Accelerated failure-time model with weighted least-squares estimation: application on survival of HIV positives

Background Survival analysis is the most appropriate method of analysis for time-to-event data. The classical accelerated failure-time model is a more powerful and interpretable model than the Cox proportional hazards model, provided that model imposed distribution and homoscedasticity assumptions satisfied. However, most of the real data are heteroscedastic which violates the fundamental assumption and consequently, the statistical inference could be erroneous in accelerated failure-time modeling. The weighted least-squares estimation for the accelerated failure-time model is an efficient semi-parametric approach for time-to-event data without the homoscedasticity assumption, which is developed recently and not often utilized for real data analysis. Thus, this study was conducted to ascertain the better performance of the weighted least-squares estimation method over the classical methods. Methods We analyzed a REAL dataset on Antiretroviral Therapy patients we recently collected. We compared the results from classical methods of estimation for the accelerated failure-time model with the results revealed from the weighted least-squares estimation. Results We found that the data are heteroscedastic and indicated that the weighted least-square method should be used to analyze this data. The weighted least-squares estimation revealed more accurate, and efficient estimates of covariates effect since its confidence intervals were shorter and it identified more significant covariates. Accordingly, the survival of HIV positives was found to be significantly linked with age, weight, functional status, CD4 (Cluster of Differentiation agent 4 glycoproteins), and clinical stages. Conclusions The weighted least-squares estimation performed the best in providing more significant effects and precise estimates than the classical accelerated failure-time methods of estimation if data are heteroscedastic. Thus, we recommend future researchers should utilize weighted least-squares estimation rather than the classical methods when the homoscedasticity assumption is violated.

The Hierarchical Rater Thresholds Model for Multiple Raters and Multiple Items

In educational measurement, various methods have been proposed to infer student proficiency from the ratings of multiple items (e.g., essays) by multiple raters. However, suitable models quickly become numerically demanding or even unfeasible as separate latent variables are needed to account for local dependencies between the ratings of the same response. Therefore, in the present paper we derive a flexible approach based on Thurstone’s law of categorical judgment. The advantage of this approach is that it can be fit using weighted least squares estimation which is computationally less demanding as compared to most of the previous approaches in the case of an increasing number of latent variables. In addition, the new approach can be applied using existing latent variable modeling software. We illustrate the model on a real dataset from the Trends in International Mathematics and Science Study (TIMMSS) comprising ratings of 10 items by 4 raters for 150 subjects. In addition, we compare the new model to existing models including the facet model, the hierarchical rater model, and the hierarchical rater latent class model.

Accelerated Failure Time Model with Weighted Least-Squares Estimation: Application on Survival of HIV Positives

BackgroundSurvival analysis is the most appropriate method of analysis for time to event data. The classical accelerated failure time model is a more powerful and interpretable model than the Cox proportional hazards model provided that, model imposed distributional and homoscedasticity assumptions satisfied. However, most of the real data are heteroscedastic which violate the fundamental assumption and consequently, the statistical inference could be erroneous in accelerated failure time modeling. Weighted least squares estimation for accelerated failure time model is an efficient semi-parametric approach for time to event data without the homoscedasticity assumption, which is developed recently and not often utilized for real data analysis. Thus, the study was conducted to ascertain the predictive performance of weighted least squares estimation method over the classical methods.MethodsWe analyzed a sample of 203 real Antiretroviral Therapy dataset. We compared the results from clasical methods of estimation for accelerated failure time model with the results revealed from the weighted least squares estimation.ResultsWe found that the data are heteroscedastic. The weighted least squares estimation revealed more accurate, and efficient estimates of covariates effect. It also detected more significant covariates. Accordingly, survival of HIV positives varies with age, weight, functional status, CD4 percent, and clinical stages.ConclusionsThe weighted least squares estimation performed best in predicting the survival of HIV patients. Thus, we recommend future researchers should utilize weighted least squares estimation rather than the classical methods when the homoscedasticity assumption is violated.

Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation.