A kernel-assisted imputation estimating method for the additive hazards model with missing censoring indicator

A Survival Analysis Incorporating Auxiliary Information by a Bayesian Generalized Method of Moments: Application to Purchase Duration Modeling

“…However, if the censoring time C i is different for each subject i and C i cannot be known to researchers, then the censoring indicator cannot be fully observed in some cases. These incomplete censoring problems are also known as unknown censoring times or missing censoring indicators (Jonker, 2003;Subramanian, 2006Subramanian, , 2011Qiu et al, 2015). For example, van der Laan and McKeague (1998) noted in studies that relevant death certificate information can be missing or autopsy results and hospital case notes can be epidemiologically inconclusive, that is, the censoring indicators are sometimes missing.…”

“…However, it is inevitable that the last observed event precedes the true censoring, which underestimates the risk of events and leads to large biases (Jonker, 2003). Subramanian (2011) and Qiu et al (2015) propose a model considering the missing censoring indicator by imputation methods. Concretely, the authors assume the missing at random (MAR) for missing censoring indicator, that is, the authors model the missing censoring indicators, which are explained by observed time-to-event and covariates using the nonparametric imputation method or the parametric multiple-imputation method.…”

“…In the split hazard model, the indicators, which show that customers will eventually purchase a product, are partially unobserved. The two customer groups are divided using a logistic regression model, and the basic idea of Sinha and Chandrashekaran (1992) is the same as that of Subramanian (2011) or Qiu et al (2015, in which there is a need to specify the missing-mechanisms. Additionally, the same situations are found in marketing fields such as customer base analysis (e.g., Schmittlein and Peterson 1994).…”

“…First, we generate artificial datasets for the usual hazard model using true parameters. Second, we create a missing indicator using a logistic regression model as in Qiu et al (2015). To be more concrete, we set the probability that the time to event is missing to be a decreasing function of the time-to-event value T i .…”

Estimation of partly linear additive hazards model with left-truncated and right-censored data

“…Later, Martinussen and Scheike (2002) and Lu and Song (2012) used a semiparametric efficient score function to improve estimation efficiency, at the cost of estimating λ0false(tfalse) separately. Some of the recent literature that considered data arising from an AHM include bivariate current status data (Tong et al, 2012), current status data with auxiliary covariates (Feng et al, 2015), informative current status data (Zhao et al, 2015), clustered interval-censored data (Li et al, 2012), gap time data of recurrent events with multiple causes (Sankaran and Anisha, 2012), left-truncated and right-censored data (Huang and Qin, 2013), right-censored data with missing covariates (Hao et al, 2014), right-censored data with missing censoring indicator (Qiu et al, 2015), left-truncated and case I interval-censored data (Wang et al, 2015), right-censored data with instrumental variable (Li et al, 2015) and error-contaminated survival data with replicate measurements (Yan and Yi, 2016), among others.…”