Giancarlo Sal y Rosas
A common study design in epidemiology and clinical
research is the follow-up study in which a fixed number of participants are
followed for a period of time in order to observe some event such as death,
disease, development of a tumor, etc. In some cases, (e.g. tumor
development, asymptomatic disease) the exact time of the event may not be
observable. Instead, the participant is tested once at some pre-determined
time and the outcome is observed to have occurred or not occurred. Such data
are referred to as current status data or type I interval censored data.
Groeneboom and Wellner (1992) proposed two methods to estimate the
cumulative distribution function of the failure times in the absence of
covariate effects. The first is based on the EM-Algorithm, which arises
naturally because we can consider current status data as an example of a
missing data problem. The second method is based on isotonic regression.
Huang (1996) extended the idea to the Cox Proportional Hazard model with
current status data.
We extend these methods to the situation where the outcome is based on an
imperfect test (sensitivity and specificity less than one), so that we
expect some false positives and false negative outcomes in our data. In
particular, we discuss the estimation of the NPMLE using the EM algorithm
and isotonic techniques in the case of no covariate effect. We also discuss
the case of covariate effect (Proportional Hazard Model).