Abstract
BackgroundDue to early colonoscopy for some participants, interval-censored observations can be introduced into the data of a colorectal polyp prevention trial. The censoring could be dependent of risk of recurrence if the reasons of having early colonoscopy are associated with recurrence. This can complicate estimation of the recurrence rate.MethodsWe propose to use midpoint imputation to convert interval-censored data problems to right censored data problems. To adjust for potential dependent censoring, we use information from auxiliary variables to define risk groups to perform the weighted Kaplan-Meier estimation to the midpoint imputed data. The risk groups are defined using two risk scores derived from two working proportional hazards models with the auxiliary variables as the covariates. One is for the recurrence time and the other is for the censoring time. The method described here is explored by simulation and illustrated with an example from a colorectal polyp prevention trial.ResultsWe first show that midpoint imputation under an assumption of independent censoring will produce an unbiased estimate of recurrence rate at the end of the trial, which is often the main interest of a colorectal polyp prevention trial, and then show in simulations that the weighted Kaplan-Meier method using the information from auxiliary variables based on the midpoint imputed data can improve efficiency in a situation with independent censoring and reduce bias in a situation with dependent censoring compared to the conventional methods, while estimating the recurrence rate at the end of the trial.ConclusionThe research in this paper uses midpoint imputation to handle interval-censored observations and then uses the information from auxiliary variables to adjust for dependent censoring by incorporating them into the weighted Kaplan-Meier estimation. This approach can handle a situation with multiple auxiliary variables by deriving two risk scores from two working PH models. Although the idea of this approach might appear simple, the results do show that the weighted Kaplan-Meier approach can gain efficiency and reduce bias due to dependent censoring.
Highlights
Due to early colonoscopy for some participants, interval-censored observations can be introduced into the data of a colorectal polyp prevention trial
Application to ursodeoxycholic acid colorectal polyp prevention (UDCA) data In 1996, the Arizona Cancer Center initiated a multicenter trial to determine whether ursodeoxycholic acid (UDCA) can prevent the recurrence of colorectal adenomas [18]
We mainly focus on comparing the estimate of recurrence rate at the end of the trial between WKMc, WKMr, WKMr+c, KM, nonparametric maximum likelihood estimator (NPMLE), logistic regression (Logit), and weighted logistic regression (WLogit) methods
Summary
Due to early colonoscopy for some participants, interval-censored observations can be introduced into the data of a colorectal polyp prevention trial. To account for censoring, modified logistic regression using a weight function, a function of follow-up length, was used to estimate the recurrence rate at the end of the trial [1] Another potential estimator is the nonparametric maximum likelihood estimator (NPMLE) [2,3], which is often used to analyze interval-censored data. Often the reasons (e.g. family history of colorectal cancer and previous polyp history) of a participant having early colonoscopy are associated with risk of recurrence and could, induce dependent censoring into the data if some of participants with early colonoscopy are censored before the end of the trial. When the censoring is dependent of risk of recurrence, both the weighted logistic regression and the NPMLE approach could produce a biased estimate of the recurrence rate at the end of the trial
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