Regression analysis for current status data using the EM algorithm

Abstract

We propose new expectation-maximization algorithms to analyze current status data under two popular semiparametric regression models: the proportional hazards (PH) model and the proportional odds (PO) model. Monotone splines are used to model the baseline cumulative hazard function in the PH model and the baseline odds function in the PO model. The proposed algorithms are derived by exploiting a data augmentation based on Poisson latent variables. Unlike previous regression work with current status data, our PH and PO model fitting methods are fast, flexible, easy to implement, and provide variance estimates in closed form. These techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy.

A Gamma-frailty proportional hazards model for bivariate interval-censored data

“…For example, specifying the degree to be one, two or three corresponds to using linear, quadratic or cubic polynomials, respectively. In general, it has been suggested that specifying the degree of the polynomial basis functions to be either two or three results in adequate smoothness; e.g., see the discussion provided in McMahan et al (2013) and Wang et al (2016). In contrast, for modeling purposes, the selection of the number and placement of the knots plays a more important role when compared to choosing the degree, thus it is suggested that the strategies discussed in McMahan et al (2013) and Wang et al (2016) be adhered to when addressing this topic.…”

Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm

“…Further, we recommend that the knot set consist of a fixed number of equally spaced points between the minimum and maximum of the censoring times. Model selection criteria, such as Akaike's information criterion (AIC) or the Bayesian information criterion (BIC), can be used to determine the appropriate number of knots, as was demonstrated in Rosenberg (1995) and McMahan et al (2013). An alternative approach would be to treat both the number and position of the knots as unknown parameters and optimize over them according to some selection criterion as in Shen (1998) among others.…”

“…In this paper, we develop a computationally efficient method of analyzing bivariate current status data under the Gammafrailty PH model, by generalizing the work of McMahan et al (2013). Our formulation approximates the unknown conditional cumulative baseline hazard functions with monotone splines, which significantly reduces the number of unknown parameters while maintaining adequate modeling flexibility.…”

“…It is important to note that Λ 0j (·) is an infinite dimensional parameter. Following the work of Cai et al (2011) and McMahan et al (2013), we propose to model these unknown functions using the monotone splines of Ramsay (1988). Specifically, we assume that Λ 0j (·) can be written as,…”

Computationally Efficient Estimation for the Generalized Odds Rate Mixture Cure Model With Interval-Censored Data

“…Recently, a two-stage poisson data augmentation was proposed by McMahan et al (2013) for the PH and PO model with current status data, and was extended to the PH model with interval censored data by Wang et al (2016). In this article, we propose a new gamma-poisson data augmentation approach for the efficient estimation of the GORMC model with interval censored data.…”