A comparison between Nonlinear Least Squares and Maximum Likelihood estimation for the prediction of tumor growth on experimental data of human and rat origin
Résumé
Several mathematical models have been developed to explain the growth of tumors and used to fit experimental or clinical data. Their predictive power – i.e. their ability to forecast the future growth on the basis of present knowledge – however, has been rarely explored. Here, we investigate whether a Hidden Markov Model (HMM) based on the well-established Gompertz tumor growth function with additive Gaussian noise could effectively be used to predict the future growth of experimental tumors. The idea behind this work is that one might achieve more accurate predictions if estimates of the unknown parameters of the HMM are used instead of those obtained by fits of the deterministic Gompertz model to the data. We use the principle of Maximum Likelihood (ML) to estimate unknown parameters related to growth dynamics and noise, and we compare its effectiveness to the classical Nonlinear Least Squares minimization approach. The analyses show that our approach can provide better growth predictions when the data contain adequate information concerning the tumors saturation phase. The forecasts could also be improved by taking into account prior knowledge about the unknown parameters when the information concerning the saturation phase was inadequate. We conclude that by using HMMs in combination with the principle of ML, one can obtain more reliable growth predictions for individual tumors.
Domaines
Systèmes et contrôle [cs.SY] Optimisation et contrôle [math.OC] Mathématique discrète [cs.DM] Traitement du signal et de l'image [eess.SP] Probabilités [math.PR] Cancer Biotechnologie Machine Learning [stat.ML] Statistiques [math.ST] Langage de programmation [cs.PL] Apprentissage [cs.LG] Intelligence artificielle [cs.AI] Mathématiques générales [math.GM] Calcul parallèle, distribué et partagé [cs.DC] Génie logiciel [cs.SE] Applications [stat.AP] Analyse numérique [math.NA] Méthodologie [stat.ME] Traitement du signal et de l'image [eess.SP] Calcul [stat.CO] Modélisation et simulation Mathématiques [math] Sciences du Vivant [q-bio]| Origine | Fichiers produits par l'(les) auteur(s) |
|---|
Loading...