In an additive model, the hazard function for the $j^{th}$ subject in the $i^{th}$ trial with random trial effect $u_i$ as well as the random treatment-by-trial interaction $v_i$ is:
$$\lambda_{ij}(t|u_i,v_i)=\lambda_0(t)exp(u_i+v_iX_{ij1}+\sum_{k=1}^{p}\beta_kX_{ijk})$$
$$u_i\sim\bold{\mathcal{N}}(0,\bold{\sigma^2}) \hspace{0.5cm} v_i\sim\bold{\mathcal{N}}(0,\bold{\tau^2})\hspace{0.5cm} \bold{cov}(u_i,v_i)=\bold{\rho\sigma\tau}$$
where $\lambda_0(t)$ is the baseline hazard function, $\beta_k$ the fixed effect associated to the covariate $X_{ijk}$ (k=1,..,p), $\beta_1$ is the treatment effect and $X_{ij1}$ the treatment variable. $\rho$ is the corresponding correlation coefficient for the two frailty terms.
additivePenal(formula, data, correlation = FALSE, recurrentAG =
FALSE, cross.validation = FALSE, n.knots, kappa1,
kappa2, maxit = 350)slope() function is requiredkappa1 (or kappa2), a solutINITIAL VALUES
The splines and the regression coefficients are initialized to 0.1. An adjusted Cox model is fitted, it provides new initial values for the splines coefficients and the regression coefficients. The variances of the frailties are initialized to 0.1. Then an additive frailty model with independent frailties is fitted. At last, an additive frailty model with correlated frailties is fitted.
print.additivePenal,
plot.additivePenal,
summary.additivePenal,
cluster,
slope,
strata,
Surv### Additive model with 1 covariate ###
data(dataAdditive)
modAdd<-additivePenal(Surv(t1,t2,event)~cluster(group)+var1+slope(var1),
correlation=TRUE,data=dataAdditive,n.knots=8,kappa1=10000)
# It takes around 4 minutes to converge. Var1 is boolean as a treatment variable. #
print(modAdd)
summary(modAdd)
plot(modAdd)Run the code above in your browser using DataLab