present - bayes-pharma

A Bayesian Dose De-Escalating Design With Stratified Minimax Regret Roland Fisch*, Georg Gutjahr†, Jean Lecot‡

Bayes 2012, Aachen, May 11, 2012 * Novartis Pharma AG; [email protected] † Universität Bremen; [email protected] ‡ Medstat; [email protected]

Outline

Motivation: Dose finding in a rare benign cancer indication

Outcomes of interest: Tumor size reduction; remission rate, stabilizing rate

Dose de-escalation design

Bayesian de-escalation design parameters

Design performance measures

What is an «optimal» design?

Regret, minimax regret, stratified minimax regret

Simulations

Summary

2 | Bayes 2012 | Fisch, Gutjahr, Lecot | 11 May, 2012 | Dose De-Escalation with Statified Minimax Regret

Dose finding in a rare benign cancer indication


Virtual «generic» example, for motivation and illustration

Indication

Rare tumor

benign, i.e. no metastases

There is an effective, but quite invasive standard treatment; however, the tumor may grow again afterwards

Proof of Concept (PoC) trial has been done, with a new treatment (an oral tablet), at one dose (vs Placebo):

Small sample size, e.g. 8

demonstrated tumor size reduction of 92% on average at 4 weeks,

75% of patients with a ≥80% reduction

dose cannot be increased beyond the chosen dose = MTD, due to safety and/or tolerability issues (as established in a first in human healthy volunteer trial); assume MTD = 10 mg

Dose finding in a rare benign cancer indication


Design a dose finding trial:

Find an efficient loading dose <=MTD to be used in pivotal phase 3 trial

Find an efficient maintenance dose to be used in pivotal phase 3 trial

Small maximal sample size, e.g. ≤ 20

Minimize number of patients with sub-therapeutic doses

Outcomes of interest


Tumor size reduction: Using imaging techniques (MRI, CT), a tumor size can be determined, at baseline, and during treatment at different time points

Clinicians prefer to dichotomize the outcome:

Remission:

Tumor size reduction to at most x% (e.g. 20%), of its original size at baseline, at 4 weeks, as a consequence of treating the patient with a «loading dose»

Remission rate = Proportion of patients achieving a remission

Relapse: After remission, the tumor grows back to more than y% (e.g. 40%) of its original size

Stabilize: After remission/relapse, treat with a «maintenance dose» to achieve another remission

Outcomes of interest: Relapse, remission, stabilize


Inference on remission / relapse / stabilizing rates can be derived from inference on the continuous outcome

Outcomes of interest: Relapse (remission, stabilize)


In this presentation: Concentrate on relapse rate, i.e. dose finding for loading dose

Adaptive dose de-escalation design (loading dose)


Start with a high loading dose, e.g. MTD

De-escalate the loading dose, in steps, in cohorts of one or more patients

Data analysis: Bayesian analysis on tumor size at 4 weeks (absolute or in % change); parametric (sigmoidal dose-response model) or ANOVA (i.e. no parametric assumption for dose-response shape)

After each cohort, update the Bayesian analysis

Use PoC data to derive an informative prior

Need to define:

Target/objective: what do we mean by efficient loading dose ?

Decision criteria: i.e. when to de-escalate, or stop ?

Target / objective


Remission rate at dose d: πd

Posterior densities for remission rate πd can be derived from the tumor size model, given data

Potential objectives for loading dose: Find smallest loading dose d with the following property (with a given level of confidence = level of proof)

πd > PRR (for a predefined target remission rate PRR, e.g. PRR = 70%)

πd > π10 – DRR (for a predefined difference DRR relative to MTD=10, e.g. DRR = 10%)

πd > π10 * RRR (relative difference RRR relative to MTD=10, e.g. RRR = 0.8)

De-escalation decision criteria


Decision criteria, in words:

If we have high confidence that the current loading dose is sufficiently effective, we try the next lower dose

If we are still uncertain whether current loading dose is effective, we allocate another cohort at this dose

If we have low confidence that the current loading dose is sufficiently effective, we stop and select the last effective dose (i.e. the previous, higher dose)

De-escalation decision criteria


Decision criteria, in probabilities (with parameters δ1, δ2):

For the current dose d (i.e. the one most recently applied), calculate the (posterior) probability qd = prob(πd > PRR)

If qd ≥ δ2 then goto next lower dose

If δ1 ≤ qd < δ2 then assign another cohort to dose d

If qd < δ1 then stop, and declare the next higher dose as the minimally effective one

De-escalation, example


Adaptive dose de-escalation design


Advantages of the design:

Find target loading dose quickly, with a small number of patients

Expected number of patients receiving an ineffective dose is small

Quantified by running simulations

Disadvantages:

Essentially unblinded

Logistically more demanding, as compared to fixed design

What is an optimal design?

Can we do simulations to find an «optimal» design?

What are reasonable criteria for optimality?

What are the scenarios to optimize over?

Find the «overall» optimal design parameters δ1, δ2

General simulation model


Elucidate biological/clinical assumptions

Build a temporal random effects dose-response model (to allow for simulating loading dose and maintenance dose effects)

For loading dose only: dose-response model (at week 4)

Loading dose simulation model


Reduce temporal model to 4 weeks: Emax-like model

Parameters with informative prior Q(μ10,σ2), from PoC trial

Effect μ10 and variance σ2 at dose 10μg, at 4 weeks

Assume homoscedasticity

Other dose-response parameters θ: Unknown

Define a design performance measure («utility») as a function of δ, θ, μ10, σ2

Overall design performance measure:

integrate out over dQ(μ10,σ2)*dP(θ) -> solution strongly depends on the choice of uninformative P(θ)

integrate out over dQ(μ10,σ2); choose a plausible metric of overall performance, under reasonable scenarios for θ: (θ1, θ2, θ3, ...)

Find the parameters δ which optimize the overall design performance

Proposals for design performance measures


Optimality criterion, first try: Minimax regret


Regret:

Maximal regret of design δ, over θ:

Minimax regret: Minimum (over all δ’s), of maximal regret (over θ) (for simulation: 0 ≤ δ1 ≤ 0.5 ≤ δ2 ≤ 0.95, in 0.05 increments)

Optimal minimax regret design


Highest values for δ1,δ2 chosen: Almost never de-escalate ??

Optimal minimax regret design


Highest value for δ2 chosen: Almost never de-escalate?? Does not make sense!

What’s wrong?

For scenarios where the highest dose is optimal, not de-escalating is the best design; this seems to dominate the minimax criterion

Need to downweight the regret for scenarios where the highest dose is optimal, in favor of the ones for lower target doses

Minimax regret design: stratified


Optimality, second try: Stratified minimax regret


Stratify the set of scenarios Θ into subsets Θ1U Θ2U Θ3U ..., such that Θi contains scenarios where the i-th dose is optimal

Stratified regret:

Standardize stratified regret to [0,1]:

Stratified minimax regret:

Optimality, second try: Stratified minimax regret


Design optimality


Minimax regret produces nonsensical optimal design

Stratified minimax seems reasonable: δopt = (δ1=0.15,δ2=0.85),

In general:

Need a design performance measure as a function of design and scenario R(δ,θ) (e.g. Regret)

Need a way to summarize R(δ,θ) over scenarios θ (e.g. maximization, stratified maximization, expectation)

Minimize over δ

Design optimality


Refine optimality / design performance measure, i.e. utility

Stratified minimax regret is just a try

Consider refining the utility:

Ideally, in units of Net Present Value

Incorporate number of patients

Incorporate number of patients on sub-therapeutic dose

Based on simulations, report aspects of design performance in tabular and graphical form

Use Decision Analysis tools to discuss utility / optimality with the team

Summary


De-esclation seems to be a reasonable approach

Stratified minimax optimal design seems to perform well

Project specifics influence design choices:

Target dose definition (PRR, DRR, RRR)

Design performance measures (L1, L2, ..)

Optimality criteria

needs a lot more work!

Additional complexity when looking at loading dose + maintenance dose

present - bayes-pharma

Documents