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Age-related reference ranges based on cubic spline or kernel-based smoothing methods lack a parametric framework with which to assess goodness of fit, as the distribution of the log-likelihood ratio comparing models with different degrees of smoothing is not known in general. Several methods have been proposed to assess goodness of fit in this case: Healy's grid test, Royston's Q tests and van Buuren's worm plot. Here we compare the performance of the various methods, including an extension of the Q tests, and show how they can be used, with other information including the appearance of the fitted curves, to inform the choice of model for age-related reference ranges of height and weight in a large Dutch data set.
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Pan et al. (2004) studied this question.
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