Cox regression was used to compare the measurement error of two tests vs. a gold standard

The use of survival analysis has been proposed to compare the diagnostic performance of two tests. We expanded it to compare two tests with a gold standard simultaneously.

In this diagnostic study, the spherical equivalent component of refraction was measured with the PowerRefractor and the Canon R-50 autorefractor. The reference test was Canon R-50 autorefraction with cycloplegic blockage of accommodation. The error of the two index tests was compared with Cox regression analysis with robust standard error estimation to take into account repeated measures on the same subject. We evaluated 1,559 children aged 5-6 from 25 schools in three urban locations in Ecuador.

The main strength of survival analysis was that it does not assume a specific distribution of measurement errors, which were not normally distributed in this study. The proportional hazards assumption, a requirement of Cox regression, was met only after removal of the bias of each test. When this was done, noncycloplegic autorefraction was better than the PowerRefractor regardless of the magnitude and direction of the error.

The potential of Cox regression can be applied to diagnostic studies that compare more tests with a gold standard.