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

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.