Table 3.

Piecewise generalized regression model for bone age minus chronological age

Parameter	Estimate	SE	95% confidence interval		P value
Intercept	-0.546	0.534	-1.593	0.500	0.31
t (treatment duration in y)	0.126	0.053	0.023	0.229	0.017
t2	-0.110	0.130	-0.366	0.145	0.040
Age at the start of therapy	-0.082	0.042	-0.164	0.000	0.049
Male (vs female)	0.156	0.381	-0.591	0.903	0.68
t + t2	0.015	0.105	-0.191	0.221	0.88

Note: For GENMOD, we set distribution=normal, link=identity, repeated measure=subject identification, covariance structure=compound symmetry; time point of slope change=6.5 (years). Parameter estimate for t is the slope before the change point (6.5 years); that for t+t₂ is the slope after the change point. The mathematical model for the piece-wise GENMOD is:

$${\displaystyle \begin{array}{l}{\displaystyle Y=b_0+b_{1}t+b_2{t}_2+c_1\left(\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{p}\mathrm{y}\right)+c_2\left(\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}\right),}\end{array}}$$

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}Y=CA-BA\mathrm{i}\mathrm{n}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s},}\end{array}}$$

$${\displaystyle \begin{array}{l}{\displaystyle t=\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{p}\mathrm{y}\mathrm{i}\mathrm{n}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s},\mathrm{a}\mathrm{n}\mathrm{d}}\end{array}}$$

$${\displaystyle \begin{array}{l}{\displaystyle t_2=\{\begin{array}{l}0,\mathrm{f}\mathrm{o}\mathrm{r}t=<6.5\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}\\ t-6.5\mathrm{f}\mathrm{o}\mathrm{r}t>6.5\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}\end{array}}\end{array}}$$

Abbreviation: GENMOD, generalized linear regression model.