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8/4/2019 1.Lecture Introduction Covariates
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8/4/2019 1.Lecture Introduction Covariates
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Intro &
Covariates
Exploratoryanalyses
Individualcovariate-parameterrelations
Buildingcovariate-parameter
models
Building
covariate-parameter
models
Time-varying
covariates
Missingcovariates
Modelevaluation
Specialmodels
&covariates
Covariatemodel use
Studydesign &
covariates
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Population analysis – nonlinear
mixed effects modeling
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Time
C
o n c e n t r a t i o n
Observed plasma drug concentrations in children after a single dose
V
Dose
CL
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Regression (population)
V
Dose
CL
+
REAL WORLD MODEL WORLD
ESTIMATION
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~ ( , )
~ ( , )
~ (0, )
CL CL
V v
CL N
V N
N
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Why do we want to include
covariates into the model?
Identify patient sub-groups at potential risk oftoxicity/suboptimal effect
Confirm absence of important influence fromcovariate
Increase the predictive performance of the model
Increase the understanding of a studied system
Increase the mechanistic interpretability of the
modelUnderstand trial characteristics
Hypothesis generation
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Covariates
Demographics
– Gender, age, size (weight, height, BSA,BMI), race
Lab values – Serum creatinine, bilirubin, albumin,
pheno/genotype
Disease parameters
– Baseline, etiology, disease duration,general status
Therapy related
– Comedication, pretreatment, dialysis
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Covariates (cont’d)
Habits / Environmental factors
– Smoking, alcohol, food, diet, time of day oryear
Study related – Center, investigator, visit
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Covariate types
Continuous
– Age
Bivariate (dichotomous)
– SexOrdered categorical
– Smoking (none, occasional, daily)
Non-ordered categorical
– Race (caucasian, black, asian)
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Skewed distributions
Non-linear relationships with covariate, or
Linear relationships with log(covariate)
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Covariate correlations3 0 4 0
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Adults Males Females
Non-smokers
1 12
Smokers 18 0
Children Males Females
Non-
smokers
15 7
Smokers 1 0
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Covariate correlations
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GENO: 1
20 25 30 35 40 45
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GENO: 2 GENO: 3
AGE
P e r c e n t a g e o
f t o t a l
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Covariate correlations
Correlated covariates partially carry the same information
To simultaneously have correlated covariates in the modelwill increase model instability and may result incounterintuitive models
The relationship between a covariate and a parameter willbe different if it is in a model alone or with a correlatedcovariate
To determine which of correlated covariates carry the mostpredictive value is often hard
Problems with correlated covariates increase withincreasing correlation
Correlation coefficient is often used to capture degree ofcorrelation, but is (alone) not an ideal measure todecide on modeling strategy
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Other covariate classifications
Time-constant / time-varying (later lecture)
Observed / missing (later lecture)
Measured with or without error (later lecture)
Directly observed or composed of other covariatesStratified or observational (later lecture)
Prior belief in covariate-parameter relation
Certain of influence, likely, unlikely, almost certainly no
influence (much more later)Clinically available versus experimental
Routine use or not for individualisation
Of predictive value or not
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Covariate models - on which
parameters
Structural parameters (almost the entire course)
Interindividual variability
Interoccasion variability
Residual variabilityCovariate relationship (covariate interactions)
On predictions directly1,2
1Bonate P, Pharm Res. 22:541-9 (2005)2Wilkins J & Looby M, PAGE (2010)
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Covariate-parameter relations
under consideration
False or irrelevantcovariate relationshipslead to:Poorer precision in prediction
Unnecessary information
gathered
Poor hypothesis generation
Less trust in true covariaterelationships
Number of covariates
N u m
b e r o f p a r a m e t e r s
1
5
30+10
1
10
ManyFew
Many
Few
Increasing problems withmodel selection bias,model interpretability,model stability and/orparameter imprecision
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Covariate model building –
a common way to do it
All covariate-parameter relationships of interest
Scientific plausibility
Statistical significance
Clinical relevance
Final covariate-parameter relationships
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Par-Cov relations to consider forinclusion
Some of the principles used for selection
– All possible relations
• Common, but may result in long model buildingprocess and many relations tested increases the riskfor false Par-Cov relations
– All scientifically justifyable• Makes sense, but may be cumbersome to select what
is plausible and what is not
– All relations that are required for documentation
• May include relations that are not plausible, but wherean absence of Par-Cov correlation needs to be
documented for regulatory purposes – All possible for the main parameter(s) of interest (e.g. CL),
but only scientifically plausible for other (e.g. V, ka)parameters
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Starting model – some
alternatives I
No Par-Cov relations – Often used. Further discussed below
Major, known, covariates are incluced – Advantage: (i) shorter model building, (ii) graphical
procedures for other covariates more informative,and (iii) ”unbiased” estimate of major covariaterelation(s)
Best-guess model – Advantage: ”unbiased” estimates for all Par-Cov
relations included in best guess model – Like the approaches above it will involve further
covariate model building (later lectures)
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Starting model – some
alternatives II
All relations of primary interest
– Full model approach (later lecture)
– May include relation with expected lack ofsignificance, but which may be of importance for
clinical/regulatory confirmation of absence ofinfluence
– Advantage: ”unbiased” estimates of all relations ofprimary interest
– Generally include few relations in order to have a
stable model – Secondary hypothesis-generating model building
step can be performed
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Selection criteria – Scientific
plausibility
Scientific plausibility
– Which Par-Cov relations?
– Sign and magnitude of Cov-Par relations
•Should be viewed in combination with otherrelations
– Problem in determining scientific basis:
• Hard to think beforehand on all scientificallysound relations
• (Too) easy afterwards to find possible rationalsfor a found relationship
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Selection criteria – Statistical
criteria
Statistical criteria (examples)
– Exploratory analysis is often used as a proxy forlikelihood of statistical significance
– Difference in objective function value (main criteria,
covered in later lecture) – SE of parameter for Par-Cov relation
– Bootstrap confidence intervals for parameter
– Predictive performance in cross-validation (laterlecture)
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Selection criteria – Clinical
importance I
Limits for what is clinically important changes inparameters can seldom be clearly defined because therelationship between a parameter value and clinicallyimportant changes in a clinically important endpoint cannot be predicted (with sufficient precision). Therefore,
interpretation of what is clinically important may differbetween persons.
An alternative, conservative, approach is to define a clinicalinsignificance criteria
Clinically not significant changes may be related toavailable dosing strengths. This is maybe relevant for
post-marketing situation, but is more difficult to justify inthe drug development setting.
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Some measures for clinical
significance
Influence at extreme percentiles of covariatedistribution
Difference between groups
Decrease in unexplained variability
Influence on some derived parameter (e.g. AUC,predicted effect, %responders)
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Covariate models and model
building strategies
Important to know covariate characteristics inorder to decide about modelling strategy
The most suitable covariate model will differbetween different intended uses of the final
model
The most suitable model building strategy willdepend on data, model, intended model use,and time and tools available
A good working knowledge of several differenttechniques is therefore desireable
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Extra slides
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Example I: Covariate model fromTDM data
Often relatively small data sets (<100 patients)
Uncertainty regarding characteristics forobserved patients compared to patientpopulation
Large heterogeneity in covariate distribution
Often low quality in dosing/sampling history
Aim can often be to create predictive model forinitial dosing or dose adjustment
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Example II: Covariate model fromPhase III study
Large study size (usually >300 patients)
Relatively heterogenous covariate distribution
Sometimes problems with low quality indosing/sampling history
Aim can be to confirm previous findingsregarding covariate relations, investigatecovariate relations not previously documented,create exposure-safety/efficacy relations
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Example III: Covariate model fromPhase II study
Varying study size (30-300 patients)
Often strict inclusion criteria resulting in exclusionof many patients from the patient population
Usually rather high quality data
Aim can often be to create model for aidingdosing strategy determination, characterizeabsence of influences and clinical trialsimulations for phase III
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Example IV: Covariate model fromcombined Phase I studies
Intermediate study size (100-200 patients)
Often only a few demographic covariates ofinterest (size, age, sex, genotype)
High quality data
Aim can often be to create model forcharacterising interactions between covariatesand clinical trial simulations for phase II