BayesAT (version 0.1.0)

Bayes_test: 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)

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, \(\pi \propto 1/\lambda\).

Arguments

data

Matrix. The data contains both survival time and event status.

alpha

Numerical. Gamma distribution alpha parameter.

beta

Numerical. Gamma distribution beta parameter (rate = 1/scale).

test

Categorical. Three types of hypothesis includes "greater", "less", or "two_sided".

threshold

Numerical. The value tested against hypothesis or evidence.

type

Categorical. The types of Bayesian inference include "Posterior" for estimation of parameters or "Predictive" for predicted survival rate.

pred

Numerical. The time point for predicted survival rate, for example, 2 years, or 5 years survival probability.

diagnosis

Logical. If diagnosis == TRUE, the Bayes factor is calculated, and the formulation of Bayesian factors is given in details.

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)