Podcast #
A easy-to-understand podcast featuring Scott Berry discusses how Bayesian Clinical Trial Design compares to Traditional Freqentist designs. This is paradigm shift happening in pharmaceutical, cancer, medical, and all types of clinical trials. Its emergence acceleration is tied to the need to adapt during the COVID pandemic and adoption of many of the techniques by public health officials and statisticians to answer the complicated questions raised in the face of emerging information.
Scott Berry podcast on Learning Bayesian Statistics #
Additional Background for Understanding Bayesian Clinical Trials #
Foundational Differences Between Frequentist and Bayesian Approaches #
Frequentist and Bayesian statistics rest on fundamentally different philosophies about probability and what inference should accomplish. Under the frequentist paradigm, probability describes the long-run frequency of events: parameters such as treatment effects are fixed but unknown constants, and the data are the random variable. In contrast, the Bayesian paradigm treats the unknown parameter itself as a random variable and assigns it a probability distribution that reflects both prior knowledge and observed data.[youtube][learnbayesstats]
What a p-Value Actually Measures #
A p-value is the probability of observing data at least as extreme as the results obtained, calculated assuming the null hypothesis is true. It does not tell you the probability that the null hypothesis is true, nor does it tell you the probability that the treatment works—these are common misinterpretations. When researchers declare a result “significant” at p ≤ 0.05, they are rejecting the null on the basis of an arbitrary threshold introduced by Ronald Fisher in 1925 largely for computational convenience.[youtube]
Because the p-value conditions on the null being true, it cannot directly answer the question clinicians care about most: “Given these trial results, how likely is it that the treatment is effective?”. In some scenarios, the false-positive risk—the probability that a treatment is actually ineffective when p ≤ 0.05—can exceed 25%, and the probability that a treatment is effective when p > 0.05 can exceed 50%.[learnbayesstats][youtube]
Confidence Intervals vs. Credible Intervals #
A 95% confidence interval means that if the same trial were repeated many times, 95% of those intervals would capture the true population effect—but any single interval either contains the true value or it does not. Crucially, a confidence interval does not say there is a 95% probability the true effect lies within that range.[youtube]
Bayesian credible intervals, by contrast, are direct probability statements: a 95% credible interval means there is a 95% probability that the parameter lies within the interval, given the observed data and prior beliefs. This interpretation aligns with what most clinicians intuitively want from an analysis.[learnbayesstats][youtube]
Updating Beliefs with Bayes’ Theorem #
Bayesian inference begins with a prior distribution that encodes what is already known or believed about a treatment effect before the trial. When new data arrive, Bayes’ theorem combines the prior with the likelihood (the probability of the observed data for each possible value of the parameter) to produce a posterior distribution. In simplified terms:[youtube]posterior∝likelihood×prior
The posterior is a complete probability distribution for the treatment effect, from which researchers can calculate the probability that the effect exceeds any clinically meaningful threshold, such as a minimum clinically important difference. This flexibility allows decision-makers to ask questions like “What is the probability that this drug reduces mortality by at least 5%?” rather than merely “Is p less than 0.05?”[youtube]
Why Bayesian Methods Suit Adaptive Trials #
Adaptive and platform trials involve multiple interim analyses, potential arm-dropping, dose reallocation, and sometimes incorporation of external data. In such designs, the frequentist notion of “probability of data this extreme under the null” becomes ill-defined because the final data depend on earlier decisions. Bayesian analyses condition only on the data actually observed and naturally accommodate sequential looks, complex decision rules, and external information without the elaborate corrections frequentist methods require.[ascopubs][youtube]
Practical Trade-Offs #
| Aspect | Frequentist Approach | Bayesian Approach |
|---|---|---|
| Probability interpretation | Long-run frequency of events [youtube] | Degree of belief given data [learnbayesstats] |
| Unknown parameter | Fixed constant [youtube] | Random variable with a distribution [youtube] |
| Prior information | Not formally incorporated | Explicitly included via prior [youtube] |
| Interim analyses | Require alpha-spending corrections [ascopubs] | Coherent under sequential updating [youtube] |
| Decision output | Dichotomous (significant/not significant) [youtube] | Posterior probabilities for any threshold [youtube] |
| Computational burden | Generally lower | Higher; relies on simulation or MCMC [youtube] |
Bayesian designs demand more up-front work—teams must agree on priors, decision rules, and simulation scenarios—but they can yield more efficient trials that expose fewer patients to inferior treatments. Frequentist designs remain simpler to implement and are still the regulatory default, though agencies such as the FDA have published guidance encouraging Bayesian approaches for medical devices and complex adaptive trials.[pmc.ncbi.nlm.nih][youtube]
