Statistical Methods in Diagnostic Medicine using SAS ® Software

An important goal in diagnostic medicine research is to estimate and compare the accuracies of diagnostic tests, which serve two purposes 1) providing reliable information about a patient’s condition and 2) influencing patient care. In developing screening tools, researchers often evaluate the discriminating power of the screening test by concentrating on the sensitivity and specificity of the test and the area under the ROC curve. We propose to give a gentle introduction to the statistical methods commonly used in diagnostic medicine covering some broad issues and scenarios. In particular, power calculations, estimation of the accuracy of a diagnostic test, comparison of accuracies of competing diagnostic tests, and regression analysis of diagnostic accuracy data will be discussed. Some existing SAS procedures and SAS macros for analyzing the data from diagnostic studies will be summarized. These concepts will be illustrated using datasets from clinical disciplines like radiology, neurology and infectious diseases. INTRODUCTION The purpose of a diagnostic test is to classify or predict the presence or absence of a condition or a disease. The clinical performance of a diagnostic test is based on its ability to correctly classify subjects into relevant subgroups. Essentially, these tests help answer a simple question: if a person tests positive, what is the probability that the person really has the disease / condition, and if a person tests negative, what is the probability that the person is really disease / condition free? As new diagnostic tests are introduced, it is important to evaluate the quality of the classification obtained from this new test in comparison to existing tests or the Gold Standard. In this review paper, we discuss the different methods used to quantify the diagnostic ability of a test (sensitivity, specificity, the likelihood ratio (LR), area under the receiver operating curve (ROC)), the probability that a test will give the correct diagnosis (positive predictive value and negative predictive value), and regression methods to analyze diagnostic accuracy data. We will also discuss comparisons of areas under two or more correlated ROC curves and provide examples of power calculations for designing diagnostic studies. These concepts will be illustrated using SAS macros and procedures. SIMPLE MEASURES OF DIAGNOSTIC ACCURACY The accuracy of any test is measured by comparing the results from a diagnostic test (positive or negative) to the true disease or condition (presence or absence) of the patient (Table 1). Table 1: Cross Classification of Test Results by Diagnosis Disease / Condition Test Results Present Absent Positive True Positive (TP) False Positive (FP) Negative False Negative (FN) True Negative (TN) The two basic measures of quantifying the diagnostic accuracy of a test are the sensitivity (SENS) and specificity (SPES) (Zhou et al., 2002). Sensitivity is defined as the ability of a test to detect the disease status or condition when it is truly present, i.e., it is the probability of a positive test result given that the patient has the disease or condition of interest. Specificity is the ability of a test to exclude the condition or disease in patients who do not have the condition or the disease i.e., it is the probability of a negative test result given that the patient does not have the disease or condition of interest. In describing a diagnostic test, both SENS and SPES are reported as they are inherently linked in that as the value of one increases, the value of the other decreases. SENS and SPES are also dependent on the patient characteristics and the disease spectrum. For example, advanced tumors are easier to detect than small benign lesions and detection of fetal maturity may be influenced by the gestational age of the patient (Hunink et al., 1990). In clinical practice, it is also important to know how good the test is at predicting the true positives, i.e., the probability that the test will give the correct diagnosis. This is captured by the predictive values. The positive predictive value (PPV) is the probability that a patient has the disease or condition given that the test results are positive, and the negative predictive value (NPV) is the probability that a patient does not have the disease or condition given that the test results are indeed negative. To illustrate these concepts, consider an example where results from a diagnostic test like x-ray or computer tomographic (CT) scan and the true disease or condition of the patient is known (Altman and Bland, 1994a). The different measures discussed above along with the 95% exact binomial confidence intervals for each estimate can be calculated (see Table 2A). Statistics and Data Analysis SUGI 30