Table 1.
Total testosterone data summary.
Figure 1.
The validated model, log-adjusted testosterone values.
Our dataset (n = 10,098) of log-adjusted observed total testosterone for ages 3–88 years, split into normative ranges determined by mean predicted values (blue line) and one (red), two (blue), three (green), and four (purple) standard deviations higher and lower than the predicted values.
Figure 2.
The residuals are the variations in log-adjusted observed values from the log-adjusted age-related mean value predicted by the model. The residuals have excellent goodness of fit to an ideal Gaussian curve (r2 = 0.99). 71% of the residuals are within one standard deviations (SD) of the mean, 95% within 2 SD, and 99% within 3SD. The percentages for an ideal Gaussian distribution are 68%, 95% and 99% respectively.
Figure 3.
Exemplar of model validation stage.
High test and training errors represent underfit (i.e. insufficient model parameters to accurately capture essential features of the dataset), and high test errors represent overfit (i.e. a model that will not generalise to accurately predict new data). The optimal number of model parameters is seven in this instance, and in the analysis of the four other cross validation sets.
Table 2.
Model parameter values.
Figure 4.
Our dataset (n = 10,098) of observed total testosterone for ages 3–88 years, split into normative ranges determined by mean predicted values (blue line) and one (red), two (blue), three (green), and four (purple) standard deviations higher and lower than the predicted values.
Figure 5.
The validated model in centiles.
Normative ranges for the model of total testosterone from ages 3–88 years. In the average case (red line) total testosterone remains constant for age >40. However, the variance in normative ranges increases for these ages, with 1st to 99th centile ranges of 5.6–27.6 nmol/L at age 35 years and 4.1–33.1 nmol/L at age 88 years.
Table 3.
Normative age-related total testosterone reference values in nmol/L.