Analysis of discrete lifetime data under middle-censoring and in the presence of covariates

Abstract

'Middle censoring' is a very general censoring scheme where the actual value of an observation in the data becomes unobservable if it falls inside a random interval (L, R) and includes both left and right censoring. In this paper, we consider discrete lifetime data that follow a geometric distribution that is subject to middle censoring. Two major innovations in this paper, compared to the earlier work of Davarzani and Parsian [3], include (i) an extension and generalization to the case where covariates are present along with the data and (ii) an alternate approach and proofs which exploit the simple relationship between the geometric and the exponential distributions, so that the theory is more in line with the work of Iyer et al. [6]. It is also demonstrated that this kind of discretization of life times gives results that are close to the original data involving exponential life times. Maximum likelihood estimation of the parameters is studied for this middle-censoring scheme with covariates and their large sample distributions discussed. Simulation results indicate how well the proposed estimation methods work and an illustrative example using time-to-pregnancy data from Baird and Wilcox [1] is included.

Middle censoring in the multinomial distribution with applications

“… Davarzani and Parsian (2011) discussed middle censoring in a discrete setup by taking observations from a geometric distribution. More recent references include Jammalamadaka and Leong (2015) where the authors discuss a middle censoring scheme for geometric random variables in the presence of covariates, and Ahmadi et al (2017) who consider middle censoring in the context of competing risks.…”

“…(4) in Iyer et al (2008) or Eqn. (1) in Jammalamadaka and Leong (2015) , except for the additional restrictions imposed by the conditions (1.1) , (1.2) due to the dependence among the categories, and their frequencies. Estimation for individual which is our main goal, becomes even more cumbersome when some of the intervals overlap.…”

An Additive Risks Regression Model for Middle-Censored Lifetime Data

“…In the presence of covariates, Sankaran & Prasad (2014) discussed a parametric proportional hazards regression model for the analysis of middle-censored lifetime data. Jammalamadaka & Leong (2015) analysed discrete middle-censored data in the presence of covariates with an accelerated failure time regression model. Recently, Jammalamadaka et al (2016) developed an iterative algorithm for analysing a semiparametric proportional hazards regression model under middle-censoring scheme, while Bennett et al (2017) considered a parametric accelerated failure time regression model under this censoring scheme.…”