An Optimum Allocation with a Family of Estimators Using Auxiliary Information in Sample Survey

The problem of obtaining optimum allocation using auxiliary information in stratified random sampling. An optimum allocation with a family of estimators is obtained and its efficiency is compared with that of Neyman allocation based on Srivastava (1971) class of estimators and the optimum allocation suggested by Zaidi et al., (1989). It is shown that the proposed allocation is better in the sense having smaller variance compared to other optimum allocation

Handling missingness value on jointly measured time-course and time-to-event data

Joint modeling technique is a recent advancement in effectively analyzing the longitudinal history of patients with the occurrence of an event of interest attached to it. This procedure is successfully implemented in biomarker studies to examine parents with the occurrence of tumor. One of the typical problem that influences the necessary inference is the presence of missing values in the longitudinal responses as well as in covariates. The occurrence of missingness is very common due to the dropout of patients from the study. This article presents an effective and detailed way to handle the missing values in the covariates and response variable. This study discusses the effect of different multiple imputation techniques on the inferences of joint modeling implemented on imputed datasets. A simulation study is carried out to replicate the complex data structures and conveniently perform our analysis to show its efficacy in terms of parameter estimation. This analysis is further illustrated with the longitudinal and survival outcomes of biomarkers' study by assessing proper codes in R programming language

Illustration of missing data handling technique generated from hepatitis C induced hepatocellular carcinoma cohort study

Background and Objectives: Missing outcome data are a common occurrence for most clinical research trials. The ’complete case analysis’ is a widely adopted method to tackle with missing observations. However, it reduced the sample size of the study and thus have an impact on statistical power. Hence every effort should be made to reduce the amount of missing data. The objective of this work is to provide the application of different analytical tools to handle missing data imputation techniques through illustration.Methods: We used Imputation techniques such as EM algorithm, MCMC, Regression, and Predictive Mean matching methods and compared the results on hepatitis C virus-induced hepatocellular carcinoma (HCV-HCC) data. The statistical models by Generalized Estimating Equations, Time-dependent Cox Regression, and Joint Modeling were applied to obtain the statistical inference on imputed data. The missing data handling technique compatible with Principle Component Analysis (PCA) was found suitable to work with high dimensional data.Results: Joint modelling provides a slightly lower standard error than other analytical methods each imputation. Accordingly, to our methodology, Joint Modeling analysis with the EM algorithm imputation method has appeared to be the most appropriate method with HCV-HCC data. However, Generalized Estimating Equations and Time-dependent Cox Regression methods were relatively easy to run.Conclusion: The multiple imputation methods are efficient to provide inference with missing data. It is technically robust than any ad hoc approach to working with missing data

Illustration of missing data handling technique generated from hepatitis C induced hepatocellular carcinoma cohort study

Background and Objectives: Missing outcome data are a common occurrence for most clinical research trials. The ’complete case analysis’ is a widely adopted method to tackle with missing observations. However, it reduced the sample size of the study and thus have an impact on statistical power. Hence every effort should be made to reduce the amount of missing data. The objective of this work is to provide the application of different analytical tools to handle missing data imputation techniques through illustration.Methods: We used Imputation techniques such as EM algorithm, MCMC, Regression, and Predictive Mean matching methods and compared the results on hepatitis C virus-induced hepatocellular carcinoma (HCV-HCC) data. The statistical models by Generalized Estimating Equations, Time-dependent Cox Regression, and Joint Modeling were applied to obtain the statistical inference on imputed data. The missing data handling technique compatible with Principle Component Analysis (PCA) was found suitable to work with high dimensional data.Results: Joint modelling provides a slightly lower standard error than other analytical methods each imputation. Accordingly, to our methodology, Joint Modeling analysis with the EM algorithm imputation method has appeared to be the most appropriate method with HCV-HCC data. However, Generalized Estimating Equations and Time-dependent Cox Regression methods were relatively easy to run.Conclusion: The multiple imputation methods are efficient to provide inference with missing data. It is technically robust than any ad hoc approach to working with missing data

Handling missingness value on jointly measured time-course and time-to-event data

Joint modeling technique is a recent advancement in effectively analyzing the longitudinal history of patients with the occurrence of an event of interest attached to it. This procedure is successfully implemented in biomarker studies to examine parents with the occurrence of tumor. One of the typical problem that influences the necessary inference is the presence of missing values in the longitudinal responses as well as in covariates. The occurrence of missingness is very common due to the dropout of patients from the study. This article presents an effective and detailed way to handle the missing values in the covariates and response variable. This study discusses the effect of different multiple imputation techniques on the inferences of joint modeling implemented on imputed datasets. A simulation study is carried out to replicate the complex data structures and conveniently perform our analysis to show its efficacy in terms of parameter estimation. This analysis is further illustrated with the longitudinal and survival outcomes of biomarkers' study by assessing proper codes in R programming language

A modified risk detection approach of biomarkers by frailty effect on multiple time to event data

Multiple indications of disease progression found in a cancer patient by loco-regional relapse, distant metastasis and death. Early identification of these indications is necessary to change the treatment strategy. Biomarkers play an essential role in this aspect. The survival chance of a patient is dependent on the biomarker, and the treatment strategy also differs accordingly, e.g., the survival prediction of breast cancer patients diagnosed with HER2 positive status is different from the same with HER2 negative status. This results in a different treatment strategy. So, the heterogeneity of the biomarker statuses or levels should be taken into consideration while modelling the survival outcome. This heterogeneity factor which is often unobserved, is called frailty. When multiple indications are present simultaneously, the scenario becomes more complex as only one of them can occur, which will censor the occurrence of other events. Incorporating independent frailties of each biomarker status for every cause of indications will not depict the complete picture of heterogeneity. The events indicating cancer progression are likely to be inter-related. So, the correlation should be incorporated through the frailties of different events. In our study, we considered a multiple events or risks model with a heterogeneity component. Based on the estimated variance of the frailty, the threshold levels of a biomarker are utilised as early detection tool of the disease progression or death. Additive-gamma frailty model is considered to account the correlation between different frailty components and estimation of parameters are performed using Expectation-Maximization Algorithm. With the extensive algorithm in R, we have obtained the threshold levels of activity of a biomarker in a multiple events scenario.Comment: 21 pages, 2 figures,7 table

A family of estimators of population mean using multi-auxiliary variate and post-stratification

This paper suggests a family of estimators of population mean using multiauxiliary variate based on post-stratified sampling and its properties are studied under large sample approximation. Asymptotically optimum estimator in the class is identified alongwith its approximate variance formulae. The proposed class of estimators is also compared with corresponding unstratified class of estimators based on estimated optimum value. At the end, an empirical study has been carried out to support the proposed methodology

A Ratio-Cum-Product Type Exponential Estimator Using Double Sampling for Stratification

This paper proposes an improved class of ratio-cum-product type exponential estimator for estimating the finite population mean of the study variate (when sampling of study variate is costly or difficult to fetch). The proposed estimator uses two auxiliary variates associated with study variate in order to increase its efficiency under the double sampling for stratification scheme. The expression for the bias and mean square error (MSE) of the proposed estimator are obtained under large sample approximation. Efficiency comparisons are made to demonstrate the performance of the proposed estimation procedure over the existing estimation procedures. We have considered the six natural population data-sets to examine the merits of the proposed estimator and carried out the empirical study in support of theoretical findings. Numerical illustration shows that the proposed estimator is more efficient