Improved accuracy when screening for human growth disorders by likelihood ratios.
The standard deviation score (SDS) is a powerful tool for screening for growth-related problems. However, referral rules of the type 'if SDS(Y)<d, then refer' (for some constant d) are not optimal for answering the question: 'Does this child with measurement Y belong to the reference or to the diseased population?'. If the growth standard for the diseased population is known, then the likelihood ratio (LR) and the log-likelihood ratio (LLR) can be calculated for individual measurements. Rules of the type 'if LLR(Y)<e, then refer' are uniformly the most powerful test for any constant e, implying that their receiver operating characteristic curves are above those for all other possible tests based on Y. As an empirical demonstration, both types of rules are applied to longitudinal growth data comparing a group with diagnosed Turner syndrome and a reference group from birth to 10 years of age. Conforming with theory, the LR rules were found to be superior to the SDS rules in terms of sensitivity and specificity. We conclude that the LR is the natural measure for two-group studies that can be easily calculated for individual measurements. The LR is firmly rooted within both statistical and decision theory and can be used to estimate the absolute probability of disease.
van Buuren
Stef
S
TNO Quality of Life, P.O. Box 2215, 2301 CE Leiden, The Netherlands. Stef.vanBuuren@tno.nl
D001699:Biometry; D002648:Child; D002675:Child, Preschool; D005260:Female; D006130:Growth Disorders / Q000175:diagnosis*; D006801:Humans; D007223:Infant; D007231:Infant, Newborn; D016013:Likelihood Functions; D008297:Male; D008403:Mass Screening / Q000706:statistics & numerical data*; D009426:Netherlands; D011336:Probability; D014424:Turner Syndrome / Q000175:diagnosis