Purpose: The likelihood ratio of a diagnostic test is used to estimate the post-test probability of disease based upon the pre-test probability of disease. When diagnostic test results are affected by a confounding variable, stratum-specific likelihood ratios may differ from the overall crude likelihood ratio (Simpson's paradox). This presentation proposes the computation of an adjusted likelihood ratio in the presence of confounding.
Methods and Materials: 635 subjects underwent both echocardiographic and lower extremity Doppler examinations. We evaluated lower extremity venous pulsatility (our "diagnostic test") as a predictor of left ventricular dysfunction (the "disease state"). In addition to an overall crude analysis, a stratified analysis was performed based upon the presence of tricuspid regurgitation. We describe a mathematical model to compute the adjusted likelihood ratio for left ventricular dysfunction based upon our stratified analysis of lower extremity venous pulsatility.
Results: The overall crude analysis demonstrated a positive likelihood ratio of 1.2 and a negative likelihood ratio of 0.84 for lower extremity venous pulsatility as a predictor of left ventricular dysfunction. Stratified analysis demonstrated confounding based upon the presence of tricuspid insufficiency; stratified positive and negative likelihood ratios were closer to unity as compared with the overall crude likelihood ratio. By analogy with the Mantel-Haenszel adjusted estimator for odds ratios, we compute an adjusted estimator of the likelihood ratio for left ventricular dysfunction in the presence of confounding.
Conclusion: Just as confounding variables may influence the exposure-disease odds ratio, confounding variables may alter the computed likelihood ratio for a diagnostic examination. A classical example of confounding is demonstrated in the likelihood ratio for left ventricular dysfunction based upon lower extremity pulsatility. In order to adjust for the confounder (tricuspid regurgitation), an adjusted estimator of the likelihood ratio is computed (by analogy with the Mantel-Hanszel technique for adjusted odds ratios). The adjusted likelihood ratio provides an overall indication of the utility of lower extremity venous pulsatility as a predictor of left ventricular dysfunction.