TwoStageSurvSurv: Assess trial-level surrogacy for two survival endpoints using...
In Surrogate: Evaluation of Surrogate Endpoints in Clinical Trials

TwoStageSurvSurv

R Documentation

Assess trial-level surrogacy for two survival endpoints using a two-stage approach

Description

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.

Usage

TwoStageSurvSurv(Dataset, Surr, SurrCens, True, TrueCens, Treat,
Trial.ID, Weighted=TRUE, Alpha=.05)

Arguments

`Dataset`	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.
`Surr`	The name of the variable in `Dataset` that contains the surrogate endpoint values.
`SurrCens`	The name of the variable in `Dataset` that contains the censoring indicator for the surrogate endpoint values (1 = event, 0 = censored).
`True`	The name of the variable in `Dataset` that contains the true endpoint values.
`TrueCens`	The name of the variable in `Dataset` that contains the censoring indicator for the true endpoint values (1 = event, 0 = censored).
`Treat`	The name of the variable in `Dataset` that contains the treatment indicators.
`Trial.ID`	The name of the variable in `Dataset` that contains the trial ID to which the patient belongs.
`Weighted`	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`.
`Alpha`	The `\alpha`-level that is used to determine the confidence intervals around `R^2_{trial}` and `R_{trial}`. Default `0.05`.

Details

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}.

Value

An object of class TwoStageSurvSurv with components,

`Data.Analyze`	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.
`Results.Stage.1`	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.
`Results.Stage.2`	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.
`Trial.R2`	A `data.frame` that contains the trial-level coefficient of determination (`R^2_{trial}`), its standard error and confidence interval.
`Trial.R`	A `data.frame` that contains the trial-level correlation coefficient (`R_{trial}`), its standard error and confidence interval.

Author(s)

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

References

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.

Examples

# 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)

Surrogate documentation built on Sept. 25, 2023, 5:07 p.m.