The function TwoStageSurvSurv uses a two-stage approach to estimate \(R^2_{trial}\). In stage 1, trial-specific Cox proportional hazard models are fitted and in stage 2 the trial-specific estimated treatment effects on \(T\) are regressed on the trial-specific estimated treatment effects on \(S\) (measured on the log hazard ratio scale). The user can specify whether a weighted or unweighted model should be fitted at stage 2. See the Details section below.
TwoStageSurvSurv(Dataset, Surr, SurrCens, True, TrueCens, Treat,
Trial.ID, Weighted=TRUE, Alpha=.05)A data.frame that should consist of one line per patient. Each line contains (at least) a surrogate value and censoring indicator, a true endpoint value and censoring indicator, a treatment indicator, and a trial ID.
The name of the variable in Dataset that contains the surrogate endpoint values.
The name of the variable in Dataset that contains the censoring indicator for the surrogate endpoint values (1 = event, 0 = censored).
The name of the variable in Dataset that contains the true endpoint values.
The name of the variable in Dataset that contains the censoring indicator for the true endpoint values (1 = event, 0 = censored).
The name of the variable in Dataset that contains the treatment indicators.
The name of the variable in Dataset that contains the trial ID to which the patient belongs.
Logical. If TRUE, then a weighted regression analysis is conducted at stage 2 of the two-stage approach. If FALSE, then an unweighted regression analysis is conducted at stage 2 of the two-stage approach. See the Details section below. Default TRUE.
The \(\alpha\)-level that is used to determine the confidence intervals around \(R^2_{trial}\) and \(R_{trial}\). Default \(0.05\).
An object of class TwoStageSurvSurv with components,
Prior to conducting the surrogacy analysis, data of trials that do not have at least three patients per treatment arm are excluded due to estimation constraints (Burzykowski et al., 2001). Data.Analyze is the dataset on which the surrogacy analysis was conducted.
The results of stage 1 of the two-stage model fitting approach: a data.frame that contains the trial-specific log hazard ratio estimates of the treatment effects for the surrogate and the true endpoints.
An object of class lm (linear model) that contains the parameter estimates of the regression model that is fitted in stage 2 of the analysis.
A data.frame that contains the trial-level coefficient of determination (\(R^2_{trial}\)), its standard error and confidence interval.
A data.frame that contains the trial-level correlation coefficient (\(R_{trial}\)), its standard error and confidence interval.
A two-stage approach is used to estimate trial-level surrogacy, following a procedure proposed by Buyse et al. (2011). In stage 1, the following trial-specific Cox proportional hazard models are fitted:
$$S_{ij}(t)=S_{i0}(t) exp(\alpha_{i}Z_{ij}),$$ $$T_{ij}(t)=T_{i0}(t) exp(\beta_{i}Z_{ij}),$$
where \(S_{i0}(t)\) and \(T_{i0}(t)\) are the trial-specific baseline hazard functions, \(Z_{ij}\) is the treatment indicator for subject \(j\) in trial \(i\), \(\mu_{Si}\), and \(\alpha_{i}\) and \(\beta_{i}\) are the trial-specific treatment effects on S and T, respectively.
Next, the second stage of the analysis is conducted:
$$\widehat{\beta_{i}}=\lambda_{0}+\lambda_{1}\widehat{\alpha_{i}}+\varepsilon_{i},$$
where the parameter estimates for \(\beta_i\), \(\mu_{Si}\), and \(\alpha_i\) are based on the full model that was fitted in stage 1.
When the argument Weighted=FALSE is used in the function call, the model that is fitted in stage 2 is an unweighted linear regression model. When a weighted model is requested (using the argument Weighted=TRUE in the function call), the information that is obtained in stage 1 is weighted according to the number of patients in a trial.
The classical coefficient of determination of the fitted stage 2 model provides an estimate of \(R^2_{trial}\).
Burzykowski, T., Molenberghs, G., Buyse, M., Geys, H., & Renard, D. (2001). Validation of surrogate endpoints in multiple randomized clinical trials with failure-time endpoints. Applied Statistics, 50, 405-422.
Buyse, M., Michiels, S., Squifflet, P., Lucchesi, K. J., Hellstrand, K., Brune, M. L., Castaigne, S., Rowe, J. M. (2011). Leukemia-free survival as a surrogate end point for overall survival in the evaluation of maintenance therapy for patients with acute myeloid leukemia in complete remission. Haematologica, 96, 1106-1112.
# NOT RUN {
# Open Ovarian dataset
data(Ovarian)
# Conduct analysis
Results <- TwoStageSurvSurv(Dataset = Ovarian, Surr = Pfs, SurrCens = PfsInd,
True = Surv, TrueCens = SurvInd, Treat = Treat, Trial.ID = Center)
# Examine results of analysis
summary(Results)
plot(Results)
# }
Run the code above in your browser using DataLab