Bland–Altman plots, rank parameters, and calibration ridit splines
Roger Newson ()
London Stata Conference 2019 from Stata Users Group
Scientists frequently work with pairs of alternative variables intended to measure the same quantity. Examples include measured and predicted disease prevalences in primary-care practices and marks awarded to student exam scripts by two different teachers. Statistical methods developed for use with such pairs of variables (A and B) may aim to measure components of disagreement between the variables (like discordance, bias, and scale differential), or they may aim to estimate one variable from the other (calibration). The Bland–Altman plot is the standard way of presenting a pair of alternative measures and allows us to visualize discordance, bias, and scale differential at the same time. However, it lacks parameters with confidence limits. The SSC packages somersd, scsomersd, and rcentile can be used to estimate rank parameters. They can measure discordance using Kendall's τa between A and B, bias using the mean sign and percentiles of A-B, and scale differential using Kendall's τa between A-B and A+B. For calibration (predicting A from B), we can use the SSC packages wridit and polyspline to define a ridit spline of A with respect to B. We can then plot the observed B and the predicted A (with confidence limits) against the ridit of B to create a continuous alternative to the standard decile plot commonly used for calibration.
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