Pred.TrialT.ContCont: Compute the expected treatment effect on the true endpoint in...

In Surrogate: Evaluation of Surrogate Endpoints in Clinical Trials

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 BimixedContCont, BifixedContCont, UnimixedContCont and UnifixedContCont. Some of the components in these fitted objects are needed to estimate E(\beta + b_0) and its variance.
mu_S0	The intercept of a regression model in the new trial i=0 where the surrogate endpoint is regressed on the true endpoint, i.e., S_{0j}=\mu_{S0} + \alpha_0 Z_{0j} + \varepsilon_{S0j}, where S is the surrogate endpoint, j is the patient indicator, and Z is the treatment. This argument only needs to be specified when a full model was used to examine surroacy.
alpha_0	The regression weight of the treatment in the regression model specified under argument mu_S0.
alpha.CI	The \alpha-level to be used to determine the confidence interval around E(\beta + b_0). Default alpha.CI=0.05.

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 \beta_0.
Variance	The variance of the prediction.
Lower	The lower bound of the confidence interval around the expected \beta_0, see Details above.
Upper	The upper bound of the confidence interval around the expected \beta_0.
alpha.CI	The \alpha-level used to establish the confidence interval.
Surr.Model	The model that was used to compute \beta_0.
alpha_0	The slope of the regression model specified in the Arguments section.

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)

Surrogate documentation built on June 22, 2024, 9:16 a.m.