**Generalized
Additive Mixed Model (available for Empower(R) only)**

This module applies generalized additive
mixed models to test for associations between risk factors and outcomes. You can specify the smoothing term to fit the
non-linear relationship and/or random effect terms (random intercept and/or
random time, time square term).

If a random effect variable (e.g. Time) is
specified, this module will examine the interactions of risk factors and the
random effect variable. It will compare 4 models and look for interaction, time-square term, and
random-slope versus random intercept.
These four models and LRT (log likelihood ratio test) test are listed in
the example below:

Outcome |
Y |

Risk factor |
X |

Model 1:Y = X + T + T |
ref. |

p-LRT(Model 2:Y = X + T + X*T + C) |
Pvalue |

p-LRT(Model 3:Y = X + T + T |
Pvalue |

p-LRT(Model 4:Y = X + T + C) |
Pvalue |

Selected Model |
1-4 |

p-LRT(random slope) |
Pvalue |

Y: Outcome, X: Exposure, T: Time, T^{2}:
Time-square, C: covariates

Model 1:Y = X + T + T^{2} + X*T + X*T^{2} + C, Random
Intercept, Method: ML

Model 2:Y = X + T + X*T + C, Random Intercept, Method: ML

Model 3:Y = X + T + T^{2} + C, Random Intercept, Method: ML

Model 4:Y = X + T + C, Random Intercept, Method: ML

p-LRT(model 2 vs. 1): P-value from LRT comparing model 2 vs
model 1

p-LRT(model 3 vs. 1): p-value from LRT comparing model 3 vs
model 1

p-LRT(model 4 vs. 1): p-value from LRT comparing model 4 vs
model 1

Selected Model: choose model with p-LRT > 0.05, in order of model
4->3->2->1

p-LRT(random slope+intercept vs
intercept): If model 3 or 4 was selected, LRT comparing model with random slope+intercept vs. random intercept only

This module was used for analyzing
repeated measurement/longitudinal data.

**Screen
shot of sample design:**

**Sample
output tables:**