Mathematical models for predicting final achieved height and its standard deviation rate in children with growth hormone deficiency in the Russian population

Abstract

Background. Predicting the efficacy of rGH therapy in patients with GH deficiency, based on the final achieved height (FAH) criterion, is an important tool for the clinician. It enables a personalized approach to the treatment of patients with GH deficiency: to recommend careful adherence to the regimen and dosage of the drug, evaluate the efficacy of therapy in different groups of patients, and clearly demonstrate the factors affecting the FAH indicator.
 Aim — to develop mathematical models for predicting FAH and its standard deviation score (SDS) in patients with GH deficiency in the Russian population.
 Material and methods. For simulation, we used the data of 121 patients diagnosed with GH deficiency who received rGH since the time of diagnosis to the time of final height and were followed-up at the Institute of Pediatric Endocrinology of the Endocrinology Research Centre in the period between 1978 and 2016. As model predictors, we used 11 indicators: the gender, chronological age at the time of GH deficiency diagnosis, puberty status, disease form, regularity of rGH therapy, height SDS at birth, height SDS at the time of GH deficiency diagnosis, bone age at the time of GH deficiency diagnosis, bone age/chronological index, SDS of a genetically predicted height, and maximum stimulated GH level in a clonidine test. To generate models, we used multiple linear regression, artificial neural networks (ANNs), and the Statistica 13 software.
 Results. The developed ANNs demonstrated a high accuracy of predicting FAH (the root-mean-square error was 4.4 cm, and the explained variance fraction was 76%) and a lower accuracy of predicting the FAH SDS (the root-mean-square error was 0.601 SDS, and the explained variance fraction was 42%). Linear regression models that were based on quantitative predictors only had a substantially worse quality. Free software implementation was developed for the best produced ANN.
 Conclusion. An ANN-based software-implemented model for predicting FAH uses indicators available for any clinician as predictors and can be used for individual prediction of FAH. In the future, the use of larger databases for simulation will improve the quality of predicting the efficacy of rGH therapy.