Estimation of Survival Function for Interval-censored Sexually Transmitted Disease Data
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Attention often pivots on the distribution of the sexually transmitted disease (STD) true infection time based on interval-censored event time data. It occurs in biological and medical studies such as medical follow-up studies and clinical trials. The underlying survival function for the interval censored data can be estimated by imputing the unknown infection time from a list of sexual encounter times. Harezlak and Tu (2006) proposed an imputation based method for the estimation of the survival function of the infection time using auxiliary behavioral information provided by daily diaries. In this study, we propose a method by considering a similar situation but using additional information, whether a condom is used or not by the subjects during their coital episodes. We incorporated the STD data introduced in Harezlak and Tu (HT) study into three methods: HT, Turnbull (Turnbull, 1976), and our proposed method and then assessed the estimates of each method. Our proposed method survival estimates behaved close to Turnbull method and even closer to HT method. The lack of true survival estimates between the three methods led us to perform simulation in order to make comparison. Our simulation results of mean integrated squared error (MISE) estimates reveal that the proposed method perform slightly better against HT method when settings have four scheduled visits and close when there are eight and sixteen number of scheduled visits and significantly better in all other scheduled visit times against Turnbull. We also compared biases in terms of sample size (n = 100) and level of right censoring (20%, 35%, 50%) in the sample at various time points (0 – 260 days). The biases for the proposed method are smaller when compared against HT and Turnbull method.