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Analyzing the Age-Related Macular Degeneration Dataset

The following command can be used to evaluate whether the change in visual acuity after 24 weeks is a good surrogate for the change in visual acuity after 52 weeks, as evaluated based on a reduced weighted mixed-effects approach in the information-theoretic framework:

> ARMD_Mixed_Fit_IT <- MixedContContIT(Dataset = ARMD,

Surr = Diff24, True = Diff52, Treat = Treat,

Trial.ID = Center, Pat.ID = Id, Model = "Reduced",

Weighted = TRUE)

Applying the summaryO function to the fitted object ARMD_Mixed_Fit_IT provides the following output:

> summary(ARMD_Mixed_Fit_IT)

# Generated output:

Function call:

MixedContContIT(Dataset = ARMD, Surr = Diff24, True = Diff52, Treat = Treat, Trial.ID = Center, Pat.ID = Id,

Model = "Reduced", Weighted = TRUE)

# Data summary and descriptives

Total number of trials: 36 Total number of patients: 181

M(SD) patients per trial: 5.0278 (2.9129) [min: 2; max: 18] Total number of patients in experimental treatment group: 84 Total number of patients in control treatment group: 97

TABLE 13.2

Surrogate package. Overview of the functions that can be used to evaluate surrogacy in the information-theoretic framework when both S and T are normally distributed endpoints.

Note. The indicator (. . .) refers to a number of required function arguments; for details see Section 13.2.2.

Full

Unweighted

Weighted

Mixed-effects

MixedContContITC..., Model="Full", Weighted=FALSE)

MixedContContITC•••, Model="Full", Weighted=TRUE)

Fixed-effects

FixedContContITC-.., Model="Full", Weighted=FALSE)

FixedContContITC-••, Model="Full", Weighted=TRUE)

Reduced

Unweighted

Weighted

Mixed-effects

MixedContContITC...,

Model="Reduced", Weighted=FALSE)

MixedContContITC•••, Model="Reduced", Weighted=TRUE)

Fixed-effects

FixedContContITC...,

Model="Reduced", Weighted=FALSE)

FixedContContITC-••, Model="Reduced", Weighted=TRUE)

Mean surrogate and true endpoint values in each treatment group:

Control.Treatment Experimental.treatment Surrogate -6.0309 -7.8095

True endpoint -11.7423 -14.6548

Var surrogate and true endpoint values in each treatment group:

Control.Treatment Experimental.treatment Surrogate 188.9261 132.6380

True endpoint 264.7975 231.7709

Correlations between the true and surrogate endpoints in the control (r_T0S0) and the experimental treatment groups (r_T1S1):

Estimate Standard Error CI lower limit CI upper limit r_T0S0 0.7693 0.0478 0.7022 0.8228

r_T1S1 0.7118 0.0525 0.6315 0.7770

# Information-theoretic surrogacy estimates summary

Trial-level surrogacy (R2_ht):

R2ht CI lower limit CI upper limit 0.6864 0.4750 0.8388

Individual-level surrogacy (R2_hind):

R2h.ind CI lower limit CI upper limit 0.5339 0.4315 0.6292

The first part of the output shows descriptives like the number of trials (here: centers) in the data, the means (variances) of S and T in the different treatment groups, and so on. The last part of the output provides the estimates of trial- and individual-level surrogacy. As can be seen, i?ht = 0.6864 with 95% confidence interval [0.4750; 0.8388], and .Rhindiv = 0.5339 with 95% confidence interval [0.4315; 0.6292] (the same results as in Section 10.2.1). These results thus indicate (i) that the uncertainty about the treatment effect on T that is reduced when the treatment effect on S becomes known (trial-level surrogacy) is moderate, and (ii) that the uncertainty about T that is reduced when S becomes known (individual-level surrogacy) is moderate as well.

The results can be further explored by applying the plot() function and by directly accessing the components in the fitted ARMD_Mixed_Fit_IT object in the same way as was illustrated in Section 13.2.1.

 
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