This function performs analysis of binary data using the Meta-Analytic-Predictive (MAP) Prior approach. The method borrows data from non-concurrent controls to obtain the prior distribution for the control response in the concurrent periods.
Usage
MAPprior_bin(
data,
arm,
alpha = 0.025,
opt = 2,
prior_prec_tau = 4,
prior_prec_eta = 0.001,
n_samples = 1000,
n_chains = 4,
n_iter = 4000,
n_adapt = 1000,
robustify = TRUE,
weight = 0.1,
check = TRUE,
...
)Arguments
- data
Data frame with trial data, e.g. result from the
datasim_bin()function. Must contain columns named 'treatment', 'response' and 'period'.- arm
Integer. Index of the treatment arm under study to perform inference on (vector of length 1). This arm is compared to the control group.
- alpha
Double. Decision boundary (one-sided). Default=0.025
- opt
Integer (1 or 2). If opt==1, all former periods are used as one source; if opt==2, periods get separately included into the final analysis. Default=2.
- prior_prec_tau
Double. Precision parameter (\(1/\sigma^2_{\tau}\)) of the half normal hyperprior, the prior for the between study heterogeneity. Default=4.
- prior_prec_eta
Double. Precision parameter (\(1/\sigma^2_{\eta}\)) of the normal hyperprior, the prior for the hyperparameter mean of the control log-odds. Default=0.001.
- n_samples
Integer. Number of how many random samples will get drawn for the calculation of the posterior mean, the p-value and the CI's. Default=1000.
- n_chains
Integer. Number of parallel chains for the rjags model. Default=4.
- n_iter
Integer. Number of iterations to monitor of the jags.model. Needed for coda.samples. Default=4000.
- n_adapt
Integer. Number of iterations for adaptation, an initial sampling phase during which the samplers adapt their behavior to maximize their efficiency. Needed for jags.model. Default=1000.
- robustify
Logical. Indicates whether a robust prior is to be used. If TRUE, a mixture prior is considered combining a MAP prior and a weakly non-informative component prior. Default=TRUE.
- weight
Double. Weight given to the non-informative component (0 < weight < 1) for the robustification of the MAP prior according to Schmidli (2014). Default=0.1.
- check
Logical. Indicates whether the input parameters should be checked by the function. Default=TRUE, unless the function is called by a simulation function, where the default is FALSE.
- ...
Further arguments passed by wrapper functions when running simulations.
Value
List containing the following elements regarding the results of comparing arm to control:
p-val- posterior probability that the log-odds ratio is less than zerotreat_effect- posterior mean of log-odds ratiolower_ci- lower limit of the (1-2*alpha)*100% credible interval for log-odds ratioupper_ci- upper limit of the (1-2*alpha)*100% credible interval for log-odds ratioreject_h0- indicator of whether the null hypothesis was rejected or not (p_val<alpha)
Details
The MAP approach derives the prior distribution for the control response in the concurrent periods by combining the control information from the non-concurrent periods with a non-informative prior.
The model for the binary response \(y_{js}\) for the control patient \(j\) in the non-concurrent period \(s\) is defined as follows:
$$g(E(y_{js})) = \eta_s$$
where \(g(\cdot)\) denotes the logit link function and \(\eta_s\) represents the control log odds in the non-concurrent period \(s\).
The log odds for the non-concurrent controls in period \(s\) are assumed to have a normal prior distribution with mean \(\mu_{\eta}\) and variance \(\tau^2\):
$$\eta_s \sim \mathcal{N}(\mu_{\eta}, \tau^2)$$
For the hyperparameters \(\mu_{\eta}\) and \(\tau\), normal and half-normal hyperprior distributions are assumed, with mean 0 and variances \(\sigma^2_{\eta}\) and \(\sigma^2_{\tau}\), respectively:
$$\mu_{\eta} \sim \mathcal{N}(0, \sigma^2_{\eta})$$
$$\tau \sim HalfNormal(0, \sigma^2_{\tau})$$
The MAP prior distribution \(p_{MAP}(\eta_{CC})\) for the control response in the concurrent periods is then obtained as the posterior distribution of the parameters \(\eta_s\) from the above specified model.
If robustify=TRUE, the MAP prior is robustified by adding a weakly-informative mixture component \(p_{\mathrm{non-inf}}\), leading to a robustified MAP prior distribution:
$$p_{rMAP}(\eta_{CC}) = (1-w) \cdot p_{MAP}(\eta_{CC}) + w \cdot p_{\mathrm{non-inf}}(\eta_{CC})$$
where \(w\) (parameter weight) may be interpreted as the degree of skepticism towards borrowing strength.
In this function, the argument alpha corresponds to \(1-\gamma\), where \(\gamma\) is the decision boundary. Specifically, the posterior probability of the difference distribution under the null hypothesis is such that:
\(P(p_{treatment}-p_{control}>0) \ge 1-\)alpha.
In case of a non-informative prior this coincides with the frequentist type I error.
References
Robust meta-analytic-predictive priors in clinical trials with historical control information. Schmidli, H., et al. Biometrics 70.4 (2014): 1023-1032.
Applying Meta-Analytic-Predictive Priors with the R Bayesian Evidence Synthesis Tools. Weber, S., et al. Journal of Statistical Software 100.19 (2021): 1548-7660.
Examples
trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")
MAPprior_bin(data = trial_data, arm = 3)
#> Using default mean for robust component of 1/2.
#> $p_val
#> [1] 0.194
#>
#> $treat_effect
#> [1] 0.3172325
#>
#> $lower_ci
#> [1] -0.4070381
#>
#> $upper_ci
#> [1] 1.05388
#>
#> $reject_h0
#> [1] FALSE
#>