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The efficacy of combining several risk factors as a screening test
Nicholas J Wald1, Joan K Morris, Simon Rish
1Wolfson Institute of Preventive Medicine, Barts and the London Queen Mary's School of Medicine and Dentistry, Charterhouse Square, London EC1 M 6BQ, UK. n.j.wald@qmul.ac.uk
Objective:
To determine the quantitative effect on overall screening performance (detection rate for a given false-positive rate) of using several moderately strong, independent risk factors in combination as screening markers.
Setting:
Theoretical statistical analysis.
Methods:
For the purposes of this analysis, it was assumed that all risk factors were independent, had Gaussian distributions with the same standard deviation in affected and unaffected individuals and had the same screening performance. We determined the overall screening performance associated with using an increasing number of risk factors together, with each risk factor having a detection rate of 10%, 15% or 20% for a 5% false-positive rate. The overall screening performance was estimated as the detection rate for a 5% false-positive rate.
Results:
Combining the risk factors increased the screening performance, but the gain in detection at a constant false-positive rate was relatively modest and diminished with the addition of each risk factor. Combining three risk factors, each with a 15% detection rate for a 5% false-positive rate, yields a 28% detection rate. Combining five risk factors increases the detection rate to 39%. If the individual risk factors have a detection rate of 10% for a 5% false-positive rate, it would require combining about 15 such risk factors to achieve a comparable overall detection rate (41%).
Conclusion:
It is intuitively thought that combining moderately strong risk factors can substantially improve screening performance. For example, most cardiovascular risk factors that may be used in screening for ischaemic heart disease events, such as serum cholesterol and blood pressure, have a relatively modest screening performance (about 15% detection rate for a 5% false-positive rate). It would require the combination of about 15 or 20 such risk factors to achieve detection rates of about 80% for a 5% false-positive rate. This is impractical, given the risk factors so far discovered, because there are too few risk factors and their associations with disease are too weak.
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