From Ethics to Clinical Algorithms
Posted on September 16, 2023 • 6 minutes • 1139 words
Table of contents
Decision-Making in Benefit-Risk Assessment (BRA) in Pharmacovigilance
In relation with clinical trials, decision-making is a critical process based on the evaluation of the Benefit-Risk Assessment (BRA). BRA measure is used to make a binary operation: support or withhold a particular medical treatment. This assessment is paramount to ensure that the benefits of a treatment outweigh the associated risks, which corresponds one of the three basic Belmont principles. But how is it actually done?
Methodologies for BRA
BRA can take into account a multitude of variables, including patient’s quality of life and treatment convenience. However, at its core, the assessment primarily revolves around two fundamental components: efficacy (as benefits) and potential negative outcomes (as risks). These components are typically represented as a ratio:
$$ \text{BRA} = \frac{\text{Benefits}}{\text{Risks}} \tag{Eq.1}$$
The complexity of BRA lies in the decision of how to compare these benefits and risks, particularly when dealing with variables that are challenging to assess. Various criteria can be employed for this task, ranging from intuition to logical rules, weightings, or value analysis based on societal considerations. Regardless of the chosen metric, the methodology for conducting the assessment is a crucial consideration, and it can be categorized into two primary approaches:
1. Qualitative Frameworks
Qualitative frameworks provide a structured and logically described set of rules to assess each variable and determine their relative importance in the BRA process. These frameworks are typically designed even before the commencement of the third clinical phase, where data collection allows for the construction of an effect’s table.
2. Quantitative Scoring Algorithms
Quantitative scoring algorithms, on the other hand, involve an analytical computation of the importance of each variable based on a structured numeric approach. While these algorithms are gaining popularity, they have yet to establish themselves as the dominant approach in BRA.
International Guidelines
Several international organizations, including the U.S. Food and Drug Administration (FDA), provide guidelines and recommendations on the best practices for implementing qualitative frameworks in BRA FDA BRA Guidelines . On the other hand, quantitative algorithms, although advancing, remain an area of ongoing development.
In summary, the process of Benefit-Risk Assessment is a multifaceted and critical component of medical decision-making. The choice between qualitative frameworks and quantitative algorithms depends on the specific context and available data, and both approaches contribute to ensuring the safety and effectiveness of medical treatments.
Model example with Bayesian statistics
The current explanation is based on the work of Kan Li et al (PMCID: PMC6681911 ). Some aspects have been simplified, as long as the purpose of this article is to explain the intution behind the maths they propose. However, a more complete explanation and the Stan code of the original work can be found in the included link.
With that said, how do we fabricate mathematical formulas to assess BRA? Let’s first of all define our data: Imagine we are studying a set of K treatments (k = 1, …, K) assessed on J criteria (j = 1, …, J) for a given patient i (i = 1, …, I). The criteria measurements corresponding to treatment k on patient i are denoted by ξᵢₖ, where ξᵢₖ = [ξᵢ₁ₖ, …, ξᵢJₖ]ᵀ, representing the performance of treatment k on each criterion j.
In a clinical trial, benefit and risk criteria are typically expressed through measurable efficacy and safety. These criteria may take various formats, such as probabilities or continuous measurements. The trade-off between benefit and risk for a specific treatment is represented by an integrated BR measure, calculated using the additive utility score:
$$ uᵢ(ξᵢₖ, wᵢ) = \sum_{j=1}^{J} wᵢuⱼ(ξᵢⱼₖ) \tag{Eq.2} $$
where: - wᵢⱼ represents the weight assigned to criterion j by patient i, assumed to follow a Dirichlet distribution. Why? Simply because, in bayesian statistics, constitutes the prior of a multinomial distribution. If you think about it weights are no more than representing a multivariate probability distribution, with values between 0 and 1.
The weights vector wᵢ denotes the relative importance of criteria elicited by patient i, reflecting their preferences on benefit and risk criteria (and they follow as well a Dirichlet distribution!). The PVF function, uⱼ(ξᵢⱼₖ) ,maps criterion values ξᵢⱼₖ to the same scale (1) making risks and benefits comparable. The PVF can be defined as follows:
$$ uⱼ(ξᵢⱼₖ) = \frac{{ξᵢⱼₖ - ξᵢ’ⱼ}}{{ξᵢ’‘ⱼ - ξᵢ’ⱼ}} \tag{Eq.3} $$
where ξᵢ’ⱼ and ξᵢ’‘ⱼ are the least and most preferable values of criterion j.
Okay, but what is a Multidimensional Latent Trait Model
The main aspects of a treatment’s response are the outcomes (benefits and risks) and the relevant covariates (such as blood pressure or presence of fever) associated to them. All these variables together are explanatory of the specific situation of the patient, and for that reason, seems logical to assume that they are not simply independant to each other. How can we model statistically their relation? One reasonable option is by assuming they are all generated by the same latent variables.
And there is more we need to assume. If we think about it, the observed outcomes from a treatment can actually have many natures. There is indeed a multivariate distributions in these variables. Under the local independce assumption, the observed outcomes yᵢ for a patient i can be written as:
For binary outcomes: $$\text{logit}(p(yᵢⱼ=1 | xᵢ, Tᵢₖ, θᵢ)) = \text{logit}(ξᵢⱼₖ) = xᵢᵀβⱼ + Tᵢₖᵀβᵗᵣⱼ + θᵢᵀλⱼ \tag{Eq.4}$$ where ξᵢⱼₖ follows a Bernoulli distribution.
For continuous outcomes: $$ yᵢⱼ’ | xᵢ, Tᵢₖ, θᵢ = ξᵢⱼ’ₖ = xᵢᵀβⱼ’ + Tᵢₖᵀβᵗᵣⱼ’ + θᵢᵀλⱼ’ + εᵢⱼ’ \tag{Eq.5} $$ where εᵢⱼ’ follows a normal distribution.
Additionally, we assume these latent variables ($\theta_{i}$) responsible of generating such a variety of differently distributed variables may be exponentially distributed. In any case, as you can see by the formulas their use and inference predicts the objective outcomes (risks and benefits) that can be used as shown in Eq.1 to generate the Benefits Risk Assesment.
Closing Thoughts on BRAs
In the end, Benefits Risk Assesments are not yet a not closed matter.There is no universal method for its computation, due to the complexity of actually comparing two different things (risks and benefits). Howver, certain essential criteria must be always met for a BRA to gain approval:
- Coherent ethical definition
- Transparent weighting reasoning
- Reproducibility with study data
It’s worth noting that the significance of these statistics is not fixed and can evolve throughout the clinical phases. Furthermore, the threshold required for a treatment to be deemed successful can vary significantly depending on factors such as the disease’s nature, its severity, and the level of competition in the market.
However, it’s crucial to remember that the ultimate decision to participate in a clinical trial should always rest with the patient, considering their unique circumstances and preferences.
Reference
Li K, Luo S, Yuan S, Mt-Isa S. A Bayesian approach for individual-level drug benefit-risk assessment. Stat Med. 2019 Jul 20;38(16):3040-3052. doi: 10.1002/sim.8166. Epub 2019 Apr 15. PMID: 30989691; PMCID: PMC6681911.