# Multiple linear regression for comparison of diagnostic tests

Hi. I’m a pathologist. I’m interested in statistics but in the category of knowing enough to be dangerous I suspect. I want to do a study where I compare two diagnostic tests. One gives a continuous result, the other is categorical (yes/no). I suspect that how well they correlate depend on a number of other factors, some are categorical, some are continuous. My sample will be randomly drawn from a large collection of samples with an expected wide range of results. Can I use multiple regression for this? I want to have my continuous test as the outcome and my categorical test, along with the different factors I think would influence the correlation as covariates. I’m not so interested in how much of the variability in the outcome would be explained by the model (one of the covariates is going to correlate strongly with the outcome) but to estimate how much the covariates affect the correlation between the two tests. I suspect I’m wrong about something because I can’t find any studies doing this for diagnostic test assessment and my PI doesn’t understand what I mean. Would be thankful for input.

Some sort of regression (not sure it’s linear regression) is probably ideal for this. See Biostatistics for Biomedical Research - 19  Diagnosis and Statistical Thinking - Statistically Efficient Ways to Quantify Added Predictive Value of New Measurements. An easy statistical test is to see if test A adds diagnostic information to test B and whether B adds to A. If only one adds information you have a simpler answer.

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