MetaAnalyticSurvSurv {Surrogate}

Compute surrogacy measures for a time-to-event surrogate and a time-to-event true endpoint in the meta-analytic multiple-trial setting.

Description

The function 'MetaAnalyticSurvSurv()' fits the model for a time-to-event surrogate and time-to-event true endpoint developed by Burzykowski et al. (2001) in the meta-analytic multiple-trial setting.

Usage

MetaAnalyticSurvSurv(
  data,
  true,
  trueind,
  surrog,
  surrogind,
  trt,
  center,
  trial,
  patientid,
  copula,
  adjustment
)

Arguments

data

A data frame with the correct columns (See Data Format).

true

Observed time-to-event for true endpoint.

trueind

Time-to-event indicator for the true endpoint.

surrog

Observed time-to-event for surrogate endpoint.

surrogind

Time-to-event indicator for the surrogate endpoint.

trt

Treatment indicator.

center

Center indicator (equal to trial if there are no different centers). This is the unit for which specific treatment effects are estimated.

trial

Trial indicator. This is the unit for which common baselines are to be used.

patientid

Patient indicator.

copula

The copula that is used, either "Clayton", "Hougaard" or "Plackett"

adjustment

The adjustment that should be made for the trial-level surrogacy, either "unadjusted", "weighted" or "adjusted"

Value

Returns an object of class "MetaAnalyticSurvSurv" that can be used to evaluate surrogacy and contains the following elements:

• Indiv.Surrogacy: a data frame that contains the measure for the individual level surrogacy and 95% confidence interval.

• Trial.R2: a data frame that contains the R^2_{trial} and 95% confidence interval to evaluate surrogacy at the trial level.

• EstTreatEffects: a data frame that contains the estimated treatment effects and sample size for each trial.

• nlm.output: output of the maximization procedure (nlm) to maximize the likelihood.

Model

In the model developed by Burzykowski et al. (2001), a copula-based model is used for the true time-to-event endpoint and the surrogate time-to-event endpoint. More specifically, three copulas can be used: the Clayton copula, Hougaard copula and Plackett copula. The marginal model for the true and surrogate endpoint is the proportional hazard model. The quality of the surrogate at the individual level can be evaluated by by either Kendall's \tau or Spearman's \rho, depending on which copula function is used. The quality of the surrogate at the trial level can be evaluated by considering the R^2_{trial} between the estimated treatment effects.

Data Format

The data frame must contains the following columns:

• a column with the observed time-to-event for the true endpoint

• a column with the time-to-event indicator for the true endpoint: 1 if the event is observed, 0 otherwise

• a column with the observed time-to-event for the surrogate endpoint

• a column with the time-to-event indicator for the surrogate endpoint: 1 if the event is observed, 0 otherwise

• a column with the treatment indicator: 0 or 1

• a column with the trial indicator

• a column with the center indicator. If there are no different centers within each trial, the center indicator is equal to the trial indicator

• a column with the patient indicator

Author(s)

Dries De Witte

References

Burzykowski T, Molenberghs G, Buyse M, Geys H, Renard D (2001). “Validation of surrogate end points in multiple randomized clinical trials with failure time end points.” Journal of the Royal Statistical Society Series C: Applied Statistics, 50(4), 405–422

Examples

## Not run: 
data("Ovarian")
fit <- MetaAnalyticSurvSurv(data=Ovarian,true=Surv,trueind=SurvInd,surrog=Pfs,surrogind=PfsInd,
                            trt=Treat,center=Center,trial=Center,patientid=Patient,
                            copula="Plackett",adjustment="unadjusted")
print(fit)
summary(fit)
plot(fit)

## End(Not run)