Loss to follow-up weighted estimation method for survival analysis

In survival studies, patient's information may loss during the follow-up period and hence results in biased survival probabilities. Hence, in the present study, loss to follow-up weighted Kaplan-Meier (LFUWKM) method was derived to reduce such bias. The LFUWKM formed as generalization of the Kaplan-Meier (K-M) method provides reliable estimates when the LFU proportion is high. The variance, 95% CI, efficiency, uniform consistency and maximum likelihood estimate of the LFUWKM method were obtained. Simulation study for varied sample sizes was done for different parametric values and comparison of K-M and other weighted K-M methods (LFUWKM, weighted K-M (WKM) and empirical weighted K-M (EWKM)) were done using root mean square error (RMSE). The simulation study observed that all the methods are equally efficient for survival data with low censoring rate and high follow-up proportion. When 50% of the cases were censored, for small sample size, LFUWKM showed the least RMSE followed by K-M method for data with sufficient follow-up and WKM for follow-up < 80%. For large sample, the same trend was followed with WKM and EWKM with minor variations. For higher censoring rate of 70%, LFUWKM has the least RMSE followed by EWKM irrespective of sample size. Further the advantage of LFUWKM was illustrated using breast and cervix-uteri cancer patient data and the better model was identified based on absolute percentage variation. From both simulation and data analysis using R program, we recommend to use LFUWKM method to get a reliable survival estimate in the presence of high censoring, lower follow-up proportion and smaller sample size.