Pharmaceutical innovation is increasingly risky, costly and at times inefficient. The drug development process to bring a new product to market can range between $800 million and $2 billion. Meanwhile, late-stage failures and rising costs of Phase II and III clinical trials often represent key components of this cost.
Drug Discovery
Therefore, it is crucial to ensure that data derived from drug development phases is conducted efficiently and cost-effectively. Moving from traditional clinical development approaches to a more integrated view that uses adaptive design tools helps increase flexibility. Further, maximizing the use of accumulated knowledge, such as Bayesian methods, has an important role in reducing attrition rates.
Drug Discovery Process
According to “The Future of Drug Development”:
“the problem of attrition is particularly acute in Phase II trials, owing to factors such as the lack of proof of relevance of the biological target in a given disease intervention and insufficient understanding of the dose-response relationship of the new molecular entity”.
Bayesian Reasoning
The Bayesian model is adaptive, parallel and data led. The reasoning is intentional: the model design allows available knowledge to be appropriately shared across development studies. The impact of Bayesian thinking is improve the quality, timeliness and efficacy of the process. This white paper will present some general issues in drug development and the conditions in which implementing the Bayesian model can lead to success.
Bayesian Theory
The drug development process is well understood, along with the goal of discovering safe and effective doses for clinical use. The data generated prior to the early drug development phase has been completed as the data during the preclinical phase involving safety assessments in animals. Bayes theorem probability is used to develop methodology and the assessment of absorption, distribution and elimination.
Bayesian Data Analysis
There is also an understanding of the relationship between dose administered, drug concentrations in the body, and efficacy/toxicity (also, referred to as pharmacokinetics). Pharmacokinetics, along with Bayesian data analysis, plays an important role in drug development.
It is critical to understand the biochemical and physiological interactions of a drug and the body. Bayesian decision theory is based on clinical drivers such as absorption, distribution, metabolism and excretion. The data derived from pharmacokinetic studies guide clinical trial design, dosage selection, development strategies.
Bayes Theorem
The Bayesian methodology relies on the use of probability models to describe knowledge about parameters of interest. It uses principles from the scientific method to combine prior beliefs with observed data.
The Bayesian approach to pharmacokinetic modeling, in specific, is appealing in that Bayes rule mimics human thinking. Bayesian probability incorporates sets of data for estimating the patients’ pharmacokinetic parameters. This uses prior pharmacokinetic parameters as the starting estimate for an individual.
Bayesian Statistics
The Bayesian approach then adjusts these estimates based on the patients measured drug levels, taking into considering the variability of the parameters. Essentially, this approach builds upon pharmacokinetic modeling because it takes data from pharmacokinetic modeling and expands by past experience.
A key success factor lies within Bayesian probability: the ability to quantitatively judge how cogent every piece of information is. In using this approach, companies will be able to first foresee all possibilities that might arise. This statistical rethinking allows the scientist to judge how likely each option may be based on data and past experiences before deciding how to proceed.
Bayesian Learning
Bayesian modeling provides coherent framework for quantifying uncertainty and making inferences in the presence of that uncertainty. The framework is the learning behind formal approaches to incremental model building, parameter estimation and other statistical inference. By contrast, frequentest methods rely solely on observed evidence for inferences and typically do not formally take into account prior information.
Biomarkers
Bayesian modeling can be a valued methodology throughout the entire drug development phase. In the exploratory phase of drug development, this model uses all available knowledge and tools. Additionally, trials that include biomarkers, modeling and Bayesian machine learning can help advance the statistical methodology success.
Proof of Concept
Trials are designed to determine proof of concept (PoC) and to establish dose selection. The level of rigor will enhance the likelihood of success in the confirmatory phase. During the confirmatory phase, modern designs, tools and knowledge are applied to larger-scale studies. The Bayes decision rule helps identify the target patient population in which the drug is efficacious. Finally, establishing the benefit/risk ratio and confirming the optimal dose directly leads to the dosing regimen.
Dosing Regimen
An important goal of a drug development program is the selection of dose and dosing regimen that achieves the target clinical benefit while minimizing undesirable adverse effects. Bayesian pharmacokinetic modeling can provide a continuous flow of information across different phases of development. Moreover, Bayesian modeling combined with use of external baseline data helps to improve efficacy and safety signal detection in early development.
Safety Signals
In early drug development studies for establishing efficacy and safety evaluation in a PoC study often uses small patient cohorts. This population is observed for a short period of time to evaluate early efficacy and safety signals that are continuously measured.
Maximum Tolerated Dose
As variables are derived from the responder and non-responder behavior, new cohorts are assigned in sequence to increasing doses until the maximum tolerated dose is reached. Most importantly, the goal is to either determine a dose range for further Phase IIb, or to conclude that no PoC can be established based on the efficacy-safety trade-off, which can be costly.
Toxicology Experiments
Bayesian pharmacokinetic modeling averaging for benchmark dose (BMD) estimation is a popular method for identifying exposure level of agents. To generate the BMD, Bayesian pharmacokinetic model averaging integrates other historical toxicological experiments and animal bioassay data with current data.
Bayesian Model Averaging
The Bayesian model averaging method qualifies a posterior probability weight for each considered dose-response model. Finally, the analysis computes a weighted average of the BMD estimate from all the individual models. In addition, the utility of PoC studies within drug development programs can be enhanced by incorporating information obtained directly into later-phase trials using Bayesian modeling.
Pharmacokinetic Modeling
One of the principal aims of drug development is to discover, for a particular agent, the relationship between dose administered, drug concentrations in the body and efficacy/toxicity. Population pharmacokinetic models provide an important aid to this understanding by identifying sources of and quantifying the remaining variability in drug concentrations and response measures.
Drug Concentrations
Pharmacokinetic data consist of drug concentrations along with (typically) known sampling times and known dosage regimens. Population data arises when quantities and subject-specific characteristics are measured in a group of individuals. Further, data can be segmented by age, sex or the level of biological marker.
Variability
Variability findings can occur when identical doses are administered to a group of individuals. Subsequently, the mechanisms which cause the variability are usually complex. Using a Bayesian approach to drug development will help improve the doses currently being determined by traditional pharmacokinetic models.
Prior Adjustments
Most importantly, the Bayesian approach allows for the incorporation of informative prior distributions. With that in mind, a Bayesian approach may actually be preferable due to the difficulties in a classical (frequentest) approach.
Dose Adjustment
The dosing recommendations that emerge from drug development studies are frequently inappropriate. When individual dose adjustment is needed, the recommendations provided may be insufficiently informative to allow the adjustment to be undertaken in an optimal manner making it extremely costly and time consuming.
For instance, PK modeling in the compartmental system for physiological analyses typically uses a large number of compartments to model the various organs and tissues of the body and only obtain data on a small number of individuals.
Dosing Regimen
Information obtained from population analyses is useful once the drug is ready for the individualization of dosing regimens. Typically only sparse data is available, so prior information on individuation of dosage regimes found through on-line therapeutic drug monitoring can help.
Above all, provide estimates of the parameters of the population distribution with the use of Bayesian sampling-based approach.
Frequentest (classical) v. Bayesian approach
While the Bayesian approach gives companies a cost effective way forward, it is critical to present classical drug development process habits. Although taking a Bayesian approach is completely sensible, it is important to present evidence that this approach will not hinder data found by frequentest.
Characterized assumptions about the underlying physiological processes are statistical and subject-matter considerations in PK/PD analysis. Both frequentest and Bayesian approaches yield similar conclusions when the data contains sufficient information.
Clinical Studies
Incorporating information from previous studies in a statistical, natural way throughout the development process is essential to success. Declining pharmaceutical industry productivity is becoming more common. Further, a key driver in the problem is clinical studies are increasingly expensive.
This Bayesian model can ensure the judicious use of limited patient resources, reduce patient exposure to ineffective or poorly tolerated doses, and lead to the recruitment of patients who, on the basis of biomarker analysis, are most likely respond to those with the most favorable benefit/risk ratio.
Model Parameter
From an estimation/statistics standpoint a Bayesian approach is preferable because of the difficulties which a classical approach encounters. This often includes the large number of parameters, nonlinearity of subject-specific models and the large numbers of variance parameters. Recent development in Bayesian methodologies do give a way forward for successful drug development.
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