FederatedApproachStage2: Fits the second stage model in the two-stage federated data...

In Surrogate: Evaluation of Surrogate Endpoints in Clinical Trials

Fits the second stage model in the two-stage federated data analysis approach.

Description

The function 'FederatedApproachStage2()' fits the second stage model of the two-stage federated data analysis approach to assess surrogacy.

Usage

FederatedApproachStage2(
  Dataset,
  Intercept.S,
  alpha,
  Intercept.T,
  beta,
  sigma.SS,
  sigma.ST,
  sigma.TT,
  Obs.per.trial,
  Trial.ID,
  R.list,
  Alpha = 0.05
)

Arguments

Dataset	A data frame with the correct columns (See Data Format).
Intercept.S	Estimated intercepts for the surrogate endpoint.
alpha	Estimated treatment effects for the surrogate endpoint.
Intercept.T	Estimated intercepts for the true endpoint.
beta	Estimated treatment effects for the true endpoint.
sigma.SS	Estimated variance of the error terms for the surrogate endpoint.
sigma.ST	Estimated covariance between the error terms of the surrogate and true endpoint.
sigma.TT	Estimated variance of the error terms for the true endpoint.
Obs.per.trial	Number of subjects in the trial.
Trial.ID	Trial indicator.
R.list	List of the variance-covariance matrices of the fixed effects.
Alpha	The \alpha-level that is used to determine the confidence intervals around R^2_{trial} and R^2_{indiv}. Default 0.05.

Value

Returns an object of class "FederatedApproachStage2()" that can be used to evaluate surrogacy.

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

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

• Fixed.Effects: a data frame that contains the average of the estimated fixed effects.

• D: estimated D matrix.

• Obs.Per.Trial: number of observations in each trial.

Model

The two-stage federated data analysis approach developed by XXX can be used to assess surrogacy in the meta-analytic multiple-trial setting (Continuous-continuous case), but without the need of sharing data. Instead, each organization conducts separate analyses on their data set using the so-called "first stage" model. The results of these analyses are then aggregated at a central analysis hub, where the aggregated results are analyzed using a "second stage" model and the necessary metrics (R^2_{trial} and R^2_{indiv}) for the validation of the surrogate endpoint are obtained. This function fits the second stage model, where a method-of-moments estimator is used to obtain the variance-covariance matrix D from which the R^2_{trial} can be derived. The R^2_{indiv} is obtained with a weighted average of the elements in \Sigma_i.

Data Format

A data frame that combines the results of the first stage models and contains:

• a column with the trial indicator

• a column with the number of subjects in the trial

• a column with the estimated intercepts for the surrogate

• a column with the estimated treatment effects for the surrogate

• a column with the estimated intercepts for the true endpoint

• a column with the estimated treatment effects for the true endpoint

• a column with the variances of the error term for the surrogate endpoint

• a column with the covariances between the error terms of the surrogate and true endpoint

• a column with the variances of the error term for the true endpoint

A list that combines all the variance-covariance matrices of the fixed effects obtained using the first stage model

Author(s)

Dries De Witte

References

Florez, A. J., Molenberghs G, Verbeke G, Alonso, A. (2019). A closed-form estimator for metaanalysis and surrogate markers evaluation. Journal of Biopharmaceutical Statistics, 29(2) 318-332.

Examples

## Not run: 
#As an example, the federated data analysis approach can be applied to the Schizo data set
data(Schizo)
Schizo <-  Schizo[order(Schizo$InvestId, Schizo$Id),]
#Create separate datasets for each investigator
Schizo_datasets <- list()

for (invest_id in 1:198) {
Schizo_datasets[[invest_id]] <- Schizo[Schizo$InvestId == invest_id, ]
assign(paste0("Schizo", invest_id), Schizo_datasets[[invest_id]])
}
#Fit the first stage model for each dataset separately
results_stage1 <- list()
invest_ids <- list()
i <- 1
for (invest_id in 1:198) {
  dataset <- Schizo_datasets[[invest_id]]

  skip_to_next <- FALSE
  tryCatch(FederatedApproachStage1(dataset, Surr=CGI, True=PANSS, Treat=Treat, Trial.ID = InvestId,
                                   Min.Treat.Size = 5, Alpha = 0.05),
                                   error = function(e) { skip_to_next <<- TRUE})
  #if the trial does not have the minimum required number, skip to the next
  if(skip_to_next) { next }

  results_stage1[[invest_id]] <- FederatedApproachStage1(dataset, Surr=CGI, True=PANSS, Treat=Treat,
                                                         Trial.ID = InvestId, Min.Treat.Size = 5,
                                                         Alpha = 0.05)
  assign(paste0("stage1_invest", invest_id), results_stage1[[invest_id]])
  invest_ids[[i]] <- invest_id #keep a list of ids with datasets with required number of patients
  i <- i+1
}

invest_ids <- unlist(invest_ids)
invest_ids

#Combine the results of the first stage models
for (invest_id in invest_ids) {
  dataset <- results_stage1[[invest_id]]$Results.Stage.1
  if (invest_id == invest_ids[1]) {
    all_results_stage1<- dataset
 } else {
    all_results_stage1 <- rbind(all_results_stage1,dataset)
  }
}

all_results_stage1 #that combines the results of the first stage models

R.list <- list()
i <- 1
for (invest_id in invest_ids) {
  R <- results_stage1[[invest_id]]$R.i
  R.list[[i]] <- as.matrix(R[1:4,1:4])
  i <- i+1
}

R.list #list that combines all the variance-covariance matrices of the fixed effects

fit <- FederatedApproachStage2(Dataset = all_results_stage1, Intercept.S = Intercept.S,
                               alpha = alpha, Intercept.T = Intercept.T, beta = beta,
                               sigma.SS = sigma.SS, sigma.ST = sigma.ST,
                               sigma.TT = sigma.TT, Obs.per.trial = n,
                               Trial.ID = Trial.ID, R.list = R.list)
summary(fit)

## End(Not run)

Surrogate documentation built on June 22, 2024, 9:16 a.m.