Imputation methods for doubly censored HIV data

Comparison performance of the Bayesian Approach with the Weibull and Birnbaum-Saunders distributions in imputation of time-to-event censors

Almost all survival data is censored, and censor imputation is necessary. This study aimed to investigate the performance of the Bayesian Approach (BA) in the imputation of censored records in simulated and Breast Cancer (BC) data. Due to the difference in the distribution of time to event in survival analysis, two well-known the Weibull and Birnbaum-Saunders (BS) distributions have been used to test the performance of the BA. For each of the censored, 10,000 times were simulated using the BA in R and BUGS software, and their median or mean was imputed instead of each censor. The eligibility of both imputation methods was investigated using different curves, different censoring percentages, and sample sizes, as well as the Deviance Information Criteria (DIC), Effective Sample Size, and the Geweke diagnostic in simulated and especially real BC data. The BC data, which contains 220 patients who were identified and followed up between 2015 and 2023, was made accessible on February 1, 2023. The Kaplan-Meier, the BA, and other survival curves were drawn for the observed times. Findings indicated that the performance of the BA under the Weibull and BS distributions in simulated data is similar. The DIC index in the BC data under the BS distribution (1510) is less than the Weibull distribution (1698). Therefore, the BS distribution is preferred over the Weibull for imputation of censoring times in real BC data.

Semiparametric efficient estimation for additive hazards regression with case II interval-censored survival data

Interval-censored data often arise naturally in medical, biological, and demographical studies. As a matter of routine, the Cox proportional hazards regression is employed to fit such censored data. The related work in the framework of additive hazards regression, which is always considered as a promising alternative, remains to be investigated. We propose a sieve maximum likelihood method for estimating regression parameters in the additive hazards regression with case II interval-censored data, which consists of right-, left- and interval-censored observations. We establish the consistency and the asymptotic normality of the proposed estimator and show that it attains the semiparametric efficiency bound. The finite-sample performance of the proposed method is assessed via comprehensive simulation studies, which is further illustrated by a real clinical example for patients with hemophilia.

A flexible semiparametric modeling approach for doubly censored data with an application to prostate cancer

Doubly censored data often arise in medical studies of disease progression involving two related events for which both an originating and a terminating event are interval-censored. Although regression modeling for such doubly censored data may be complicated, we propose a simple semiparametric regression modeling strategy based on jackknife pseudo-observations obtained using nonparametric estimators of the survival function. Inference is carried out via generalized estimating equations. Simulations studies show that the proposed method produces virtually unbiased covariate effect estimates, even for moderate sample sizes. A prostate cancer study example illustrates the practical advantages of the proposed approach.

Approximating the baseline hazard function by taylor series for interval-censored time-to-event data

In many oncology clinical trials, time-to-event data are generated from scanning for cancer within a specific interval, resulting in interval censoring along with complete-time and right-left-censored time-to-event data. A common practice in analyzing data from this type of trial is to impute the interval-censored event time using the midpoint or right endpoint (i.e., the first observed time) of the interval so that well-known statistical methods developed for right-censored time-to-event data, such as Cox regression, may be used for the requisite analyses. This may introduce bias and lead to erroneous conclusions. In this paper, a Taylor series is proposed to approximate the log baseline hazard function in Cox proportional hazards regression to mitigate the bias arising from analyzing the imputed time-to-event data. With this formulation, the likelihood ratio test can be used to select an appropriate order for this Taylor series approximation and maximum likelihood techniques used to estimate model parameters and provide statistical inference, for example, on treatment effect. The application of this novel method is demonstrated by a simulation study and application to data from a breast cancer clinical trial.