Kernel Estimation of Probability Density Functions for Interval-censored Sexually Transmitted Disease Data with Diary Information




Schmidt, Martin

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The purpose of this study is to propose a method to reliably estimate the survival function of the true infection time of a sexually transmitted disease (STD) based on interval-censored data with diary information. The survival function for interval-censored data can be estimated with Turnbull’s self-consistency algorithm (Turnbull, 1976) and Braun and Stafford’s (2005) proposed method. However, this data includes additional auxiliary behaviorial information, known as the diary information, in which patients record a list of sexual encounter times. In this study, we propose a method that incorporates a kernel smoothing (utilized by Braun and Stafford) and uses the addition diary information. The motivation for the study is with interval-censored data with auxiliary diary inforation provided by the Indiana University School of Medicine. Harzelak and Tu (2006) have a proposed method with the data we received but is a piecewise function like Turnbull’s that incorporated a product limit estimator. Hence, we will briefly mention Turbull’s algorthim and Harezlak and Tu’s method in the methods section. Furthermore, the advantage of using a kernel density estimate over a piecewise estimate allows for a continuous, smooth estimate that is flexible and easy to interpret. So in this research, we will focus the estimate of the true survival function with Braun and Stafford’s method and our proposed method. With data generated from a known true survival function in simulation, knowing the true survival function or desnity function we make comparisons between the two methods. We calculate the mean integrated squared error (MISE), mean square error (MSE) and bias estimates of the two methods. The results show that our method performs significantly better in most settings considered at different levels of right censoring (15%, 30%, and 40%).



Kernel, Estimation, Probability, Density, Function, STD


Schmidt, M. (2018). <i>Kernel estimation of probability density functions for interval-censored sexually transmitted disease data with diary information</i> (Unpublished thesis). Texas State University, San Marcos, Texas.


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