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To assess the non-linear association of sleep duration and difficulties with mortality outcomes, we calculated P-values for non-linear trend across categories of sleep duration and difficulties, using a quadratic term for the sleep variables.
We thereafter reanalysed our data using a quadratic term for each of the exposure variables to examine potential non-linear associations.
The possibility of a local maximum was tested using a quadratic term for year.
However, there was no statistical evidence for this possibility when investigated using a quadratic term (P = 0.38).
The possibility of a non-linear relationship between cortisol and depression was investigated using a quadratic term.
A nonlinear relationship between deprivation and survival was also modelled using a quadratic term (y= a+ bx+ cx).
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Likewise, LINE-1 hypomethylation was inversely linearly associated with CIMP-high (p for trend <0.0001), and there was no significant non-linearity by the likelihood ratio test, using a quadratic (or cubic) term (p≥0.078).
Model I: star experiment design using a quadratic polynomial without cross-terms; Model II: minimum experiment design using a quadratic polynomial with cross-terms; Model III: composite experiment design using a quadratic polynomial with cross-terms.
The time course of REE was analyzed by repeated-measures regression, using a quadratic curve of REE vs. time to describe the dip suggested by the data and confirming the significance of the quadratic term by the appropriate F-test.
In the analysis procedure, the approximation of the response, y, was determined using a quadratic polynomial regression model as a function of the pyrolysis parameters using Eq. 1, which has linear and quadratic terms in addition to an interaction term, where b is the regression coefficient, χ is the independent parameter, and e is the experimental error.
The results were analyzed using a quadratic loglog curve fit.
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