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Abstract: Parametric Analysis of Renal Failure Data using the Exponentiated Odd Weibull Distribution
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Abstract: In this article, we analyze renal failure data from patients with mesangioproliferative glomerulonephritis (MPGN) which was modeled by [1] non-parametrically using the Kaplan-Meier curve. In their work, they showed that the clinical variables, large increase serum creatinine (LISC) and systolic blood pressure >160 mmHg (SBP>160), and morphological variables, benign nephrosclerosis present (BNP) and interstitial score group 5-6 (IS5-6) were part of the variables which indicated progression to end-stage renal failure (ESRF). Though survival curves associated with these variables may be difficult to model by existing parametric distributions in literature. Therefore, we introduce a four-parameter Odd Weibull extension, the exponentiated Odd Weibull (EOW) distribution which is very versatile in modeling lifetime data that its hazard function exhibits ten different hazard shapes as well as various density shapes. Basic properties of the EOW distribution are presented. In the presence of random censoring, a small simulation study is conducted to assess the coverage probabilities of the estimated parameters of the EOW distribution using the maximum likelihood method. Our results show that the EOW distribution is very convenient and reliable to analyze the MPGN data since it provides an excellent fit for the variables LISC, SBP>160, BNP, and IS5-6. Furthermore, advantages of using the EOW distribution over the Kaplan-Meier curve are discussed. Comparisons of the EOW distribution with other Weibull-related distributions are also presented. Keywords: Coverage probability, hazard function, maximum likelihood, random censoring, survival function. |
Abstract: A Simulation Based Evaluation of Sample Size Methods for Biomarker Studies
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Abstract: Cancer researchers are often interested in identifying biomarkers that are indicative of poor outcomes (prognostic biomarkers) or response to specific therapies (predictive biomarkers). In designing a biomarker study, the first statistical issue encountered is the sample size requirement for adequate detection of a biomarker effect. In biomarker studies, the desired effect size is typically larger than those targeted in therapeutic trials and the biomarker prevalence is rarely near the optimal 50%. In this article, we review sample size formulas that are routinely used in designing therapeutic trials. We then conduct simulation studies to evaluate the performances of these methods when applied to biomarker studies. In particular, we examine the impact that deviations from certain statistical assumptions (i.e., biomarker positive prevalence and effect size) have on statistical power and type I error. Our simulation results indicate that when the true biomarker prevalence is close to 50%, all methods perform well in terms of power regardless of the magnitude of the targeted biomarker effect. However, when the biomarker positive prevalence rate deviates from 50%, the empirical power based on some existing methods may be substantially different from the nominal power, and this discrepancy becomes more profound for large biomarker effects. The type I error is maintained close to the 5% nominal level in all scenarios we investigate, although there is a slight inflation as the targeted effect size increases. Based on these results, we delineate the range of parameters within which the use of some sample size methods may be sufficiently robust. Keywords: Sample size methods, biomarker study, prognostic biomarker, predictive biomarker, survival data. |
Abstract: On Comparing Survival Curves with Right-Censored Data According to the Events Occur at the Beginning, in the Middle and at the End of Study Period
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Abstract: In clinical practice the event of interest does not always occur equally across the study time period. Depending on the disease being investigated, the event that is of interest can occur intensively in different periods of the follow-up time. In such cases, choosing the correct survival comparison test has importance. This study aims to examine and discuss the results of survival comparison tests under some certain circumstances. A simulation study was conducted. We discussed the result of different tests such as Logrank, Gehan-Wilcoxon, Tarone-Ware, Peto-Peto, Modified Peto-Peto tests and tests belonging to Fleming-Harrington test family with (p, q) values; (1, 0), (0.5, 0.5), (1, 1), (0, 1) ve (0.5, 2) by means of Type I error rate that obtained from simulation study, when the event of interest occurred intensively at the beginning of the study, in the middle of the study and at the end of the study time period. As a result of simulation study, Type I error rate of tests is generally lower or higher than the nominal value. In the light of the results, it is proposed to re-examine the tests for cases where events are observed intensively at the beginning, middle and late periods, to carry out new simulation studies and to develop new tests if necessary. Keywords: Survival analysis, survival curves, comparison of survival curves, right censored observations. |
Abstract: A Correlation Technique to Reduce the Number of Predictors to Estimate the Survival Time of HIV/ AIDS Patients on ART
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Abstract: Till now, many research papers have been published which aims to estimate the survivle time of the HIV/AIDS patients taking into consideration all the predictors viz, Age, Sex, CD4, MOT, Smoking, Weight, HB, Coinfection, Time, BMI, Location Status, Marital Status, Drug etc, although all the predictors need not to be included in the model. Since some of the predictors may be correlated/ associated and may have some influence on the outcome variable, therefore, instead of taking both the significantly correlated/ associated predictors, we may take only one of the two. In this way, we may be able to reduce the number of predictors without affecting the estimated survival time. In this paper we have tried to reduce the number of predictors by determining the highly positively correlated predictors and then evaluating the effect of correlation/ association on the survival time of HIV/AIDS patients. These predictors that we have considered in the starting are Age, Sex, State, Smoking, Alcohol, Drugs, Opportunistic Infections (OI), Living Status (LS), Occupation (OC), Marital Status (MS) and Spouse for the data collected from 2004 to 2014 of AIDS patients in an ART center of Delhi, India. We have performed one – way ANOVA to test the association between a quantitative and a categorical variable and Chi-square test to test between two categorical variables. To select one of the two highly correlated/ associated predictors, a suitable model is fitted keeping one predictor independent at a time and other dependent and the model having the smaller AIC is considered and the independent variable in the model is included in the modified model. The fitted models are logistic, linear and multinomial logistic depending on the type of the independent variable to be fitted. Then the true model (having all the predictors) and the modified model (with reduced number of predictors) are compared on the basis of their AICs and the model having minimum AIC is chosen. In this way we could reduce the number of predictors by almost 50% without affecting the estimated survival time with a reduced standard error. Keywords: AIDS, AFT, Correlation, Chi- Square test, One- Way ANOVA. |
