Determining the Sensitivity and Specificity of a Substitute Test as a Diagnostic for its Gold Standard in the presence of Severe Missingness.

Abstract

When the need arises to identify a disease, substitute tests or screening tests are commonly used to recommend patients for its respective “Gold Standard”. Since it is seldom that these gold standards are carried out for those who pass the substitute tests, calculating the sensitivity and specificity of the substitute test has become a near impossible task using conventional methods. However, due to the life threatening nature of certain diseases such as coronary artery disease (CAD), understanding the effectiveness of these substitute tests in detecting the disease for sub-regions of the world is of utmost importance. Therefore, the primary objective of this study was to develop a theoretical framework to determine the sensitivity and specificity of a diagnostic test in the presence of severe missingness in the results of its gold standard. The methodology involves missing value imputation for the missing response, which is the result of the gold standard for those who have passed the substitute test. Logistic models were used to predict the existence of the disease using pre-defined risk factors. Subsequently, receiver operator characteristic (ROC) curves were used to confirm the existing cut-off for the substitute test. This procedure is illustrated on data from a retrospective study carried out in a General Hospital in Sri Lanka. The ROC curve analysis verified the existing Bruce protocol method cut-off as being the best to classify the existence of CAD. The study confirms that the results conform to world standards.