# TrialLevelIT: 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., α_{i}), intercepts on S (i.e., μ_{i}) and T (i.e., β_{i}) in the different trials. See the Details section below.

### Usage

 1 2 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., α_{i}. Mu_S.Vector The vector of intercepts for S in the different trials, i.e., μ_{Si}. Only required when a full model is requested. Beta.Vector The vector of treatment effects on T in the different trials, i.e., β_{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 α-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:

{β}_{i}=λ_{0}+λ_{1}{μ_{Si}}+λ_{2}{α}_{i}+ \varepsilon_{i}, (1)

where β_i = the trial-specific treatment effects on T, μ_{Si} = the trial-specific intercepts for S, and α_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 ({β}_{i}=λ_{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 ≤ft(-\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:

{β}_{i}=λ_{0}+λ_{1}{α}_{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 ({β}_{i}=λ_{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.

UnimixedContCont, UnifixedContCont, BifixedContCont, BimixedContCont, plot.TrialLevelIT
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 # 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)