Single covariate log-logistic model adequacy with right and interval censored data

Abstract

This research aims to analyze and examine the adequacy of the log-logistic model for a covariate, right, and interval censored data by using various types of imputation methods. We started by incorporating a covariate to the log-logistic model with right and interval censored data and obtained its parameter estimates via maximum likelihood estimation (MLE). Performance of the parameter estimates using the left, mid, and right point imputation methods is assessed and compared at various sample sizes and censoring proportions via a simulation study. The best imputation method is chosen based on minimum values of standard error (SE), and root mean square error (RMSE). Also, newly proposed Modified Cox-Snell residuals based on the geometric mean (GMCS) and harmonic mean (HMCS) were compared with Cox-Snell (CS) and Modified Cox-Snell (MCS) residuals via simulation study by comparing the range of residual’s intercept, slope, and R-square at different settings. Conclusions are then made based on the simulation results. The proposed residual worked well with real data and provided simple and easy interpretation of the results using log(-log(estimated survivor function of residual)) versus log(residual) plot. The results show the data is fitted well with the log-logistic model and gender of patients is not giving any significant impact on the development of diabetic nephropathy.