ECADE {covadap}

Efficient Covariate-Adaptive Design

Description

Implements the Efficient Covariate-Adaptive DEsign by Baldi Antognini et al. (2022) for assigning patients to two treatments A and B. The procedure works with qualitative and quantitative covariates.

Usage

ECADE(data, all.cat, rho = 0.85, alloc.function = "Efron",
      print.results = TRUE)

Arguments

data

a data frame or a matrix. It can be a matrix only when all.cat = TRUE. Each row of data corresponds to the covariate profile of a patient.

all.cat

logical. If all the covariates in data are qualitative must be set equal to TRUE, otherwise must be set equal to FALSE.

rho

biasing probability, to be used only with the Efron allocation function (1/2 \leq \rho \leq 1). The default value is 0.85.

alloc.function

a character specifying the allocation function used in the randomization procedure: ="Efron" for Efron's, if the assignment probability to A is e+(1-2e)[1-\Phi(x)] with e=0.1 alloc.function="norm1" while alloc.function="norm2" for e=0.2.

print.results

logical. If TRUE a summary of the results is printed.

Details

The function assigns patients to treatments A or B with the Efficient Covariate-Adaptive Design as described in Baldi Antognini et al. (2022).

This randomization procedure can be used when data contains only qualitative covariate, in this case set all.cat = TRUE, when data contains only quantitative covariates or when covariates of mixed nature are present, in these two latter cases set all.cat = FALSE. The function's output is slighly different according to these three scenarios as described in Value.

The assignment probability to A of each patient is based on the Efron's allocation function (Efron, 1971) with biasing probability equal to rho if alloc.function = "Efron". Otherwise the allocation ptobability to A is based on the cumulative distribution function of the standard normal distribution \Phi (see Arguments).

At the end of the study the imbalance measures reported are the loss of estimation precision as described in Atkinson (1982), the Mahalanobis distance and the overall imbalance, defined as the difference in the total number of patients assigned to treatment A and B.

Only when all.cat = TRUE, the function returns the strata imbalances measures, that report, for each stratum, the total number of patients assigned (N.strata), the number of patients assigned to A (A.strata) and the within-stratum imbalance (D.strata), calculated as 2*A.strata-N.strata.

If at least one qualitative covariate is present, the function returns the within-covariate imbalances reporting, for each level of each qualitative covariate, the difference in the number of patients assigned to A and B.

If at least one quantitative covariate is present, the function returns the difference in means. For each quantitative covariate, is reported the difference in the mean in group A and B.

See Value for more details.

Value

It returns an object of class "covadap", which is a list containing the following elements:

summary.info

Design name of the design.

Sample_size number of patients.

n_cov number of covariates.

n_categorical_variables number of levels of each covariate. Is NULL if all.cat = TRUE or only quantitative covariates are present).

n_levels number of levels of each qualitative covariate. Is NULL if only quantitative covariates are present.

var_names name of the covariates.

cov_levels_names levels of each qualitative covariate. Is NULL if only quantitative covariates are present.

n_quantitative_variables number of quantitative covariates. Is NULL if all.cat = TRUE.

Assignments

a vector with the treatment assignments.

Imbalances.summary

summary of overall imbalance measures at the end of the study (Loss loss, Mahal Mahalanobis distance, overall.imb difference in the total number of patients assigned to A and B ).

Strata.measures

(only if all.cat = TRUE) a data frame containing for each possiblue stratum the corresponding imbalances: N.strata is the total number of patients assigned to the stratum; A.strata is the total number of patients assigned to A within the stratum; D.strata is the within-stratum imbalance, i.e. difference in the total number of patients assigned to A and B within the stratum).

Imbalances

a list containing all the imbalance measures.

Imb.measures summary of overall imbalances (Loss loss, Mahal Mahalanobis distance, overall.imb difference in the total number of patients assigned to A and B).

Within.strata (only if all.cat = TRUE) within-stratum imbalance for all strata.

Within.cov within-covariate imbalance: difference in the number of patients assigned to A and B for each level of each qualitative covariate (is NULL if only quantitative covariates are present).

data

the data provided in input.

diff_mean

(only if all.cat = FALSE) the difference in mean of the quantitative covariates in group A and B.

observed.strata

(only if all.cat = TRUE) a data frame with all the observed strata.

References

Baldi Antognini A, Frieri R, Zagoraiou M, Novelli M. The Efficient Covariate-Adaptive Design for high-order balancing of quantitative and qualitative covariates. Statistical Papers, 2022.

Atkinson A. C. Optimum biased coin designs for sequential clinical trials with prognostic factors. Biometrika, 1982, 69(1): 61-67.

Efron B, Forcing a sequential experiment to be balanced. Biometrika, 1971, 58(3): 403-418.

See Also

See Also as ECADE.sim for allocating patients by simulating their covariate profiles.

Examples

require(covadap)
# Assume we choose Efron's allocation function with rho  = 0.85

### Implement with qualitative covariates (set all.cat = TRUE)
# Create a sample dataset with qualitative covariates
df1 <- data.frame("gender" = sample(c("female", "male"), 100, TRUE, c(1 / 3, 2 / 3)),
                  "age" = sample(c("18-35", "36-50", ">50"), 100, TRUE),
                  "bloodpressure" = sample(c("normal", "high", "hyper"), 100, TRUE),
                   stringsAsFactors = TRUE)
# To just view a summary of the metrics of the design
ECADE(data = df1,  all.cat = TRUE, alloc.function = "Efron",
      rho = 0.85, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res1 <- ECADE(data = df1,  all.cat = TRUE, alloc.function = "Efron",
              rho = 0.85, print.results = TRUE)
res1


### Implement with quantitative or mixed covariates
# Create a sample dataset with covariates of mixed nature
ff1 <- data.frame("gender" = sample(c("female", "male"), 100, TRUE, c(1 / 3, 2 / 3)),
                 "age" = sample(c("0-30", "30-50", ">50"), 100, TRUE),
                 "bloodpressure" = sample(c("normal", "high", "hypertension"), 10,
                  TRUE),
                 "smoke" = sample(c("yes", "no"), 100, TRUE, c(2 / 3, 1 / 3)),
                 "cholesterol" = round(rnorm(100, 200, 8),1),
                 "height" = rpois(100,160),
                  stringsAsFactors = TRUE)

### With quantitative covariates only (set all.cat = FALSE)
# select only column 5 and 6 of the sample dataset
# To just view a summary of the metrics of the design
ECADE(data = ff1[,5:6],  all.cat = FALSE, alloc.function = "Efron",
      rho = 0.85, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res2 <- ECADE(data = ff1[,5:6],  all.cat = FALSE, alloc.function = "Efron",
              rho = 0.85, print.results = TRUE)
res2

### With mixed covariates (set all.cat = FALSE)
# To just view a summary of the metrics of the design
ECADE(data = ff1, all.cat = FALSE, alloc.function = "Efron",
      rho = 0.85, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res3 <- ECADE(data = ff1, all.cat = FALSE, alloc.function = "Efron",
              rho = 0.85, print.results = TRUE)
res3