Composite Likelihoods with Bounded Weights in Extrapolation of Data Margaret Gamalo Yoonji Kim Fan Zhang Junjing Lin

2025-04-27 0 0 506.05KB 28 页 10玖币
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Composite Likelihoods with Bounded Weights in Extrapolation of
Data
Margaret Gamalo, Yoonji Kim, Fan Zhang, & Junjing Lin
ABSTRACT
Among many efforts to facilitate timely access to safe and effective medicines to
children, increased attention has been given to extrapolation. Loosely, it is the
leveraging of conclusions or available data from adults or older age groups to draw
conclusions for the target pediatric population when it can be assumed that the course
of the disease and the expected response to a medicinal product would be sufficiently
similar in the pediatric and the reference population. Extrapolation then can be
characterized as a statistical mapping of information from the reference (adults or
older age groups) to the target pediatric population. The translation, or loosely
mapping of information, can be through a composite likelihood approach where the
likelihood of the reference population is weighted by exponentiation and that this
exponent is related to the value of the mapped information in the target population.
The weight is bounded above and below recognizing the fact that similarity (of
the disease and the expected response) is still valid despite variability of response
between the cohorts. Maximum likelihood approaches are then used for estimation
of parameters and asymptotic theory is used to derive distributions of estimates for
use in inference. Hence, the estimation of effects in the target population borrows
information from reference population. In addition, this manuscript also talks about
how this method is related to the Bayesian statistical paradigm.
Keywords
extrapolation, composite likelihood; random effects methods, exchangeability, Bayesian
methods
Corresponding Author: Margaret Gamalo, PhD is Statistics Therapeutic Area Head, Inflammation and Immunology, Pfizer;
Email:margaret.gamalo@pfizer.com. Yoonji Kim is a PhD Candidate at the Department of Statistics, The Ohio State University,
Fan Zhang is Associate Director, Global Biometrics and Data Sciences, Pfizer, Junjing Lin is Associate Director, Statistical and
Quantitative Sciences, Takeda. The views expressed in this paper are those of the authors and not necessarily those of the author’s
employer.
arXiv:2210.01862v1 [stat.ME] 4 Oct 2022
1 Introduction
Despite the requirement and associated incentives to address the economic burdens of pediatric drug
development, the typical delay in getting pediatric labeling after the initial adult approval is still an
average of 9 years with many pediatric trials ending up not finishing, abandoned, or delayed [
1
,
2
].
Nearly one out of five trials ended early, primarily due to recruitment challenges, with a proportion
of trials withdrawn before recruitment began [
3
]. In a related investigation, completion of many
pediatric studies required under the European Union (EU) Paediatric Regulation is generally delayed
[
4
]. For this reason, extrapolation is promoted as a means to reduce “the amount of, or general
need for, additional information (e.g., types of studies, design modifications, number of patients
required) needed to reach conclusions” when it can be assumed that the course of the disease and
the expected response to a medicinal product will be sufficiently similar in the pediatric (or target)
and the reference (or source) population [
5
,
6
]. This is also justified as children are considered
avulnerable population, i.e., children should only be enrolled in research if the scientific and/or
public health goal(s) cannot be met through enrolling subjects who can consent personally [7].
The right number of pediatric patients also implies that extrapolation should be a default strategy
in pediatric development and warrants a further use of efficient innovative designs. This includes
innovative analytical strategies with appropriately designed adult clinical trials. Of note, extrapola-
tion as a reduction of extent of development, i.e., number of trials and sample size, includes two
steps: (1) determining the trial type based on the degree of information that can be translatable from
the reference to the target population within the current indication and the risk associated with the
development; and (2) quantitative or innovative methodologies to be implemented. These novel
analytical strategies further reduce the required evidence to be obtained from the target pediatric
population following the predicted degree of similarity to the source population.
The manuscript aims to offer a translation of the extrapolation concept into statistics to provide
some guidance on the extent of development in a pediatric trial. In particular, it discusses composite
likelihood to borrow information from the reference population. The manuscript is organized in
the following sequence. The next section discusses the concept of extrapolation as defined in the
International Conference on Harmonization (ICH) E11 (R1). Section 3 discusses the composite
likelihood and bounded weights. Bounded weights is a unique concept that recognizes similarity of
diseases/response precedes variability in outcomes. Hence, minor changes in response, in a disease
2
that is known to be similar in both cohorts, should not be used as penalty for down-weighting or
reduction in accessible information. Section 4 provides an example of a streamlined pediatric drug
development with analysis on its operating characteristics and its relationship to the concept of
tolerable uncertainty. The last section gives a discussion of the key messages of the manuscript.
Figure 1: Extrapolation Framework as outlined in the EMA’s Reflection paper on the use of
extrapolation in the development of medicines for paediatrics.
2 Extrapolation in Pediatric Clinical Development
In the EMA’s reflection paper, in particular, extrapolation starts with initial substantiation, i.e.,
assumptions forming the extrapolation concept should be evidence-based. This establishes a “line
of reasoning” about the relation between the disease pathogenesis or underlying cause and in
tissue findings, clinical presentation or manifestation of disease, criteria for disease diagnosis
and onset, disease stage or severity, co-morbidities, and treatment.” Additional data that may
3
help establish similarity of the disease include time course of the disease, portability of response
measures, i.e., measurement can be used in target population, as well as physiologically based
mathematical representations of biological, pathophysiological, and pharmacological processes in
as much molecular detail as possible.
To establish similarity in response, a systematic assessment and synthesis of available data from
clinical trials is needed. Other relevant evidence from clinical practice (e.g., from other pediatric age
groups, related pediatric indications, adult indications for (similar) pediatric indications, real-world
evidence, or historical or placebo controls) may also provide information on the degree of similarity
between adults and children in the course of the disease and the response to treatment. Reference
population information to justify similarity of clinical response may come from products used to
treat the same indication, other formulations of the same active ingredient, or surrogate endpoints
and data from other clinical trials and observational studies. There is no universal answer to “when
is it reasonable to assume similarity of response?” as the assessment of similarity depends on the
indication, clinical consensus, and the definition of the criteria for delineating when “similar is
similar enough.”
These criteria should not be construed that the goal in the substantiation of extrapolation is to
show dissimilarity between the reference population and the target pediatric population. Most
research has been about measuring the right outcomes that define disease progression or emphasis
on tailoring treatment options; hence, these researches have been about differences in disease than
comparability. In addition, the identification of knowledge gaps can be confusing, since it focuses
on disease manifestation and progression, i.e., differences between reference and target or adults
and children. However, the gaps seem to be equated with knowledge of efficacy, safety, and PK.
The question should be how the similarity in these parameters reduces the amount of information
needed to establish, efficacy, safety, and PK. Ultimately, the mindset needs toward ensuring safe
and appropriate usage in children should be emphasized rather than establishing necessary metrics
of disease similarity. In the real world, clinical judgment presides over pharmacologic rationale —
the dire need to provide pediatric patients the treatment they need will force a clinician to guess the
appropriate administered dose once adult approval.
4
3 Statistical Translation of Information through Composite Likelihoods
Statistically, the conditions for applying extrapolation are stringent as similarity in disease progres-
sion implies similarity at baseline and disease prognosis. Furthermore, the criteria of similarity of
treatment response imply clinical meaningful consistency of response. The challenge has often
led to its limited use. However, many have argued that extrapolation should not be all or nothing
and that there are degrees of extrapolation that can be accommodated [
8
]. The clinical assessment
of dissimilarity on disease progression/response to intervention may not be sufficient ground for
withholding treatment to a child in the light of the benefit that could be potentially achieved [
9
].
Hence, some form of extrapolation or should be a default strategy in any pediatric drug development.
In view of these arguments and to facilitate a statistical translation, suppose that we call a disease
Dr
for the reference population and when it appears in the target population as
Dt
. We say
Dr
is
similar to
Dt
if any information (disease progression, response to intervention) in
Dr
, called
Dr
, has
corresponding information in
Dt
, called
Dt
. For example, a simple case would be that
Dr
similar to
Dt
if information in
Dr
is proportional to some data in
Dt
. Hence, if
A
is quantifiable evidence in
Dr
then we can determine its projected information in
Dt
. Call this projection as the translatable
information which is only worth
γ|A|
in
Dt
, for some
γ∈R
. In general, we are interested in a
function that will map information in Drto information in Dt.
Suppose the extrapolation plan for a drug developed for
Dt
is to have sufficient information
S
in
the form of an adequate and well-controlled trial to warrant label extension in children. Since
γ|A|
is already available, the objective is to conduct a trial with information size
B
such that
γ|A|+|B|=|S|
.
B
then is just the right amount of pediatric patients to fill the knowledge gap or
uncertainty in the currently available data. Note that the more similar the diseases are then the less
B
is needed to reach
S
. Furthermore, while
B
can come from a continuum of evidence, there are
only a few trial types from which information can be extracted, e.g.,
• PK/PD or dose-ranging study;
• single arm descriptive efficacy and/or safety study;
• randomized controlled efficacy and/or safety study.
From these types, the extent of the trial in terms of sample size can be increased or decreased. The
reduction can be similarly based on the perceived similarity of the two diseases and can be derived
5
摘要：

CompositeLikelihoodswithBoundedWeightsinExtrapolationofDataMargaretGamalo,YoonjiKim,FanZhang,&JunjingLinABSTRACTAmongmanyeffortstofacilitatetimelyaccesstosafeandeffectivemedicinestochildren,increasedattentionhasbeengiventoextrapolation.Loosely,itistheleveragingofconclusionsoravailabledatafromadultso...

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