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Editor’s Choice : A Bayesian Approach for the Cox Proportional Hazards Model with Covariates Subject to Detection Limit
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Abstract: The research on biomarkers has been limited in its effectiveness because biomarker levels can only be measured within the thresholds of assays and laboratory instruments, a challenge referred to as a detection limit (DL) problem. In this paper, we propose a Bayesian approach to the Cox proportional hazards model with explanatory variables subject to lower, upper, or interval DLs. We demonstrate that by formulating the time-to-event outcome using the Poisson density with counting process notation, implementing the proposed approach in the OpenBUGS and JAGS is straightforward. We have conducted extensive simulations to compare the proposed Bayesian approach to the other four commonly used methods and to evaluate its robustness with respect to the distribution assumption of the biomarkers. The proposed Bayesian approach and other methods were applied to an acute lung injury study, in which a panel of cytokine biomarkers was studied for the biomarkers’ association with ventilation-free survival. Keywords: Bayesian, Biomarker, Detection limit, Lung Injury, Proportional hazards models.Download Full Article |
Editor’s Choice : Interpreting Long-Term Trends in Time Series Intervention Studies of Smoke-Free Legislation and Health
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Abstract: Background: Numerous studies have investigated the impact of smoke-free laws on health outcomes. Large differences in estimates are in part attributable to how the long-term trend is modelled. However, the choice of appropriate trend is not always straightforward. We explore these complexities in an analysis of myocardial infarction (MI) mortality in England before and after the introduction of smoke-free legislation in July 2007. Methods: Weekly rates of MI mortality among men aged 40+ between July 2002 and December 2010 were analysed using quasi-Poisson generalised additive models. We explore two ways of modelling the long-term trend: (1) a parametric approach, where we fix the shape of the trend, and (2) a penalised spline approach, in which we allow the model to decide on the shape of the trend. Results: While both models have similar measures of fit and near identical fitted values, they have different interpretations of the legislation effect. The parametric approach estimates a significant immediate reduction in mortality rate of 13.7% (95% CI: 7.5, 19.5), whereas the penalised spline approach estimates a non-significant reduction of 2% (95% CI:-0.9, 4.8). After considering the implications of the models, evidence from sensitivity analyses and other studies, we conclude that the second model is to be preferred. Conclusions: When there is a strong long-term trend and the intervention of interest also varies over time, it is difficult for models to separate out the two components. Our recommendations will help further studies determine the best way of modelling their data. Keywords: Smoke-free law, myocardial infarction, mortality, second-hand smoke, passive smoke.Download Full Article |
Editor’s Choice : Factors Affecting Self-Image in Patients with a Diagnosis of Eating Disorders on the Basis of a Cluster Analysis
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Abstract: The aim of this study was to assess the relationship between self-image in eating disorders and age, duration and severity of the disorder, comorbidity, depressiveness and self-evaluation of eating problems. The results of the Offer self-image questionnaire for adolescents (QSIA) were compared in four groups: anorexia nervosa restrictive subtype (ANR, n: 47), anorexia nervosa binge/purge subtype (ANBP, n: 16), bulimia nervosa (BUL, n: 34) and eating disorders NOS (EDNOS, n: 19). The control group was age matched female pupils (NOR, n = 76). The Kruskal-Wallis test revealed significant differences between the age of patients from the ANR (16.34, SD 1.58) and BUL (17.56, SD 0.96) groups (p = .008). The self-image of schoolgirls from the NOR group was on most scales significantly better than the self-image of girls from clinical groups. On four scales differences between the (better) self-image in the ANR group and that in the BUL group were observed. Next, a cluster analysis using a generalised k-means algorithm with v-fold cross validation of QSIA questionnaire results was conducted in the group of clinical eating disorders (ANR, ANBP, and BUL). Three clusters were obtained. The first was characterized by very good self-image (above the averagefor the general population), the second by poor self-image and the third by negative self-image. Severity of depressiveness measured using the Beck Depression Inventory turned out to be the only factor which differentiated the clusters of self-image in eating disorders. Keywords: Anorexia, bulimia, QSIA, DATA MINING, cluster analysis.Download Full Article |
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Abstract: The purpose of this study was to assess the duration of breastfeeding among women of reproductive age in Ethiopia and to identify determinants associated with early cessation of breastfeeding. Data for the study were drawn from the Ethiopia Demographic and Health Survey 2005. The study included mothers of 9,066 children from nine regional states and two city administrations. The Kaplan-Meier and stratified Cox’s hazard model were employed for the analysis of breastfeeding-related data. The Kaplan-Meier survival estimate showed that the probability of mothers who continue to breastfeeding was high (97.3%) for the first month. The breastfeeding rates then declined to 92.5% at 6 months, 78.4% at 12 months, 37% at 24 months and 8.3% at 48 months. The mean and median duration of breastfeeding in Ethiopia were 25.64 and 24.00 months respectively. The stratified Cox regression analysis revealed that younger mothers, mothers who had lived in urban area, mothers having higher education, higher maternal parity, early pregnant and being a Muslim and protestant were significant determinants of early cessation of breastfeeding in Ethiopia. Then, we recommend that the breastfeeding-promotion programs in Ethiopia should give special attention to young mothers, those who lived in urban areas, mothers with higher education, those who have higher parity, those who have early pregnancy and who are Muslims and Protestants since these mothers tend to breastfeed their child for a relatively shorter period of time. Keywords: Breastfeeding duration, Kaplan-Meier estimator, Determinants, Stratified- Cox regression model, Hazard-Ratio, Ethiopia.Download Full Article |
Editor’s Choice : Modified Kaplan-Meier Estimator Based on Competing Risks for Heavy Censoring Data
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Abstract: Most follow-up studies are conducted to determine the survival rates of subjects affected by a specific risk. These subjects are also exposed to other risks. Every subject in a medical follow-up is exposed not only to the risk of dying, but also to the risk of being censored. In case of heavy censoring, the Kaplan-Meier estimates are biased and overestimate the survival distribution. A new methodology based on competing risks is proposed to estimate the survival function by using net and crude probabilities. These estimates reduce the bias and overestimation of the survival distribution noted in Kaplan-Meier estimators. In this study, the method of modified Kaplan-Meier (MKM) is compared with the Kaplan-Meier (KM), Huang’s method and also the two other methods namely Weighted Kaplan-Meier (WKM) and Modified Weighted Kaplan-Meier (MWKM). Either of the weighted methods depends heavily on the event times and censoring distributions. Due to this fact, the weighted methods can have misleading results when the censoring patterns are different in the individual samples. The results showed that the MKM estimator considers not only the problem of heavy censoring but also the problem of weighted methods and competing risks in complicated data. In this study “Stanford Heart Transplant Data” was used to investigate the effectiveness of the proposed methods. Keywords: Competing risks, Kaplan-Meier estimator, Heavy Censoring, Net and Crude probabilities.Download Full Article |