Multivariate probability-based detection of drug-induced hepatic signals

Clinical signal detection of drug-induced hepatic effects is a very inexact science. Ordinary clinical laboratory tests are the primary biomarkers for liver changes. Heuristic rules have been developed by clinicians for diagnosing liver disease and monitoring these changes. These are based on laboratory reference limits, which are also largely heuristic. This article reviews some of the statistical characteristics of univariate reference limits and shows how they can and should be extended to multivariate reference regions. For instance, in the univariate approach, the probability of a false positive cannot be specified and grows with increasing numbers of analytes evaluated. However, accurate reference regions require very large samples from reference populations. Although the uniformly minimum variance unbiased estimator can greatly improve the mean-squared-error efficiency relative to a maximum likelihood estimator, it still requires tens of thousands of reference samples to estimate the 95% reference region for 20 analytes to an order of 95 +/- 1%, for example. Methods for constructing the elliptical reference region estimators and for sample size determination are provided. It is not feasible for small laboratories to make these calculations unless more rigorous methods of standardisation can be imposed and data merged across institutions. Large healthcare systems with electronic medical records and large pharmaceutical companies singly or in collaboration could generate sufficient sample sizes for accurate reference regions if techniques to make inter-laboratory results comparable are implemented. Exiting a reference region, whether population-based or individualised, can only tell you when the patient has changed from steady state. The region into which the patient's results enter and dynamics of this change are likely to contain considerable biological information. An example of this is Hy's rule. As the number of new, expensive biomarkers grows, it may be more cost-effective to find better ways to use the data we already collect, using the new biomarkers for validation. Mathematics and computers can help do this.