Bayesian adaptive trial interim analysis

Description

BayesAT conducts Bayesian adaptive trials through multiple-stage interim analysis.

Usage

BayesAT(
  data,
  D,
  stage,
  threshold,
  start,
  objective,
  alpha,
  beta,
  boundary = NULL
)

Arguments

Value

Interim analysis reporting Bayesian adaptive trial results.

If there is one data set applied to BayesAT, the result will provide a table containing:

⁠Upper bound⁠ can be used as stopping criterion for efficacy;

⁠Lower bound⁠ can be used as stopping criterion for futility;

⁠Z score⁠ Z statistic is calculated based on the predicted survival probability:

\frac{\hat{S} - S_0}{SD( \hat{S} )}

with predicted mean survival rate \hat{S} and test evidence or threshold S_0.

⁠Efficacy Prob⁠ and ⁠Futility Prob⁠ Predictive probability measures the efficacy or futility, such as P(\hat{S} > \text{Efficacy}) and P(\hat{S} < \text{Futility}).

Efficacy and Futility indicate the interim analysis results: + means the trial reach the stopping criterion, otherwise it is -.

Examples

data <- Simulate_Enroll(n = c(30,20,20,15,30), lambda = 0.03,
                        event = 0.1, M = 3, group = 5, maxt = 5,
                        accrual = 3,  censor = 0.9, followup = 2,
                        partition = "Uneven")
## assign patients in each group analyzed at each stage of time points
IA <- BayesAT(data,D = 3,stage = 5,threshold = 0.9, start = 1.5,
              objective = 2, alpha = 3, beta = 82)
summary(IA)
plot(IA)

Bayesian inference for survival analysis

Description

Bayes_test conduct hypothesis test through Bayesian survival model

Usage

Bayes_test(data, alpha, beta, test, threshold, type, pred, diagnosis = FALSE)

Arguments

Value

Bayesian test provide mean, sd, CI, z_score, prob, and bf.

mean Posterior mean is estimated by calculating the mean of MCMC outputs.

sd Posterior standard deviation is estimated as the standard deviation of MCMC outputs.

CISummary statistics provides the credible intervals and specific quantile.

z_score Standardized test of statistics is calculated based on MCMC outputs. For example,

\frac{\hat{\lambda} - \lambda_0}{SD( \hat{\lambda} )} \text{ or } \frac{ \hat{S} - S_0}{SD( \hat{S} )},

where \hat{\lambda} is the estimated posterior mean of hazard rate, and \hat{S} is the predicted survival probability. Both \lambda_0 and S_0 are threshold used for test against hypothesis or evidence.

prob Posterior probability: P(\hat{\lambda} > \lambda_0) if test is "greater", P(\hat{\lambda} \le \lambda_0) if test is "less", and 2 min( P(\hat{\lambda} > \lambda_0),P(\hat{\lambda} \le \lambda_0)) if test is "two-sided".

bf Bayes Factor is calculated if diagnosis = TRUE, and the comparison model is non-informative prior, Jeffreys prior, \pi \propto 1/\lambda.

References

Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 186(1007), 453-461.

Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the american statistical association, 90(430), 773-795.

Examples

data <- Simulate_Enroll(n = c(50,20,20), lambda = 0.03,
                        event = 0.1, M = 1, group = 3,
                        maxt = 5, accrual = 3, censor = 0.9,
                        followup = 2,partition = "Uneven")
test <- Bayes_test(data, alpha = 3, beta = 82, test = "greater",
                   pred = 2, threshold = 0.9, type = "Predictive",
                   diagnosis = TRUE)
print(test)

Survival data simulation

Description

Simulate_Enroll generates multiple streams of data sets with survival time, censoring status, and enrollment time.

Usage

Simulate_Enroll(
  n,
  lambda,
  event,
  M,
  group,
  maxt,
  accrual,
  censor,
  followup,
  partition = "Even"
)

Arguments

Value

Simulated survival data contain both survival time, censoring status, and enrollment time.

Examples

data <- Simulate_Enroll(n = c(50,20,20), lambda = 0.03,
                        event = 0.1, M = 3, group = 3, maxt = 5,
                        accrual = 3,  censor = 0.9, followup = 2,
                        partition = "Uneven")
head(data[[1]])
head(data[[2]])
head(data[[3]])