| Pred.TrialT.ContCont {Surrogate} | R Documentation |
Compute the expected treatment effect on the true endpoint in a new trial (when both S and T are normally distributed continuous endpoints)
Description
The key motivation to evaluate a surrogate endpoint is to be able to predict the treatment effect on the true endpoint T based on the treatment effect on S in a new trial i=0. The function Pred.TrialT.ContCont allows for making such predictions based on fitted models of class BimixedContCont, BifixedContCont, UnimixedContCont and UnifixedContCont.
Usage
Pred.TrialT.ContCont(Object, mu_S0, alpha_0, alpha.CI=0.05)
Arguments
Object |
A fitted object of class |
mu_S0 |
The intercept of a regression model in the new trial |
alpha_0 |
The regression weight of the treatment in the regression model specified under argument |
alpha.CI |
The |
Details
The key motivation to evaluate a surrogate endpoint is to be able to predict the treatment effect on the true endpoint T based on the treatment effect on S in a new trial i=0.
When a so-called full (fixed or mixed) bi- or univariate model was fitted in the surrogate evaluation phase (for details, see BimixedContCont, BifixedContCont, UnimixedContCont and UnifixedContCont), this prediction is made as:
E(\beta + b_0 | m_{S0}, a_0) = \beta + \left(\begin{array}{c}
d_{Sb}\\
d_{ab}
\end{array}\right)^T \left(\begin{array}{cc}
d_{SS} & D_{Sa}\\
d_{Sa} & d_{aa}
\end{array}\right)^{-1} \left(\begin{array}{c}
\mu_{S0} - \mu_S\\
\alpha_0 - \alpha
\end{array}\right)
Var(\beta + b_0 | m_{S0}, a_0) = d_{bb} + \left(\begin{array}{c}
d_{Sb}\\
d_{ab}
\end{array}\right)^T \left(\begin{array}{cc}
d_{SS} & D_{Sa}\\
d_{Sa} & d_{aa}
\end{array}\right)^{-1} \left(\begin{array}{c}
d_{Sb}\\
d_{ab}
\end{array}\right),
where all components are defined as in BimixedContCont. When the univariate mixed-effects models are used or the (univariate or bivariate) fixed effects models, the fitted components contained in D.Equiv are used instead of those in D.
When a reduced-model approach was used in the surrogate evaluation phase, the prediction is made as:
E(\beta + b_0 | a_0) = \beta + \frac{d_{ab}}{d_{aa}} + (\alpha_0 - \alpha),
Var(\beta + b_0 | a_0) = d_{bb} - \frac{d_{ab}^2}{d_{aa}},
where all components are defined as in BimixedContCont. When the univariate mixed-effects models are used or the (univariate or bivariate) fixed effects models, the fitted components contained in D.Equiv are used instead of those in D.
A (1-\gamma)100\% prediction interval for E(\beta + b_0 | m_{S0}, a_0) can be obtained as E(\beta + b_0 | m_{S0}, a_0) \pm z_{1-\gamma/2} \sqrt{Var(\beta + b_0 | m_{S0}, a_0)} (and similarly for E(\beta + b_0 | a_0)).
Value
Beta_0 |
The predicted |
Variance |
The variance of the prediction. |
Lower |
The lower bound of the confidence interval around the expected |
Upper |
The upper bound of the confidence interval around the expected |
alpha.CI |
The |
Surr.Model |
The model that was used to compute |
alpha_0 |
The slope of the regression model specified in the |
Author(s)
Wim Van der Elst, Ariel Alonso, & Geert Molenberghs
References
Burzykowski, T., Molenberghs, G., & Buyse, M. (2005). The evaluation of surrogate endpoints. New York: Springer-Verlag.
See Also
UnifixedContCont, BifixedContCont, UnimixedContCont
Examples
## Not run: #time-consuming code parts
# Generate dataset
Sim.Data.MTS(N.Total=2000, N.Trial=15, R.Trial.Target=.8,
R.Indiv.Target=.8, D.aa=10, D.bb=50, Fixed.Effects=c(1, 2, 30, 90),
Seed=1)
# Evaluate surrogacy using a reduced bivariate mixed-effects model
BimixedFit <- BimixedContCont(Dataset = Data.Observed.MTS, Surr = Surr,
True = True, Treat = Treat, Trial.ID = Trial.ID, Pat.ID = Pat.ID,
Model="Reduced")
# Suppose that in a new trial, it was estimated alpha_0 = 30
# predict beta_0 in this trial
Pred_Beta <- Pred.TrialT.ContCont(Object = BimixedFit,
alpha_0 = 30)
# Examine the results
summary(Pred_Beta)
# Plot the results
plot(Pred_Beta)
## End(Not run)