2 dependent tests, 1 population, no gold standard
WinBUGS 1.4 code to accompany the paper entitled "Branscum AJ, Gardner IA, Johnson WO. Estimation of diagnostic-test sensitivity and specificity through Bayesian modeling. Prev Vet Med. 2005 May 10;68(2-4):145-63".
Code prepared by Adam Branscum, November 18, 2003
branscum@ms.uky.edu
Departments of Biostatistics and Statistics
University of Kentucky
Example from section 3.3.3.1.
Two dependent tests / One population.
Estimation of the Se and Sp of two FAT tests.
Classical swine fever virus.
Data source: Bouma A, Stegeman JA, Engel B, de Kluijver EP, Elbers AR, De Jong MC.
Evaluation of diagnostic tests for the detection of classical swine fever in the field without a gold standard. J Vet Diagn Invest. 2001 Sep;13(5):383-8.
model;
{
x[1:4] ~ dmulti(p[1:4], n)
p[1] <- pi*(Sefat1*Sefat2+covDp) + (1-pi)*((1-Spfat1)*(1-Spfat2)+covDn)
p[2] <- pi*(Sefat1*(1-Sefat2)-covDp) + (1-pi)*((1-Spfat1)*Spfat2-covDn)
p[3] <- pi*((1-Sefat1)*Sefat2-covDp) + (1-pi)*(Spfat1*(1-Spfat2)-covDn)
p[4] <- pi*((1-Sefat1)*(1-Sefat2)+covDp) + (1-pi)*(Spfat1*Spfat2+covDn)
ls <- (Sefat1-1)*(1-Sefat2)
us <- min(Sefat1,Sefat2) - Sefat1*Sefat2
lc <- (Spfat1-1)*(1-Spfat2)
uc <- min(Spfat1,Spfat2) - Spfat1*Spfat2
pi ~ dbeta(13.322, 6.281) ### Mode=0.70, 95% sure > 0.50
Sefat1 ~ dbeta(9.628,3.876) ### Mode=0.75, 95% sure > 0.50
Spfat1 ~ dbeta(15.034, 2.559) ### Mode=0.90, 95% sure > 0.70
Sefat2 ~ dbeta(9.628, 3.876) ### Mode=0.75, 95% sure > 0.50
Spfat2 ~ dbeta(15.034, 2.559) ### Mode=0.90, 95% sure > 0.70
covDn ~ dunif(lc, uc)
covDp ~ dunif(ls, us)
rhoD <- covDp / sqrt(Sefat1*(1-Sefat1)*Sefat2*(1-Sefat2))
rhoDc <- covDn / sqrt(Spfat1*(1-Spfat1)*Spfat2*(1-Spfat2))
}
list(n=214, x=c(121,6,16,71))
list(pi=0.7, Sefat1=0.75, Spfat1=0.90, Sefat2=0.75, Spfat2=0.90)
node |
mean |
sd |
MC error |
2.50% |
median |
97.50% |
start |
sample |
Sefat1 |
0.7691 |
0.06151 |
9.16E-04 |
0.6497 |
0.7693 |
0.887 |
10001 |
100000 |
Sefat2 |
0.8147 |
0.06045 |
9.83E-04 |
0.6959 |
0.8156 |
0.9281 |
10001 |
100000 |
Spfat1 |
0.8851 |
0.0581 |
5.35E-04 |
0.7533 |
0.8924 |
0.975 |
10001 |
100000 |
Spfat2 |
0.8485 |
0.07411 |
5.83E-04 |
0.6856 |
0.8566 |
0.9667 |
10001 |
100000 |
rhoD |
0.6814 |
0.1484 |
0.001845 |
0.3135 |
0.7049 |
0.9071 |
10001 |
100000 |
rhoDc |
0.3629 |
0.2655 |
0.002054 |
-0.09339 |
0.361 |
0.858 |
10001 |
100000 |