Abstract
In epidemiological studies where subjects are seen periodically on follow-up visits, interval-censored data occur naturally. The exact time the change of state (such as HIV seroconversion) occurs is not known exactly, only that it occurred sometime within a specific time interval. This paper considers estimation of parameters when HIV infection times are intervalcensored and correlated. It is assumed that each sexual partnership has a specific unobservable random effect that induces association between infection times. Parameters are estimated using the expectation-maximization algorithm and the Gibbs sampler. The results from the two methods are compared. Both methods yield fixed effects and baseline hazard estimates that are comparable. However, standard errors and frailty variance estimates are underestimated in the expectation-maximization algorithm compared to those from the Gibbs sampler. The Gibbs sampler is considered a plausible alternative to the expectation-maximization algorithm.
Highlights
Interval-censored data arise in research settings where the exact time an event occurs is not observed directly, but only the time interval to which the observation belongs is observed
The conjugate gamma frailty distribution often assumed in standard survival frailty model (Klein, 1992) is no longer conjugate in the interval-censored likelihood (Finkelstein, 1986; Huang and Wellner, 1997)
The conditional expectation E[bitij |Lij < tij ≤ Uij ; θ] is calculated using f where f is the joint conditional distribution obtained by first integrating out the remaining sexual partnership unobserved infection times tij, for j = j from Li(bi, vi, ti; θ)
Summary
Interval-censored data arise in research settings where the exact time an event occurs is not observed directly, but only the time interval to which the observation belongs is observed. Lurie (2003a; 2003b), and is the subject of our analysis, see Section 2 This dependency is often modelled as random effects or frailties. The conjugate gamma frailty distribution often assumed in standard survival frailty model (Klein, 1992) is no longer conjugate in the interval-censored likelihood (Finkelstein, 1986; Huang and Wellner, 1997). In this paper, both the interval-censored infection time and frailties are treated as missing data.
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