Big Stick Design

Description

Implements the Big Stick Design by Soares and Wu (1963) for assigning patients to two treatments A and B. The procedure works with qualitative covariates only.

Usage

BSD(data, bound = 3, print.results = TRUE)

Arguments

Details

The function assigns patients to treatments A or B with the Big Stick Design as described in Soares and Wu (1983).

The argument bound is the maximum tolerated imbalance that the experiment can accept: complete randomization is used as long as the imbalance of the treatment allocation does not exceed bound. When the imbalance reaches the value set in bound, a deterministic assignment is made to lower the imbalance.

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. The strata imbalances measures 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. The within-covariate imbalances report, for each level of each qualitative covariate, the difference in the number of patients assigned to A and B. See also Value.

Value

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

References

Soares F, Wu CFJ. Some restricted randomization rules in sequential designs. Communications in Statistics Theory and Methods 1963, 12: 2017-2034.

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

See Also

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

Examples

require(covadap)

# Create a sample dataset
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
BSD(data = df1, bound = 3, print.results = TRUE)
# To view a summary and create a list containing all the metrics of the design
res <- BSD(data = df1, bound = 3, print.results = TRUE)
res

Simulations of the Big Stick Design

Description

Implements the Big Stick Design by Soares and Wu (1963) for assigning patients to two treatments A and B by simulating the covariate profile of each patient using an existing dataset or specifying number and levels of the covariates. The procedure works with qualitative covariates only.

Usage

#With existing dataframe
BSD.sim(data, covar = NULL, n = NULL, bound = 3, nrep = 1000,
        print.results = TRUE)
#With covariates
BSD.sim(data = NULL, covar, n, bound = 3, nrep = 1000,
        print.results = TRUE)

Arguments

Details

This function simulates nrep times a clinical study assigning patients to treatments A and B with the Big Stick Design by Soares and Wu (1983) (see BSD).

When covar is provided, the function finds all the possible combination of the levels of the covariates, i.e., the strata and, at each trial replication, the patients' covariate profiles are uniformly sampled within those strata. The specification of covar requires the specification of the number of patients n.

When data is provided, at each trial replication, the patients' covariate profiles are sampled from the observed strata with uniform distribution. In this case the number of patients equals the number of rows of data.

The summary printed when print.results = TRUE reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications. See also BSD.

Value

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

References

Soares F, Wu CFJ. Some restricted randomization rules in sequential designs. Communications in Statistics Theory and Methods 1963, 12: 2017-2034.

See Also

See Also BSD.

Examples

require(covadap)
# Here we set nrep = 100 for illustrative purposes,
# Set it equal to at least 5000 for more reliable Monte Carlo estimates.


### With existing dataframe
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)
# Simulate the design
res1 <- BSD.sim(data = df1, covar = NULL, n = NULL, bound = 3, nrep = 100,
                print.results = TRUE)
### With covariates
# e.g. two binary covariates and one with three levels and 100 patients
res2 <- BSD.sim(data = NULL, covar = c(2,2,3), n = 100, bound = 3,  nrep = 100,
                print.results = TRUE)

Covariate-Adjusted Biased Coin Design

Description

Implements the Covariate-adjusted Biased Coin Design by Baldi Antognini and Zagoraiou (2011), a stratified randomization procedure for two treatments A and B. The procedure works with qualitative covariates only.

Usage

CABCD(data, a = 3, print.results = TRUE)

Arguments

Details

The function assigns patients to treatments A or B as described in Baldi Antognini and Zagoraiou (2011).

The parameter a determines the degree of randomness of the procedure.

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. The strata imbalances measures 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. The within-covariate imbalances report, for each level of each qualitative covariate, the difference in the number of patients assigned to A and B. See also Value.

Value

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

References

Baldi Antognini A and Zagoraiou M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika, 2011, 98(3): 519-535.

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

See Also

CABCD.sim for allocating patients by simulating their covariate profiles.

Examples

require(covadap)

# Create a sample dataset
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
CABCD(data = df1, a = 3)
# To view a summary
# and create a list containing all the metrics of the design
res <- CABCD(data = df1, a = 3)
res

Simulations of the Covariate-Adjusted Biased Coin Design

Description

Implements the Covariate-adjusted Biased Coin Design by Baldi Antognini and Zagoraiou (2011) by simulating the covariate profile of each patient using an existing dataset or specifying number and levels of the covariates. The procedure works with qualitative covariates only.

Usage

#With existing dataframe
CABCD.sim(data, covar = NULL, n = NULL, a = 3, nrep = 1000,
          print.results = TRUE)
#With covariates
CABCD.sim(data = NULL, covar, n, a = 3, nrep = 1000,
          print.results = TRUE)

Arguments

Details

This function simulates nrep times a clinical study assigning patients to treatments A and B with the Covariate-Adjusted Biased Coin Design (see CABCD).

When covar is provided, the function finds all the possible combination of the levels of the covariates, i.e., the strata and, at each trial replication, the patients' covariate profiles are uniformly sampled within those strata. The specification of covat requires the specification of the number of patients n.

When data is provided, at each trial replication, the patients' covariate profiles are sampled from the observed strata with uniform distribution. In this case the number of patients equals the number of rows of data.

The summary printed when print.results = TRUE reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications. See also CABCD.

Value

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

References

Baldi Antognini A and Zagoraiou M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika, 2011, 98(3): 519-535.

See Also

See Also CABCD.

Examples

require(covadap)
# Here we set nrep = 100 for illustrative purposes,
# Set it equal to at least 5000 for more reliable Monte Carlo estimates.


### With existing dataframe
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)
# Simulate the design
res1 <- CABCD.sim(data = df1, n = NULL, a = 3, nrep = 100)
### With covariates
# e.g. two binary covariates and one with three levels and 100 patients
res2 <- CABCD.sim(covar = c(2,2,3), n = 100, a = 3,  nrep = 100)

D_A-optimum biased coin design

Description

Implements the D_A-optimum BCD by A. Atkinson (1982) for assigning patients to two treatments A and B in order to minimize the variance of the estimated treatment difference sequentially. The procedure works with qualitative and quantitative covariates.

Usage

DABCD(data, all.cat, print.results = TRUE)

Arguments

Details

The function assigns patients to treatments A or B with the D_A-optimum BCD as described in Atkinson (1982).

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.

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:

References

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

See Also

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

Examples

require(covadap)

### 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
DABCD(data = df1,  all.cat = TRUE, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res1 <- DABCD(data = df1, all.cat = TRUE, 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
DABCD(data = ff1[,5:6],  all.cat = FALSE, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res2 <- DABCD(data = ff1[,5:6], all.cat = FALSE, print.results = TRUE)
res2

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

Simulations of the D_A-optimum biased coin design

Description

Implements the D_A-optimum biased coin design BCD by A. Atkinson (1982) for assigning patients to two treatments A and B in order to minimize the variance of the estimated treatment difference sequentially by simulating the covariate profile of each patient using an existing dataset or specifying number and levels of the covariates. The procedure works with qualitative and quantitative covariates.

Usage

#With existing dataframe provided in data
DABCD.sim(data, covar = NULL,  n = NULL, all.cat, nrep = 1000,
          print.results = TRUE)
#With covariates
DABCD.sim(data = NULL, covar, n, all.cat, nrep = 1000,
          print.results = TRUE)

Arguments

Details

This function simulates nrep times a clinical study assigning patients to treatments A and B with the D_A-optimum BCD by Atkinson (see DABCD).

When covar is provided, the function finds all the possible combination of the levels of the covariates, i.e., the strata and, at each trial replication, the patients' covariate profiles are uniformly sampled within those strata. The specification of covar requires the specification of the number of patients n.

When data is provided, at each trial replication, the patients' covariate profiles are sampled from the observed strata with uniform distribution. In this case the number of patients equals the number of rows of data.

The summary printed when print.results = TRUE reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications according to the nature of the covariates. See also DABCD.

Value

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

References

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

See Also

See Also as DABCD.

Examples

require(covadap)

# Here we set nrep = 50 for illustrative purposes,
# Set it equal to at least 5000 for more reliable Monte Carlo estimates.

### Implement with qualitative covariates (set all.cat = TRUE)
#### With an existing dataset
# 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
DABCD.sim(data = df1,  covar = NULL, n = NULL, all.cat = TRUE, nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res1 <- DABCD.sim(data = df1, covar = NULL, n = NULL, all.cat = TRUE,
                  nrep = 50)
#### By specifying the covariates
# e.g. two binary covariates and one with three levels and 100 patients
res2 <- DABCD.sim(data = NULL, covar = c(2,3,3), n = 100,
                  all.cat = TRUE, nrep = 50)


### 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)
#### With an existing dataset
# select only column 5 and 6 of the sample dataset
# To just view a summary of the metrics of the design
DABCD.sim(data = ff1[,5:6], covar = NULL, n = NULL,  all.cat = FALSE,
          nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res3 <- DABCD.sim(data = ff1[,5:6],  covar = NULL, n = NULL,
                  all.cat = FALSE, nrep = 50)
#### By specifying the covariates
# e.g. 2 quantitative covariates:
# BMI normally distributed with mean 26 and standard deviation 5
# cholesterol normally distributed with mean 200 and standard deviation 34
covar = list(quant = list(BMI = c(26, 5), cholesterol = c(200, 34)))
# To just view a summary of the metrics of the design
DABCD.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
          nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res4 <- DABCD.sim(data = NULL, covar = covar, n = 100,
                  all.cat = FALSE,  nrep = 50)


### With mixed covariates (set all.cat = FALSE)
#### With an existing dataset
# To just view a summary of the metrics of the design
DABCD.sim(data = ff1, covar = NULL, n = NULL,  all.cat = FALSE,
          nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res5 <- DABCD.sim(data = ff1, covar = NULL, n = NULL,
                  all.cat = FALSE, nrep = 50)
#### By specifying the covariates
# e.g. one qualitative covariate and 2 quantitative covariates:
# gender with levels M and F
# BMI normally distributed with mean 26 and standard deviation 5
# cholesterol normally distributed with mean 200 and standard deviation 34
covar = list(cat = list(gender = c("M", "F")),
             quant = list(BMI = c(26, 5), cholesterol = c(200, 34)))
#To just view a summary of the metrics of the design
DABCD.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
          nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res6 <- DABCD.sim(data = NULL, covar = covar, n = 100,
                  all.cat = FALSE,  nrep = 50)

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

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:

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

Simulations of the 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 by simulating the covariate profile of each patient using an existing dataset or specifying number and levels of the covariates. The procedure works with qualitative and quantitative covariates.

Usage

#With existing dataframe provided in data
ECADE.sim(data, covar = NULL, n = NULL, all.cat, nrep = 1000,
          rho = 0.85, alloc.function = "Efron", print.results = TRUE)
#With covariates
ECADE.sim(data = NULL, covar, n, all.cat, nrep = 1000, rho = 0.85,
          alloc.function = "Efron", print.results = TRUE)

Arguments

Details

This function simulates nrep times a clinical study assigning patients to treatments A and B with the Efficient Covariate-Adaptive Design as described in Baldi Antognini et al. (see ECADE).

When covar is provided, the function finds all the possible combination of the levels of the covariates, i.e., the strata and, at each trial replication, the patients' covariate profiles are uniformly sampled within those strata. The specification of covar requires the specification of the number of patients n.

When data is provided, at each trial replication, the patients' covariate profiles are sampled from the observed strata with uniform distribution. In this case the number of patients equals the number of rows of data.

The summary printed when print.results = TRUE reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications according to the nature of the covariates. See also ECADE.

Value

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

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.

See Also

See Also ECADE.

Examples

require(covadap)
# Here we set nrep = 50 for illustrative purposes,
# Set it equal to at least 5000 for more reliable Monte Carlo estimates.


### Implement with qualitative covariates (set all.cat = TRUE)
#### With an existing dataset
# 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.sim(data = df1,  covar = NULL, n = NULL, all.cat = TRUE,
          alloc.function = "Efron", rho = 0.85, nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res1 <- ECADE.sim(data = df1, covar = NULL, n = NULL, all.cat = TRUE,
                  alloc.function = "Efron", rho = 0.85, nrep = 50)

#### By specifying the covariates
# e.g. two binary covariates and one with three levels and 100 patients
res2 <- ECADE.sim(data = NULL, covar = c(2,3,3), n = 100, all.cat = TRUE,
                  alloc.function = "Efron",  rho = 0.85, nrep = 50)



### 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)
#### With an existing dataset
# select only column 5 and 6 of the sample dataset
# To just view a summary of the metrics of the design
ECADE.sim(data = ff1[,5:6], covar = NULL, n = NULL,  all.cat = FALSE,
          alloc.function = "Efron", rho = 0.85, nrep = 50)
# To view a summary and create a list containing all the metrics of the design
res3 <- ECADE.sim(data = ff1[,5:6],  covar = NULL, n = NULL, all.cat = FALSE,
                  alloc.function = "Efron", rho = 0.85, nrep = 50)
#### By specifying the covariates
# e.g. 2 quantitative covariates:
# BMI normally distributed with mean 26 and standard deviation 5
# cholesterol normally distributed with mean 200 and standard deviation 34
covar = list(quant = list(BMI = c(26, 5), cholesterol = c(200, 34)))
# To just view a summary of the metrics of the design
ECADE.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
          alloc.function = "Efron", rho = 0.85, nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res4 <- ECADE.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
                  alloc.function = "Efron", rho = 0.85,  nrep = 50)



### With mixed covariates (set all.cat = FALSE)
#### With an existing dataset
# To just view a summary of the metrics of the design
ECADE.sim(data = ff1, covar = NULL, n = NULL,  all.cat = FALSE,
          alloc.function = "Efron",  rho = 0.85, nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res5 <- ECADE.sim(data = ff1, covar = NULL, n = NULL,  all.cat = FALSE,
                  alloc.function = "Efron", rho = 0.85, nrep = 50)
#### By specifying the covariates
# e.g. one qualitative covariate and 2 quantitative covariates:
# gender with levels M and F
# BMI normally distributed with mean 26 and standard deviation 5
# cholesterol normally distributed with mean 200 and standard deviation 34
covar = list(cat = list(gender = c("M", "F")),
             quant = list(BMI = c(26, 5), cholesterol = c(200, 34)))
# To just view a summary of the metrics of the design
ECADE.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
          alloc.function = "Efron", rho = 0.85, nrep = 50)
# To view a summary and
# create a list containing all the metrics of the design
res6 <- ECADE.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
                  alloc.function = "Efron", rho = 0.85, nrep = 50)

Covariate-Adaptive randomization by Hu and Hu

Description

Implements the Covariate-Adaptive randomization by Hu and Hu (2012) for assigning patients to two treatments A and B. The procedure works with qualitative covariates only.

Usage

HuHu(data, p = 0.85, omega = NULL, print.results = TRUE)

Arguments

Details

The function assigns patients to treatments A or B as described in Hu and Hu (2012).

The assignment probability to A of each patient is based on the Efron's allocation function (Efron, 1971) with biasing probability equal to p.

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. The strata imbalances measures 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. The within covariate imbalances report, for each level of each qualitative covariate, the difference in the number of patients assigned to A and B. See also Value.

Value

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

References

Hu Y, Hu F. Asymptotic properties of covariate-adaptive randomization. The Annals of Statistics, 2012, 40(3): 1794-1815.

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

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

See Also

HuHu.sim for allocating patients by simulating their covariate profiles.

Examples

require(covadap)


# Create a sample dataset
df1 <- data.frame("gender" = sample(c("female", "male"), 200, TRUE, c(1 / 3, 2 / 3)),
                  "age" = sample(c("18-35", "36-50", ">50"), 200, TRUE),
                  "bloodpressure" = sample(c("normal", "high", "hyper"), 200, TRUE),
                   stringsAsFactors = TRUE)
# To view a summary of the metrics of the design
HuHu(df1, p = 0.85, omega = NULL, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res <- HuHu(df1, p = 0.85, omega = NULL, print.results = TRUE)
res

Simulations of the Covariate-Adaptive randomization by Hu and Hu

Description

Implements the Covariate-Adaptive randomization by Hu and Hu (2012) for assigning patients to two treatments A and B by simulating the covariate profile of each patient using an existing dataset or specifying number and levels of the covariates. The procedure works with qualitative covariates only.

Usage

#With existing dataframe
HuHu.sim(data, covar = NULL, n = NULL, p = 0.85,
         omega = NULL, nrep = 1000, print.results = TRUE)
#With covariates
HuHu.sim(data = NULL, covar, n, p = 0.85, omega = NULL,
         nrep = 1000, print.results = TRUE)

Arguments

Details

This function simulates nrep times a clinical study assigning patients to treatments A and B with the Covariate-Adaptive randomization procedure proposed by Hu and Hu (see HuHu).

When covar is provided, the function finds all the possible combination of the levels of the covariates, i.e., the strata and, at each trial replication, the patients' covariate profiles are uniformly sampled within those strata. The specification of covar requires the specification of the number of patients n.

When data is provided, at each trial replication, the patients' covariate profiles are sampled from the observed strata with uniform distribution. In this case the number of patients equals the number of rows of data.

The summary printed when print.results = TRUE reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications. See also HuHu.

Value

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

References

Hu Y, Hu F. Asymptotic properties of covariate-adaptive randomization. The Annals of Statistics, 2012, 40(3): 1794-1815.

See Also

See Also HuHu.

Examples

require(covadap)
# Here we set nrep = 100 for illustrative purposes,
# Set it equal to at least 5000 for more reliable Monte Carlo estimates.


### With existing dataframe
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)
# Simulate the design
res2 <- HuHu.sim(data = df1, covar = NULL, n = NULL, p = 0.85,  omega = NULL,
                 nrep = 100)
### With covariate
# e.g. two binary covariates and one with three levels and 100 patients
res2 <- HuHu.sim(data = NULL, covar = c(2,2,3), n = 100, p = 0.85,  omega = NULL,
                 nrep = 100)

Covariate-Adaptive randomization by Ma and Hu

Description

Implements the Covariate-Adaptive randomization by Ma and Hu (2013) for assigning patients to two treatments A and B in order to minimize the distance between the covariate distribution in the two treatment groups. The procedure works with qualitative and quantitative covariates.

Usage

KER(data, all.cat, p = 0.8, print.results = TRUE)

Arguments

Details

The function assigns patients to treatments A or B with the Covariate-Adaptive randomization based on kernel density estimation as described in Ma and Hu (2013).

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 p.

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:

References

Ma Z and Hu F. Balancing continuous covariates based on Kernel densities. Contemporary Clinical Trials, 2013, 34(2): 262-269.

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 KER.sim for allocating patients by simulating their covariate profiles.

Examples

require(covadap)

### 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
KER(data = df1,  all.cat = TRUE, p = 0.8, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res1 <- KER(data = df1,  all.cat = TRUE, p = 0.8, 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
KER(data = ff1[,5:6],  all.cat = FALSE, p = 0.8, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res2 <- KER(data = ff1[,5:6], p = 0.8, all.cat = FALSE, print.results = TRUE)
res2

### With mixed covariates
# In this case the user must set all.cat = FALSE
# To just view a summary of the metrics of the design
KER(data = ff1, all.cat = FALSE, p = 0.8, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res3 <- KER(data = ff1, all.cat = FALSE, p = 0.8, print.results = TRUE)
res3

Simulations of the Covariate-Adaptive randomization by Ma and Hu

Description

Implements the Covariate-Adaptive randomization by Ma and Hu (2013) for assigning patients to two treatments A and B in order to minimize the distance between the covariate distribution in the two treatment groups by simulating the covariate profile of each patient using an existing dataset or specifying number and levels of the covariates. The procedure works with qualitative and quantitative covariates.

Usage

#With existing dataframe
KER.sim(data, covar = NULL, n = NULL, all.cat, nrep = 1000,
        p = 0.8, print.results = TRUE)
#With covariates
KER.sim(data = NULL, covar, n, all.cat, nrep = 1000,
        p = 0.8, print.results = TRUE)

Arguments

Details

This function simulates nrep times a clinical study assigning patients to treatments A and B with the Efficient Covariate-Adaptive Design as described in Ma and Hu (see KER).

When covar is provided, the function finds all the possible combination of the levels of the covariates, i.e., the strata and, at each trial replication, the patients' covariate profiles are uniformly sampled within those strata. The specification of covar requires the specification of the number of patients n.

When data is provided, at each trial replication, the patients' covariate profiles are sampled from the observed strata with uniform distribution. In this case the number of patients equals the number of rows of data.

The summary printed when print.results = TRUE reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications according to the nature of the covariates. See also KER.

Value

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

References

Ma Z and Hu F. Balancing continuous covariates based on Kernel densities. Contemporary Clinical Trials, 2013, 34(2): 262-269.

See Also

See Also as KER.

Examples

require(covadap)
# Here we set nrep = 50 for illustrative purposes,
# Set it equal to at least 5000 for more reliable Monte Carlo estimates.


### Implement with qualitative covariates (set all.cat = TRUE)
#### With an existing dataset
# 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
KER.sim(data = df1,  covar = NULL, n = NULL, all.cat = TRUE,
        p = 0.8, nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res1 <- KER.sim(data = df1, covar = NULL, n = NULL, all.cat = TRUE,
                p = 0.8, nrep = 50)
#### By specifying the covariates
# e.g. two binary covariates and one with three levels and 100 patients
res2 <- KER.sim(data = NULL, covar = c(2,3,3), n = 100, all.cat = TRUE,
                p = 0.8, nrep = 50)



### 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)
#### With an existing dataset
# select only column 5 and 6 of the sample dataset
# To just view a summary of the metrics of the design
KER.sim(data = ff1[,5:6], covar = NULL, n = NULL,  all.cat = FALSE, p = 0.8,
        nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res3 <- KER.sim(data = ff1[,5:6],  covar = NULL, n = NULL, all.cat = FALSE,
                p = 0.8, nrep = 50)

#### By specifying the covariates
# BMI normally distributed with mean 26 and standard deviation 5
# cholesterol normally distributed with mean 200 and standard deviation 34
covar = list(quant = list(BMI = c(26, 5), cholesterol = c(200, 34)))
# To just view a summary of the metrics of the design
KER.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
        p = 0.8, nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res4 <- KER.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
                  p = 0.8,  nrep = 50)

### With mixed covariates (set all.cat = FALSE)
#### With an existing dataset
# To just view a summary of the metrics of the design
KER.sim(data = ff1, covar = NULL, n = NULL, all.cat = FALSE, p = 0.8,
        nrep = 50)
# To view a summary
# and create a list containing all the metrics of the design
res5 <- KER.sim(data = ff1, covar = NULL, n = NULL, all.cat = FALSE,
                 p = 0.8, nrep = 50)
#### By specifying the covariates
# e.g. one qualitative covariate and 2 quantitative covariates:
# BMI normally distributed with mean 26 and standard deviation 5
# cholesterol normally distributed with mean 200 and standard deviation 34
# gender with levels M and F
covar = list(cat = list(gender = c("M", "F")),
             quant = list(BMI = c(26, 5), cholesterol = c(200, 34)))
# To just view a summary of the metrics of the design
KER.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
        p = 0.8, nrep = 50)
# To view a summary and create a list containing all the metrics of the design
res6 <- KER.sim(data = NULL, covar = covar, n = 100, all.cat = FALSE,
                  p = 0.8, nrep = 50)

Pocock and Simon's minimization method

Description

Implements the Pocock and Simon's minimization method by Pocock and Simon (1975) for assigning patients to two treatments A and B. The procedure works with qualitative covariates only.

Usage

PocSim(data, p = 0.85, print.results = TRUE)

Arguments

Details

The function assigns patients to treatments A or B as described in Pocock and Simon (1975).

The assignment probability to A of each patient is based on the Efron's allocation function (Efron, 1971) with biasing probability equal to p.

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. The strata imbalances measures 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. The within-covariate imbalances report, for each level of each qualitative covariate, the difference in the number of patients assigned to A and B. See also Value.

Value

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

References

Pocock S J, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics, 1975, 31(1): 103-115.

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

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

See Also

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

Examples

require(covadap)

# Create a sample dataset
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
PocSim(df1, p = 0.85, print.results = TRUE)
# To view a summary
# and create a list containing all the metrics of the design
res <- PocSim(df1, p = 0.85, print.results = TRUE)
res

Simulations of the Pocock and Simon's minimization method

Description

Implements the Pocock and Simon's minimization method by Pocock and Simon (1975) for assigning patients to two treatments A and B by simulating the covariate profile of each patient using an existing dataset or specifying number and levels of the covariates. The procedure works with qualitative covariates only.

Usage

#With existing dataframe
PocSim.sim(data, covar = NULL, n = NULL, p = 0.85, nrep = 1000,
           print.results = TRUE)
#With covariates
PocSim.sim(data = NULL, covar, n, p = 0.85, nrep = 1000,
           print.results = TRUE)

Arguments

Details

This function simulates nrep times a clinical study assigning patients to treatments A and B with the minimization method by Pocock and Simon (see PocSim).

When covar is provided, the function finds all the possible combination of the levels of the covariates, i.e., the strata and, at each trial replication, the patients' covariate profiles are uniformly sampled within those strata. The specification of covar requires the specification of the number of patients n.

When data is provided, at each trial replication, the patients' covariate profiles are sampled from the observed strata with uniform distribution. In this case the number of patients equals the number of rows of data.

The summary printed when print.results = TRUE reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications. See also PocSim.

Value

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

References

Pocock S J, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics, 1975, 31(1): 103-115.

See Also

See Also as PocSim.

Examples

require(covadap)
# Here we set nrep = 100 for illustrative purposes,
# Set it equal to at least 5000 for more reliable Monte Carlo estimates.

### With existing dataframe
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)
# Simulate the design
res1 <- PocSim.sim(data = df1, covar = NULL, n = NULL, p = 0.85, nrep = 100)
### With covariates
# e.g. two binary covariates and one with three levels and 100 patients
res2 <- PocSim.sim(data = NULL, covar = c(2,2,3), n = 100,
                   p = 0.85, nrep = 100)

Internal covadap Functions

Description

Internal covadap functions.

Value

No return value, called for side effects.

Note

These functions are not to be called by the user (or in some cases are just waiting for proper documentation to be written).

covadap: Implements Covariate-Adaptive Randomization procedures

Description

Implementing seven Covariate-Adaptive Randomization to assign patients to two treatments. Three of these procedures can also accommodate quantitative and mixed covariates. Given a set of covariates, the user can generate a single sequence of allocations or replicate the design multiple times by simulating the patients' covariate profiles. At the end, an extensive assessment of the performance of the randomization procedures is provided, calculating several imbalance measures.

Acknowledgement

This work was supported by the EU funding within the NextGenerationEU PRIN2022 Optimal and adaptive designs for modern medical experimentation (2022TRB44L).

Author(s)

R. Frieri rosamarie.frieri2@unibo.it, M. Novelli m.novelli@unibo.it

References

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

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.

Baldi Antognini A and Zagoraiou M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika, 2011, 98(3): 519-535.

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

Hu Y, Hu F. Asymptotic properties of covariate-adaptive randomization. The Annals of Statistics, 2012, 40(3): 1974-1815.

Ma Z and Hu F. Balancing continuous covariates based on Kernel densities. Contemporary Clinical Trials, 2013, 34(2): 262-269.

Pocock S J, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics, 1975, 31(1): 103-115.

Soares F, Wu CFJ. Some restricted randomization rules in sequential designs. Communications in Statistics Theory and Methods 1983, 12: 2017-2034.

See Also

CABCD, HuHu, PocSim, BSD, DABCD, ECADE, KER.

Summary of Covariate-Adaptive Designs

Description

This function automatically recognizes the design implemented and provides a summary of the results.

Usage

summary_covadap(res)

Arguments

Details

When applied to an object of class "covadap": 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 instead at least one quantitative covariate is present, the function returns the difference in means. For each quantitative covariate, the difference in the mean in group A and B is reported.

When applied to an object of class "covadapsim", it reports the averages, in absolute value, of the imbalance measures, strata imbalances and within-covariate imbalances of the nrep trial replications according to the nature of the covariates.

Value

The form of the value returned by summary_covadap depends on the class of the argument provided (see Details).

Examples

#Create a sample dataset
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)

res1 <- ECADE(data = df1, all.cat = TRUE,
                  alloc.function = "Efron", rho = 0.85)
summary_covadap(res1)


res2 <- ECADE.sim(data = df1, cov = NULL, n = NULL, all.cat = TRUE,
                  alloc.function = "Efron", rho = 0.85, nrep = 100)
summary_covadap(res2)