title: Reconciling the Log-Linear and Non-Log-Linear Nature of the TSH-Free T4 Relationship: Intra-Individual Analysis of a Large Population.
abstract: BACKGROUND
  The TSH-T4 relationship was thought to be inverse log-linear, but recent cross-sectional studies report a complex, nonlinear relationship; large, intra-individual studies are lacking.
  
  
  OBJECTIVE
  Our objective was to analyze the TSH-free T4 relationship within individuals.
  
  
  METHODS
  We analyzed data from 13 379 patients, each with six or more TSH/free T4 measurements and at least a 5-fold difference between individual median TSH and minimum or maximum TSH. Linear and nonlinear regression models of log TSH on free T4 were fitted to data from individuals and goodness of fit compared by likelihood ratio testing.
  
  
  RESULTS
  Comparing all models, the linear model achieved best fit in 31% of individuals, followed by quartic (27%), cubic (15%), null (12%), and quadratic (11%) models. After eliminating least favored models (with individuals reassigned to best fitting, available models), the linear model fit best in 42% of participants, quartic in 43%, and null model in 15%. As the number of observations per individual increased, so did the proportion of individuals in whom the linear model achieved best fit, to 66% in those with more than 20 observations. When linear models were applied to all individuals and averaged according to individual median free T4 values, variations in slope and intercept indicated a nonlinear log TSH-free T4 relationship across the population.
  
  
  CONCLUSIONS
  The log TSH-free T4 relationship appears linear in some individuals and nonlinear in others, but is predominantly linear in those with the largest number of observations. A log-linear relationship within individuals can be reconciled with a non-log-linear relationship in a population.
authors.affiliation: Department of Endocrinology and Diabetes (K.M.R., S.J.B., J.P.W.), Sir Charles Gairdner Hospital, Nedlands, Western Australia 6009, Australia; Department of Clinical Biochemistry (K.M.R., N.C.H., R.W.), PathWest Laboratory Medicine, Queen Elizabeth II Medical Centre, Nedlands, Western Australia 6009, Australia; Western Diagnostic Pathology (N.C.H.), Myaree, Western Australia 6154, Australia; School of Pathology and Laboratory Medicine, The University of Western Australia (N.C.H.), Crawley, Western Australia 6009, Australia; and School of Medicine and Pharmacology (J.P.W.), The University of Western Australia, Crawley, Western Australia 6009, Australia.
authors.forename: Karen M
authors.initials: KM
authors.lastname: Rothacker
authors.affiliation: Department of Endocrinology and Diabetes (K.M.R., S.J.B., J.P.W.), Sir Charles Gairdner Hospital, Nedlands, Western Australia 6009, Australia; Department of Clinical Biochemistry (K.M.R., N.C.H., R.W.), PathWest Laboratory Medicine, Queen Elizabeth II Medical Centre, Nedlands, Western Australia 6009, Australia; Western Diagnostic Pathology (N.C.H.), Myaree, Western Australia 6154, Australia; School of Pathology and Laboratory Medicine, The University of Western Australia (N.C.H.), Crawley, Western Australia 6009, Australia; and School of Medicine and Pharmacology (J.P.W.), The University of Western Australia, Crawley, Western Australia 6009, Australia.
authors.forename: Suzanne J
authors.initials: SJ
authors.lastname: Brown
authors.affiliation: Department of Endocrinology and Diabetes (K.M.R., S.J.B., J.P.W.), Sir Charles Gairdner Hospital, Nedlands, Western Australia 6009, Australia; Department of Clinical Biochemistry (K.M.R., N.C.H., R.W.), PathWest Laboratory Medicine, Queen Elizabeth II Medical Centre, Nedlands, Western Australia 6009, Australia; Western Diagnostic Pathology (N.C.H.), Myaree, Western Australia 6154, Australia; School of Pathology and Laboratory Medicine, The University of Western Australia (N.C.H.), Crawley, Western Australia 6009, Australia; and School of Medicine and Pharmacology (J.P.W.), The University of Western Australia, Crawley, Western Australia 6009, Australia.
authors.forename: Narelle C
authors.initials: NC
authors.lastname: Hadlow
authors.affiliation: Department of Endocrinology and Diabetes (K.M.R., S.J.B., J.P.W.), Sir Charles Gairdner Hospital, Nedlands, Western Australia 6009, Australia; Department of Clinical Biochemistry (K.M.R., N.C.H., R.W.), PathWest Laboratory Medicine, Queen Elizabeth II Medical Centre, Nedlands, Western Australia 6009, Australia; Western Diagnostic Pathology (N.C.H.), Myaree, Western Australia 6154, Australia; School of Pathology and Laboratory Medicine, The University of Western Australia (N.C.H.), Crawley, Western Australia 6009, Australia; and School of Medicine and Pharmacology (J.P.W.), The University of Western Australia, Crawley, Western Australia 6009, Australia.
authors.forename: Robert
authors.initials: R
authors.lastname: Wardrop
authors.affiliation: Department of Endocrinology and Diabetes (K.M.R., S.J.B., J.P.W.), Sir Charles Gairdner Hospital, Nedlands, Western Australia 6009, Australia; Department of Clinical Biochemistry (K.M.R., N.C.H., R.W.), PathWest Laboratory Medicine, Queen Elizabeth II Medical Centre, Nedlands, Western Australia 6009, Australia; Western Diagnostic Pathology (N.C.H.), Myaree, Western Australia 6154, Australia; School of Pathology and Laboratory Medicine, The University of Western Australia (N.C.H.), Crawley, Western Australia 6009, Australia; and School of Medicine and Pharmacology (J.P.W.), The University of Western Australia, Crawley, Western Australia 6009, Australia.
authors.forename: John P
authors.initials: JP
authors.lastname: Walsh
mesh_terms: D000328:Adult; D000368:Aged; D003430:Cross-Sectional Studies; D005260:Female; D006801:Humans; D007206:Individuality; D016014:Linear Models; D008297:Male; D008875:Middle Aged; D017711:Nonlinear Dynamics; D015588:Observer Variation; D011156:Population Density; D013960:Thyroid Function Tests / Q000706:statistics & numerical data*; D013972:Thyrotropin / Q000032:analysis / Q000097:blood*; D013974:Thyroxine / Q000032:analysis / Q000097:blood*
chemical_list: D013972:Thyrotropin; D013974:Thyroxine