sample_size {snSMART}

Sample size calculation for snSMART with 3 active treatments and a binary outcome

Description

conduct Bayesian sample size calculation for a snSMART design with 3 active treatments and a binary outcome to distinguish the best treatment from the second-best treatment using the Bayesian joint stage model.

Usage

sample_size(pi, beta1, beta0, coverage, power, mu, n, verbose = FALSE)

## S3 method for class 'sample_size'
summary(object, ...)

## S3 method for class 'summary.sample_size'
print(x, ...)

## S3 method for class 'sample_size'
print(x, ...)

Arguments

pi

a vector with 3 values (piA, piB, piC). piA is the the response rate (ranges from 0.01 to 0.99) for treatment A, piB is the response rate (ranges from 0.01 to 0.99) for treatment B, piC is the response rate (ranges from 0.01 to 0.99) for treatment C

beta1

the linkage parameter (ranges from 1.00 to 1/largest response rate) for first stage responders. (A smaller value leads to more conservative sample size calculation because two stages are less correlated)

beta0

the linkage parameter (ranges from 0.01 to 0.99) for first stage non-responders. A larger value leads to a more conservative sample size calculation because two stages are less correlated

coverage

the coverage rate (ranges from 0.01 to 0.99) for the posterior difference of top two treatments

power

the probability (ranges from 0.01 to 0.99) for identify the best treatment

mu

a vector with 3 values (muA, muB, muC). muA is the prior mean (ranges from 0.01 to 0.99) for treatment A, muB is the prior mean (ranges from 0.01 to 0.99) for treatment B, muC is the prior mean (ranges from 0.01 to 0.99) for treatment C

n

a vector with 3 values (nA, nB, nC). nA is the prior sample size (larger than 0) for treatment A. nB is the prior sample size (larger than 0) for treatment B. nC is the prior sample size (larger than 0) for treatment C

verbose

TRUE or FALSE. If FALSE, no function message and progress bar will be printed.

object

object to summarize.

...

further arguments. Not currently used.

x

object to print

Details

Note that this package does not include the JAGS library, users need to install JAGS separately. Please check this page for more details: https://sourceforge.net/projects/mcmc-jags/ This function may take a few minutes to run

Value

final_N

the estimated sample size per arm for this snSMART

critical_value

critical value based on the provided coverage value

grid_result

for each iteration we calculate l, where l belongs to {2 * (pi_(1) - pi_(2)), ..., 0.02, 0.01}; E(D): the mean of the posterior distribution of D, , where D = pi_(1) = pi_(2); Var(D): the variance of the posterior distribution of D; N: the corresponding sample size; and power: the resulting power of this iteration

References

Wei, B., Braun, T.M., Tamura, R.N. and Kidwell, K.M., 2018. A Bayesian analysis of small n sequential multiple assignment randomized trials (snSMARTs). Statistics in medicine, 37(26), pp.3723-3732.

Wei, B., Braun, T.M., Tamura, R.N. and Kidwell, K., 2020. Sample size determination for Bayesian analysis of small n sequential, multiple assignment, randomized trials (snSMARTs) with three agents. Journal of Biopharmaceutical Statistics, 30(6), pp.1109-1120.

See Also

BJSM_binary

Examples

## Not run: 
# short running time example
sampleSize <- sample_size(
  pi = c(0.7, 0.5, 0.25), beta1 = 1.4, beta0 = 0.5, coverage = 0.9,
  power = 0.3, mu = c(0.65, 0.55, 0.25), n = c(10, 10, 10)
)

## End(Not run)


sampleSize <- sample_size(
  pi = c(0.7, 0.5, 0.25), beta1 = 1.4, beta0 = 0.5, coverage = 0.9,
  power = 0.8, mu = c(0.65, 0.55, 0.25), n = c(4, 2, 3)
)