Comparison of two or more measurement techniques to a standard

With advancing medical technology come new and less invasive ways to measure the extent of a patient's disease. These techniques may be preferred to an invasive standard even if they are not quite as accurate. They may also be the only available tools because some patients are not sufficiently stable to be measured the standard way. The question then becomes, does one newer method more closely match the standard than another? For comparison of a single new method to a standard, one measures patients using each method and assesses the distribution of differences. But how does one compare the distributions of differences when there are multiple newer techniques? At least two components of these distributions are important. One is the mean difference or bias, but its absolute value is what is most relevant; a bias of -3 is better than a bias of +4. Another important component is the variance of the differences. If two methods have similar and small absolute bias, the one yielding a smaller variance of differences is preferred. We derive methods of comparing absolute biases, variances of errors, and parameters that combine biases and variances.