become of interest. Keywords: Multivariate longitudinal data, mixed models, covariance structures.Download Full Article |
Editor's Choice : Survival Functions in the Presence of Several Events and Competing Risks: Estimation and Interpretation Beyond Kaplan-Meier
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Abstract: Evaluation of a therapeutic strategy is complex when the course of a disease is characterized by the occurrence of different kinds of events. Competing risks arise when the occurrence of specific events prevents the observation of other events. A particular case is semi-competing risks when only fatal events can prevent the observation of the non fatal ones. Kaplan-Meier is the most popular method to estimate overall or event free survival. On the other hand when a subset of events is considered and net survival is of concern, different estimators have been proposed. Kaplan-Meier method can be used only under the independence assumptions otherwise estimators based on multivariate distribution of times are needed. If causes of death are unknown, relative survival can approximate net survival only under specific assumptions on the mortality pattern. Kaplan-Meier method cannot be used to estimate crude cumulative incidence of specific events. The aim of this work is to present the survival functions used in competing risks framework, their non parametric estimators and semi parametric estimators for net survival based on Archimedean Copulas. This would be a help for the reader who is not experienced in competing risks analysis. A simulation study is performed to evaluate performances of net survival estimators. To illustrate survival functions in presence of different causes of death and of different kind of events a numerical example is given, a literature dataset on prostate cancer and a case series of breast cancer patients have been analysed. Keywords: Survival analysis, competing risks, crude cumulative incidence, net survival, relative survival, breast cancer.Download Full Article |
Editor's Choice : Time Profile of Time-Dependent Area Under the ROC Curve for Survival Data
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Abstract: In the setting of survival analysis, the time-dependent area under the receiver operating characteristic curve (AUC) has been proposed as a discrimination measure of interest. In contrast with the diagnostic setting, the definitions of time-dependent sensitivity and specificity are required. This paper evaluates the time-dependent profile of the resulting AUC(t), which has not been previously assessed. We show that, even when the effect of a binary biomarker on the hazard rate is constant, the value of AUC(t) varies over time according to the prevalence of the marker. The Time-profile of the continuous biomarker is illustrated with numerical integration, and data on several prognostic factors in AML are examined. Keywords: Survival analysis, Prognostic models, Time-dependent AUC, Proportional hazards models.Download Full Article |