MetaAnalyticSurvCat {Surrogate}

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

Description

The function 'MetaAnalyticSurvCat()' fits the model for a categorical (ordinal) surrogate and time-to-event true endpoint developed by Burzykowski et al. (2004) in the meta-analytic multiple-trial setting.

Usage

MetaAnalyticSurvCat(
  data,
  true,
  trueind,
  surrog,
  trt,
  center,
  trial,
  patientid,
  adjustment
)

Arguments

data

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

true

Observed time-to-event (true endpoint).

trueind

Time-to-event indicator.

surrog

Ordinal surrogate endpoint, coded as 1 2 3 ... K.

trt

Treatment indicator, coded as 0 or 1.

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.

adjustment

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

Value

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

• Indiv.Surrogacy: a data frame that contains the Global Odds and 95% confidence interval to evaluate surrogacy at the individual level.

• 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 function.

Model

In the model developed by Burzykowski et al. (2004), a copula-based model is used for the true endpoint and a latent continuous variable, underlying the surrogate endpoint. More specifically, the Plackett copula is used. The marginal model for the surrogate endpoint is a proportional odds model. For the true endpoint, the proportional hazards model is used. The quality of the surrogate at the individual level can be evaluated by using the copula parameter \Theta, which takes the form of a global odds ratio. 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 (true endpoint)

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

• a column with the ordinal surrogate endpoint: 1 2 3 ... K

• 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. (2004). The validation of surrogate end points by using data from randomized clinical trials: a case-study in advanced colorectal cancer. Journal of the Royal Statistical Society Series A: Statistics in Society, 167(1), 103-124.

Examples

## Not run: 
data("colorectal4")
fit <- MetaAnalyticSurvCat(data = colorectal4, true = truend, trueind = trueind, surrog = surrogend,
                           trt = treatn, center = center, trial = trialend, patientid = patid,
                           adjustment="unadjusted")
print(fit)
summary(fit)
plot(fit)

## End(Not run)