Parallel Weibull regression model.

This paper focuses on the lifetime analysis of parallel systems consisting of Weibull components with independent failures and covariates. The performance of the parameter estimates of two and three-component parallel systems at different values of the shape parameter, σ, are compared and some confidence interval procedures are analyzed via a coverage probability study for m = 2, using simulated data

Interval estimation for parameters of a bivariate time varying covariate model

This paper investigates several asymptotic confidence interval estimates, based on the Wald, likelihood ratio and the score statistics for the parameters of a parallel two-component system model, with dependent failure and a time varying covariate, when data is censored. This model is an extension of the bivariate exponential model. The procedures are investigated via a coverage probability study using the simulated data. The results clearly indicate that the interval estimates, based on the likelihood ratio method, work better than any of the other two methods when dealing with the censored data

Survival model of a parallel system with dependent failures and time varying covariates

In this paper, we extended a parallel system survival model based on the bivariate exponential to incorporate a time varying covariate. We calculated the bias, standard error and rmse of the parameter estimates of this model at different censoring levels using simulated data. We then compared the difference in the total error when a fixed covariate model was used instead of the true time varying covariate model. Following that, we studied three methods of constructing confidence intervals for such models and conclusions were drawn based on the results of the coverage probability study. Finally, the results obtained by fitting the diabetic retinopathy study data to the model were analysed

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 subject's 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

Bayesian estimation for Poisson process models with grouped data and covariate

This paper looks into the Bayesian approach for analyzing and selecting the best Poisson process model for grouped failure data from a repairable system with covariate. The extended powerlaw model with a recurrence rate that incorporates both time and covariate effect is compared to the powerlaw, log-linear and HPP models. We propose the use of both informative and noninformative priors depending on the nature of the parameter. The MCMC technique is utilized to obtain samples from the posterior distribution which was implemented via WinBUGS. We then apply the Bayesian Deviance Information Criteria (DIC) to select the best model for real data from ball bearing failures where information regarding previous failures are available. The credible interval is used to check the significance of the parameters of the selected model. We also used the posterior predictive distribution for model checking by comparing the observed and posterior predictive mean number of failures

Modeling repairable system failures with interval failure data and time dependent covariate

An application of a repairable system model for interval failure data with a time dependent covariate is examined. The performance of several models based on the NHPP when applied to real data on ball bearing failures is also explored. The best model for the data was selected based on results of the likelihood ratio test. The bootstrapping technique was applied to obtain the variance estimate for the estimated expected number of failures. Results demonstrate that the proposed model works well and is easy to implement, in addition the bootstrap variance estimate provides a simple substitute for the traditional estimate

Double Bootstrap Confidence Interval Estimates with Censored and Truncated Data

Traditional inferential procedures often fail with censored and truncated data, especially when sample sizes are small. In this paper we evaluate the performances of the double and single bootstrap interval estimates by comparing the double percentile (DB-p), double percentile-t (DB-t), single percentile (B-p), and percentile-t (B-t) bootstrap interval estimation methods via a coverage probability study when the data is censored using the log logistic model. We then apply the double bootstrap intervals to real right censored lifetime data on 32 women with breast cancer and failure data on 98 brake pads where all the observations were left truncated

Robust heteroscedasticity consistent covariance matrix estimator based on robust mahalanobis distance and diagnostic robust generalized potential weighting methods in linear regression

The violation of the assumption of homoscedasticity and the presence of high leverage points (HLPs) are common in the use of regression models. The weighted least squares can provide the solution to heteroscedastic regression model if the heteroscedastic error structures are known. Based on Furno (1996), two robust weighting methods are proposed based on HLP detection measures (robust Mahalanobis distance based on minimum volume ellipsoid and diagnostic robust generalized potential based on index set equality (DRGP(ISE)) on robust heteroscedasticity consistent covariance matrix estimators. Results obtained from a simulation study and real data sets indicated the DRGP(ISE) method is superior

Robust Heteroscedasticity Consistent Covariance Matrix Estimator based on Robust Mahalanobis Distance and Diagnostic Robust Generalized Potential Weighting Methods in Linear Regression

The violation of the assumption of homoscedasticity and the presence of high leverage points (HLPs) are common in the use of regression models. The weighted least squares can provide the solution to heteroscedastic regression model if the heteroscedastic error structures are known. Based on Furno (1996), two robust weighting methods are proposed based on HLP detection measures (robust Mahalanobis distance based on minimum volume ellipsoid and diagnostic robust generalized potential based on index set equality (DRGP(ISE)) on robust heteroscedasticity consistent covariance matrix estimators. Results obtained from a simulation study and real data sets indicated the DRGP(ISE) method is superior

Interval estimations for parameters of gompertz model with time-dependent covariate and right censored data

There are numerous parametric models for analyzing survival data such as exponential, Weibull, log-normal and gamma. One of such models is the Gompertz model which is widely used in biology and demography. Most of these models are extended to new forms for accommodating different types of censoring mechanisms and different types of covariates. In this paper the performance of the Gompertz model with time-dependent covariate in the presence of right censored data was studied. Moreover, the performance of the model was compared at different censoring proportions (CP) and sample sizes. Also, the model was compared with fixed covariate model. In addition, the effect of fitting a fixed covariate model wrongly to a data with time-dependent covariate was studied. Finally, two confidence interval estimation techniques, Wald and jackknife, were applied to the parameters of this model and the performance of the methods was compared