1.Lecture Introduction Covariates

8/4/2019 1.Lecture Introduction Covariates

http://slidepdf.com/reader/full/1lecture-introduction-covariates 1/31



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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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0

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0 5 10 15

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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ALT distribution

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0.7 1.4 2.0 2.7 3.3 4.0 4.7 5.3

log(ALT) distribution



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Covariate correlations3 0 4 0

5 0 6 0

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GE

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Adults Males Females

Non-smokers

1 12

Smokers 18 0

Children Males Females

Non-

smokers

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Smokers 1 0



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Covariate correlations

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GENO: 1

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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

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1.Lecture Introduction Covariates

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