TrialLevelIT {Surrogate}

Estimates trial-level surrogacy in the information-theoretic framework

Description

The function TrialLevelIT estimates trial-level surrogacy based on the vectors of treatment effects on S (i.e., \alpha_{i}), intercepts on S (i.e., \mu_{i}) and T (i.e., \beta_{i}) in the different trials. See the Details section below.

Usage

TrialLevelIT(Alpha.Vector, Mu_S.Vector=NULL, 
Beta.Vector, N.Trial, Model="Reduced", Alpha=.05)

Arguments

Alpha.Vector

The vector of treatment effects on S in the different trials, i.e., \alpha_{i}.

Mu_S.Vector

The vector of intercepts for S in the different trials, i.e., \mu_{Si}. Only required when a full model is requested.

Beta.Vector

The vector of treatment effects on T in the different trials, i.e., \beta_{i}.

N.Trial

The total number of available trials.

Model

The type of model that should be fitted, i.e., Model=c("Full") or Model=c("Reduced"). See the Details section below. Default Model=c("Reduced").

Alpha

The \alpha-level that is used to determine the confidence intervals around R^2_{trial} and R_{trial}. Default 0.05.

Details

When a full model is requested (by using the argument Model=c("Full") in the function call), trial-level surrogacy is assessed by fitting the following univariate model:

{\beta}_{i}=\lambda_{0}+\lambda_{1}{\mu_{Si}}+\lambda_{2}{\alpha}_{i}+ \varepsilon_{i}, (1)

where \beta_i = the trial-specific treatment effects on T, \mu_{Si} = the trial-specific intercepts for S, and \alpha_i = the trial-specific treatment effects on S. The -2 log likelihood value of model (1) (L_1) is subsequently compared to the -2 log likelihood value of an intercept-only model ({\beta}_{i}=\lambda_{3}; L_0), and R^2_{ht} is computed based based on the Variance Reduction Factor (for details, see Alonso & Molenberghs, 2007):

R^2_{ht}= 1 - exp \left(-\frac{L_1-L_0}{N} \right),

where N is the number of trials.

When a reduced model is requested (by using the argument Model=c("Reduced") in the function call), the following model is fitted:

{\beta}_{i}=\lambda_{0}+\lambda_{1}{\alpha}_{i}+\varepsilon_{i}.

The -2 log likelihood value of this model (L_1 for the reduced model) is subsequently compared to the -2 log likelihood value of an intercept-only model ({\beta}_{i}=\lambda_{3}; L_0), and R^2_{ht} is computed based on the reduction in the likelihood (as described above).

Value

An object of class TrialLevelIT with components,

Alpha.Vector

The vector of treatment effects on S in the different trials.

Beta.Vector

The vector of treatment effects on T in the different trials.

N.Trial

The total number of trials.

R2.ht

A data.frame that contains the trial-level coefficient of determination (R^2_{ht}), its standard error and confidence interval.

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.

Buyse, M., Molenberghs, G., Burzykowski, T., Renard, D., & Geys, H. (2000). The validation of surrogate endpoints in meta-analysis of randomized experiments. Biostatistics, 1, 49-67.

See Also

UnimixedContCont, UnifixedContCont, BifixedContCont, BimixedContCont, plot.TrialLevelIT

Examples

# Generate vector treatment effects on S
set.seed(seed = 1)
Alpha.Vector <- seq(from = 5, to = 10, by=.1) + runif(min = -.5, max = .5, n = 51)

# Generate vector treatment effects on T
set.seed(seed=2)
Beta.Vector <- (Alpha.Vector * 3) + runif(min = -5, max = 5, n = 51)

# Apply the function to estimate R^2_{h.t}
Fit <- TrialLevelIT(Alpha.Vector=Alpha.Vector,
Beta.Vector=Beta.Vector, N.Trial=50, Model="Reduced")

summary(Fit)
plot(Fit)