Causal Modeling to Estimate Sensitivity and Specificity of a Test when Prevalence Changes

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Abstract
The objective of this paper is to demonstrate, by causal modeling, whether the sensitivity and specificity of a test are constant, or whether they change with prevalence. I use three assumptions, diagnostic, predictive, and correlational, in three sets of mathematical models. A diagnostic test measures an outcome of a disease and is based on the assumption that the "gold standard" result indicates a disease state that causes a test result. A predictive test measures a risk factor for a disease and is based on the assumption that the test result indicates a risk factor that causes a disease state. A correlational test measures a condition which is an outcome of an underlying causal risk factor for a disease and is based on the assumption that the disease and the test result are noncausally related. I find that sensitivity and specificity are constant for diagnostic tests but change with prevalence for predictive and correlational tests. I present equations to show the effects on various test performance indices when prevalence changes. Different equations must be used to estimate the sensitivity, specificity, and other test performance indicators for various types of tests that are under different causal assumptions.

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