Case Study: The Age-Related Macular Degeneration Trial

The methodology that was detailed in the earlier sections of the current chapter is illustrated based on the data of the ARMD trial. The results of the case study are discussed without reference to the software tools that can be used to conduct the analyses. In Sections 12.3, 13.2.1, and 14.2, it is detailed how the analyses can be conducted in R, R Shiny, and SAS, respectively.

The ARMD study is a multi-center clinical trial in which the efficacy of interferon-a to treat age-related macular degeneration (ARMD) was evaluated (for details, see Section 2.2.1). Obviously, since the ARMD dataset consists of a single clinical trial, it is not possible to use trial as the clustering unit. Instead, center is used as the clustering unit in the analysis. A total of N = 36 such centers were available.

Analyses

The hierarchical modeling approach and the different simplifying model-fitting strategies (detailed in Sections 4.2 and 4.3) were applied to the data of the ARMD study. Table 4.2 summarizes the results. As can be seen, no trial- and

TABLE 4.2

Age-Related Macular Degeneration (ARMD) Trial. Trial- and individual-level surrogacy estimates and their 95% confidence intervals.

Note. — : model did not, converge.

Full

Reduced

Unweighted

Weighted

Unweighted

Weighted

Mixed-effects approach

Bivariate

p2

^Hrial

r>2

-“indiv

Univariate

c>2

^trial

f>2

-“indiv

0.6772 [0.4959; 0.8584] 0.5387 [0.3772; 0.7001]

0.8126 [0.6973; 0.9279] 0.5387 [0.3772; 0.7001]

0.6888 [0.5125; 0.8650] 0.5469 [0.4172; 0.6765]

0.8151 [0.7012; 0.9290] 0.5469 [0.4172; 0.6765]

Fixed-effects approach

Bivariate

p2

^trial

p2

?^Mndiv

0.6968 [0.5240; 0.8695] 0.4866 [0.3814; 0.5919]

0.7031 [0.5333; 0.8730] 0.4866 [0.3814; 0.5919]

0.6423 [0.4466; 0.8379] 0.5318 [0.4315; 0.6321]

0.6585 [0.4695; 0.8476] 0.5318 [0.4315; 0.6321]

Univariate

p2

-^trial

p2

?^Mndiv

0.6968 [0.5240; 0.8695] 0.4866 [0.2941; 0.6792]

0.7031 [0.5333; 0.8730] 0.4866 [0.2941; 0.6792]

0.6423 [0.4466; 0.8379] 0.5318 [0.3876; 0.6761]

0.6585 [0.4695; 0.8476] 0.5318 [0.3876; 0.6761]

FIGURE 4.1

Age-Related Macular Degeneration Trial. Scatter plot of the estimated вг (the treatment effect on the true endpoint, i.e., visual acuity after 52 weeks) against аг (the treatment effect on the surrogate endpoint, i.e., visual acuity after 24 weeks) based on the weighted and unweighted full bivariate fixed-effects model (left and right figures, respectively).

individual-level surrogacy estimates are provided for the (full and reduced) bivariate mixed-effects (hierarchical) models. The reason for this is that these models did not converge, a problem that often occurs in real-life datasets.

 
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