Genetic

and

Environmental

Influences

on

the

Relation

Between

Attention

Problems

and

Attention

Deficit

Hyperactivity

Disorder

Objective

The

assessment

of

symptoms

of

ADHD

in

children

is

usually

based

on

a

clinical

interview

or

a

behavior

checklist

The

aim

of

the

present

study

is

to

investigate

the

extent

to

which

these

instruments

measure

an

underlying

construct

and

to

estimate

the

genetic

and

environmental

influences

on

individual

differences

in

ADHD

Methods

Maternal

ratings

were

collected

on

twins

from

families

Child

Behavior

Checklist

-LRB-

CBCL

-RRB-

ratings

were

available

for

and

twins

at

the

ages

and

respectively

The

Conners

Rating

Scale

-LRB-

twins

-RRB-

and

the

DSM

interview

-LRB-

twins

-RRB-

were

completed

at

age

The

magnitude

of

genetic

and

environmental

influences

on

the

variance

of

the

three

measures

of

ADHD

and

the

covariance

among

the

three

measures

of

ADHD

was

obtained

Results

Phenotypic

correlations

range

between

and

Variances

and

covariances

of

the

measurements

were

explained

mainly

by

genetic

influences

The

model

that

provided

the

best

account

of

the

data

included

an

independent

pathway

for

additive

and

dominant

genetic

effects

The

genetic

correlations

among

the

measures

collected

at

age

varied

between

and

Conclusions

The

genetic

overlap

between

questionnaire

ratings

and

the

DSM-IV

diagnosis

of

ADHD

is

high

Clinical

and

research

implications

of

these

findings

are

presented

Introduction

As

is

the

case

for

all

psychiatric

disorders

the

diagnosis

of

attention

deficit

hyperactivity

disorder

-LRB-

ADHD

-RRB-

is

not

based

on

a

specific

pathological

agent

such

as

a

microbe

a

toxin

or

a

genetic

mutation

but

rather

on

the

collection

of

signs

and

symptoms

and

evidence

of

impairment

that

occur

together

more

frequently

than

expected

by

chance

-LRB-

Todd

et

al.

-RRB-

The

presence

of

these

symptoms

is

usually

established

by

direct

observation

or

by

the

completion

of

a

clinical

interview

or

questionnaire

by

the

parent

or

teacher

of

a

child

Instruments

vary

with

respect

to

the

included

symptoms

the

exact

manner

of

data

collection

-LRB-

checklist

or

interview

-RRB-

and

the

response

format

-LRB-

e.g.

yes/no

versus

Likert

scale

-RRB-

In

the

present

paper

we

investigated

if

-LRB-

co

-RRB-

variance

of

the

scores

on

different

instruments

can

be

explained

by

a

common

underlying

construct

and

to

what

extent

this

common

factor

is

influenced

by

genetic

and

environmental

factors

The

focus

is

on

three

widely

used

instruments

the

Child

Behavior

Checklist

-LRB-

CBCL

Achenbach

-RRB-

the

Conners

Parent

Rating

Scale-Revised

Short

version

-LRB-

CPRS-R

S

Conners

-RRB-

and

the

Diagnostic

and

Statistical

Manual

of

Mental

edition

-LRB-

DSM-IV

American

Psychiatric

Association

-RRB-

The

CBCL-Attention

Problem

scale

-LRB-

CBCL-AP

-RRB-

was

developed

by

means

of

factor

analyses

and

includes

eleven

items

The

psychometric

properties

and

methods

to

establish

the

reliability

of

the

syndrome

are

discussed

in

detail

elsewhere

-LRB-

Achenbach

-RRB-

Despite

its

name

the

scale

assesses

problems

related

both

to

attention

and

hyperactivity

The

CBCL

has

sex

and

age-specific

norms

which

are

useful

in

assessing

a

child

's

risk

for

ADHD

The

CPRS-R

S

ADHD-index

comprises

the

best

items

for

distinguishing

children

with

ADHD

from

children

without

ADHD

as

assessed

by

the

DSM

-LRB-

Conners

-RRB-

As

with

the

CBCL

sex

and

age-specific

norm

scores

are

available

allowing

the

clinician

to

determine

whether

a

given

child

is

at

risk

for

ADHD

DSM-IV

ADHD

is

assessed

on

the

basis

of

symptoms

nine

relate

to

inattention

and

nine

relate

to

hyperactivity/impulsivity

In

the

DSM

framework

ADHD

is

viewed

as

a

categorical

trait

i.e.

children

either

do

or

do

not

meet

criteria

for

ADHD

The

norms

for

clinical

diagnosis

do

not

vary

as

a

function

of

sex

or

age

of

the

child

Table

contains

the

symptoms

included

in

the

CBCL-AP

scale

the

CPRS-R

S

ADHD-index

and

DSM-IV

ADHD

Table

overview

of

the

Child

Behaviour

Checklist

-LRB-

CBCL

-RRB-

Conners

Parent

Rating

Scale-Revised

Short

version

-LRB-

CPRS-R

S

-RRB-

and

the

Diagnostic

and

Statistical

Manual

of

Mental

edition

symptomsScaleSymptomCBCL

Attention

ProblemsActs

too

young

for

his/her

ageCa

n't

concentrate

ca

n't

pay

attention

for

longCa

n't

sit

still

restless

or

hyperactiveConfused

or

seems

to

be

in

a

fogDaydreams

or

gets

lost

in

his/her

thoughtsImpulsive

or

acts

without

thinkingNervous

high-strung

or

tenseNervous

movements

or

twitchingPoor

school

workPoorly

coordinated

or

clumsyStares

blanklyCPRS-R

S

ADHD-indexInattentive

easily

distractedShort

attention

spanFidgets

with

hands

or

feet

or

squirms

in

seatMessy

or

disorganized

at

home

or

schoolOnly

attends

if

it

is

something

he/she

is

very

interested

inDistractibility

or

attention

span

a

problemAvoids

expresses

reluctance

about

or

has

difficulties

engaging

in

tasks

that

require

sustained

mental

effort

-LRB-

such

as

schoolwork

or

homework

-RRB-

Gets

distracted

when

given

instructions

to

do

somethingHas

trouble

concentrating

in

classLeaves

seat

in

classroom

or

in

other

situations

in

which

remaining

seated

is

expectedDoes

not

follow

through

on

instructions

and

fails

to

finish

schoolwork

chores

or

duties

in

the

workplace

-LRB-

not

due

to

oppositional

behavior

or

failure

to

understand

directions

-RRB-

Easily

frustrated

in

effortsDSM-IV

ADHDInattentionOften

fails

to

give

close

attention

to

details

or

makes

careless

mistakes

in

schoolwork

work

or

other

activitiesOften

has

difficulty

sustaining

attention

in

tasks

or

play

activitiesOften

does

not

seem

to

listen

when

spoken

to

directlyOften

does

not

follow

through

on

instructions

and

fails

to

finish

schoolwork

chores

or

duties

in

the

workplace

-LRB-

not

due

to

oppositional

behavior

or

failure

to

understand

instructions

-RRB-

Often

has

difficulty

organizing

tasks

and

activitiesOften

avoids

dislikes

or

is

reluctant

to

engage

in

tasks

that

require

sustained

mental

effort

-LRB-

such

as

schoolwork

or

homework

-RRB-

Often

loses

things

necessary

for

tasks

or

activities

-LRB-

e.g.

toys

school

assignments

pencils

books

or

tools

-RRB-

Is

often

easily

distracted

by

extraneous

stimuliIs

often

forgetful

in

daily

activitiesHyperactivityOften

fidgets

with

hands

or

feet

or

squirms

in

seatOften

leaves

seat

in

classroom

or

in

other

situations

in

which

remaining

seated

is

expectedOften

runs

about

or

climbs

excessively

in

situations

in

which

it

is

inappropriateOften

has

difficulty

playing

or

engaging

in

leisure

activities

quietlyIs

often

on

the

go

or

often

acts

as

if

driven

by

a

motor

Often

talks

excessivelyOften

blurts

out

answers

before

questions

have

been

completedOften

has

difficult

awaiting

turnOften

interrupts

or

intrudes

on

others

-LRB-

e.g.

butts

into

conversations

or

games

-RRB-

Although

the

CBCL

DSM

and

CPRS-R

S

focus

on

different

symptoms

and

are

based

on

distinct

assumptions

the

scores

of

these

instruments

are

strongly

related

CBCL-AP

scores

predict

the

presence

of

ADHD

-LRB-

Gould

et

al.

Chen

et

al.

Eiraldi

et

al.

Lengua

et

al.

Sprafkin

et

al.

Hudziak

et

al.

-RRB-

In

a

non-referred

sample

enriched

for

ADHD

about

of

the

children

with

a

high

CBCL-AP

score

were

diagnosed

with

ADHD

compared

to

of

the

children

with

a

low

CBCL-AP

score

-LRB-

Derks

et

al.

-RRB-

Although

these

results

imply

a

good

convergence

between

the

CBCL

and

a

DSM-IV

interview

the

relation

is

clearly

less

than

perfect

The

CPRS-R

S

ADHD-I

was

developed

for

assessing

children

at

risk

for

ADHD

based

on

a

DSM-IV

diagnosis

-LRB-

Conners

-RRB-

Conners

-LRB-

-RRB-

showed

that

the

CPRS-R

S

ADHD-I

is

a

good

screening

instrument

for

DSM-IV

ADHD

with

a

sensitivity

of

a

specificity

of

and

an

overall

correct

classification

rate

of

As

far

as

we

know

the

relation

between

CBCL-AP

and

the

CPRS-R

S

ADHD-I

has

not

been

studied

but

given

that

they

are

both

related

to

DSM-IV

ADHD

these

are

likely

to

be

correlated

Genetic

studies

of

psychiatric

disorders

are

complicated

by

the

lack

of

clear

diagnostic

tests

-LRB-

Hudziak

-RRB-

Heritability

estimates

in

epidemiological

genetic

studies

and

the

results

of

gene-finding

studies

may

depend

on

the

exact

instrument

that

is

used

to

assess

ADHD

Although

a

number

of

papers

have

established

the

convergence

between

CBCL-AP

and

DSM-IV

ADHD

the

causal

factors

underpinning

this

relationship

remain

unclear

Is

it

the

result

of

genetic

overlap

environmental

overlap

or

both

This

is

an

important

question

which

may

determine

the

progress

in

gene

finding

studies

If

variance

in

alternative

measures

of

ADHD

is

explained

by

different

genes

we

would

expect

disagreement

in

the

results

of

studies

using

different

instruments

If

the

same

genes

explain

variance

in

these

measures

the

data

from

studies

using

different

instruments

may

be

combined

in

order

to

increase

statistical

power

-LRB-

Boomsma

Boomsma

and

Dolan

-RRB-

Assuming

that

the

convergence

between

different

instruments

will

be

less

than

perfect

part

of

the

variance

will

be

attributable

by

instrument-specific

factors

It

is

important

to

investigate

the

nature

of

such

factors

If

the

divergence

among

instruments

is

merely

a

matter

of

measurement

error

we

would

expect

no

genetic

influences

on

the

instrument-specific

factors

Genetic

influences

on

the

instrument-specific

factors

on

the

other

hand

would

suggest

that

the

instruments

tap

partly

unique

aspects

of

children

's

behavior

Genetic

and

environmental

influences

on

individual

differences

in

behavior

can

be

studied

in

genetically

informative

designs

such

as

the

classical

twin

design

Such

studies

have

shown

that

genetic

influences

explain

between

and

of

the

variance

in

clinical

diagnoses

of

ADHD

-LRB-

Eaves

et

al.

Sherman

et

al.

-RRB-

Shared

environmental

influences

were

nearly

always

absent

Likewise

about

of

the

variance

in

CBCL-AP

scores

is

explained

by

genetic

influences

The

remaining

variance

is

explained

by

non-shared

environmental

influences

-LRB-

Rietveld

et

al.

Hudziak

et

al.

Gjone

et

al.

-RRB-

Kuntsi

and

Stevenson

-LRB-

-RRB-

used

the

Conners

Rating

Scale

to

assess

symptoms

of

ADHD

and

reported

a

heritability

of

A

review

of

genetic

studies

on

AP

HI

and

ADHD

suggested

the

absence

of

qualitative

and

quantitative

sex

differences

in

the

genetic

etiology

of

parent

ratings

of

ADHD

-LRB-

Derks

et

al.

in

press

-RRB-

Interestingly

in

parent

ratings

but

not

in

teacher

ratings

the

DZ

twin

concordances

and

correlations

are

lower

than

would

be

expected

under

a

purely

additive

genetic

model

For

example

in

maternal

structured

interview

reports

the

concordance

rate

is

in

MZ

twins

but

in

DZ

twins

-LRB-

Sherman

et

al.

-RRB-

Similarly

in

CBCL

ratings

the

DZ

twin

correlations

are

less

than

half

the

MZ

correlations

-LRB-

Rietveld

et

al.

-RRB-

In

the

literature

two

explanations

are

offered

for

these

low

DZ

correlations

Firstly

the

DZ

correlation

can

be

less

than

half

the

MZ

correlation

due

to

the

presence

of

non-additive

genetic

effects

-LRB-

i.e.

genetic

dominance

-RRB-

-LRB-

Lynch

and

Walsh

-RRB-

Secondly

the

low

DZ

correlation

may

be

explained

by

social

interaction

effects

which

may

be

the

result

of

interaction

among

siblings

-LRB-

i.e.

the

behavior

of

a

twin

influences

the

behavior

of

the

other

twin

-RRB-

or

rater

bias

-LRB-

i.e.

the

behavior

of

a

twin

is

compared

to

the

behavior

of

the

other

twin

-RRB-

-LRB-

Eaves

Carey

Boomsma

-RRB-

In

previous

studies

support

was

found

both

for

the

presence

of

genetic

dominance

-LRB-

Rietveld

et

al.

Martin

et

al.

-RRB-

and

sibling

interaction

-LRB-

Simonoff

et

al.

Kuntsi

and

Stevenson

Vierikko

et

al.

Eaves

et

al.

-RRB-

A

high

heritability

of

attention

problems

and

ADHD

has

been

reported

irrespective

of

the

instrument

that

is

used

However

based

on

the

findings

of

univariate

studies

we

can

not

conclude

that

CBCL

Conners

Rating

Scale

and

DSM

ratings

measure

the

same

construct

or

that

they

are

influenced

by

the

same

set

of

genes

To

address

this

question

multivariate

analyses

are

needed

Although

a

number

of

studies

have

focused

on

the

genetic

and

environmental

influences

on

either

AP

or

ADHD

only

the

study

of

Nadder

and

Silberg

-LRB-

-RRB-

included

multivariate

analyses

Nadder

and

Silberg

-LRB-

-RRB-

analyzed

data

obtained

in

a

sample

of

male

and

female

same-sex

twin

pairs

aged

years

They

modelled

the

genetic

influences

on

nine

measures

of

ADHD

symptomatology

including

maternal

and

paternal

DSM-III-R

interview

data

-LRB-

three

dimensions

hyperactivity

inattention

and

impulsivity

-RRB-

maternal

questionnaire

data

-LRB-

the

Rutter

Parental

Scale

and

the

CBCL

-RRB-

and

a

questionnaire

completed

by

the

twin

's

teacher

The

aim

of

this

study

was

to

determine

whether

overactivity

inattention

and

impulsivity

reflect

the

same

underlying

genetic

liability

while

taking

method

-LRB-

i.e.

instrument-specific

-RRB-

variance

into

account

In

males

of

the

genetic

variance

was

explained

by

a

common

factor

that

loaded

on

all

nine

indicators

A

second

and

third

factor

loaded

on

the

three

dimensions

of

the

maternal

and

paternal

interview

data

respectively

The

remaining

variance

-LRB-

-RRB-

was

explained

by

factors

that

were

specific

to

each

measure

In

females

there

was

also

one

factor

common

to

all

indicators

-LRB-

explaining

of

the

variance

-RRB-

and

a

second

and

third

factor

which

loaded

on

the

three

dimensions

of

the

interview

data

In

contrast

to

the

males

a

fourth

factor

loaded

on

the

three

behavioral

questionnaires

This

factor

explained

of

the

genetic

variance

In

total

measurement

specific

factors

explained

of

the

genetic

variance

The

purpose

of

the

present

paper

is

to

investigate

the

construct

validity

of

CBCL-AP

CPRS-R

S

ADHD-I

and

DSM-IV

ADHD

Three

questions

are

addressed

First

what

are

the

phenotypic

correlations

between

the

three

instruments

Second

do

the

instruments

reflect

a

common

underlying

factor

Third

what

are

the

genetic

and

environmental

influences

on

the

common

and

the

instrument-specific

factors

Methods

Subjects

This

study

is

part

of

an

ongoing

longitudinal

twin

study

in

the

Netherlands

The

subjects

were

all

registered

at

birth

with

the

Netherlands

Twin

Register

-LRB-

Boomsma

et

al.

Bartels

et

al.

-RRB-

Mothers

of

the

registered

twin

pairs

receive

the

CBCL

and

the

CPRS

at

the

ages

and

years

A

subsample

of

the

twins

was

selected

based

on

their

longitudinal

CBCL

scores

The

mothers

of

these

pairs

completed

a

diagnostic

interview

The

twins

with

an

age

range

of

years

-LRB-

mean

age

SD

-RRB-

at

the

time

of

the

interview

were

born

between

and

The

mean

time-span

between

the

completion

of

the

interview

and

the

questionnaires

was

-LRB-

SD

-RRB-

-LRB-

SD

-RRB-

and

-LRB-

SD

-RRB-

years

for

the

questionnaires

completed

at

age

age

and

age

respectively

Questionnaires

were

sent

to

all

families

that

agreed

to

participate

with

the

research

of

the

Netherlands

Twin

Registry

when

the

children

were

born

-LRB-

N

families

birth

cohorts

-RRB-

at

the

ages

and

years

At

least

one

measurement

is

available

for

twins

from

families

so

the

response

rate

is

CBCL

ratings

were

available

in

twins

at

age

twins

at

age

and

twins

at

age

CPRS-R

S

ratings

were

available

for

twins

at

age

and

DSM-IV

interviews

were

available

for

twins

Complete

data

were

available

in

twins

The

fact

that

the

number

of

CPRS-R

S

ratings

is

lower

than

the

number

of

CBCL

ratings

can

be

explained

by

the

fact

that

the

CPRS-R

S

was

not

included

for

children

born

before

The

number

of

available

questionnaires

decreases

over

time

as

a

result

of

the

longitudinal

character

of

the

study

-LRB-

i.e.

a

number

of

children

in

the

study

had

yet

to

reach

the

age

of

-RRB-

Zygosity

diagnosis

was

based

on

DNA

in

same-sex

twin

pairs

In

the

remaining

same-sex

pairs

zygosity

was

assessed

using

a

item

questionnaire

Zygosity

determination

using

this

questionnaire

is

almost

accurate

-LRB-

Rietveld

et

al.

-RRB-

Of

the

twin

pairs

there

were

monozygotic

male

-LRB-

MZM

-RRB-

pairs

dizygotic

male

-LRB-

DZM

-RRB-

pairs

monozygotic

female

-LRB-

MZF

-RRB-

pairs

dizygotic

female

-LRB-

DZF

-RRB-

pairs

and

dizygotic

opposite

sex

-LRB-

DOS

-RRB-

pairs

Selection

for

the

diagnostic

interview

For

the

diagnostic

interview

subjects

were

selected

on

the

basis

of

their

standardized

maternal

CBCL

ratings

-LRB-

T-scores

mean

SD

-RRB-

at

the

ages

and

years

-LRB-

Derks

et

al.

-RRB-

Subjects

were

excluded

if

maternal

ratings

were

available

at

only

one

time-point

or

if

they

suffered

from

a

severe

handicap

which

disrupted

daily

functioning

Twin

pairs

were

selected

if

at

least

one

of

the

twins

scored

high

on

AP

-LRB-

affected

pairs

-RRB-

or

if

both

twins

scored

low

on

AP

-LRB-

control

pairs

-RRB-

A

high

score

was

defined

as

a

T-score

above

at

all

available

time-points

-LRB-

age

and

years

-RRB-

and

a

T-score

above

at

least

once

A

low

score

was

defined

as

a

T-score

below

at

all

available

time-points

The

control

pairs

were

matched

with

the

affected

pairs

on

the

basis

of

sex

cohort

maternal

age

and

social

economic

status

-LRB-

SES

-RRB-

T-scores

were

computed

in

boys

and

girls

separately

In

other

words

girls

were

selected

if

they

scored

low

or

high

compared

to

other

girls

and

boys

were

selected

if

they

scored

low

or

high

compared

to

other

boys

This

procedure

resulted

in

the

selection

of

similar

numbers

of

boys

-LRB-

N

-RRB-

and

girls

-LRB-

N

-RRB-

Measures

The

Child

Behavior

Checklist

-LRB-

CBCL

-RRB-

-LRB-

Achenbach

-RRB-

is

a

standardized

questionnaire

designed

for

parents

to

report

the

frequency

and

intensity

of

their

children

's

behavioral

and

emotional

problems

as

exhibited

in

the

past

months

It

consists

of

items

that

measure

problem

behavior

The

items

are

rated

on

a

scale

ranging

from

not

true

somewhat

or

sometimes

true

to

very

true

or

often

true

The

Attention

Problem

scale

contains

items

The

test

retest

correlation

and

the

internal

consistency

of

this

scale

are

and

respectively

-LRB-

Verhulst

et

al.

-RRB-

In

the

statistical

analyses

we

included

the

CBCL

ratings

at

the

ages

and

years

in

order

to

correct

for

the

selection

as

explained

below

The

Conners

Parent

Rating

Scale-Revised

is

a

widely

used

instrument

to

assess

behavior

problems

in

the

past

month

-LRB-

CPRS-R

Conners

Conners

et

al.

-RRB-

The

short

version

contains

items

The

items

are

rated

on

a

scale

ranging

from

not

true

at

all

to

very

much

true

The

CPRS-R

S

ADHD-I

which

was

used

in

the

present

study

comprises

the

best

items

for

distinguishing

children

with

ADHD

from

children

without

ADHD

as

assessed

by

the

DSM-IV

-LRB-

American

Psychiatric

Association

Conners

-RRB-

The

internal

consistency

of

this

scale

at

age

years

is

in

boys

and

in

girls

The

weeks

test

retest

correlation

is

The

Diagnostic

Interview

Schedule

for

Children

-LRB-

DISC

-RRB-

-LRB-

Shaffer

et

al.

-RRB-

is

a

structured

diagnostic

interview

It

can

be

used

to

assess

the

presence

of

DSM-IV

diagnoses

including

ADHD

The

Dutch

translation

is

by

Ferdinand

and

van

der

Ende

-LRB-

-RRB-

The

mothers

of

twins

were

interviewed

by

ten

experienced

research

assistants

to

determine

which

symptoms

of

ADHD

were

displayed

by

the

twins

during

the

last

year

Maternal

ratings

of

DISC

symptoms

in

their

children

were

assessed

by

the

same

interviewer

for

each

twin

in

a

given

pair

We

analyzed

the

total

number

of

symptoms

Statistical

analyses

Transformation

to

categorical

data

The

distributions

of

the

CBCL

CPRS-R

S

and

DSM

symptom

data

are

characterized

by

excessive

skewness

and

kurtosis

Derks

et

al.

-LRB-

-RRB-

showed

that

bias

in

parameter

estimates

due

to

non-normality

of

the

data

may

be

avoided

by

using

categorical

data

analysis

In

this

approach

a

liability

threshold

model

is

applied

to

the

ordinal

scores

-LRB-

Lynch

and

Walsh

-RRB-

It

is

assumed

that

a

person

is

unaffected

if

his

or

her

liability

is

below

a

certain

threshold

and

that

he

or

she

is

affected

if

his

or

her

liability

is

above

this

threshold

In

the

present

paper

the

scores

were

recoded

in

such

a

way

that

three

thresholds

divide

the

latent

liability

distribution

into

four

categories

of

about

equal

size

The

liability

threshold

model

was

identified

by

constraining

the

variance

of

the

observed

variables

at

The

CBCL

AP

score

was

calculated

by

summing

the

responses

on

the

items

which

resulted

in

a

sum

score

with

a

possible

maximum

of

The

four

categories

consisted

of

a

score

of

and

or

higher

respectively

The

CPRS-R

S

ADHD-I

score

was

calculated

by

summing

the

responses

on

the

items

which

resulted

in

a

sum

score

with

a

possible

maximum

of

The

four

categories

consisted

of

a

score

of

and

or

higher

respectively

The

DISC

sumscore

with

a

range

of

to

was

transformed

into

an

ordinal

variable

with

four

categories

The

four

categories

were

-LRB-

i

-RRB-

not

affected

-LRB-

symptoms

-RRB-

-LRB-

ii

-RRB-

mildly

affected

-LRB-

symptoms

-RRB-

-LRB-

iii

-RRB-

moderately

affected

-LRB-

symptoms

-RRB-

and

-LRB-

iv

-RRB-

highly

affected

-LRB-

more

than

symptoms

-RRB-

The

use

of

this

four

category

variable

provides

greater

resolution

and

so

better

statistical

power

than

the

use

of

a

dichotomous

variable

-LRB-

ADHD

absent

versus

ADHD

present

-RRB-

Correcting

for

the

selection

Diagnostic

interview

data

were

collected

only

in

a

subsample

of

the

twins

The

probability

of

selection

for

the

interview

depends

on

a

measured

variable

namely

the

twin

's

CBCL

scores

at

age

and

The

data

of

the

complete

sample

may

be

partitioned

as

the

observed

-LRB-

selected

-RRB-

and

missing

-LRB-

unselected

-RRB-

parts

The

data

are

missing

at

random

-LRB-

MAR

-RRB-

if

the

probability

of

missingness

depends

only

on

the

observed

part

of

the

data

and

not

on

the

missing

part

-LRB-

Little

and

Rubin

-RRB-

Given

that

the

data

are

MAR

unbiased

parameter

estimates

can

be

obtained

by

full

information

-LRB-

i.e.

raw

data

-RRB-

maximum

likelihood

estimation

of

the

parameters

in

a

statistical

model

that

includes

the

variables

that

were

used

for

selection

It

is

essential

to

include

all

variables

that

were

used

for

selection

because

the

probability

of

missingness

should

not

depend

on

the

missing

part

of

the

data

in

which

case

the

data

would

be

missing

not

at

random

-LRB-

MNAR

-RRB-

and

parameter

estimates

would

be

biased

We

therefore

included

the

CBCL

ratings

obtained

at

the

ages

and

years

in

the

statistical

analyses

All

twin

pairs

in

which

at

least

one

measure

is

available

are

included

in

the

analyses

Prevalences

To

investigate

if

the

prevalences

of

AP

and

ADHD

depend

on

the

twin

's

sex

or

zygosity

we

performed

with

the

five

ordinal

measures

as

dependent

variables

and

sex

and

zygosity

as

independent

variables

Genetic

modeling

Genetic

and

environmental

influences

on

variance

in

ADHD

scores

were

estimated

using

structural

equation

modeling

All

model

fitting

was

performed

on

raw

data

with

Mx

-LRB-

Neale

et

al.

-RRB-

a

statistical

software

package

well

suited

for

conducting

genetic

analyses

The

influence

of

the

relative

contributions

of

genetic

and

environmental

factors

to

individual

differences

in

ADHD

can

be

inferred

from

the

differences

in

correlations

across

MZ

and

DZ

twin

pairs

as

MZ

and

DZ

twins

differ

in

their

genetic

relatedness

-LRB-

Plomin

et

al.

-RRB-

Using

the

twin

method

phenotypic

variance

may

be

attributed

to

additive

genetic

effects

-LRB-

A

-RRB-

dominant

genetic

effects

-LRB-

D

-RRB-

or

shared

environmental

effects

-LRB-

C

-RRB-

and

non-shared

environmental

-LRB-

E

-RRB-

effects

The

genetic

effects

-LRB-

A

and

D

-RRB-

correlate

in

MZ

twins

as

they

are

genetically

identical

In

DZ

twins

A

correlates

and

D

correlates

C

correlates

in

both

MZ

and

DZ

twins

E

or

non-shared

environmental

effects

are

by

definition

uncorrelated

Uncorrelated

measurement

error

if

present

is

absorbed

in

the

E

term

Note

that

estimating

C

and

D

at

the

same

time

is

not

possible

in

a

design

using

only

data

from

MZ

and

DZ

twins

reared

together

If

the

correlations

of

DZ

twins

are

less

than

half

the

correlations

of

MZ

twins

which

is

the

case

for

maternal

ratings

of

attention

problems

and

ADHD

D

is

included

in

the

genetic

model

The

proportion

of

the

variance

accounted

for

by

heritability

or

environmental

influences

is

calculated

by

calculating

the

ratio

of

variance

due

to

A

D

or

E

to

the

total

phenotypic

variance

For

instance

let

a

d

and

e

denote

the

regression

coefficients

in

the

regression

of

the

phenotype

on

the

standardized

latent

variables

A

D

and

E

respectively

The

variance

due

to

A

is

then

and

the

-LRB-

narrow-sense

-RRB-

heritability

is

calculated

as

-LRB-

-RRB-

Social

interactions

may

be

an

additional

source

of

variance

Social

interaction

effects

lead

to

differences

in

variances

in

MZ

and

DZ

twins

in

continuous

data

-LRB-

Carey

-RRB-

Using

ordinal

data

the

presence

of

an

interaction

component

can

be

tested

by

equating

the

prevalences

of

AP/ADHD

between

MZ

and

DZ

twins

The

absence

of

significant

prevalence

differences

suggests

that

the

presence

of

sibling

interaction

or

rater

bias

is

considered

implausible

Three

multivariate

models

were

tested

a

triangular

-LRB-

Cholesky

-RRB-

decomposition

an

independent

pathway

model

and

a

common

pathway

model

-LRB-

Neale

and

Cardon

-RRB-

The

triangular

decomposition

is

the

least

restrictive

model

as

no

specific

hypotheses

regarding

the

covariance

matrices

of

A

D

and

E

are

tested

These

matrices

are

merely

assumed

to

be

positive

-LRB-

semi

-RRB-

definite

This

is

a

saturated

model

that

can

be

used

to

obtain

-LRB-

otherwise

unconstrained

-RRB-

genetic

and

environmental

correlations

among

traits

In

the

independent

pathway

model

common

and

specific

genetic

and

environmental

factors

are

included

In

our

data

analyses

of

the

five

variables

we

specified

a

common

factor

and

five

instrument-specific

factors

for

each

of

the

factors

A

D

and

E

which

we

denote

Ac

Dc

and

Ec

An

independent

pathway

model

provides

a

good

fit

to

the

data

if

the

covariance

between

the

five

variables

is

due

to

the

common

factors

Ac

Dc

and

Ec

Finally

in

the

common

pathway

model

a

model

that

is

nested

under

the

independent

pathway

model

it

is

assumed

that

genes

and

environment

explain

variance

in

a

latent

phenotype

This

latent

factor

of

which

the

variance

is

constrained

at

explains

variance

in

the

five

variables

In

addition

the

variance

of

the

five

variables

is

allowed

to

be

influenced

by

instrument-specific

influences

of

A

D

and

E

In

other

words

the

common

pathway

model

would

provide

a

good

fit

to

the

data

if

the

covariance

between

the

five

variables

can

be

explained

by

a

latent

construct

Because

the

number

of

twins

for

whom

interview

data

are

available

is

relatively

small

and

sex

differences

in

heritability

are

usually

not

found

the

data

from

male

and

female

twins

were

combined

in

the

analyses

To

allow

for

prevalence

differences

between

boys

and

girls

sex

was

included

as

a

covariate

on

the

thresholds

The

type-I

error

rate

of

all

statistical

tests

was

set

at

Results

Descriptives

The

prevalences

for

the

five

measures

were

compared

between

MZ

and

DZ

twins

and

between

boys

and

girls

The

first

model

that

was

fitted

to

the

data

was

a

fully

saturated

model

In

this

model

correlations

were

estimated

in

MZ

twins

and

in

DZ

twins

In

addition

the

model

included

thresholds

in

each

of

the

following

groups

MZ

boys

DZ

boys

MZ

girls

and

DZ

girls

which

results

in

a

total

of

estimated

thresholds

Next

a

model

was

fitted

that

included

a

number

of

constraints

on

the

thresholds

This

model

included

thresholds

sex

effect

on

the

thresholds

and

zygosity

effects

on

the

thresholds

-LRB-

one

for

each

of

the

five

measurements

-RRB-

As

this

model

fitted

the

data

well

it

was

used

as

the

reference

model

to

test

for

prevalence

differences

as

a

function

of

zygosity

for

each

of

the

five

measurements

The

results

of

these

analyses

are

summarized

in

Table

Zygosity

did

not

affect

the

prevalences

of

the

CBCL

CPRS-R

S

and

DSM

scores

In

view

of

the

absence

of

prevalence

differences

in

MZ

and

DZ

twins

social

interaction

effects

were

not

included

in

the

genetic

model

The

model

that

was

used

as

the

reference

model

to

test

for

sex

differences

included

as

free

parameters

thresholds

zygosity

effect

on

the

thresholds

and

five

sex

effects

on

the

thresholds

one

for

each

measurement

The

results

showed

that

boys

have

significantly

more

problems

than

girls

on

all

five

measurements

therefore

sex

was

included

as

a

covariate

on

the

thresholds

Because

of

the

use

of

categorical

scores

in

the

present

paper

we

did

not

report

means

and

standard

deviations

of

the

CBCL

CPRS-R

S

and

DSM

scores

These

descriptives

can

be

requested

from

the

corresponding

author

by

interested

readers

Twin

correlations

The

polychoric

correlations

between

the

five

measurements

are

shown

in

Table

for

MZ

and

DZ

twins

The

MZ

-LRB-

DZ

-RRB-

twin

correlations

are

reported

above

-LRB-

below

-RRB-

the

diagonal

As

expected

the

phenotypic

correlations

-LRB-

i.e.

the

correlation

between

traits

within

the

same

individual

-RRB-

are

similar

in

first

and

second-born

twins

and

in

MZ

and

DZ

twins

The

correlations

range

from

to

with

slightly

lower

correlations

between

different

assessment

methods

-LRB-

e.g.

CBCL

questionnaire

versus

clinical

interview

-RRB-

than

similar

assessment

methods

-LRB-

e.g.

CBCL

questionnaire

versus

CPRS-R

S

questionnaire

-RRB-

Equating

the

correlations

of

first

and

second-born

twins

at

age

the

phenotypic

correlation

between

CBCL-AP

and

CPRS-R

S

was

while

the

correlations

between

CBCL-AP

and

DSM

and

CPRS-R

S

and

DSM

were

The

fact

that

the

cross-twin

and

the

cross-trait

cross-twin

correlations

are

higher

in

MZ

than

DZ

twins

indicates

that

genetic

influences

contribute

to

the

variance

of

the

three

measures

and

to

the

covariance

between

them

Table

correlations

in

monozygotic

-LRB-

above

diagonal

-RRB-

and

dizygotic

-LRB-

below

diagonal

-RRB-

twinsFirst-bornSecond-bornCBCL

CBCL

CBCL

CPRS

DSM

CBCL

CBCL

CBCL

CPRSDSMFirst-bornCBCL

age

CBCL

age

CBCL

age

S

DSM.51.55.59.681.34.41.46.46.64Second-bornCBCL

age

CBCL

age

CBCL

age

S

DSM

Note

CBCL

Child

Behavior

Checklist

CPRS

Conners

Parent

Rating

Scale-Revised

Short

version

ADHD-index

DSM

Diagnostic

Statistical

Manual

of

Mental

Disorders

Genetic

analyses

A

Cholesky

decomposition

that

included

additive

genetic

influences

-LRB-

A

-RRB-

dominant

genetic

influences

-LRB-

D

-RRB-

and

non-shared

environmental

influences

-LRB-

E

-RRB-

was

fitted

to

the

data

The

full

ADE

cholesky

decomposition

fitted

the

data

well

-LRB-

χ2

-LRB-

-RRB-

P

-RRB-

see

Table

for

an

overview

of

the

model

fitting

results

Next

an

independent

pathway

model

was

fitted

to

the

data

Imposition

of

the

independent

pathway

model

for

A

D

and

E

resulted

in

a

significant

deterioration

in

fit

compared

to

the

fit

of

a

cholesky

decomposition

-LRB-

χ2

-LRB-

-RRB-

P

-RRB-

Additional

analyses

showed

that

the

influence

of

A

and

D

were

consistent

with

the

independent

pathway

model

whereas

the

influence

of

E

was

not

A

model

that

incorporated

an

independent

pathway

model

for

A

and

D

and

a

cholesky

decomposition

for

E

fitted

well

compared

to

the

full

cholesky

decomposition

-LRB-

χ2

-LRB-

-RRB-

P

-RRB-

The

fit

of

the

common

factor

model

was

poor

-LRB-

χ2

-LRB-

-RRB-

P

-RRB-

Next

we

tested

if

the

instrument-specific

influences

of

A

and

D

could

be

constrained

at

zero

The

instrument-specific

additive

genetic

factors

could

not

be

dropped

from

the

model

-LRB-

χ2

-LRB-

-RRB-

P

-RRB-

In

contrast

the

dominant

genetic

variance

could

be

explained

by

one

common

factor

-LRB-

χ2

-LRB-

-RRB-

P

-RRB-

In

other

words

the

covariance

structure

of

D

did

not

include

specific

variances

This

means

that

this

covariance

matrix

has

rank

one

and

that

the

correlations

-LRB-

obtained

by

standardizing

the

covariance

matrix

of

D

-RRB-

were

all

one

Figure

provides

a

graphical

representation

of

the

genetic

part

of

the

best

fitting

model

and

includes

the

unstandardized

factor

loadings

of

the

additive

genetic

and

dominant

genetic

factors

Table

model

fitting

of

maternal

ratings

on

CBCL

CPRS-R

S

and

DSM-IV

ratings

on

attention

problems

and

ADHD

in

children

log

LLN

parWith

Fully

Thresholds

MZ/DZ

free

thresholds

boys/girls

equated

a.

Thresholds

CBCL

age

equated

in

b.

Thresholds

CBCL

age

equated

in

c.

Thresholds

CBCL

age

equated

in

d.

Thresholds

Conners

age

equated

in

e.

Thresholds

DSM

age

equated

in

Thresholds

boys/girls

free

thresholds

MZ/DZ

equated

a.

Thresholds

CBCL

age

b.

Thresholds

CBCL

age

c.

Thresholds

CBCL

age

d.

Thresholds

Conners

age

e.

Thresholds

DSM

age

Cholesky

decomposition

a.

Independent

pathway

model

D

Cholesky

decomposition

b.

Independent

pathway

model

A

Cholesky

decomposition

c.

Independent

pathway

model

E

Cholesky

decomposition

d.

Independent

pathway

AD

Cholesky

decomposition

e.

Independent

pathway

model

f.

Independent

pathway

AD

Cholesky

decomposition

E

instrument-specific

A

factors

g.

Independent

pathway

AD

Cholesky

decomposition

E

instrument-specific

D

factors

Common

pathway

Fig.

graphical

representation

of

the

unstandardized

additive

genetic

-LRB-

A

-RRB-

and

dominant

genetic

-LRB-

D

-RRB-

effects

on

five

measurements

of

Attention

Problems

and

ADHD

In

this

figure

a

graphical

representation

of

the

best-fitting

model

and

the

estimated

factor

loadings

is

provided

for

one

individual

twin

Additive

genetic

effects

correlate

in

MZ

twins

and

in

DZ

twins

Dominant

genetic

effects

correlate

in

MZ

twins

and

in

DZ

twins

To

identify

the

model

the

variances

of

the

five

categorical

measurements

are

constrained

at

Child

Behavior

Checklist

at

age

Child

Behavior

Checklist

at

age

Child

Behavior

Checklist

at

age

CPRS-R

S

Conners

Parental

Rating

Scale-Revised

Short

version

at

age

DSM

DISC-IV

ADHD

at

a

mean

age

of

years

Although

the

influence

of

the

nonshared

environment

was

not

included

in

Fig.

the

fact

that

the

total

variances

of

the

five

measurements

are

constrained

at

in

order

to

identify

the

model

allows

a

calculation

of

the

additive

and

dominant

genetic

variance

based

on

the

unstandardized

factor

loadings

For

example

-LRB-

i.e.

-RRB-

of

the

variance

in

the

CBCL

rating

at

age

is

attributable

to

additive

genetic

effects

-LRB-

-RRB-

is

attributable

to

dominant

genetic

effects

The

remaining

variance

is

explained

by

nonshared

environmental

effects

The

additive

genetic

variance

on

the

five

measurements

can

be

decomposed

into

variance

due

to

the

common

factor

and

variance

due

to

instrument-specific

factors

For

the

CBCL

rating

at

age

-LRB-

-RRB-

of

the

total

variance

is

attributable

to

common

additive

genetic

effects

and

-LRB-

-RRB-

is

attributable

to

instrument-specific

genetic

effects

The

influence

of

common

additive

genetic

effects

on

the

total

variance

accounts

for

and

for

the

CBCL

at

age

the

CBCL

at

age

the

CPRS-R

S

and

the

DSM

respectively

Likewise

the

influences

of

instrument-specific

effects

account

for

and

of

the

variance

respectively

Table

shows

an

overview

of

the

standardized

influences

of

A

D

and

E

on

the

variance

and

covariance

of

the

five

measurements

The

three

diagonals

of

the

five

by

five

tables

of

A

D

and

E

contained

the

standardized

variance

components

The

results

indicate

a

high

heritability

irrespective

of

measurement

instrument

or

age

On

the

off-diagonals

in

Table

one

can

find

the

standardized

influences

of

A

D

and

E

on

the

covariance

between

the

measurements

For

example

the

covariance

between

and

DSM

is

for

explained

by

A

by

D

and

by

E.

To

obtain

the

unstandardized

amount

of

variances

explained

the

standardized

influences

should

be

multiplied

with

the

phenotypic

covariance

between

the

measures

which

is

for

and

DSM

The

most

interesting

comparison

is

between

the

data

that

were

collected

at

approximately

the

same

time

The

covariance

between

the

CBCL

at

age

and

the

DSM

is

explained

largely

by

genetic

effects

-LRB-

A

D

and

E

-RRB-

Similar

results

were

found

for

the

covariance

between

CPRS-R

S

and

the

DSM

-LRB-

A

and

D

-RRB-

and

for

the

covariance

between

the

CBCL

age

and

CPRS-R

S

-LRB-

A

and

D

-RRB-

Table

genetic

and

environmental

influences

on

the

variances

and

covariances

of

five

ratings

of

ADHD

and

attention

problemsADECBCL

SDSMCBCL

SDSMCBCL

SDSMCBCL

age

CBCL

age

CBCL

age

CPRS-R

S.

DSM

.51.57.68.67.56.25.17.09.07.04.24.26.23.25.40

Note

CBCL

Child

Behavior

Checklist

CPRS-R

S

Conners

Parent

Rating

Scale-Revised

Short

version

ADHD-index

DSM

Diagnostic

Statistical

Manual

of

Mental

Disorders

A

additive

genetic

effects

D

dominant

genetic

effects

E

non-shared

environmental

effects

Table

includes

the

genetic

and

environmental

correlation

matrices

in

the

best-fitting

model

which

represent

the

overlap

between

the

genetic

and

environmental

influences

on

the

five

measurement

instruments

The

additive

genetic

correlations

range

between

and

All

dominant

genetic

correlations

are

which

is

a

result

of

the

absence

of

specifics

in

the

one-factor

model

used

to

model

the

dominant

genetic

covariance

structure

The

non-shared

environmental

correlations

range

from

to

Table

and

environmental

correlations

of

five

ratings

of

ADHD

and

attention

problemsADECBCL

SDSMCBCL

SDSMCBCL

SDSMCBCL

age

CBCL

age

CBCL

age

S.

DSM

.52.62.68.631.01.01.01.01.01.0.39.52.45.621.0

Note

CBCL

Child

Behavior

Checklist

CPRS-R

S

Conners

Parent

Rating

Scale-Revised

Short

version

ADHD-index

DSM

Diagnostic

Statistical

Manual

of

Mental

Disorders

A

additive

genetic

effects

D

dominant

genetic

effects

E

non-shared

environmental

effects

Discussion

The

aim

of

this

study

was

to

determine

the

extent

to

which

three

different

instruments

which

are

commonly

used

to

assess

ADHD

attention

problems

and

hyperactivity

measure

a

common

construct

The

instruments

considered

are

two

scales

based

on

items

from

questionnaires

-LRB-

CBCL-AP

and

CPRS-R

S

ADHD-I

-RRB-

and

a

DSM-IV

ADHD

interview

First

we

considered

the

phenotypic

correlations

Second

we

tested

if

the

variance

in

the

different

instruments

reflects

one

common

underlying

factor

Third

we

estimated

the

genetic

and

environmental

influences

on

individual

differences

in

ADHD

This

is

the

first

study

that

includes

multivariate

genetic

analyses

of

behavior

rating

scales

and

DSM-IV

interview

data

collected

in

a

large

sample

of

twins

of

approximately

the

same

age

The

CBCL

scores

collected

at

age

and

years

were

included

only

to

correct

for

the

selection

In

the

discussion

we

focus

mainly

on

the

CBCL

CPRS-R

S

and

DSM

interview

data

which

were

collected

at

a

mean

age

of

years

The

phenotypic

correlation

between

CBCL-AP

and

the

CPRS-R

S

ADHD-I

was

high

-LRB-

r

-RRB-

The

correlations

between

the

CBCL

and

the

DSM

and

between

the

CPRS-R

S

and

the

DSM

were

slightly

lower

-LRB-

r

-RRB-

These

lower

correlations

can

both

be

the

result

of

the

different

time-points

at

which

the

behavior

checklists

and

the

DSM

interview

data

were

collected

-LRB-

the

mean

time-span

between

measurement

occasions

was

months

-RRB-

the

differences

in

the

time

frame

for

the

assessment

of

the

items

-LRB-

e.g.

month

for

the

CPRS-R

S

months

for

the

CBCL

and

year

for

the

DSM

-RRB-

and

of

instrument

or

method

variance

-LRB-

e.g.

interview

versus

behavior

checklists

-RRB-

The

genetic

analyses

show

that

the

covariance

between

CBCL

and

CPRS

is

for

explained

by

genetic

factors

while

the

covariance

between

CBCL

and

DSM

was

for

explained

by

genetic

factors

Therefore

the

higher

phenotypic

correlation

between

CBCL

and

CPRS

is

not

caused

by

a

relatively

higher

genetic

covariance

As

noted

the

AP

scale

of

the

CBCL

questions

relate

to

both

inattention

and

hyperactivity/impulsivity

The

fact

that

the

correlation

between

the

CPRS-R

S

ADHD-I

and

DSM-IV

ADHD

is

identical

to

the

correlation

between

CBCL-AP

and

DSM-IV

ADHD

implies

that

the

CPRS-R

S

and

the

CBCL

measure

ADHD

equally

well

The

description

of

the

eleven

item

CBCL

scale

as

an

inattention

scale

seems

to

be

too

limited

because

both

the

item

content

and

the

current

results

suggest

that

the

CBCL

also

signals

problems

related

to

hyperactivity/impulsivity

Although

the

phenotypic

correlations

provide

an

interesting

insight

regarding

the

similarities

and

dissimilarities

of

the

quantitative

and

qualitative

approaches

towards

child

psychopathology

an

important

question

concerns

the

etiological

influences

on

the

variances

and

covariances

In

agreement

with

previous

studies

-LRB-

Eaves

et

al.

Sherman

et

al.

Rietveld

et

al.

Hudziak

et

al.

-RRB-

individual

differences

in

AP

and

ADHD

are

mainly

explained

by

genetic

factors

An

independent

pathway

model

provided

a

better

fit

than

a

common

factor

model

A

common

factor

model

implies

a

similar

structure

for

the

additive

genetic

dominant

genetic

and

nonshared

environmental

influences

so

the

poor

fit

is

probably

due

to

the

fact

that

there

are

instrument-specific

additive

genetic

factors

while

these

are

absent

for

the

dominant

genetic

factors

As

referees

of

earlier

drafts

of

this

paper

noted

alternative

models

might

be

fit

to

our

data

a

model

including

three

common

factors

-LRB-

one

loading

on

all

ratings

a

second

loading

on

CBCL

ratings

and

a

third

loading

on

age

ratings

might

offer

a

good

solution

but

because

the

structure

of

A

D

and

E

differ

-LRB-

with

no

rating-specific

influences

for

D

-RRB-

we

did

not

fit

this

model

to

our

data

An

independent

pathway

model

allows

for

the

inclusion

of

common

and

instrument-specific

genetic

and

environmental

factors

The

model

that

provided

the

best

fit

to

the

data

included

common

additive

and

dominant

genetic

effects

instrument-specific

additive

genetic

effects

and

nonshared

environmental

effects

The

relative

influence

of

common

and

instrument-specific

genetic

effects

varies

by

rating

Two

third

of

the

additive

genetic

variance

of

the

CBCL

ratings

at

age

age

and

the

CPRS-R

S

rating

at

age

was

explained

by

common

effects

More

specifically

Instrument-specific

effects

played

a

more

important

role

in

the

CBCL

ratings

at

age

and

in

the

DSM

ratings

For

these

ratings

the

ratio

of

common

and

instrument-specific

effects

was

about

Apparently

the

overlapping

genes

explain

less

of

the

variance

in

these

ratings

compared

to

the

other

ratings

probably

as

a

result

of

developmental

changes

in

behavior

and

of

method

variance

-LRB-

i.e.

questionnaire

versus

interview

-RRB-

The

dominant

genetic

effects

overlapped

completely

between

ratings

as

the

instrument-specific

effects

could

be

dropped

from

the

model

Our

results

show

some

agreement

with

the

findings

of

Nadder

and

Silberg

-LRB-

-RRB-

who

fit

an

independent

pathway

model

to

ADHD

symptomatology

based

on

maternal

and

paternal

questionnaire

and

interview

data

and

to

teacher

reports

Although

their

best-fitting

model

included

contrast

effects

instead

of

genetic

dominance

our

finding

of

both

common

and

specific

genetic

influences

on

the

questionnaire

and

interview

data

on

ADHD

is

supported

by

their

results

The

poor

fit

of

the

common

factor

model

suggests

that

the

construct

validity

of

the

instruments

is

not

perfect

However

it

is

interesting

to

consider

the

implications

of

the

overlap

between

the

sets

of

genes

that

explained

variance

in

the

three

instruments

High

genetic

correlations

imply

that

the

detection

of

the

specific

genes

that

play

a

role

for

ADHD

does

not

depend

much

on

the

instrument

that

is

used

At

age

the

additive

genetic

correlations

of

the

CBCL

CPRS-R

S

and

DSM

varied

between

and

while

the

dominant

genetic

correlations

could

be

constrained

at

The

non-shared

environmental

correlations

are

also

quite

high

and

vary

between

and

The

dominant

genetic

correlations

of

suggest

that

there

is

a

subset

of

genes

whose

effect

is

not

instrument

or

age

dependent

In

contrast

the

correlations

of

the

additive

genetic

effects

are

high

but

less

than

perfect

This

suggests

that

the

influence

of

most

genes

with

an

additive

effect

are

not

sensitive

to

the

particular

instrument

that

is

used

although

there

are

some

genes

that

explain

variance

only

in

a

particular

measurement

-LRB-

e.g.

CBCL

-RRB-

but

not

in

another

-LRB-

e.g.

DSM

-RRB-

What

are

the

implications

of

the

present

findings

for

gene

finding

studies

Thus

far

five

groups

have

conducted

genome-wide

linkage

scans

in

an

attempt

to

find

genomic

regions

which

are

involved

in

ADHD

and

a

number

of

regions

that

may

be

of

interest

have

been

identified

Linkage

peaks

with

a

LOD

score

above

-LRB-

P

-RRB-

were

reported

at

chromosomes

and

-LRB-

Ogdie

et

al.

-RRB-

chromosomes

and

-LRB-

Bakker

et

al.

-RRB-

chromosomes

and

-LRB-

Arcos-Burgos

et

al.

-RRB-

chromosomes

and

chromosome

-LRB-

Hebebrand

et

al.

-RRB-

and

chromosomes

and

-LRB-

Gayan

et

al.

-RRB-

All

these

studies

based

diagnosis

on

DSM-IV

-LRB-

Ogdie

et

al.

Bakker

et

al.

Arcos-Burgos

et

al.

Hebebrand

et

al.

-RRB-

or

DSM-III

-LRB-

Gayan

et

al.

-RRB-

criteria

The

discrepancy

in

the

results

of

these

five

studies

could

be

due

to

low

statistical

power

The

present

study

showed

that

the

genetic

overlap

between

behavior

checklist

scores

and

the

DSM-IV

diagnosis

of

ADHD

is

high

This

implies

that

the

detection

of

genes

which

play

a

role

for

ADHD

can

be

based

on

questionnaire

scores

rather

than

diagnostic

interviews

This

will

reduce

the

costs

of

collecting

phenotypic

data

Resources

may

then

be

reallocated

to

the

collection

of

genotypic

data

An

increased

number

of

subjects

can

be

genotyped

and

the

statistical

power

to

detect

a

QTL

will

be

increased

Limitations

The

results

of

this

study

should

be

interpreted

bearing

in

mind

the

following

limitations

First

further

study

is

required

to

investigate

if

the

results

of

the

current

study

which

was

based

on

a

Dutch

population

sample

generalize

to

population

samples

outside

the

Netherlands

Second

clinical

diagnoses

were

based

on

structured

diagnostic

interviews

with

the

mother

The

results

may

be

different

when

the

assessment

of

ADHD

is

based

on

expert

clinical

diagnoses

Third

no

distinction

was

made

between

problems

related

to

inattention

and

problems

related

to

hyperactivity

Since

the

CBCL

does

not

distinguish

between

inattention

and

hyperactivity

-LRB-

and

probably

the

number

of

items

is

too

small

to

reliably

measure

these

two

factors

-RRB-

we

did

not

distinguish

between

the

subscales

Fourth

we

did

not

allow

for

sex

differences

in

the

genetic

and

environmental

influences

based

on

the

results

of

univariate

studies

Because

of

the

increased

statistical

power

in

the

multivariate

model

it

is

possible

that

sex

differences

do

exist

However

due

to

the

categorical

nature

of

the

data

and

the

fact

that

some

of

the

cells

in

the

contingency

tables

contain

few

individuals

in

a

two-group

analysis

statistical

problems

will

arise

in

a

four-group

analysis

Fifth

as

a

result

of

the

categorical

nature

of

the

data

computational

limitations

prohibited

inclusion

of

confidence

intervals

Clinical

implications

Two

general

approaches

towards

the

measurement

of

ADHD

can

be

distinguished

In

the

DSM-IV

framework

ADHD

is

viewed

as

a

categorical

trait

Using

behavior

checklists

children

can

show

variation

in

a

continuum

from

not

affected

at

all

to

severely

affected

The

current

study

shows

that

variance

in

DSM-IV

symptoms

the

CBCL-AP

scale

and

the

CPRS-R

S

ADHD-I

is

explained

mostly

by

genetic

effects

The

correlations

between

the

genetic

influences

on

variance

in

these

three

measurements

of

ADHD

are

high

This

implies

that

different

measurements

tap

the

same

genetic

liability

O O O O O O O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O B O O O O O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O

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Genetic algorithm for multi-objective experimental optimization A new software tool making use of a genetic algorithm for multi-objective experimental optimization -LRB- GAME.opt -RRB- was developed based on a strength Pareto evolutionary algorithm . The software deals with high dimensional variable spaces and unknown interactions of design variables . This approach was evaluated by means of multi-objective test problems replacing the experimental results . A default parameter setting is proposed enabling users without expert knowledge to minimize the experimental effort -LRB- small population sizes and few generations -RRB- . Introduction In many technical problems scientists face the problem of identifying optimal process conditions like pH , temperature , concentrations or other variables . A typical example is fermentation medium development . The composition of a fermentation medium consisting of carbon sources , nitrogen sources , mineral salts , trace elements , amino acids and/or peptides , vitamins and other growth factors determines the chemical and nutritional environment of cells in a bioreactor and is thus vital for the effective manufacturing of bioproducts . Due to the large number of process variables and the metabolic complexity of microorganisms or cells methods of experimental design need to be applied in order to identify values of the relevant variables resulting in an improved performance . Considering several objectives to be optimal there is per definition not one optimal solution but a set of efficient solutions . Mathematically such a multi-objective optimization problem -LRB- MOP -RRB- can be described in terms of Eq . 1 . The functional relation between the m design variables and the objective functions φ does not necessarily need to be known , as y will be obtained from n experimental observations . An important criteria for MOPs is that of Pareto optimality , shortly saying that a member of the efficient set is not dominated by any other . In Fig. 1 the principle of dominance is exemplified in the objective space , where for the case of maximizing two objectives the efficient solutions are indicated . Fig. 1Efficient points -LRB- black -RRB- are not dominated by any other point . For a dominated point -LRB- white -RRB- there exist at least one other point that has greater values in both objectives y1 and y2 Classical statistical experimental design methods -LRB- Plackett -- Burman Design , Response Surface Method -RRB- have drawbacks like screening for principal components and assuming an unimodal objective function , reviewed in -LSB- 1 -RSB- . More sophisticated stochastic search strategies like genetic algorithms -LRB- GAs -RRB- have grown in popularity since Rechenberg -LSB- 2 -RSB- and Holland -LSB- 3 -RSB- first published their work on this subject . GAs are based on evolutionary principles , encoding several sets of design variables on binary strings -LRB- individuals in a population -RRB- which are processed by GA operators -LRB- crossover and mutation -RRB- throughout several generations . The principle `` survival of the fittest '' assures a convergence towards optimal values in the design variables with proceeding generations . The first GA dealing with multiple objectives was the Vector Evaluated Genetic Algorithm -LRB- VEGA -RRB- proposed by Schaffer -LSB- 4 -RSB- . This multi-objective optimization strategy has already been applied successfully for experimental medium optimization in many cases -LSB- 1 -RSB- . The most recent published multi-objective GAs are the Non-Dominated Sorting Genetic Algorithm-II -LSB- 5 -RSB- and the Strength Pareto Evolutionary Algorithm -LRB- SPEA -RRB- -LSB- 6 -RSB- . The SPEAs main feature is processing two populations : besides a normal population an external population serves as a kind of archive , keeping track of the efficient set . Especially in the case of experimental design with a limited number of experiments the SPEA is supposed to have advantages compared to VEGA with respect to the experimental effort . The new software tool with a genetic algorithm for multi-objective experimental optimization making use of SPEA will be outlined . The performance of GAME.opt will be evaluated with the help of special test-functions to achieve appropriate parameter settings for experimental design . Methods GAME.opt was developed with LabVIEW 7 -LRB- National Instruments -RRB- . The Application Builder was used to create a stand alone application running under Windows platforms . Data handling is based on spreadsheet files , which can be accessed via a text editor or Microsoft Excel . GAME.opt will be made available on request by the Technical University of Munich . As the core algorithm is based on the SPEA , fitness assignment , selection and clustering is described in detail by Zitzler and Thiele -LSB- 6 -RSB- . To abstract the algorithm : fitness assignment is either based on the strength of an individuals dominance or on the degree an individual is dominated by others . A mating pool equal to the population size is filled by selecting individuals using binary tournament without replacement -LSB- 7 -RSB- . Crossover is performed between two parental binary strings from the mating pool at the specified number of crossover points in order to create two off-springs . Each bit of these new strings is inverted with a probability which is defined by the mutation rate . Clustering is used in order to bound the external population to a maximal value Nextern . Each time the external population exceeds this value it is pruned to a size of Ncluster by means of average clustering . The first step when using GAME.opt is to create a new project where all information on the experimental design is defined . For this purpose the user is led through the steps explained together with some recommendations in the following . Design variables The design variables considered in the problem -LRB- x in Eq . 1 -RRB- need to be defined initially . Alternatively to choosing the amount of bits encoding a variable GAME.opt gives the opportunity to choose the amount of levels , resulting from the variable 's bounds and its increment . The choice of levels can be necessary for practical purposes but causes problems in the coding of a decision variable as follows . A general decoding function linearly transforms an n-bit-long binary string -LRB- a1 ... an -RRB- into a bounded real number x ∈ -LSB- xL , xU -RSB- : where a1 is the most significant bit and an is the least significant bit -LSB- 8 -RSB- . This kind of transformation is just unique if the amount of levels equals -LRB- 2n − 1 -RRB- . In other words , like its natural paradigm , the binary code is degenerated if there are more bit combinations than levels -LRB- the opposite case will not occur as the program computes the minimal amount of required bits -RRB- . Considering the above mentioned the following points are important when defining the design variables : If the experimental setup prevents an adequate choice of levels the coding can be made visible in GAME.opt . In order to assure equal processing of all variables the amount of levels among the variables should not vary too much.From the amount of levels results the length of the binary string that is needed to encode the design variables , which is shown in GAME.opt in terms of bits for each variable . From a set of M binary strings with the length l each point in the search space -LRB- X in Eq . 1 -RRB- can be reached with a probability p . The relation is given in Eq . 3 and GAME.opt will display p when selecting the number of individuals -LRB- M -RRB- -LSB- 9 -RSB- . The value of p should be higher than 0.99 . As each individual corresponds to one experiment , the experimental effort will be correlated to the chosen amount of levels.The increment should be higher than the possible precision in the experiment . Experimental results The experimental observations y have to be specified in GAME.opt just in terms of their names and units . The following items should be considered when planning the experiments : All parameters different from the design variables have to remain fixed in all experiments throughout the optimization procedure.The experimental error should be lower than the differences that are expected to result from different levels in the design variables . Objective functions The objective functions in GAME.opt can be any linear combination of the experimental results and the decision variables . GAME.opt will maximize all objective values . If for example one objective is minimizing a certain experimental result , the objective function is -- 1 times the according result . When defining the objective functions it is important to make sure that they are independent from each other . For example it is no use maximizing simultaneously the amount of a reaction 's product and minimizing the amount of non-converted reactants at the end of a batch process , because a high product concentration is correlated to low resting concentrations of reactants . A reasonable combination is for example maximization of an experimental result while minimizing the sum of decision variables , possibly reducing the costs of a process . Optimization procedure Once the MOP is defined by the above mentioned steps a random generated initial population is available . This set of design variables can be exported from GAME.opt and the according experiments are performed . After the experimental results are entered in GAME.opt the next population is generated and checked for individuals that have already appeared in order to prevent repeated experiments . This iterative process is performed until satisfying results are obtained . The external population contains the efficient set recovered so far and thus constitutes the result of the optimization process . The experimental results in the external population are already assigned because their members originate from former populations . Results A previous version of GAME.opt was used for experimental design for media optimization -LRB- 13 medium components , 20 individuals/generation , 91 bits/binary string , eight generations -RRB- and gave comparable results to another GA making use of VEGA with half the number of experiments -LSB- 10 -RSB- . Further process optimizations considering media composition together with process parameters are currently performed in our laboratory . In order to evaluate the software for a proper processing and its general ability to solve MOPs it was tested by means of several multi-objective test problems in such a way that the experimental results are replaced by evaluation of mathematical functions . An exemplary MOP with three objectives and six design variables is given in Eq . 4 . This MOP is based on Deb et al. -LSB- 11 -RSB- , where the development of test problems is described . The MOP in Eq . 4 was solved with GAME.opt , therefore the six design variables have been defined in the program together with the bounds , being 0 and 1 for each variable . As mentioned above the choice of the increment and thus the amount of levels is crucial for a proper processing of the variables . An increment of 0.1 will give 11 Levels , namely -LSB- 0 , 0.1 , 0.2 , ... , 1 -RSB- encoded with 4 bits giving 16 levels . According to Eq . 2 an adequate increment for a given number of bits n results from : Table 1 confronts a proper coding with 4 bits with a degenerated coding for a variable range from 0 to 1 . Table 1Four bit binary coding of the design variables in Eq . 4 for different increments -LRB- incr -RRB- Binary codeDegenerated codingDecoded value -LRB- incr = 0.1 -RRB- Proper codingDecoded value -LRB- incr = 1/15 -RRB- 0 0 0 0000 0 0 10.11 / 150 0 1 00.12 / 150 0 1 10.23 / 150 1 0 00.34 / 150 1 0 10.35 / 150 1 1 00.46 / 150 1 1 10.57 / 151 0 0 00.58 / 151 0 0 10.69 / 151 0 1 00.710 / 151 0 1 10.711 / 151 1 0 00.812 / 151 1 0 10.913 / 151 1 1 00.914 / 151 1 1 111 Using the proper coding shown in Table 1 the GA was run eight generations with 20 individuals in the normal population and 10 individuals in the external population . Two crossover points and a mutation probability of 1 % was chosen what has been identified as a reasonable default setting in other problems . As a rule of thumb the size of the external population should be half of the normal population , for which a minimal number can be estimated by Eq . 3 . Table 2 summarizes the default parameter setting . Table 2Default parameter setting for the genetic algorithmParameterValueCrossover points2Mutation rate1 % Individuals in normal population -LRB- N -RRB- Eq . 3Individuals in external population -LRB- Nextern -RRB- N/2Individuals in external population after cluster analysis -LRB- Ncluster -RRB- N/2 The results are shown in Fig. 2 , by means of the objective values f1 , f2 , f3 of the ten individuals in the external population after eight generations . Fig. 2The objective space of the test problem lies between the surfaces . Optimal solutions are located on the unit sphere in the first quadrant . The black dots indicate the efficient set after eight generations of GAME.opt -LRB- external population -RRB- . The two views of the plot point out the closeness of the efficient set to the Pareto front -LRB- a -RRB- and its equal distribution -LRB- b -RRB- The two spherical surfaces in Fig. 2 constitute the objective space of Eq . 4 . For the minimization problem the first quadrant of the unit sphere constitutes the Pareto optimal frontier where g -LRB- x -RRB- = 0 and it is already approximated well by the ten members of an external population after eight generations -LRB- Fig. 2a -RRB- . Beside the closeness to the Pareto frontier the distribution of the solutions is an important performance criteria . Figure 2b reveals the equal distribution of the ten solutions resulting amongst other things from the cluster analysis . Optimal solutions are characterized by xi = 0.5 for i = 1 , 2 , 3 , 4 , whereas x5 and x6 can take any value in the given range . Splitting the design variables in such a way allows to test the algorithm for a crucial feature of GAs , the populations diversity . On the one hand the algorithm is expected to converge fast to the optimal solutions but on the other the populations diversity must be high enough to ensure exploration of the whole Pareto optimal frontier . This fact is reflected in the box plots of the initial and the eighth generation together with their corresponding external populations in Fig. 3 . Fig. 3Box plot of the initial population -LRB- a -RRB- , the first external generation -LRB- b -RRB- , the eighth generation -LRB- c -RRB- and the eighth external generation -LRB- d -RRB- . The boxes contain the middle of 50 % of the data . The line in the box indicates the median . The bold dashed line separates variables with an optimal solution -LRB- x1 , x2 , x3 , x4 = 0.5 -RRB- from variables without optimal value -LRB- x5 , x6 -RRB- Initially the individuals are randomly distributed , what is reflected by the box plots of the six design variables in Fig. 3a . A trend towards 0.5 is already visible in Fig. 3b where box plots are shown for the first external population . In Fig. 3c , d , depicting the box plots of the corresponding populations after eight generations , a clear distinction between the variables with optimal value and those without can be made . After eight generations the diversity of x5 and x6 is still high in both populations . The remaining variables show the expected divergence towards 0.5 in the external population but remain in parts distributed over a wider range in the normal population . From this result it gets obvious that GAME.opt performs well with a small amount of individuals and a short evolution on a MOP considered a benchmark of evolutionary computing . Conclusions In order to keep the experimental effort low , GAME.opt will use small population sizes and fewer generations compared to other GA applications , where the amount of objective function evaluations is mostly limited by the computational costs . For this reason the external population is expected to be only a rough approximation of the true Pareto optimal frontier . Nevertheless in all test problems a satisfying performance of GAME.opt was achieved in spite of the relatively low number of experiments -LRB- 160 compared to 166 possible design variable combinations with the test problem presented -RRB- . In the near future , efficient parallel search strategies for experimental design are becoming more and more important in bioprocess optimization due to the availability of new parallel stirred-tank bioreactor technologies -LSB- 12 -RSB- .

B I O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O

experimental design
genetic algorithm
software tool