hiv: Intervals for infection time and disease onset for 257...
In Icens: NPMLE for Censored and Truncated Data

Description Format Details Source Examples

The hiv data frame has 257 rows and 4 columns.

This data frame contains the following columns:

yL: The left end point of the infection time interval.
yR: The right end point of the infection time interval.
zL: The left end point of the disease onset interval.
zR: The right end point of the disease onset interval.
Age: Coded as 1 if the estimated age at infection was less than 20 and 2 if the estimated age at infection was greater than 20.
Trt: Treatment, Light or Heavy

The setting is as follows. Individuals were infected with the HIV virus at some unknown time they subsequently develop AIDS at a second unknown time. The data consist of two intervals, (y_L, y_R) and (z_L,z_R), such that the infection time was in the first interval and the time of disease onset was in the second interval. A quantity of interest is the incubation time of the disease which is T=Z-Y. The authors argue persuasively that this should be considered as bivariate interval censored data. They note that simply forming the differences (z_L-y_R, z_R-y_L) and analysing the resultant data assumes an incorrect likelihood. DeGruttola and Lagakos transform the problem slightly to study the joint distribution of Y and T=Z-Y. This is equivalent to estimating the joint distribution of Z and Y then transforming. The data, as reported, have been discretized into six month intervals.

We use the data as reported in Table 1 of DeGruttola and Lagakos, 1989. The patients were 257 persons with Type A or B hemophilia treated at two hospitals in France. They were then examined intermittently (as they came in for treatment?) and their HIV and AIDS status was determined. Kim, De Gruttola and Lagakos report some covariate information and their paper is concerned with the modeling of that information. In this paper we concentrate only on the event times and ignore the covariate information; that topic being worthy of separate investigation.

DeGruttola, V. and Lagakos, S.W., 1989, Analysis of doubly-censored survival data, with application to AIDS, Biometrics.

Kim, Mimi Y. and De Gruttola, Victor G. and Lagakos, Stephen W., 1993, Analyzing Doubly Censored Data With Covariates, With Application to AIDS, Biometrics.