Reconciling the log-linear and non-log-linear nature of the TSH-free T4 relationship: Intra-individual analysis of a large population

K.M. Rothacker, S.J. Brown, Narelle Hadlow, R. Wardrop, John Walsh

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    Abstract

    © 2016 by the Endocrine Society. Context: 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:Weanalyzed 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.
    Original languageEnglish
    Pages (from-to)1151-1158
    JournalJournal of Clinical Endocrinology and Metabolism
    Volume101
    Issue number4
    DOIs
    Publication statusPublished - 2016

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    Linear Models
    Population
    Nonlinear Dynamics
    Individuality
    Cross-Sectional Studies
    Testing

    Cite this

    @article{ece242b41cdb408798e96e7306944eb4,
    title = "Reconciling the log-linear and non-log-linear nature of the TSH-free T4 relationship: Intra-individual analysis of a large population",
    abstract = "{\circledC} 2016 by the Endocrine Society. Context: 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:Weanalyzed 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.",
    author = "K.M. Rothacker and S.J. Brown and Narelle Hadlow and R. Wardrop and John Walsh",
    year = "2016",
    doi = "10.1210/jc.2015-4011",
    language = "English",
    volume = "101",
    pages = "1151--1158",
    journal = "Journal of Endocrinology & Metabolism",
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    publisher = "ENDOCRINE SOC",
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    TY - JOUR

    T1 - Reconciling the log-linear and non-log-linear nature of the TSH-free T4 relationship: Intra-individual analysis of a large population

    AU - Rothacker, K.M.

    AU - Brown, S.J.

    AU - Hadlow, Narelle

    AU - Wardrop, R.

    AU - Walsh, John

    PY - 2016

    Y1 - 2016

    N2 - © 2016 by the Endocrine Society. Context: 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:Weanalyzed 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.

    AB - © 2016 by the Endocrine Society. Context: 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:Weanalyzed 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.

    U2 - 10.1210/jc.2015-4011

    DO - 10.1210/jc.2015-4011

    M3 - Article

    VL - 101

    SP - 1151

    EP - 1158

    JO - Journal of Endocrinology & Metabolism

    JF - Journal of Endocrinology & Metabolism

    SN - 0021-972X

    IS - 4

    ER -