Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 46

Sensitivity, Specificity, and Receiver Operator Characteristic (ROC) Methods

Helena Chmura Kraemer

46.1 Evaluating a Single Binary Test Against a Binary Criterion

The basic problem is to evaluate a single binary test against a binary criterion. Consider a population in which the probability of a positive “gold standard” or “reference” diagnosis (D+) is P and a binary test in which the probability of a positive test (T+) is Q. The diagnosis represents the best criterion currently available to identify the disorder in question, but it is not usually available for routine use in clinical decision making (e.g., a result obtained on autopsy or from long-term follow-up). P may be a prevalence at the time of testing or an incidence during a fixed follow-up in the population of interest. The probability situation in the population is described in Table 1.

Table 1: Mathematical Definitions of, and Relationships Between, Odds Ratio and Other Common Measures of 2 × 2 Association, where a, b, c, and d Are the Probabilities of the Four Possible Responses in Relating Diagnosis (D+ and D−) To Medical Test (T+ and T−)

Odds ratio (OR) (also called the cross-product ratio) and resettled versions:

OR = ad/bc = (Se Sp)/(Se′Sp′) = (PVP PVN)/(PVP′PVN′) = RR₁RR₂ = RR₃RR₄

Gamma = (OR − 1)/(OR + 1) Yules index =

Risk ratios (also called likelihood ratios or relative risks): RR₁ = Se/(1 − Sp) ...