The FACTS core engine allows for the design and simulation of fixed and adaptive clinical trials, especially focused on, but not limited to, Bayesian designs with multiple active arms.
Sub-tabs of the Design Tab
Trials designed in the core engines are comprised of a number of elements:
The dose response model: the user must specify how the doses are related to each other in the primary analysis, though there is a simple ‘no model’ option that estimates the mean treatment effect of each arm independently. A fixed trial uses the dose response model for the final Bayesian analysis of the data; an adaptive trial uses the same model both for the final analysis and at the interim updates. For time-to-event endpoints, there is an additional tab for estimating the control arm hazard rate called hazard model.
The longitudinal model or predictor model: whether the trial is adaptive or fixed, the user may select whether to use a longitudinal model for continuous or dichotomous primary endpoints or a predictor model when using a time-to-event primary endpoint. In a fixed trial the longitudinal model can be used to multiply impute final values for subjects that have dropped out. In an adaptive trial it is also used at the interim updates to multiply impute final values for subjects who have been recruited but do not yet have final values. In a fixed trial with no subject dropouts using a longitudinal model would have no effect on the outcome, analysis, or conduct of the trial.
Allocation rules: in a fixed trial the user just specifies the proportion of subjects to be recruited to each arm, and the same can be done in an adaptive trial (i.e. an adaptive trial does not have to adapt the allocation), but an adaptive trial has a range of options that the user can use to adapt how subjects are allocated to the different treatment arms as the trial progresses.
Early stopping rules: in an adaptive trial the user can select the criteria and specify the thresholds at which trial should be stopped at any interim where the conditions are satisfied. Early stopping is optional, and even in an adaptive design the user can opt to always recruit the maximum permitted number of subjects. In a fixed trial there are no interim analyses and hence no opportunity to stop early.
Final evaluation criteria: the same Bayesian evaluation criteria are available whether the trial is fixed or adaptive. The user selects which criteria to use and what thresholds will constitute success or failure. The success and failure criteria do not have to be complements of eachother, and any analysis that doesn’t completely satisfy either the success or futility criteria is called, “inconclusive.”
Frequentist analysis: frequentist p-values can be calculated comparing each dose to the control arm (or a fixed value if there is no control). P-values can be used as decision making quantities at interim updates or final analyses. p-value cannot benefit from the dose reponse models or longitudinal models, which are specific to the Bayesian model in FACTS.
The tab layout for multiple endpoint designs is slightly different when compared to the single endpoint engines. The multiple endpoint engine must allow for separate Dose Response, Frequentist Analysis, and Longitudinal specifications for each endpoint.
To allow for this, there is a “Response Models” tab as a first level sub-tab of the Design tab. There is 1 sub-tab below Response Models for each endpoint. Within the endpoint tab there will be a Dose Response, Frequentist Analysis, and Longitudinal tab (if applicable).
Evaluation of Bayesian Posterior Estimates
At every interim and final analysis there is a Bayesian model fit to the data observed up to that point in the trial. The Bayesian model contains a dose response model and, often, a longitudinal model. In the absence of a longitudinal model, the posterior is calculated as:
\[p(\omega|Y) \propto \prod_{i = 1}^{n}{p(y_{i}|\phi)p(\phi)}\]
where \(\phi\) is the set of parameters of the selected response model, \(p(\phi)\) is the prior for those parameters, \(y_i\) is the final response for each subject and \(n\) is the number of subjects with complete data.
With a longitudinal model, this becomes:
\[p(\omega|Y) \propto \prod_{i = 1}^{n}{p(y_{i}|\phi)p(\phi)\prod_{i = 1}^{n}{\prod_{j = 1}^{L}{p(y_{ij}|\psi)p(\psi)}}}\]
where \(\psi\) is the set of parameters of the selected longitudinal model, \(p(\psi)\) is the prior for those parameters, \(y_{ij}\) is the response for each subject \(i\) at each visit \(j\) and \(L\) is the number of visits.
The posterior is evaluated using MCMC Markov Chain Monte Carlo with individual parameters updated by Metropolis Hastings (or Gibbs sampling where possible), using only the \(y_i\) and \(y_{ij}\) data available at the time of the update.
The likelihood and priors for each of the dose response models are provided in the description of the Dose Response tab, and the likelihood and priors for the multiple imputation models are provided in the description of the Longitudinal Models tab.