Computation of profile likelihood-based confidence intervals for reference limits with covariates

Many biochemical quantities depend on age or some other covariate. Reference limits that allow for these dependencies help physicians to interpret the results of biochemical tests. Because reference limits must be estimated, it is important to assess their precision with, for example, confidence intervals. This paper relies on the assumption that data can be modeled by a generalized linear model and presents a method for calculating approximate profile likelihood-based confidence intervals for reference limits. The calculation of confidence intervals is based on a new method that draws on profile likelihood-based confidence intervals in general statistical models. The asset of this new method is that only two constrained optimization problems have to be solved instead of several in the standard method. We motivate our confidence interval calculation method with two applications. The first is for data on immunoglobulin concentration in the context of a generalized linear model with gamma distribution. This model is compared with the often used lognormal model. The second application handles data on serum alpha-fetoprotein and is presented in a linear regression situation. In the latter application the widths of the calculated profile confidence intervals are compared with exact and approximate regression-based intervals and the actual confidence levels are determined by simulation.