Jayanthi Arasan

Gompertz model with time-dependent covariate in the presence of interval-, right- and left-censored data

In this paper, the Gompertz model is extended to incorporate time-dependent covariates in the presence of interval-, right-, left-censored and uncensored data. Then, its performance at different sample sizes, study periods and attendance probabilities are studied. Following that, the model is compared to a fixed covariate model. Finally, two confidence interval estimation methods, Wald and likelihood ratio (LR), are explored and conclusions are drawn based on the results of the coverage probability study. The results indicate that bias, standard error and root mean square error values of the parameter estimates decrease with the increase in study period, attendance probability and sample size. Also, LR was found to work slightly better than the Wald for parameters of the model.

Rank-based inference for the accelerated failure time model in the presence of interval censored data

Semiparametric analysis and rank-based inference for the accelerated failure time model are complicated in the presence of interval censored data. The main difficulty with the existing rank-based methods is that they involve estimating functions with the possibility of multiple roots. In this paper a class of asymptotically normal rank estimators is developed which can be aquired via linear programming for estimating the parameters of the model, and a two-step iterative algorithm is introduce for solving the estimating equations. The proposed inference procedures are assessed through a real example.

Jackknife and bootstrap inferential procedures for censored survival data

Confidence interval is an estimate of a certain parameter. Classical construction of confidence interval based on asymptotic normality (Wald) often produces misleading inferences when dealing with censored data especially in small samples. Alternative techniques allow us to construct the confidence interval estimation without relying on this assumption. In this paper, we compare the performances of the jackknife and several bootstraps confidence interval estimates for the parameters of a log logistic model with censored data and covariate. We investigate their performances at two nominal error probability levels and several levels of censoring proportion. Conclusions were then drawn based on the results of the coverage probability study.

The effect of high leverage points on the maximum estimated likelihood for separation in logistic regression

This article is concerned with the performance of the maximum estimated likelihood estimator in the presence of separation in the space of the independent variables and high leverage points. The maximum likelihood estimator suffers from the problem of non overlap cases in the covariates where the regression coefficients are not identifiable and the maximum likelihood estimator does not exist. Consequently, iteration scheme fails to converge and gives faulty results. To remedy this problem, the maximum estimated likelihood estimator is put forward. It is evident that the maximum estimated likelihood estimator is resistant against separation and the estimates always exist. The effect of high leverage points are then investigated on the performance of maximum estimated likelihood estimator through real data sets and Monte Carlo simulation study. The findings signify that the maximum estimated likelihood estimator fails to provide better parameter estimates in the presence of both separation, and high leverage points.

Semiparametric binary model for clustered survival data

This paper considers a method to analyze semiparametric binary models for clustered survival data when the responses are correlated. We extend parametric generalized estimating equation (GEE) to semiparametric GEE by introducing smoothing spline into the model. A backfitting algorithm is used in the derivation of the estimating equation for the parametric and nonparametric components of a semiparametric binary covariate model. The properties of the estimates for both are evaluated using simulation studies. We investigated the effects of the strength of cluster correlation and censoring rates on properties of the parameters estimate. The effect of the number of clusters and cluster size are also discussed. Results show that the GEE-SS are consistent and efficient for parametric component and nonparametric component of semiparametric binary covariates.

A Parametric Non-Mixture Cure Survival Model with Censored Data

In some medical studies, there is often an interest in the number of patients who are not susceptible to the event of interest (recurrence of disease) and expected to be cured. This article investigates the cure rate estimation based on non-mixture cure model in the presence of left, right and interval censored data. The model proposed based on log-normal distribution that incorporates the effects of covariates on the cure probability. The maximum likelihood estimation (MLE) approach is employed to estimate the model parameters and a simulation study is provided for assessing the efficiency of the proposed estimation procedure under various conditions.

Assessing the performance of the log-normal distribution with left truncated survival data

This research focuses on assessing the performance of the log-normal distribution with left truncated and right censored (LTRC) survival data. Simulation studies were carried out to compare the bias, standard error and root mean square error (RMSE) of the parameter estimates for two different models for which the model ignores left truncation (model 1) and left truncation is accounted for (model 2) when right censored (setting 1) or complete observations (setting 2) are available. The results demonstrate that the bias and RMSE of the parameter estimates for model 1 are relatively higher compared to model 2 for both settings. Furthermore, the standard error appears to be underestimated for model 1 compared to model 2. Finally, a coverage probability study was conducted to assess the performance of Wald confidence interval estimates.

The application of simple errors in variables model on real data

The Ordinary Least Squares (OLS) method is the most widely used method to estimate the parameters of regression model. One of the critical assumption of the OLS estimation method is that the regression variables are measured without error. However, in many practical situations this assumption is often violated, whereby both dependent and independent variables are measured with errors. In these situations the OLS estimates lead to inconsistent and biased estimates. Consequently, the parameter estimates do not come closer to the true values, even in very large sample. To remedy this problem, instrumental variables (IV) estimation technique is utilized. In this article we examine some interesting numerical examples which are related to measurement errors. The results show that the IV estimates is more appropriate than the OLS estimates in such situations.

SIMULATION OF INTERVAL CENSORED DATA IN MEDICAL AND BIOLOGICAL STUDIES

This research looks at the simulation of interval censored data when the survivor function of the survival time is known and attendance probability of the subjects for follow-ups can take any number between 0 to 1. Interval censored data often arise in the medical and biological follow-up studies where the event of interest occurs somewhere between two known times. Regardless of the methods used to analyze these types of data, simulation of interval censored data is an important and challenging step toward model building and prediction of survival time. The simulation itself is rather tedious and very computer intensive due to the interval monitoring of subjects at prescheduled times and subjects incomplete attendance to follow-ups. In this paper the simulated data by the proposed method were assessed using the bias, standard error and root mean square error (RMSE) of the parameter estimates where the survival time T is assumed to follow the Gompertz distribution function.