title: Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism.
abstract: OBJECTIVE
  This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it.
  
  
  METHODS
  The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4).
  
  
  RESULTS
  From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one.
  
  
  CONCLUSIONS
  The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second degree where the parabola is its graphical representation.
authors.affiliation: Camelia C. Scarneciu, MD, PhD. Faculty of Medicine, Transilvania University of Brasov, Brasov, Romania.
authors.forename: Camelia C
authors.initials: CC
authors.lastname: Scarneciu
authors.affiliation: Livia Sangeorzan, PhD. Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, Romania.
authors.forename: Livia
authors.initials: L
authors.lastname: Sangeorzan
authors.affiliation: Horatiu Rus, MD, PhD. Faculty of Medicine, Transilvania University of Brasov, Brasov, Romania.
authors.forename: Horatiu
authors.initials: H
authors.lastname: Rus
authors.affiliation: Vlad D. Scarneciu, MD, PhD. Candidate. Faculty of Medicine, Transilvania University of Brasov, Brasov, Romania.
authors.forename: Vlad D
authors.initials: VD
authors.lastname: Scarneciu
authors.affiliation: Mihai S. Varciu, MD, PhD. Faculty of Medicine, Transilvania University of Brasov, Brasov, Romania.
authors.forename: Mihai S
authors.initials: MS
authors.lastname: Varciu
authors.affiliation: Oana Andreescu, MD, PhD. Faculty of Medicine, Transilvania University of Brasov, Brasov, Romania.
authors.forename: Oana
authors.initials: O
authors.lastname: Andreescu
authors.affiliation: Ioan Scarneciu, MD, PhD. Faculty of Medicine, Transilvania University of Brasov, Brasov, Romania.
authors.forename: Ioan
authors.initials: I
authors.lastname: Scarneciu
keywords: Hyperthyroidism; Linear and Non-linear Regression; Pulmonary hypertension