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Analyzing the Ovarian Cancer Dataset

After the Surrogate package and the Ovarian dataset are loaded into memory (see Section 13.1), the following command can be used to examine whether progression-free survival (PFS) is an appropriate surrogate for overall survival (OS):

> Ovarian_SurvSurv <- SurvSurv(Dataset = Ovarian, Surr = Pfs, SurrCens = PfsInd, True = Surv, TrueCens = SurvInd,

Treat = Treat, Trial.ID = Center)

• Generated output:

Note. The trial with ID 28 did not have >=3 observations in each treatment arm and was excluded from the trial-level analyses (estimation of R2_ht) due to estimability constraints.

(...)

Note. The trial with ID 66 did not have >=3 observations in each treatment arm and was excluded from the trial-level analyses (estimation of R2_ht) due to estimability constraints.

Note that trials (clusters) with less than 3 observations are not considered in the analyses due to estimability constraints (Burzykowski et al., 2001). When such trials (clusters) are present in the dataset, the user is warned that these will not be considered in the analysis.

The fitted object Ovarian_SurvSurv (of class SurvSurv) is placed in the R workspace and it can subsequently be examined. To explore the results, the summary() function can be applied:

> summary(Ovarian_SurvSurv)

# Generated output:

Function call:

SurvSurv(Dataset = Ovarian, Surr = Pfs, SurrCens = PfsInd, True = Surv, TrueCens = SurvInd, Treat = Treat,

Trial.ID = Center)

# R"2_trial results

R2_trial Standard Error CI lower limit CI upper limit 0.9184 0.0261 0.8674 0.9695

# R"2_{h.ind} (LRF) results

Overall R~2_{h.ind> (LRF):

R2h.ind CI lower limit CI upper limit 0.7446 0.7152 0.7720

# R"2_{h.ind.QF} (LRF_a; O'Quinly and Flandre, 2006) results

Overall R~2_{h.ind.QF> (LRF_a):

R2h.ind.QF CI lower limit CI upper limit 0.8193 0.7928 0.8433

R"2_{h.ind.QF} (LRF_a) per trial:

TrialID R2h.ind R2h_low R2h_up

  • 1 -4.0000 0.8408 0.7555 0.9021
  • 2 -3.0000 0.7279 0.6578 0.7884
  • 3 2.0000 0.7847 0.3171 0.9687
  • (...)

4 3.0000 0.8313 0.5220 0.9621 42 109.0000 0.9757 0.8185 0.9985 43 111.0000 0.8048 0.5635 0.9334

The top of the output shows that R%rial = 0.9184, with 95% confidence interval [0.8674; 0.9695]. This result thus indicates that PFS is a good surrogate for

05 at the level of the trial (cluster), i.e., the treatment effect on OS can be predicted with a high level of accuracy based on the predicted treatment effect on PFS.

The individual-level results are shown below the trial-level results. As can be seen, the estimated LRF = 0.7446 with 95% confidence interval [0.7152; 0.7720], and LRFa = 0.8193 with 95% confidence interval [0.7928; 0.8433]. Thus, the amount of uncertainty in T = OS that is removed when the value of S = PFS becomes known is quite high as well. Overall, the results indicate that PFS is a good surrogate for OS at both the levels of the individual patients and the trials (clusters).

At the end of the output, estimates of LRFa (and their 95% confidence intervals) are provided for each of the trials (clusters) separately. For example, when attention is restricted to the first trial (cluster) in the dataset (coded as TriallD = -4 in the Ovarian dataset), it is obtained that LRFai = 0.8408 with 95% confidence interval [0.7555; 0.9021].

The results can be graphically explored by applying the plot() function to the fitted 0varian_SurvSurv object:

# Plot of trial-level surrogacy

> plot(Ovarian_SurvSurv, Indiv.Level.By.Trial = FALSE,

Trial.Level = TRUE)

# Generated output:

The R Package Surrogate

237

# Plot of individual-level surrogacy (per cluster)

> plot(Ovarian_SurvSurv, Indiv.Level.By.Trial = TRUE, Trial.Level = FALSE)

# Generated output:

The first figure (trial-level plot) confirms the earlier conclusion that the treatment effect on T = OS (i.e., /%) can be accurately predicted based on the treatment effect on S = PFS (i.e., <%). The second figure shows the individual- level surrogacy estimates LRFa per trial (cluster). As can be seen, the point estimates for LRFa were similar in most clusters (units) and tended to be above 0.65. In cluster 59, the point estimate of the LRFa equaled only 0.0639, though its 95% confidence interval overlapped with many of the confidence intervals of the other clusters. This indicates that the individual-level association between S = PFS and T = OS is of the same magnitude across trials (centers).

 
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