A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data

The log-normal distribution is often used to model lifetime data due to its non-monotonic hazard rate. However, with left-truncated data the normal approximation fails due to the increased skewness in this distribution. This sometimes results in the poor performance of the confidence interval estimation based on the asymptotic normality of the maximum likelihood estimates, especially when the sample sizes are small. The purpose of this research is to compare and analyze the performance of the Wald, likelihood ratio and jackknife confidence intervals based on the widths of the intervals for the parameters of the log-normal model with fixed covariates through a coverage probability study. A lifetime data is therefore simulated under six different settings; model 1 (no truncation with exact observations), model 2 (low truncation with exact observations), model 3 (high truncation with exact observations), model 4 (no truncation with low censoring), model 5 (low truncation with low censoring) and model 6 (high truncation with low censoring). The comparative study indicates that the Wald, likelihood ratio and jackknife intervals performed reasonably well when no truncation or truncation is present and exact observations are available (model 1, model 2 and model 3) compared to when no truncation or truncation is observed with the presence of censoring (model 4, model 5 and model 6). Additionally, it is also evident from the results that the jackknife method outperformed the Wald and likelihood ratio methods specifically for the covariate parameter of the log-normal model even with small sample sizes when data is left-truncated with the presence of low censoring