Marginal versus joint Box–Cox transformation with applications to percentile curve construction for IgG subclasses and blood pressures

Abstract

When age-specific percentile curves are constructed for several correlated variables, the marginal method of handling one variable at a time has typically been used. We address the question, frequently asked by practitioners, of whether we can achieve efficiency gains by joint estimation. We focus on a simple but common method of Box-Cox transformation and assess the statistical impact of a joint transformation to multivariate normality on the percentile curve estimation for correlated variables. We find that there is little gain from the joint transformation for estimating percentiles around the median but a noticeable reduction in variances is possible for estimating extreme percentiles that are usually of main interest in medical and biological applications. Our study is motivated by problems in constructing percentile charts for IgG subclasses of children and for blood pressures in adult populations, both of which are discussed in the paper as examples, and yet our general findings are applicable to a wide range of other problems.

Classification using longitudinal trajectory of biomarker in the presence of detection limits

“…Several papers have discussed the Box-Cox transformation for censored data 24,25 and for correlated data. 26,27 Application of Box-Cox transformation to censored multivariate data merits further research. Although we introduce the discriminant analysis based on a single censored longitudinal biomarker, the extension to the multiple censored longitudinal biomarkers is possible because a complex covariance structure can be used in the linear mixed model to account for the correlations within subjects and between biomarkers.…”