Biomedical Engineering Reference
In-Depth Information
6.4
Illustrative Real-Life Example
A multi-center prospective study was conducted in the 1980s to investigate
HIV-1 infection rate among people with hemophilia. The patients were at risk
from HIV-1 infection from blood products made from donors' plasma. In this
study, 544 patients were categorized into one of four groups according to the
average annual dose of the blood products they received: high-, median-, low-,
or no-dose group. The goal of this study was to compare the HIV-1 infection
rates between these dose groups and to quantify the dose effect. The exact
HIV-1 infection times were never observed, and only interval-censored data
are available. Among all the patients, 63 of them were left-censored, 204 were
interval-censored, and 277 were right-censored. More details about this study
can be found in Goedert et al. (1989) and Kroner et al. (1994). This typical
interval-censored data set has been analyzed by several researchers, including
Zhang et al. (2005) and Sun (2006), among others.
To analyze the data, we took three dummy variables xi3 i1 , x i2 , and x i3 to
indicate subject i to be in the low-, median-, and high-dose groups, respec-
tively. We specified monotone splines by taking 20 equally spaced knots within
(0; 60) and degree equal to 3 to ensure adequate smoothness. To allow for com-
parison, we used independent N(0; 100) priors for all j and took G(1; 1) prior
for the hyperparameter under all three models. The prior of 0 was taken
to be N(0; 100) under the Probit and PO models. A total of 10,000 iterations
were run for each method and fast convergence was observed. We summarized
the results based on the latter 10,000 iterations after discarding the first 1,000
iterations as a burn-in.
Table 6.1 presents the posterior means and the corresponding 95% credible
intervals of 1 , 2 , 3 , 2 1 , and 3 2 under each model. Note that the re-
gression parameters have different interpretations under different models; thus
it is not surprising that these estimates are different in Table 6.1. However, the
 
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