A database of 389 medicinal plants for diabetes Medicinal plants used to treat hypoglycemic and hyperglycemic conditions are of considerable interest to ethno-botanical community as they are recognized to contain valuable medicinal properties in different parts of the plant . The active principles of many plant species with desired properties are isolated to cure ailments such as diabetes type-1 and type-2 , respectively . Here , we describe DiaMedBase , a database containing information of medicinal plants for diabetes . Background Since olden days , plants are used to treat many ailments . India has about 45,000 plant species and several thousands have been claimed to possess medicinal properties . -LSB- 1 -RSB- Medicinal plants used to treat hypoglycemic or hyperglycemic conditions are of considerable interest for ethno-botanical community as they are recognized to contain valuable medicinal properties in different parts of the plant and a number of plants have shown varying degree of hypoglycemic and anti-hyperglycemic activity . -LSB- 1 -RSB- The active principles of many plant species are isolated for direct use as drugs , lead compounds or pharmacological agents . -LSB- 3 -RSB- Several species of medicinal plants are used in the treatment of diabetes mellitus , a disease affecting large number of people world-wide . Traditional plant medicines or herbal formulations might offer a natural key to unlock diabetic complications . -LSB- 2 -RSB- Diabetes mellitus is the major endocrine disorder -LSB- 4 -RSB- responsible for renal failure , blindness or diabetic cataract -LSB- 5 -RSB- , poor metabolic control -LSB- 6 -RSB- , increased risk of cardiovascular disease including atherosclerosis and AGE -LRB- advanced glycation end -RRB- products . -LSB- 7 -RSB- Antioxidants play an important role to protect against damage by reactive oxygen species and their role in diabetes has been evaluated . Many plant extracts and products were shown to possess significant antioxidant activity . -LSB- 8 -RSB- Hence , we created DiaMedBase , a diabetes literature database of medicinal plants with abstract , plant parts , objective and a ` disease link ' to diseases other than diabetes for each medicinal plant . Methodology Construction of DiaMedBase DiaMedBase is constructed using html and can be accessed at http://www.progenebio.in/DMP/DMP.htm . Data were collected from various literature sources such as , PubMed -LSB- 9 -RSB- , ScienceDirect -LSB- 10 -RSB- , Mary Ann Liebert -LSB- 11 -RSB- , BlackWell Synergy -LSB- 12 -RSB- , IngentaConnect -LSB- 13 -RSB- , Scirus -LSB- 14 -RSB- , Bentham Publishers -LSB- 15 -RSB- , Wiley journals -LSB- 16 -RSB- and others . DiaMedBase includes 742 records , containing about 309 genus and 389 species of plants described to possess medicinal properties against diabetes . The complete list can be found at http://www.progenebio.in/DMP/listz.htm . However , the list is not complete . They are provided alphabetically and the records are organized to simplify the task of finding relevant data for any plant . The database can be accessed alphabetically using genus name for information on specific plants . Features of DiaMedBase Each entry in DiaMedBase is provided with a unique accession number DMPXX001 , where , XX represents the first letter of genus and species , respectively . Digits refer to the record number in the database . For example , the accession number of Aloe vera is DMPAv042 , where , 042 represent record entry in the DiaMedBase . The Medicinal Plant row in some records display a list of medicinal plants and the representative plants are highlighted . DiaMedBase contains 30 entries for genus Trigonella , 22 entries for Momordica , 19 for Gymnema , 13 entries for Opuntia and Panax , 11 for Allium species and 10 each for Aloe , Tinospora , respectively . A screen-shot of the DiaMedBase is given in Figure 1 . Of the collected data , 36 % whole plant , 26 % leaves , 12 % seeds , 10 % roots , and 4 % fruits . The characteristic feature of DiaMedBase is ` Disease Link ' , provided in each record displays the list of diseases other than diabetes as a pop-up window indicating the importance of medicinal values of plants . Utility DiaMedBase emphasizes the importance of hypoglycemic and hyperglycemic properties possessed by medicinal plants . The database finds utility to the scientific community for a quick review on the number of plants and plant parts for diabetes medicinal plant research . Future development Continuous updates shall be released to include other plants of medicinal value periodically . The present access method shall be upgraded to browse records on the studied plant parts . We plan to develop provisions to search the database to identify plants of interest using keywords .

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

medicinal plants
diabetes
database
data
literature


Lichen

planus

remission

is

associated

with

a

decrease

of

human

herpes

virus

type

protein

expression

in

plasmacytoid

dendritic

cells

The

cause

of

lichen

planus

is

still

unknown

Previously

we

showed

human

herpes

virus

-LRB-

-RRB-

DNA

and

proteins

in

lesional

lichen

planus

skin

and

significantly

less

in

non-lesional

lichen

planus

psoriasis

or

healthy

skin

Remarkably

lesional

lichen

planus

skin

was

infiltrated

with

plasmacytoid

dendritic

cells

If

is

associated

with

lichen

planus

then

replication

would

reduce

upon

lichen

planus

remission

DNA

detection

was

performed

by

nested

PCR

and

protein

by

immunohistochemistry

on

lesional

skin

biopsies

from

lichen

planus

patients

before

treatment

and

after

remission

Biopsies

were

obtained

from

lichen

planus

lesions

before

treatment

-LRB-

n

patients

-RRB-

and

after

remission

-LRB-

n

-RRB-

Before

treatment

biopsies

contained

DNA

versus

after

remission

-LRB-

P

-RRB-

positive

cell

numbers

diminished

significantly

after

remission

in

both

dermis

and

epidermis

Expression

of

was

mainly

detected

in

positive

plasmacytoid

dendritic

cells

rather

than

positive

lymphocytes

replicates

in

plasmacytoid

dendritic

cells

in

lesional

lichen

planus

skin

and

diminishes

after

remission

This

study

further

supports

our

hypothesis

that

is

associated

with

lichen

planus

pathogenesis

Introduction

Lichen

planus

is

clinically

characterized

by

flat

topped

polygonal

itchy

erythematous

papules

with

Wickams

striae

nail

deformation

and

white

mucosal

patches

-LSB-

-RSB-

The

histopathological

substrate

comprises

a

dermal

band

like

-LRB-

lichenoid

-RRB-

lymphocytic

infiltrate

directed

towards

the

basal

epidermal

layer

with

destruction

of

the

basal

membrane

and

apoptosis

of

epidermal

cells

-LRB-

colloid

bodies

-RRB-

A

viral

cause

infecting

skin

cells

has

been

proposed

Hepatitis

C

virus

was

epidemiologically

linked

to

lichen

planus

-LSB-

-RSB-

but

this

finding

could

not

be

confirmed

in

later

studies

-LSB-

-RSB-

We

recently

described

an

association

of

human

herpes

virus

type

-LRB-

-RRB-

DNA

and

large

infiltrates

of

plasmacytoid

dendritic

cells

-LRB-

associated

with

virally

induced

inflammatory

processes

-RRB-

in

lesional

skin

of

lichen

planus

patients

but

not

in

non-lesional

skin

of

the

same

patients

-LSB-

-RSB-

Moreover

skin

of

healthy

volunteers

and

of

patients

with

another

inflammatory

skin

condition

like

psoriasis

showed

significantly

less

activity

Others

have

described

plasmacytoid

dendritic

cell

recruitment

with

interferon-alpha

and

antiviral

protein

MxA

production

in

oral

and

cutaneuous

lichen

planus

lesions

-LSB-

-RSB-

The

presence

of

in

lesional

skin

could

play

a

role

in

the

pathogenesis

of

lichen

planus

is

an

ubiquitous

organism

affecting

more

than

of

the

adult

population

worldwide

and

primary

infection

occurs

mainly

during

early

childhood

-LSB-

-RSB-

Like

Epstein

Barr

virus

reactivation

is

associated

with

Burkitt

lymphoma

reactivation

of

during

adulthood

could

be

associated

with

lichen

planus

To

support

this

hypothesis

we

quantified

and

compared

the

presence

of

DNA

and

protein

in

lesional

lichen

planus

skin

before

and

after

treatment-induced

remission

Materials

and

methods

The

hospital

medical

ethics

review

board

approved

this

study

Before

entering

the

study

patients

gave

their

written

informed

consent

to

participate

Skin

biopsies

were

collected

in

a

follow

up

study

from

the

same

patient

group

with

lichen

planus

as

described

before

-LSB-

-RSB-

In

short

before

treatment

was

initiated

two

mm

full

thickness

skin

biopsies

were

obtained

from

lesional

skin

Patients

were

treated

with

mg

prednisone

per

os

daily

diminished

with

mg

every

other

day

until

a

daily

dose

of

mg

was

reached

From

that

point

on

the

prednisone

dosage

was

diminished

with

mg

per

week

If

new

lichen

planus

lesions

recurred

the

previous

dose

was

administered

and

diminishment

halted

for

weeks

In

case

prednisone

treatment

was

contra-indicated

other

treatment

options

like

topical

corticosteroids

oral

acitretin

-LRB-

mg/kg

body

weight

-RRB-

and

psoralen

ultraviolet

A

combined

photo

therapy

were

considered

depending

on

the

extent

of

lesions

and

underlying

medical

conditions

Treatment

was

terminated

after

complete

clinical

remission

was

achieved

and

weeks

later

provided

no

disease

activity

had

recurred

another

two

biopsies

were

collected

from

recovered

lesional

skin

adjacent

to

the

pretreatment

biopsy

sites

Both

time

points

biopsies

were

taken

one

biopsy

was

processed

for

routine

histopathology

and

examined

by

both

a

pathologist

and

a

dermatologist

separately

to

confirm

the

lichen

planus

diagnosis

or

signs

of

ongoing

inflammation

The

final

diagnosis

was

made

on

mutual

agreement

and

based

on

typical

lichen

planus

associated

dermatopathological

signs

like

parakeratosis

wedge

shaped

hypergranulosis

saw-tooth

configured

rete

ridges

vacuolar

degeneration

of

the

basal

layer

colloid

bodies

a

band-like

dermal

inflammatory

infiltration

and

pigment

incontinence

-LSB-

-RSB-

The

second

biopsy

of

each

time

point

was

snap

frozen

in

liquid

nitrogen

stored

at

minus

°C

and

thawed

later

for

molecular

biological

analysis

-LRB-

DNA

-RRB-

DNA

isolation

and

the

nested

PCR

techniques

have

been

previously

described

-LSB-

-RSB-

The

amplified

fragment

-LRB-

bp

-RRB-

was

identified

by

gel

electrophoresis

The

lower

limit

of

detection

of

the

PCR

is

copies

of

DNA

We

performed

immunohistochemistry

as

described

before

-LSB-

-RSB-

The

antibodies

used

in

this

study

were

directed

against

clone

and

clone

both

resulting

in

a

similar

specific

staining

pattern

-LRB-

data

not

shown

Advanced

Biotechnologies

Inc.

Columbia

MD

-RRB-

-LRB-

pan

T

cell

marker

clone

FITC-conjugated

BD

Biosciences

San

Jose

CA

-RRB-

and

-LRB-

plasmacytoid

dendritic

cell

marker

clone

FITC

conjugated

Miltenyi

Biotec

Bergisch

Gladbach

Germany

-RRB-

In

the

single-staining

experiments

we

used

clone

-LRB-

directed

against

tegument

protein

-RRB-

but

unfortunately

this

clone

was

no

longer

available

at

the

time

we

performed

the

double

staining

For

this

reason

we

used

in

the

double

staining

experiments

clone

-LRB-

directed

against

an

unknown

epitope

-RRB-

In

brief

the

following

sequence

of

steps

was

applied

for

single

staining

blocking

endogenous

peroxidase

activity

-LRB-

clone

-RRB-

biotin-conjugated

goat

anti-mouse

antibody

-LRB-

Dako

-RRB-

horseradish

peroxidase-conjugated

streptavidin

and

for

clone

a

TSA

amplification

step

-LRB-

Perkin

Elmer

-RRB-

was

applied

In

four

patients

specimens

obtained

before

and

after

remission

were

double

stained

for

and

or

for

and

In

this

case

the

following

incubation

steps

were

performed

blocking

endogenous

peroxidase

activity

-LRB-

clone

-RRB-

biotin-conjugated

goat

anti-mouse

antibody

-LRB-

Dako

-RRB-

horseradish

peroxidase-conjugated

streptavidin

TSA

amplification

according

to

the

manufacturer

's

protocol

-LRB-

Perkin

Elmer

-RRB-

an

AEC

kit

to

visualize

the

peroxidase

activity

-LRB-

Vector

-RRB-

blocking

potential

available

biotin

anti-mouse

immunoglobulin

and

peroxidase

activity

or

antibody

rabbit

anti-FITC

-LRB-

Dako

-RRB-

peroxidase-conjugated

goat

anti-rabbit

-LRB-

Dako

-RRB-

for

and

phosphatase-conjugated

goat

anti-rabbit

-LRB-

Dako

-RRB-

for

for

a

TSA

amplification

step

followed

by

phosphatase-conjugated

streptavidin

and

finally

an

AP

kit

-LRB-

Vector

-RRB-

to

visualize

the

phosphatase

activity

All

single-stained

sections

were

counterstained

with

Mayer

's

hematoxylin

-LRB-

Fluka

-RRB-

The

expression

of

single

and

double

stained

cells

was

counted

in

each

entire

section

at

magnification

using

a

standard

binocular

light

microscope

-LRB-

Olympus

Tokyo

Japan

-RRB-

equipped

with

a

mm

ocular

grid

The

number

of

cells

in

the

epidermis

was

expressed

per

mm

and

the

number

in

the

dermis

per

During

a

follow

up

period

of

year

visits

were

scheduled

every

months

In

case

a

patient

experienced

a

relapse

in

between

follow

up

visits

or

after

the

initial

year

follow

up

period

extra

visits

were

performed

at

the

patient

's

initiative

for

additional

monitoring

and

treatment

Patients

without

a

relapse

on

record

were

interviewed

by

telephone

to

exclude

disease

reoccurrence

The

Wilcoxon

rank

sum

test

was

used

for

statistical

analysis

of

cell

counts

between

samples

before

and

after

remission

and

the

McNemar

test

for

binominal

data

P

was

considered

significant

Results

Eighteen

patients

entered

this

study

with

a

mean

age

of

years

at

the

time

of

inclusion

-LRB-

mean

age

of

males

was

and

for

females

years

-RRB-

The

mean

disease

duration

was

months

-LRB-

Table

-RRB-

Lesional

biopsies

were

taken

from

the

lower

leg

in

cases

times

from

the

trunk

and

in

patient

from

the

wrist

Fourteen

patients

were

treated

with

oral

prednisone

two

patients

received

local

corticosteroid

treatment

one

psoralen

and

ultraviolet

A

photo

therapy

and

one

acitretin

Three

patients

were

lost

to

follow

up

two

patients

refused

biopsies

after

remission

but

their

relapse

data

could

be

recorded

From

the

remaining

patients

biopsies

could

be

collected

after

remission

The

mean

treatment

duration

until

remission

was

days

-LRB-

in

the

prednisone

treated

subgroup

days

in

the

subgroup

who

received

other

treatment

modalities

days

-RRB-

In

out

of

biopsies

a

minimal

remnant

inflammatory

infiltrate

around

the

basal

layer

was

still

present

in

spite

of

clinical

remission

Table

characteristics

and

data

before

treatment

and

after

remissionPatientDisease

duration

-LRB-

months

-RRB-

Treatment

modalityTreatment

duration

-LRB-

days

-RRB-

Biopsy

siteRelapse

interval

-LRB-

months

-RRB-

Before

treatmentAfter

positive

epidermal

positive

dermal

cells

positive

double

positive

positive

epidermal

positive

dermal

positive

double

positive

NegativeNormalThe

relapse

interval

was

counted

from

discontinuation

of

treatment

until

the

first

relapse

immunohistochemical

positive

dermal

and

epidermal

cells

and

positive

cells

were

counted

per

Some

biopsies

after

remission

showed

minimal

basal

layer

inflammatory

activity

-LRB-

inflam

-RRB-

not

available

During

follow

up

-LRB-

with

a

minimum

period

of

months

-RRB-

out

of

patients

experienced

a

relapse

of

lichen

planus

symptoms

patients

within

year

within

years

All

relapses

occurred

in

patients

treated

with

oral

prednisone

In

patients

with

relapses

remnant

inflammation

after

remission

had

been

noticed

In

-LRB-

-RRB-

patients

lichen

planus

affected

skin

contained

specific

DNA

before

treatment

compared

to

-LRB-

-RRB-

patients

after

remission

-LRB-

P

McNemar

test

-RRB-

In

one

patient

-LRB-

no.

-RRB-

DNA

was

detected

after

remission

whereas

before

treatment

no

DNA

was

found

Immunohistochemical

single

staining

for

the

presence

of

tegument

protein

revealed

that

before

treatment

the

mean

number

of

positive

cells

was

per

in

the

dermis

and

per

mm

in

the

epidermis

-LRB-

Fig.

-RRB-

After

remission

the

number

of

positive

cells

had

dropped

to

and

respectively

-LRB-

P

with

the

paired

samples

t

test

-RRB-

Fig.

cell

count

-LRB-

in

mm

for

the

epidermis

and

for

the

dermis

-RRB-

of

tegument

positive

cells

with

immunohistochemical

staining

in

lichen

planus

affected

epidermis

and

dermis

before

treatment

-LRB-

white

bars

-RRB-

and

after

remission

-LRB-

black

bars

-RRB-

and

P

with

the

Wilcoxon

rank

sum

test

Immunohistochemical

double

staining

was

performed

on

skin

specimens

of

four

patients

to

investigate

whether

protein

expression

may

be

associated

with

T

cells

or

plasmacytoid

dendritic

cells

which

both

represent

major

constituents

of

the

inflammatory

infiltrate

We

found

a

considerable

number

of

double

positive

cells

in

lesional

lichen

planus

skin

before

treatment

but

not

after

treatment

-LRB-

Fig.

-RRB-

The

number

of

single

stained

positive

cells

decreased

approximately

twofold

before

treatment

compared

to

after

remission

-LRB-

Table

-RRB-

With

double

staining

we

predominantly

observed

single

stained

or

cells

whereas

only

an

occasional

double

positive

cell

could

be

found

-LRB-

Fig.

-RRB-

Fig.

positive

stained

plasmacytoid

dendritic

cells

reflects

intracellular

protein

positive

plasmacytoid

dendritic

cells

-LRB-

blue

stain

-RRB-

containing

protein

-LRB-

red

stain

-RRB-

in

lesional

LP

skin

before

-LRB-

a

-RRB-

and

after

-LRB-

b

-RRB-

treatment

-LRB-

overview

and

inlay

magnification

-RRB-

Fig.

replication

does

not

coincide

with

lymphocytes

positive

cells

-LRB-

red

stain

-RRB-

and

positive

lymphocytes

-LRB-

blue

stain

-RRB-

cells

in

lesional

lichen

planus

skin

are

in

majority

mutually

exclusive

-LRB-

magnification

-RRB-

Discussion

Lichen

planus

is

characterized

by

a

band-like

lymphocytic

infiltrate

which

seems

to

be

involved

in

an

attack

of

the

basal

epidermal

layer

It

is

suggested

that

these

T

lymphocytes

are

directed

towards

infected

skin

cells

expressing

viral

antigens

Molecular

mimicry

is

a

second

conceivable

inflammatory

mechanism

initiated

by

microbial

antigens

or

microbial-reactive

T

lymphocytes

that

cross

react

with

self

antigens

sharing

homology

-LRB-

i.e.

basal

layer

structures

-RRB-

In

our

previous

study

we

localized

antigen

containing

cells

in

lesional

lichen

planus

tissue

around

de

dermo-epidermal

junction

coinciding

with

the

location

of

the

inflammatory

infiltrate

-LSB-

-RSB-

In

addition

we

detected

high

numbers

of

plasmacytoid

dendritic

cells

-LRB-

cells

that

are

associated

with

the

clearance

of

virally

induced

diseases

-RRB-

within

the

infiltrate

The

presence

of

DNA

and

antigen

did

not

coincide

with

non-lesional

lichen

planus

skin

psoriatic

skin

and

normal

skin

from

healthy

donors

Since

was

not

found

in

psoriatic

skin

-LRB-

which

is

also

characterized

by

a

lymphocytic

infiltrate

-RRB-

it

is

unlikely

that

in

lichen

planus

is

a

reflection

of

an

innocent

bystander

in

a

dense

influx

of

lymphocytes

Moreover

in

the

current

study

we

could

localize

protein

mainly

in

positive

plasmacytoid

dendritic

cells

and

sporadic

in

positive

lymphocytes

This

is

remarkable

since

has

been

characterized

as

a

T-lymphotropic

virus

-LSB-

-RSB-

Our

results

suggest

that

plasmacytoid

dendritic

cells

can

also

host

This

is

conceivable

since

plasmacytoid

dendritic

cells

express

-LSB-

-RSB-

which

is

the

main

receptor

used

by

to

enter

target

cells

-LSB-

-RSB-

Here

we

investigated

the

effect

of

therapy-induced

remission

of

lichen

planus

on

replication

Both

the

number

of

DNA

containing

skin

samples

and

the

absolute

number

of

antigen

containing

skin

cells

-LRB-

in

dermis

and

epidermis

-RRB-

diminished

significantly

after

treatment-induced

remission

Since

we

included

a

washout

period

between

treatment

termination

and

obtaining

the

post

remission

biopsies

a

direct

medication

effect

on

viral

replication

is

unlikely

In

contrast

to

a

fourfold

diminution

in

positive

cells

after

treatment

there

was

only

a

twofold

reduction

in

the

number

of

positive

plasmacytoid

dendritic

cells

This

makes

it

unlikely

that

the

diminished

expression

only

depends

on

a

reduced

number

of

plasmacytoid

dendritic

cells

after

treatment

Whether

plasmacytoid

dendritic

cells

are

carriers

of

driving

the

disease

activity

or

that

these

cells

are

infected

as

innocent

bystanders

or

actively

induce

the

inflammatory

process

is

not

yet

clear

and

needs

further

study

a

member

of

the

beta

herpes

virus

subfamily

was

first

discovered

by

Frenkel

et

al.

-LSB-

-RSB-

in

positive

T

lymphocytes

of

healthy

individuals

It

is

an

ubiquitous

virus

with

a

worldwide

prevalence

exceeding

Most

of

the

primo

infections

occur

during

infancy

-LSB-

-RSB-

Since

the

discovery

of

as

the

causative

agent

for

Kaposi

sarcoma

-LSB-

-RSB-

all

three

human

herpes

viruses

-LRB-

and

-RRB-

discovered

in

the

last

few

decades

have

been

subjected

to

studies

on

their

role

in

skin

diseases

of

unknown

origin

like

pitryasis

rosea

-LSB-

-RSB-

and

exanthema

subitum

-LSB-

-RSB-

A

shared

characteristic

of

all

herpes

viruses

is

their

unique

ability

to

persist

in

the

host

after

primary

infection

and

become

reactivated

later

in

life

-LRB-

sometimes

after

many

years

of

latency

-RRB-

Symptomatic

reactivation

of

herpes

viruses

is

a

well-known

phenomenon

in

the

daily

dermatological

practice

For

example

shingles

afflicting

patients

later

in

life

after

acquisition

of

the

causative

varicella

zoster

virus

during

childhood

and

the

recurrence

of

labial

and

genital

herpes

simplex

virus

lesions

after

reactivation

of

viral

DNA

Human

herpes

virus

reactivation

is

believed

to

cause

the

drug

related

exanthema

and

systemic

side

effect

syndrome

-LRB-

DRESS

-RRB-

-LSB-

-RSB-

It

is

unlikely

that

primary

infections

cause

lichen

planus

since

first

transmission

mostly

occurs

during

childhood

whereas

lichen

planus

affects

mainly

patients

during

midlife

Yet

it

is

conceivable

that

reactivation

triggers

lichen

planus

in

the

same

fashion

as

Epstein-Barr

virus

reactivation

is

associated

with

Burkitt

lymphoma

The

apparent

paradoxical

efficacy

of

steroid

therapy

in

lichen

planus

and

a

considered

viral

cause

can

be

explained

by

a

hit

and

run

model

where

the

actual

viral

reactivation

would

be

short

lived

but

subsequently

responsible

for

an

independently

propagated

inflammatory

skin

reaction

This

could

also

explain

why

not

in

all

patients

was

detected

at

the

time

of

inclusion

Moreover

in

one

patient

-LRB-

no.

-RRB-

DNA

was

detected

after

remission

It

is

this

patient

that

experienced

a

relapse

month

later

and

returned

to

the

clinic

for

additional

treatment

Possibly

can

trigger

lichen

planus

episodes

including

relapses

but

resolve

before

clinical

lichen

planus

symptoms

appear

The

other

patient

-LRB-

no.

-RRB-

with

a

relapse

within

month

unfortunately

refused

us

a

post

remission

skin

sample

On

the

other

hand

the

absence

of

replication

in

some

of

our

patients

could

also

be

explained

assuming

a

multi

causal

pathogenesis

for

lichen

planus

Further

evidence

for

the

causal

association

of

and

lichen

planus

could

come

from

clinical

studies

on

the

efficacy

of

anti-herpetic

medication

Which

drug

would

be

the

best

option

is

not

yet

clear

Guanoside

analogons

with

little

side

effects

like

acyclovir

show

little

activity

against

-LSB-

-RSB-

is

more

susceptible

to

cidofovir

and

foscarnet

but

these

drugs

are

known

for

serious

side

effects

-LSB-

-RSB-

Fredericks

and

Relman

proposed

a

reconsideration

of

Koch

's

postulates

for

the

identification

of

microbial

antigens

as

causative

agents

in

diseases

-LSB-

-RSB-

With

data

presented

here

and

in

our

previous

study

-LSB-

-RSB-

we

were

able

to

meet

with

three

out

of

their

seven

postulates

for

the

establishment

of

a

causal

relationship

between

and

lichen

planus

-LRB-

-RRB-

Microbial

nucleic

acid

sequences

were

present

in

most

cases

in

diseased

sites

and

not

in

sites

that

lack

pathology

-LRB-

-RRB-

Fewer

nucleic

acid

sequences

were

found

in

hosts

without

the

disease

-LRB-

-RRB-

Nucleic

acid

sequences

correlates

were

present

at

a

cellular

level

The

fourth

postulate

a

decrease

of

the

number

of

nucleic

acid

sequences

during

resolution

of

the

disease

and

increase

with

relapse

was

met

in

this

study

as

far

as

disease

resolution

is

concerned

Unfortunately

we

did

not

collect

lesional

biopsies

in

those

patients

that

suffered

from

relapses

reactivation

during

relapses

will

have

to

be

investigated

in

future

studies

-LRB-

-RRB-

The

number

of

nucleic

acid

sequences

should

correlate

with

disease

severity

and

-LRB-

-RRB-

reproducibility

of

the

evidence

will

have

to

be

met

in

future

longitudinal

studies

The

seventh

postulate

clinical

features

and

pathology

should

be

consistent

with

known

biological

characteristics

of

the

microbe

will

also

have

to

be

addressed

in

future

studies

since

still

little

is

known

about

the

effects

of

in

vivo

yet

The

hypothesis

of

as

the

causative

agent

for

lichen

planus

deserves

further

research

in

larger

studies

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

human herpes virus 7
lichen planus
plasmacytoid dendritic cells


Power

Calculations

Using

Exact

Data

Simulation

A

Useful

Tool

for

Genetic

Study

Designs

Statistical

power

calculations

constitute

an

essential

first

step

in

the

planning

of

scientific

studies

If

sufficient

summary

statistics

are

available

power

calculations

are

in

principle

straightforward

and

computationally

light

In

designs

which

comprise

distinct

groups

-LRB-

e.g.

MZ

DZ

twins

-RRB-

sufficient

statistics

can

be

calculated

within

each

group

and

analyzed

in

a

multi-group

model

However

when

the

number

of

possible

groups

is

prohibitively

large

-LRB-

say

in

the

hundreds

-RRB-

power

calculations

on

the

basis

of

the

summary

statistics

become

impractical

In

that

case

researchers

may

resort

to

Monte

Carlo

based

power

studies

which

involve

the

simulation

of

hundreds

or

thousands

of

replicate

samples

for

each

specified

set

of

population

parameters

Here

we

present

exact

data

simulation

as

a

third

method

of

power

calculation

Exact

data

simulation

involves

a

transformation

of

raw

data

so

that

the

data

fit

the

hypothesized

model

exactly

As

in

power

calculation

with

summary

statistics

exact

data

simulation

is

computationally

light

while

the

number

of

groups

in

the

analysis

has

little

bearing

on

the

practicality

of

the

method

The

method

is

applied

to

three

genetic

designs

for

illustrative

purposes

Introduction

The

importance

of

statistical

power

in

-LRB-

behavior

-RRB-

genetic

analyses

is

evident

in

the

number

of

articles

devoted

to

power

calculations

Power

has

been

studied

in

virtually

all

research

designs

ranging

from

the

classical

twin

design

-LRB-

Martin

et

al.

Neale

et

al.

-RRB-

to

extended

family

designs

-LRB-

e.g.

Heath

et

al.

Heath

and

Eaves

Posthuma

and

Boomsma

-RRB-

to

sibpair

and

family

linkage

and

association

designs

either

in

or

excluding

gene

by

environment

interaction

-LRB-

Abecasis

et

al.

b

Boomsma

and

Dolan

Dolan

et

al.

Fulker

and

Cherny

Purcell

Purcell

and

Sham

Sham

et

al.

Sham

and

Hewitt

Sham

et

al.

Van

den

Oord

-RRB-

For

a

wide

range

of

genetic

designs

the

Genetic

Power

-LRB-

Purcell

et

al.

-RRB-

can

be

used

to

calculate

power

However

for

customized

designs

and

specific

research

questions

researchers

may

have

to

resort

to

their

own

procedure

to

carry

out

power

calculations

Power

calculation

based

on

the

likelihood

with

the

general

Pearson

Nyman

statistical

decision

theory

takes

two

forms

First

the

non-centrality

parameter

λ

of

the

non-null

can

be

calculated

in

the

analysis

of

exact

sufficient

statistics

-LRB-

e.g.

Dolan

et

al.

-RRB-

If

the

distribution

of

the

data

is

multivariate

normal

the

expected

variance

covariance

matrix

Σ

and

the

means

vector

μ

are

sufficient

statistics

as

they

define

the

likelihood

of

the

data

up

to

an

arbitrary

constant

-LRB-

Azzelini

-RRB-

Second

when

Σ

and

μ

are

not

sufficient

statistics

the

non-centrality

parameter

λ

of

the

non-null

can

be

estimated

on

the

basis

of

the

analysis

of

simulated

data

using

Monte

Carlo

simulation

methods

-LRB-

e.g.

Fulker

and

Cherny

Abecasis

et

al.

b

Purcell

van

den

Oord

-RRB-

The

latter

is

computationally

intensive

but

does

not

require

the

presence

of

sufficient

summary

statistics

whereas

the

former

is

computationally

light

but

does

require

sufficient

summary

statistics

The

aim

of

the

present

note

is

to

discuss

a

third

method

of

power

calculation

which

we

refer

to

as

exact

data

simulation

This

method

is

suitable

when

data

are

multivariate

normal

and

sufficient

summary

statistics

are

in

principle

available

but

the

number

of

possible

groups

is

prohibitively

large

-LRB-

say

in

the

hundreds

-RRB-

The

large

number

of

distinct

groups

renders

power

calculations

on

the

basis

of

the

summary

statistics

impractical

Usually

researchers

resort

to

Monte

Carlo

based

power

studies

under

such

circumstances

However

exact

data

simulation

in

combination

with

the

definition

variable

facilities

in

packages

like

Mplus

-LRB-

fourth

edition

Muthén

and

Muthén

-RRB-

or

the

freely

available

Mx

-LRB-

Neale

et

al.

-RRB-

is

also

applicable

and

is

more

efficient

than

raw

data

simulation

Exact

data

simulation

was

used

by

Dolan

et

al.

-LRB-

-RRB-

to

evaluate

the

effects

of

missing

data

on

the

power

in

structural

equation

modeling

and

by

Van

der

Sluis

et

al.

-LRB-

Under

revision

-RRB-

to

evaluate

the

power

to

detect

gene

by

environment

interaction

in

sib-pair

association

studies

Although

the

technique

of

exact

simulation

is

in

itself

not

new

-LRB-

Bollen

and

Stine

provided

the

basics

in

and

the

technique

of

exact

data

simulation

has

recently

been

integrated

as

a

distinct

function

in

the

freely

available

-RRB-

we

wish

to

bring

it

to

the

attention

of

geneticists

since

this

method

of

calculating

power

has

general

value

in

the

field

of

genetic

modeling

Below

we

shortly

recapitulate

the

basics

of

power

analysis

and

then

outline

the

procedure

of

exact

simulation

which

may

be

implemented

readily

-LRB-

we

use

the

freely

available

R

program

-RRB-

The

method

is

illustrated

in

three

genetic

designs

Although

we

confine

ourselves

in

this

paper

to

illustrations

in

the

context

of

genetic

designs

we

stress

that

this

form

of

simulation

can

be

used

for

power

calculations

in

a

wide

range

of

other

designs

such

as

random

effects

models

growth

curve

and

simplex

models

and

structural

models

Power

calculation

The

concept

of

power

is

closely

related

to

the

two

types

of

statistical

errors

the

Type

I

error

-LRB-

i.e.

the

probability

of

rejecting

a

true

hypothesis

α

-RRB-

and

the

Type

II

error

-LRB-

i.e.

the

probability

of

accepting

a

false

hypothesis

β

-RRB-

Power

is

defined

as

β

i.e.

the

probability

of

rejecting

a

false

hypothesis

or

the

probability

of

not

making

a

Type

II

error

The

basic

aim

of

a

power

study

is

to

determine

the

sample

size

N

which

is

required

to

achieve

adequate

power

given

chosen

α

and

a

particular

effect

size

For

example

suppose

that

we

want

to

fit

a

classical

univariate

ACE

twin-model

-LRB-

see

Fig.

-RRB-

and

we

expect

that

additive

genetic

effects

-LRB-

a

-RRB-

account

for

of

the

phenotypic

variance

besides

effects

of

shared

-LRB-

c

-RRB-

and

unique

-LRB-

e

-RRB-

environment

We

denote

this

model

or

hypothesis

Under

model

four

parameters

are

estimated

the

path

coefficient

for

the

additive

genetic

effects

A

-LRB-

a

-RRB-

the

path

coefficient

for

the

shared

environment

C

-LRB-

c

-RRB-

the

path

coefficient

for

the

unique

environment

E

-LRB-

e

which

includes

measurement

error

-RRB-

and

the

means

of

the

twins

-LRB-

μ

-RRB-

which

are

usually

set

to

be

equal

within

twin

pairs

and

across

MZ

and

DZ

twins

The

parameter

vector

θ

for

this

model

with

degrees

of

freedom

is

θ1

-LCB-

a

c

e

μ

-RCB-

from

which

the

covariance

matrices

and

and

mean

vector

μ1

can

be

derived

Now

consider

a

second

model

which

we

denote

model

or

in

which

the

additive

genetic

effects

are

assumed

to

account

for

only

of

the

phenotypic

variance

This

alternative

model

will

be

characterized

by

parameter

vector

θ0

-LCB-

c

e

μ

-RCB-

Note

that

in

model

parameter

a

is

not

estimated

-LRB-

and

thus

not

part

of

θ

-RRB-

but

fixed

at

a

value

that

corresponds

exactly

to

of

the

phenotypic

variation

being

explained

by

additive

genetic

effects

This

model

has

degrees

of

freedom

covariance

matrices

and

mean

vector

μ0

This

alternative

model

is

nested

in

the

null-model

because

the

parameters

in

θ0

represent

a

subset

of

the

parameters

in

θ1

-LRB-

e.g.

Bollen

Satorra

and

Saris

-RRB-

The

study

of

power

is

subsequently

concerned

with

the

probability

of

rejecting

the

false

model

in

favor

of

the

true

model

given

α

the

true

value

of

parameter

a

-LRB-

the

effect

size

-RRB-

and

sample

size

N.

Fig.

univariate

ACE-twin

model

To

calculate

power

we

adopt

the

method

of

Satorra

and

Saris

-LRB-

see

also

Saris

and

Satorra

-RRB-

which

is

based

on

the

normal

theory

log-likelihood

ratio

test

statistic

T

In

a

single

group

T

is

calculated

as

follows

where

N

is

the

sample

size

p

denotes

the

number

of

variables

in

the

analysis

and

Σ

and

μ

and

S

and

m

represent

the

theoretical

and

observed

variance

covariance

matrix

and

the

means

vector

respectively

Given

that

the

assumptions

of

normal

theory

maximum

likelihood

are

met

-LRB-

e.g.

multivariate

normality

and

a

large

sample

of

independently

and

identically

distributed

cases

-RRB-

and

under

the

assumption

that

Σ

and

μ

represent

the

true

model

-LRB-

Σ1

and

μ1

-RRB-

the

test

statistic

T

follows

a

χ2

distribution

with

degrees

of

freedom

i.e.

T

χ2

-LRB-

-RRB-

-LRB-

Azzeline

Bollen

-RRB-

If

Σ

and

μ

do

not

represent

the

true

model

but

the

alternative

model

-LRB-

Σ0

and

μ0

-RRB-

and

given

regularity

conditions

are

satisfied

-LRB-

practically

amounting

to

multivariate

normality

limited

misfit

and

large

sample

size

N

-RRB-

the

test

statistic

T

follows

a

non-central

χ2

distribution

with

degrees

of

freedom

and

non-centrality

parameter

λ

i.e.

T

χ2

-LRB-

λ

-RRB-

where

λ

Given

the

significance

level

of

the

test

α

and

the

difference

in

degrees

of

freedom

between

the

true

model

and

the

alternative

model

the

criterion

level

cα

can

be

obtained

from

a

χ2

table

If

the

test

statistic

T

exceeds

this

criterion

level

i.e.

T

cα

then

the

alternative

model

is

rejected

in

favor

of

the

true

model

-LRB-

i.e.

the

fit

of

the

alternative

model

to

the

data

is

significantly

worse

than

the

fit

of

the

true

model

-RRB-

The

aim

of

power

studies

is

to

determine

the

probability

of

observing

T

cα

i.e.

P

-LRB-

χ2

-LRB-

λ

-RRB-

cα

-RRB-

given

Σ0

μ0

Σ1

μ1

N

and

α

i.e.

the

probability

of

rejecting

the

alternative

model

in

favor

of

the

true

model

The

non-centrality

parameter

λ

can

be

obtained

by

fitting

the

alternative

model

to

the

true

Σ1

and

μ1

whereby

λ

equals

the

difference

in

the

χ2

fit

statistic

of

the

model

and

the

χ2

fit

statistic

of

the

alternative

model

That

is

-LRB-

again

in

a

single

group

-RRB-

and

the

non-null

distribution

of

this

test

statistic

is

χ2

-LRB-

λ

-RRB-

A

variety

of

programs

can

subsequently

be

used

to

integrate

the

non-null

distribution

to

obtain

the

power

-LRB-

e.g.

R

Mx

see

also

Hewitt

and

Heath

-RRB-

Note

that

some

packages

such

as

the

Mx

program

also

compute

the

total

sample

size

that

would

be

required

-LRB-

given

the

reported

proportion

of

subjects

in

each

group

-RRB-

to

reject

the

hypothesis

at

various

power

levels

As

stated

in

the

introduction

power

calculations

usually

take

on

one

of

two

forms

First

one

may

be

in

the

position

that

all

information

present

in

the

raw

data

can

be

summarized

in

the

covariance

matrix

Σ

and

the

means

vector

μ

in

which

case

Σ

and

μ

are

sufficient

statistics

because

they

define

the

likelihood

of

the

data

up

to

an

arbitrary

constant

-LRB-

Azzelini

-RRB-

In

that

case

one

can

derive

the

expected

population

statistics

Σ

and

μ

for

every

group

in

the

study

design

under

and

and

base

the

power

calculations

on

these

summary

statistics

The

second

method

of

power

calculation

is

applied

when

sufficient

summary

statistics

are

not

available

For

example

the

population

statistics

Σ

and

μ

do

not

summarize

all

information

present

in

the

raw

data

when

the

continuous

data

are

a

mixture

-LRB-

i.e.

a

convex

combination

of

different

distributions

McLachlan

and

Peel

-RRB-

or

when

data

are

missing

at

random

-LRB-

MAR

Shafer

and

Graham

-RRB-

In

family

studies

gene

by

environment

interaction

may

render

the

summary

statistics

insufficient

For

instance

Purcell

-LRB-

-RRB-

showed

how

environmental

moderation

on

the

means

and

variances

can

be

modeled

-LRB-

see

Fig.

-RRB-

For

both

MZ

and

DZ

twins

the

variance

of

twin

i

is

calculated

as

while

the

for

MZ

twins

covariance

between

twin

i

and

twin

j

is

calculated

as

and

for

DZ

twins

as

The

expected

values

of

means

for

all

twins

are

calculated

as

Fig.

ACE-twin

model

including

moderation

on

the

variances

and

the

means

If

the

environmental

moderator

is

categorical

or

ordinal

-LRB-

e.g.

gender

or

affection

status

-RRB-

the

sufficient

statistics

-LRB-

Σ

and

μ

-RRB-

are

available

assuming

that

the

data

are

normally

distributed

conditional

on

the

levels

of

the

moderator

In

that

instance

the

twins

in

a

pair

may

be

concordant

with

respect

to

the

moderator

-LRB-

i.e.

both

twins

score

or

both

twins

score

-RRB-

or

the

twins

may

be

discordant

with

respect

to

the

moderator

-LRB-

i.e.

scoring

and

respectively

-RRB-

For

both

MZ

and

DZ

twins

Σ

and

μ

can

be

formulated

for

all

possible

combinations

such

that

all

information

present

in

the

raw

data

is

summarized

with

different

variance

covariance

matrixes

Σ

-LRB-

for

the

MZ

twins

and

for

the

DZ

twins

-RRB-

and

different

means

vectors

μ

-LRB-

assuming

no

relation

between

zygosity

and

mean

-RRB-

as

such

distinguishing

different

groups

By

comparing

the

fit

of

the

model

including

moderator

effects

on

both

the

means

and

the

variances

to

a

model

in

which

the

moderator

only

affects

the

means

-LRB-

say

-RRB-

one

can

obtain

an

estimate

of

non-centrality

parameter

λ

from

which

the

power

to

detect

the

effect

of

the

moderator

can

be

derived

However

if

the

moderator

is

continuously

distributed

sufficient

statistics

can

not

be

calculated

In

the

absence

of

sufficient

statistics

power

calculation

may

be

conducted

by

means

of

Monte

Carlo

simulation

This

design

implies

determination

of

the

values

of

the

parameters

of

interest

-LRB-

e.g.

based

on

previous

studies

or

corresponding

to

realistic

effect

sizes

-RRB-

and

subsequent

-LRB-

quasi

-RRB-

random

data

generation

according

to

the

true

model

with

realistic

sample

size

N.

By

fitting

the

false

model

to

the

data

simulated

according

to

the

true

model

an

indication

of

the

power

is

obtained

However

in

contrast

to

the

situation

in

which

sufficient

summary

statistics

are

available

parameter

values

are

not

recovered

exactly

when

the

model

is

fitted

as

the

random

data

are

the

outcome

of

a

stochastic

sample

process

Therefore

the

difference

in

the

χ2

statistic

of

the

model

and

the

model

can

not

be

taken

as

an

exact

estimate

of

the

non-centrality

parameter

λ

To

solve

this

a

large

number

of

datasets

are

usually

generated

and

λ

is

estimated

as

the

mean

of

the

difference

in

χ2

obtained

in

these

data

sets

minus

the

number

of

degrees

of

freedom

-LRB-

-RRB-

Since

power

studies

often

concern

multiple

parameters

with

multiple

values

such

Monte

Carlo

simulation

studies

can

be

prohibitively

intensive

As

an

alternative

simulated

sample

sizes

may

be

chosen

very

large

to

induce

asymptotic

behavior

of

the

χ2

statistic

However

how

large

a

sample

size

should

be

chosen

depends

on

the

study

design

in

question

and

very

large

sample

sizes

also

render

the

analyses

computationally

intensive

Exact

data

simulation

Power

calculations

based

on

sufficient

summary

statistics

are

computationally

relatively

efficient

to

carry

out

However

the

actual

feasibility

of

this

type

of

power

calculation

depends

on

the

number

of

distinct

groups

If

the

number

of

groups

is

large

-LRB-

i.e.

-RRB-

it

may

be

more

convenient

to

carry

out

Monte

Carlo

based

power

calculations

We

now

introduce

the

concept

of

exact

data

simulation

which

shares

the

virtues

of

the

power

studies

based

on

summary

statistics

but

is

more

practicable

given

a

large

number

of

distinct

groups

The

idea

of

exact

data

simulation

is

that

data

which

are

randomly

generated

to

begin

with

can

subsequently

be

transformed

to

fit

the

null-model

exactly

That

is

first

a

data

file

is

generated

using

a

normal

distribution

quasi-random

number

generator

These

data

are

then

transformed

using

a

transformation

proposed

by

Bollen

and

Stine

-LRB-

-RRB-

so

that

the

variance

covariance

matrix

and

means

are

exactly

as

specified

under

the

model

Assume

a

total

sample

size

of

N

and

k

distinct

groups

with

known

probability

pk

Let

Y

denote

the

Nk

q

data

matrix

for

group

k

where

Nk

is

N

pk

-LRB-

possibly

rounded

to

the

nearest

integer

-RRB-

and

q

is

the

number

of

variables

Let

m

denote

the

q

vector

of

observed

means

and

S

YtY

-LRB-

N

-RRB-

mmt

be

the

observed

covariance

matrix

Σ

the

expected

covariance

matrix

implied

by

model

and

μ

the

expected

means

vector

implied

by

the

model

Let

and

then

denote

the

square

root

factorization

of

the

positive

definite

matrices

S

and

Σ

such

as

given

by

a

Cholesky

factorization

It

can

then

be

shown

that

the

covariance

matrix

and

mean

vector

of

data

matrix

Z

which

is

obtained

through

the

following

transformation

of

Yequals

Σ

and

μ

exactly

-LRB-

Bollen

and

Stine

-RRB-

In

Eq

J

is

a

unit

vector

of

length

q

and

denotes

the

Kronecker

product

This

transformation

allows

one

to

create

raw

data

for

numerous

groups

that

fit

the

null-model

exactly

Consequently

when

the

null-model

used

for

the

generation

of

the

data

is

fitted

to

these

transformed

data

all

parameter

values

used

for

the

simulation

are

recovered

exactly

Let

Log

and

Log

LA

denote

the

maximum

values

of

log-likelihood

functions

The

difference

LA

equals

the

non-centrality

parameter

λ

Compared

to

multi-group

power

calculation

with

summary

statistics

which

becomes

unpractical

when

the

number

of

groups

is

large

the

practicality

of

exact

data

simulation

is

unaffected

by

the

number

of

groups

in

the

analysis

However

one

issue

does

require

attention

When

the

number

of

groups

is

large

-LRB-

e.g.

see

Illustration

below

-RRB-

the

probability

pk

that

a

subject

belongs

to

a

group

k

may

be

relatively

small

In

order

to

calculate

the

Cholesky

decomposition

of

the

observed

variance

covariance

matrix

S

the

number

of

observations

in

a

group

Nk

should

equal

at

least

q

-LRB-

i.e.

to

ensure

that

S

is

positive

definite

and

the

Cholesky

decomposition

is

possible

-RRB-

There

are

two

ways

to

handle

this

problem

First

one

can

choose

N

to

be

sufficiently

large

that

all

groups

even

those

with

small

probabilities

by

choosing

a

very

large

overall

sample

size

N

for

the

simulation

Power

analyses

based

on

this

very

large

sample

size

produce

non-centrality

parameters

which

can

subsequently

be

used

to

calculate

power

for

other

more

realistic

sample

sizes

Second

one

can

choose

a

smaller

overall

sample

size

and

accept

that

not

all

possible

groups

will

be

represented

in

the

power

calculations

This

choice

is

usually

justified

since

very

small

groups

-LRB-

e.g.

including

subjects

out

of

a

possible

-RRB-

do

not

contribute

much

to

the

power

However

power

calculations

are

more

precise

when

all

groups

are

represented

in

the

simulation

i.e.

overall

N

is

large

Furthermore

it

is

in

principle

possible

that

the

presence

of

all

groups

is

required

for

model

identification

Note

that

packages

like

Mx

and

R

will

estimate

the

number

of

data

vectors

required

for

a

power

of

e.g.

given

the

proportion

of

subjects

in

each

group

So

while

Nk

q

is

required

for

exact

simulation

Mx

will

return

an

overall

sample

size

N

in

which

many

groups

may

represented

by

fewer

than

q

observations

which

is

in

line

with

what

one

would

expect

to

observe

in

research

practice

Using

the

exact

data

simulation

script

subsequently

to

simulate

data

with

the

sample

size

advertised

by

Mx

would

not

result

in

a

power

of

since

the

groups

with

Nk

q

observations

are

not

represented

in

the

simulated

data

and

thus

do

not

contribute

to

the

power

Having

discussed

the

concept

of

power

and

the

exact

data

simulation

procedure

we

will

now

illustrate

the

virtues

of

exact

data

simulation

with

three

behavior

genetics

examples

We

chose

Mx

to

analyze

the

simulated

data

because

of

the

program

's

inbuilt

option

to

calculate

the

sample

size

required

for

different

power

levels

given

the

non-centrality

parameter

However

the

non-centrality

parameter

can

also

be

obtained

through

other

software

-LRB-

e.g.

LISREL

Mplus

-RRB-

The

calculation

of

sample

sizes

required

for

different

power

levels

can

then

be

done

using

other

programs

like

R

The

R-scripts

used

to

simulate

the

data

and

the

Mx

scripts

used

to

analyze

the

data

are

available

in

the

Mx

scripts

library

A

small

R-script

for

power

computations

based

on

non-centrality

parameters

can

be

downloaded

from

the

library

as

well

Illustration

multivariate

ACE-model

with

data

MCAR

Let

us

consider

a

four-variate

ACE-model

with

data

obtained

from

MZ

and

DZ

twins

-LRB-

no

additional

family

members

-RRB-

We

assume

a

model

with

one

common

genetic

factor

one

common

shared

environmental

factor

and

specifics

for

A

C

and

E

for

all

four

traits

The

model

is

illustrated

in

Fig.

Parameter

values

are

chosen

such

that

additive

genetic

influences

shared

environmental

influences

and

non-shared

environmental

influences

explain

and

of

the

total

variance

respectively

Of

the

additive

genetic

variance

is

attributable

to

the

common

genetic

factor

-LRB-

i.e.

of

the

total

variance

-RRB-

and

to

the

specifics

of

A

-LRB-

i.e.

of

the

total

variance

-RRB-

Of

the

shared

environmental

variance

is

attributable

to

the

common

shared

environmental

factor

-LRB-

i.e.

of

the

total

variance

-RRB-

and

to

the

specifics

of

C

-LRB-

i.e.

of

the

total

variance

-RRB-

Table

contains

the

correlation

matrices

for

the

MZ

and

DZ

twins

in

the

case

that

data

are

not

missing

Means

for

all

traits

are

equal

to

zero

We

consider

the

power

to

reject

the

alternative

hypothesis

that

the

genetic

specifics

for

all

four

traits

explain

not

but

only

of

the

total

variance

i.e.

one

common

genetic

factor

is

-LRB-

almost

-RRB-

sufficient

to

explain

all

genetic

variance

and

covariance

in

the

four

traits

If

there

are

no

missing

data

-LRB-

situation

-RRB-

then

one

could

simply

use

summary

statistics

to

obtain

power

information

as

this

is

a

analysis

However

suppose

we

want

to

study

the

influence

of

data

missing

completely

at

random

-LRB-

MCAR

-RRB-

on

the

power

to

reject

the

hypothesis

that

all

genetic

specifics

are

zero

Here

we

consider

two

scenarios

First

we

study

the

case

that

the

probability

of

data

being

MCAR

is

for

all

variables

-LRB-

situation

-RRB-

Given

that

we

have

q

observations

per

family

this

kind

of

missingness

could

yield

possible

data

patterns

i.e.

different

groups

-LRB-

we

discard

the

group

in

which

all

data

are

missing

-RRB-

In

that

case

power

calculations

using

summary

statistics

are

impractical

whereas

exact

data

simulation

is

feasible

Note

that

some

data

patterns

are

rather

unlikely

e.g.

the

probability

of

observing

a

valid

observation

for

the

first

trait

of

the

first

twin

only

while

all

other

observations

in

the

family

are

missing

is

-LRB-

-RRB-

Remember

that

the

Cholesky

decomposition

can

not

be

calculated

if

the

number

of

observations

in

a

group

Nk

does

not

equal

at

least

q

so

the

simulated

N

needs

to

be

very

large

if

one

wants

all

data

patterns

to

be

present

in

the

simulated

data

set

-LRB-

about

-LRB-

q

-RRB-

-RRB-

Yet

as

very

rare

observations

will

hardly

contribute

to

the

power

-LRB-

of

the

cases

in

the

present

example

-RRB-

one

can

just

as

well

adopt

a

smaller

sample

size

and

accept

the

fact

that

some

groups

-LRB-

i.e.

patterns

of

observations

-RRB-

will

not

be

represented

and

calculate

power

given

the

most

likely

patterns

of

observations

Fig.

ACE-model

with

common

factors

for

additive

genetic

and

shared

environmental

effects

and

specifics

for

A

C

and

ETable

Four-variate

cross-trait-cross-twin

MZ

correlations

-LRB-

below

diagonal

-RRB-

and

DZ

correlation

-LRB-

above

diagonal

-RRB-

for

data

without

missingnessTwin

Twin

Note

Sample

size

N

is

not

reported

as

the

simulations

are

exact

this

correlation

matrix

should

result

independent

of

the

sample

size

chosen

for

the

simulations

when

data

are

not

missing

Second

we

study

the

case

where

the

probability

of

data

being

MCAR

is

for

the

first

two

variables

and

zero

for

the

second

two

-LRB-

situation

-RRB-

This

could

be

a

realistic

scenario

in

practice

for

example

when

a

questionnaire

study

that

measures

two

traits

is

extended

during

the

data

collection

to

include

two

additional

traits

or

when

data

from

different

studies

are

combined

-LRB-

one

study

in

which

all

four

traits

were

measured

while

another

study

only

included

measurements

of

two

traits

for

e.g.

economical

reasons

-RRB-

Given

that

we

have

q

observations

per

family

of

which

only

four

variables

show

missingness

this

would

yield

possible

data

patterns

i.e.

different

groups

With

only

groups

power

calculations

using

summary

statistics

would

be

feasible

However

one

efficiently

setup

exact

data

simulation

script

can

handle

both

this

simple

pattern

of

missingness

and

more

complex

For

the

simulations

we

chose

an

overall

sample

size

of

families

-LRB-

MZ

DZ

-RRB-

which

means

that

for

situations

and

all

groups

-LRB-

data

patterns

-RRB-

are

represented

-LRB-

and

cases

simulated

respectively

-RRB-

while

for

situation

only

the

most

likely

groups

of

the

possible

are

represented

-LRB-

cases

simulated

-RRB-

The

three

simulated

data

sets

were

subsequently

analyzed

in

Mx.

In

the

Mx-script

we

specify

different

groups

for

the

MZ

and

DZ

twins

Because

we

use

full

information

maximum

likelihood

to

accommodate

the

missingness

we

do

not

need

to

specify

different

groups

for

all

possible

missing

data

patterns

The

Mx

command

option

power

-LRB-

α

df

-RRB-

was

used

to

obtain

an

estimation

of

the

total

sample

size

that

would

be

required

for

a

power

of

given

the

current

proportions

of

subjects

in

each

group

We

find

that

for

situation

-LRB-

no

missingness

-RRB-

families

are

required

for

power

to

reject

the

alternative

hypothesis

that

the

genetic

specifics

for

all

four

traits

explain

rather

than

of

the

variance

each

while

for

situations

-LRB-

missingness

for

all

variables

-RRB-

and

-LRB-

missingness

for

only

variable

and

-RRB-

the

number

of

families

required

to

obtain

power

is

estimated

at

and

respectively

We

hasten

to

note

that

these

results

are

not

informative

for

the

case

that

data

are

missing

at

random

-LRB-

MAR

-RRB-

rather

than

MCAR

-LRB-

see

Schafer

and

Graham

for

a

comprehensive

review

on

missingness

and

statistical

procedures

for

handling

missing

data

-RRB-

These

power

calculations

took

about

min

for

each

situation

S.

Within

the

Monte

Carlo

framework

acquisition

of

similar

power

results

would

take

at

least

T

times

as

long

for

each

situation

S

-LRB-

where

T

is

the

number

of

replications

one

chooses

to

do

-RRB-

Given

that

the

time

required

to

write

the

data

simulation

script

is

equal

for

Monte

Carlo

simulation

and

exact

simulation

it

is

clear

that

exact

simulation

saves

a

lot

of

time

Illustration

gene

by

environment

interaction

with

latent

G

and

measured

categorical

E

Gene

by

Environment

-LRB-

G

E

-RRB-

interaction

is

an

important

issue

From

the

perspective

of

the

power

study

a

problem

with

the

presence

of

G

E

when

the

E

is

continuously

distributed

is

that

it

renders

single

summary

statistics

insufficient

in

the

presence

of

G

E

-LRB-

co

-RRB-

variances

and

means

depend

on

the

level

of

the

environmental

moderator

as

we

have

seen

in

Eqs

Purcell

-LRB-

-RRB-

showed

how

G

E

on

the

means

and

variances

can

be

modeled

if

G

is

latent

and

E

is

measured

In

power

calculations

in

the

G

E

context

one

can

adopt

a

multi-group

design

if

the

environmental

moderator

is

categorical

For

example

consider

a

classical

ACE-twin

design

If

the

environmental

moderator

is

dichotomous

-LRB-

e.g.

males

versus

females

young

versus

old

smoking

versus

non-smoking

-RRB-

the

sample

consisting

of

MZ

and

DZ

twin

pairs

can

be

split

up

into

twin

pairs

who

are

concordant

with

respect

to

the

moderator

-LRB-

e.g.

both

twins

do

or

do

not

smoke

-RRB-

and

twin

pairs

who

are

discordant

with

respect

to

the

moderator

-LRB-

only

one

of

the

twins

in

a

pair

smokes

-RRB-

With

a

dichotomous

moderator

and

only

two

subjects

per

family

power

calculations

using

summary

statistics

are

feasible

as

there

are

only

three

distinguishable

groups

-LRB-

not

accounting

for

the

distinction

between

MZ

and

DZ

twins

-RRB-

However

suppose

that

you

have

measured

an

environmental

moderator

with

levels

-LRB-

coded

-RRB-

in

twin-pairs

and

their

parents

With

four

persons

per

family

and

four

possible

moderator

levels

there

are

possible

family

configurations

In

that

case

multi-group

analysis

with

summary

statistics

is

impractical

and

exact

data

simulation

may

be

used

instead

For

this

illustration

parameters

a

c

and

e

were

all

set

to

such

that

the

total

variance

equaled

-LRB-

excluding

moderating

and

main

effects

-RRB-

The

moderator

which

was

assumed

independent

of

genotype

in

this

illustration

was

coded

to

such

that

the

group

with

on

the

moderator

can

be

considered

the

baseline

condition

The

probability

for

all

moderation

levels

was

set

to

and

moderation

levels

were

modeled

as

independent

across

family

members

-LRB-

i.e.

the

probability

for

each

family

member

's

moderation

level

was

independent

of

the

moderation

levels

of

the

other

family

members

-RRB-

Moderation

in

C

E

and

the

means

was

fixed

to

but

the

regression

weight

of

the

moderator

was

set

to

for

the

additive

genetic

effects

such

that

the

moderator

explained

of

the

variance

in

the

total

population

-LRB-

i.e.

and

of

the

variance

respectively

depending

on

the

level

of

the

moderator

-RRB-

The

model

is

illustrated

in

Fig.

For

the

simulation

we

chose

an

overall

sample

size

N

of

-LRB-

MZ

and

DZ

twins

-RRB-

Fig.

ACE-model

for

parents

and

twin-offspring

including

moderation

on

the

variances

and

the

means

Given

these

simulated

data

we

want

to

estimate

the

power

to

reject

the

alternative

hypothesis

that

all

moderator

effects

on

the

variances

are

zero

-LRB-

i.e.

no

G

E

or

C

E

or

E

E

-RRB-

In

practice

one

would

fix

all

regression

weights

concerning

the

moderating

effects

on

the

variances

-LRB-

βa

βc

and

βe

-RRB-

to

zero

at

once

resulting

in

a

test

with

degrees

of

freedom

The

data

were

analyzed

in

Mx

different

groups

were

specified

for

the

MZ

and

DZ

twins

and

the

moderator

featured

as

a

so-called

definition

variable

The

option

power

command

-LRB-

α

df

-RRB-

was

again

used

to

obtain

an

estimation

of

the

total

sample

size

that

would

be

required

for

a

power

of

given

the

current

proportions

of

subjects

in

each

group

With

the

probability

for

all

moderation

levels

fixed

to

all

groups

were

represented

in

both

the

MZ

and

the

DZ

twins

in

the

simulated

data

file

-LRB-

cases

simulated

-RRB-

and

for

the

chosen

values

the

analysis

shows

that

we

would

need

families

for

a

power

of

If

we

were

to

change

the

moderator

level

probabilities

from

for

every

level

to

and

for

levels

and

respectively

then

and

groups

would

be

represented

in

MZ

and

DZ

twins

respectively

-LRB-

cases

simulated

-RRB-

In

that

case

families

would

be

required

for

a

power

of

even

though

the

moderator

effect

-LRB-

βa

-RRB-

is

unchanged

These

power

calculations

took

at

most

minute

in

total

Again

acquisition

of

similar

power

results

would

take

at

least

T

times

as

long

within

the

Monte

Carlo

framework

-LRB-

where

T

is

the

number

of

replications

-RRB-

Assembling

the

data

simulation

script

takes

equally

long

for

both

types

of

simulation

so

overall

exact

simulation

saves

time

Illustration

association

for

a

tri-allelic

locus

with

different

allele

frequencies

The

aim

of

association

studies

is

to

determine

whether

genetic

variation

is

associated

with

the

risk

for

disease

or

the

expression

of

a

continuously

distributed

trait

Association

studies

may

produce

false

positives

i.e.

significant

association

in

the

absence

of

any

true

genetic

effects

Population

stratification

is

one

source

of

false

positives

i.e.

the

mixture

of

two

populations

with

different

allele

frequencies

and

different

phenotypic

means

Fulker

et

al.

-LRB-

-RRB-

showed

that

this

type

of

spurious

association

can

be

avoided

in

a

family-based

study

design

In

this

illustration

we

focus

on

the

situation

in

which

data

are

available

for

pairs

of

siblings

Although

this

design

allows

for

the

simultaneous

modeling

of

linkage

and

association

we

limit

the

analysis

to

the

association

but

note

that

linkage

information

-LRB-

i.e.

IBD

sharing

estimation

-RRB-

could

be

included

in

exact

data

simulation

scripts

For

the

present

illustration

however

we

assume

that

the

locus

under

study

is

the

QTL

itself

and

not

a

marker

in

linkage

disequilibrium

with

the

QTL

If

a

locus

is

diallelic

genotypes

can

be

distinguished

AA

AB

BA

and

BB

-LRB-

of

course

in

practice

there

are

only

distinguishable

groups

as

AB

and

BA

are

the

same

but

when

simulating

the

data

exactly

it

is

convenient

simply

to

treat

them

as

different

groups

-RRB-

These

genotypes

give

rise

to

-LRB-

-RRB-

possible

combinations

of

siblings

-LRB-

not

accounting

order

-RRB-

i.e.

a

group

analysis

Note

that

this

is

the

simplest

case

with

alleles

the

number

of

possible

sib-pairs

is

already

-LRB-

-RRB-

and

when

the

locus

under

study

is

a

polymorphic

marker

with

say

possible

alleles

the

number

of

distinguishable

sib-pairs

is

-LRB-

-RRB-

Clearly

multi-group

analyses

with

sufficient

summary

statistics

quickly

become

impractical

as

the

number

of

alleles

or

loci

increases

We

illustrate

the

use

of

exact

data

simulation

in

the

context

of

the

sib-pair

association

design

for

a

tri-allelic

locus

with

alleles

A

B

and

C

with

frequencies

p

q

and

r

respectively

The

aim

of

this

particular

power

calculation

is

to

determine

the

influence

of

the

allele

frequencies

on

the

power

to

detect

a

QTL

The

biometrical

model

for

a

tri-allelic

locus

is

summarized

in

Table

As

with

the

more

familiar

diallelic

case

the

expected

genotypic

value

is

assumed

zero

so

that

everything

is

scaled

in

terms

of

deviations

In

the

case

of

three

alleles

genotypic

values

are

distinguished

which

were

both

fixed

to

so

that

AA

was

associated

with

an

increase

of

BB

with

an

increase

of

and

CC

with

a

decrease

of

to

Dominance

was

assumed

to

be

absent

so

the

genotypic

effect

for

the

heterozygous

genotypes

AB

AC

and

BC

was

calculated

as

the

mean

of

the

effects

of

the

homozygous

groups

In

the

case

of

equal

allele

frequencies

-LRB-

p

q

r

-RRB-

this

QTL

explains

of

the

variance

-LRB-

as

determined

using

regular

regression

with

the

phenotype

as

dependent

variable

and

genotype

as

predictor

-RRB-

Note

that

the

variance

explained

by

the

QTL

depends

on

the

allele

frequencies

so

even

though

the

genotypic

values

remain

the

same

across

all

simulations

varying

the

allele

frequencies

affects

the

effect

size

of

the

QTL

effect

For

all

simulations

background

variance

was

decomposed

such

that

additive

genetic

effects

explained

and

unique

environmental

influences

-LRB-

E

-RRB-

explained

of

the

variance

that

remained

after

the

QTL-effects

was

taken

into

account

Overall

sample

size

N

was

fixed

to

-LRB-

note

that

because

of

rounding

the

actual

N

modeled

will

not

be

equal

to

the

overall

sample

size

N

of

see

Table

-RRB-

Table

for

a

tri-allelic

locus

following

the

standard

biometric

model

when

dominance

is

assumed

absentGenotypeAAABBBACBCCCGenotype

frequency

value

gijx

-LRB-

x

y

-RRB-

p

q

and

r

denote

the

frequencies

of

alleles

A

B

and

C

respectively

x

is

the

genotypic

value

associated

with

genotype

AA

y

the

genotypic

value

associated

with

genotype

BB

As

the

genotypic

value

for

genotype

CC

is

z

x

y

-LRB-

i.e.

x

y

z

-RRB-

μqtl

denotes

the

expected

contribution

of

the

QTL

to

the

population

mean

and

denotes

the

expected

contribution

of

the

QTL

to

the

population

variance

-LRB-

adapted

from

Falconer

and

Mackay

-RRB-

Table

for

illustration

Power

calculations

for

sib-pair

association

with

a

tri-allelic

locus

with

fixed

genotypic

valuesFrequencies

alleles

A

B

CEffect

size

-LRB-

-RRB-

Actual

NNr

of

groups

represented

χ2

-LRB-

-RRB-

Observed

power

N

required

for

power

of

Note

Effect

size

is

defined

as

of

variance

explained

by

QTL

Actual

N

refers

to

actual

number

of

sib-pairs

in

the

analysis

Nr

of

groups

represented

refers

to

the

number

of

groups

of

the

possible

that

were

represented

in

the

analysis

χ2

-LRB-

-RRB-

the

of

the

test

for

association

when

the

genotypic

effects

for

all

distinguishable

genotypes

are

fixed

to

zero

Observed

power

refers

to

the

power

observed

for

the

modeled

sample

size

N

Note

that

between

and

within

effects

were

exactly

equal

-LRB-

i.e.

B

W

-RRB-

as

we

did

not

model

population

stratification

all

between

and

within

parameters

can

thus

be

fixed

to

be

equal

without

loss

of

fit

The

overall

test

for

genetic

association

then

involves

fixing

the

genotypic

effects

for

all

distinguishable

genotypes

-LRB-

AA

AB

AC

BB

BC

and

CC

-RRB-

to

zero

i.e.

degrees

of

freedom

The

simulated

sib-pair

data

were

analyzed

in

Mx

using

the

option

power

command

-LRB-

α

df

-RRB-

to

obtain

the

sample

size

required

for

a

power

of

given

the

current

proportions

of

subjects

in

each

group

The

results

presented

in

Table

show

that

the

power

to

detect

a

QTL

with

certain

genotypic

values

depends

on

the

allele

frequencies

As

expected

the

power

is

greatest

when

the

frequency

for

the

allele

with

the

largest

genotypic

value

-LRB-

allele

C

-RRB-

is

highest

With

exact

data

simulation

these

power

calculations

took

about

min

for

each

choice

of

allele

frequencies

Again

it

would

take

at

least

T

times

as

long

to

obtain

similar

power

results

within

the

Monte

Carlo

framework

-LRB-

where

T

is

the

number

of

replications

-RRB-

while

the

time

required

to

write

the

data

simulation

script

takes

equally

long

for

both

types

of

simulation

Conclusion

In

this

paper

we

discussed

a

third

method

of

power

calculation

which

can

be

useful

when

sufficient

summary

statistics

are

available

in

principle

but

the

number

of

possible

groups

is

so

large

to

render

a

multi-group

analysis

impractical

The

illustrations

presented

in

this

paper

represent

only

a

few

of

the

possible

-LRB-

behavior

genetics

-RRB-

designs

in

which

exact

data

simulation

may

prove

useful

Other

models

for

which

exact

data

simulation

can

be

used

include

random-effects

models

latent

growth

curve

models

simplex

models

and

-LRB-

hierarchical

-RRB-

structural

models

either

or

not

in

the

context

of

genetics

just

to

name

a

few

Exact

data

simulation

does

not

require

more

programming

skills

or

programming

time

than

Monte

Carlo

simulation

but

one

may

save

a

lot

of

time

analyzing

the

simulated

data

and

calculating

power

especially

when

one

wishes

to

construct

graphs

of

power

vs.

effect

size

In

this

paper

we

used

the

Mx

program

to

analyze

the

simulated

data

because

of

its

inbuilt

power

calculation

function

Another

useful

option

of

Mx

in

this

context

is

the

possibility

to

output

individual

likelihood

statistics

for

each

raw

data

group

This

information

can

be

used

to

identify

the

groups

that

contribute

most

to

the

power

to

detect

the

effects

of

interest

Of

course

various

other

statistical

software

packages

-LRB-

e.g.

QTDT

LISREL

MPlus

R

-RRB-

can

also

be

used

in

combination

with

exact

data

simulation

to

obtain

the

non-centrality

parameters

required

for

power

calculations

We

emphasize

that

the

power

results

obtained

through

exact

data

simulation

are

exactly

similar

to

power

results

obtained

through

the

analysis

of

summary

statistics

and

just

like

power

calculation

using

summary

statistics

asymptotically

similar

to

results

obtained

through

Monte

Carlo

simulation

-LRB-

depending

on

the

number

of

runs

used

in

Monte

Carlo

-RRB-

Differences

between

those

two

customary

method

of

power

calculation

and

exact

data

simulation

only

occur

when

subgroups

have

very

low

probabilities

and

the

simulated

overall

sample

size

is

not

large

enough

to

include

all

possible

groups

to

sufficient

extent

these

small

groups

may

then

not

be

represented

in

the

exact

power

simulation

while

they

may

be

-LRB-

more

or

less

-RRB-

represented

in

other

methods

However

as

stated

previously

the

ensuing

differences

with

respect

to

the

power

results

are

very

small

as

such

small

groups

hardly

contribute

to

the

power

anyway

Even

so

to

avoid

the

exclusion

of

small

groups

one

should

choose

a

sufficiently

large

overall

sample

size

in

exact

simulation

such

that

all

groups

are

represented

This

is

perfectly

doable

and

does

not

alter

the

practicability

of

the

method

as

it

still

involves

analyzing

a

single

-LRB-

yet

larger

-RRB-

dataset

The

non-centrality

parameter

obtained

in

the

analysis

of

the

large

simulated

data

set

can

subsequently

be

used

to

calculate

the

power

for

smaller

more

realistic

sample

sizes

Alternatively

one

may

decide

to

accept

the

absence

of

certain

groups

and

the

implied

slight

underestimation

of

power

Happily

the

discrepancy

between

the

intended

N

and

the

realized

N

is

simple

to

calculate

-LRB-

as

demonstrated

in

the

R

script

available

in

the

Mx

scripts

library

-RRB-

so

that

one

can

readily

obtain

an

impression

of

the

implications

of

this

decision

Throughout

the

paper

we

have

assumed

that

the

data

conditional

on

group

are

normally

distributed

so

that

sufficient

statistics

are

in

principle

available

With

respect

to

situations

that

preclude

sufficient

statistics

the

present

method

may

still

have

some

use

For

instance

a

continuous

moderator

in

a

G

E

model

as

discussed

by

Purcell

-LRB-

-RRB-

might

be

approximated

by

a

point

or

point

Likert

scale

which

would

render

exact

simulation

possible

in

principle

-LRB-

see

illustration

-RRB-

Finally

we

note

that

the

extension

of

this

method

to

discrete

data

would

obviously

be

very

useful

and

does

seem

feasible

B 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 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 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 B 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 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 B 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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