Purpose: The purpose of this study was to examine the impact of two vague priors on a Bayesian bivariate binomial model (BBBM) for meta-analysis of diagnostic tests.
Methods: Two vague priors were applied to a previously developed BBBM, which was created to analyze pairs of sensitivity and specificity values, while incorporating the correlation between these outcome variables. The vague priors used for the standard deviations of sensitivity and specificity respectively were a Uniform(0,2) and a half-Normal(0,100). Two thousand simulations were applied to four simulation scenarios to examine the impact of these priors on the posterior distributions of the model parameters compared to two previously used priors. All computations were implemented with Markov Chain Monte Carlo techniques using WinBUGS 1.4.2.
Results: Table 1 compares the posterior medians and standard errors obtained from the simulation studies of the BBBM using four different priors. The two new priors were conducted for the first 2,000 datasets while the inverse Wishart and Uniform(0,100) priors were extracted from previous simulation studies using 10,000 datasets. The point estimates of sensitivity and specificity were close to the true values and robust to changes of the four priors on the covariance matrix. However, the point estimates of the correlation coefficient between sensitivity and specificity (rho) were sensitive to changes of priors when the sample size was small (n=25 subjects per group). Specifically, rho obtained from the Uniform(0,2) and half-Normal(0,100) priors were -0.4899 and -0.4901 respectively, much closer to the true value (-0.5) when the sensitivity was set at 0.7 and the specificity at 0.8. Additionally, differences in rho estimates resulting from the two new priors and inverse Wishart were greater when both sensitivity and specificity were close to 1 (rho = -0.4953 and -0.4948 vs. -0.7271 when sensitivity = 0.9, specificity = 0.95). Deviations from the true value were consistently smaller with a sample size of 250 vs. 25 individuals per group.
Conclusions: When sample sizes are small, the rho estimate is sensitive to the change of prior distributions for BBBM for meta-analysis of diagnostic tests. Specifically, Uniform and half-Normal priors provide more accurate estimates than inverse-Wishart prior. These results indicate the importance of conducting sensitivity analyses using a range of different priors whenever new models are developed. 
Candidate for the Lee B. Lusted Student Prize Competition