| In an ideal study of diagnostic tests, the new diagnostic test and the gold standard should be applied to each patient suspected of the disease. But the reality is that the gold standard is not applicable due to many limitations, such as its invasiveness, high cost, or technical challenge. This project was motivated by the meta-analysis of diagnostic tests for deep vein thrombosis (DVT). In diagnosing DVT, the gold standard is venography, which is invasive and often not applicable to every patient. In fact, it was applied only in a small number of studies. A concurrent reference is ultrasonography, which is not risky to patients and has well known diagnostic characteristics. D-dimer is a new test of interest for DVT. Among the studies of d-dimer, a substantial amount of studies applied ultrasonography as the reference. The aim of this project is to develop statistical methods to estimate the diagnostic performance of d-dimer by synthesizing studies using both references.In summary, this project provided statistical methods for the meta-analysis of diagnostic tests in the absence of complete data. Results between the test of interest and an imperfect reference can be used to estimate the diagnostic performance of the test of interest, provided that appropriate adjustments were performed. This finding has a strong impact in the literature of diagnostic tests: the gold standard may not be necessary in assessing a new test. This is a real milestone in diagnostic tests where the gold standard diagnosis is invasive or harmful to patients.By assuming known values of sensitivity and specificity of ultrasonography, maximum likelihood estimation was applied to acquire estimates of coefficients in the log-linear model. When the sensitivity and specificity of ultrasonography were not available, data from a systematic review of ultrasonography [6] were employed. Two approaches to estimating the diagnostic accuracy of d-dimer were compared: admitting the difference between the two references and ignoring the difference. Taking into account heterogeneity across studies, the log-linear model was fitted with random disease prevalence and random association between d-dimer and gold standard. Two algorithms, the Gaussian Hermite integration and the Gibbs sampling, were applied to derive estimates in the random effects model. In the model with two random effects, a new design matrix of random effects based on -1 1 contrast was applied to improve estimates. This project was a novel application of the Gaussian Hermite integration and the Gibbs sampling in the meta-analysis of incomplete multinomial data. |
