Analyzing the Data of Five Clinical Trials in Schizophrenia
Here, it is examined whether the dichotomized BPRS score (1 = clinically relevant change on the BPRS at the end of the treatment; 0 = no clinically relevant change at the end of the treatment) is an appropriate surrogate for the dichotomized PANSS score (1 = clinically relevant change on PANSS at the end of the treatment; 0 = no clinically relevant change at the end of the treatment) using the data of the five clinical trials in schizophrenia (for details, see Section 2.2.2). The data of only five trials were available, which is insufficient to use clinical trial as the cluster-level unit (see Section 4.4). In the different trials, information was also available regarding the psychiatrists who treated the patients. Hence, treating physician was used as the clustering unit in the analysis below.
After the Surrogate package and the Schizo dataset are loaded in memory (see Section 13.1), the function FixedBinBinIT() is called to conduct the analysis. Different models can be fitted (see Table 13.3). By means of illustration, a full weighted model is requested here:
> Schizo_BinBin <- FixedBinBinIT(Dataset = Schizo,
Surr = BPRS_Bin, True = PANSS_Bin, Treat = Treat,
Model = "Full", Weighted = TRUE, Trial.ID = InvestId,
Pat.ID = Id, Seed = 1) # Seed used for reproducibility
Applying the summary () function to the fitted object Schizo_BinBin provides the following output:
# Generated output:
FixedBinBinIT(Dataset = Schizo, Surr = BPRS_Bin,
Surrogate package. Overview of the functions that can be used to evaluate surrogacy in the information-theoretic framework when both S and T are binary endpoints.
Note. The indicator (. . .) refers to a number of required function arguments; for details see Section 13. f.
True = PANSS_Bin, Treat = Treat, Trial.ID = InvestId,
Pat.ID = Id, Model = "Full", Weighted = TRUE, Seed = 1)
# Data summary and descriptives
Total number of trials: 144
Total number of patients: 1988
M(SD) patients per trial: 13.8056 (10.1522) [min: 2; max: 52] Total number of patients in experimental treatment group: 1472
Total number of patients in control treatment group: 516
# Information-theoretic surrogacy estimates summary
Trial-level surrogacy (R2_ht):
R2ht CI lower limit CI upper limit 0.7414 0.6510 0.8155
Individual-level surrogacy (R2_h.ind):
R2h.ind CI lower limit CI upper limit 0.5392 0.5089 0.5688
The first part of the output shows descriptives like the number of trials in the data and the number of patients in the different treatment groups. Note that a total of 2128 patients participated in the five clinical trials, though the output shows that the data of only 1988 patients were actually included in the analyses.
The reason for this is that, prior to conducting the surrogacy analysis, data of patients who have a missing value for the surrogate and/or the true endpoint are excluded. In addition, the data of trials (or: clusters, treating physicians, . . . ) (i) in which only one type of the treatment was administered (i.e., all patients received the experimental treatment or all patients received the control treatment), and (ii) in which either the surrogate or the true endpoint was a constant (i.e., all patients within a trial had exactly the same surrogate and/or true endpoint value) are excluded because trial-specific treatment effects cannot be estimated in such trials (clusters). The subset of the dataset that was included in the analysis can be obtained by using the Schizo_BinBin$Data.Analyze command.
The second part of the output provides the estimates of trial- and individual-level surrogacy. The Rt = 0.7414 with 95% confidence interval
[0.6510; 0.8155], indicating that the uncertainty about the treatment effect on T = clinically relevant change on the PANSS that is reduced when the treatment effect on S = clinically relevant change on the BPRS becomes known (trial-level surrogacy) is relatively high. The individual-level surrogacy estimate equaled Rhindiv = 0.5392 with 95% confidence interval [0.5089; 0.5688] (see also the results in Section 10.7). These results thus indicate that the uncertainty about T that is reduced when S becomes known (individual-level surrogacy) is moderate. Overall, it can be concluded that clinically relevant change on the BPRS is a moderately good surrogate for clinically relevant change on the PANSS.
The results can be further graphically explored by applying the plot() function to the fitted Schizo_BinBin object. For example, a plot of the individual-level surrogacy estimates for each cluster can be obtained using the command:
# Plot of individual-level surrogacy (per cluster)
> plot(Schizo_BinBin, Indiv.Level.By.Trial = TRUE,
Trial.Level = FALSE)
# Generated output:
The figure shows the individual-level surrogacy estimates Rhindiv per cluster (treating physician). As can be seen, there was substantial variability in the point estimates for Rhind across clusters. Nonetheless, the 95% confidence intervals largely overlapped, indicating that the individual-level surrogacy estimates were of similar magnitude across trials.