1 the design of animal experiments michael fw festing c/o understanding animal research, 25...
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The design of animal experiments
Michael FW Festingc/o Understanding Animal Research, 25 Shaftsbury
Av. London, UK. [email protected]
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Replacement e.g. in-vitro methods, less sentient animals
Refinement e.g. anaesthesia and analgesia, environmental
enrichment Reduction
Research strategy Controlling variability Experimental design and statistics
Principles of Humane Experimental Technique
(Russell and Burch 1959)
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A well designed experiment Absence of bias
Experimental unit, randomisation, blinding High power
Low noise (uniform material, blocking, covariance) High signal (sensitive subjects, high dose) Large sample size
Wide range of applicability Replicate over other factors (e.g. sex, strain): factorial
designs Simplicity Amenable to a statistical analysis
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The animal as the experimental unit
Animals individually treated. May be individually housed or grouped
N=8n=4
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A cage as the Experimental Unit.
Treatment in water or diet.
N=4n=2
Treated TreatedControl Control
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An animal for a period of time: repeated measures or crossover design
Animal
1
2
3
Treatment 1
Treatment 2
N
4
4
4
N=12n= 6
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Teratology: mother treated, young measured
Mother is the experimental unit.
N=2n=1
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Failure to identify the experimental unit correctly in a 2(strains) x 3(treatments) x 6(times) factorial design
ELD groupELD group
Single cage of 8 mice killed at each time point (288 mice in total)
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Experimental units must be randomised to treatments
Physical: numbers on cards. Shuffle and take one
Tables of random numbers in most text books
Use computer. e.g. EXCEL or a statistical package such as MINITAB
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Randomisation
Original Randomised1 21 31 31 12 22 12 22 13 33 23 33 1
NB Randomisation should include housing and order in which observations are made
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Failure to randomise and/or blind leads to more “positive” results
Blind/not blind odds ratio 3.4 (95% CI 1.7-6.9)
Random/not random odds ratio 3.2 (95% CI 1.3-7.7)
Blind Random/ odds ratio 5.2 (95% CI 2.0-13.5)not blind random
290 animal studies scored for blinding, randomisation and positive/negative outcome, as defined by authors
Babasta et al 2003 Acad. emerg. med. 10:684-687
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Some factors (e.g. strain, sex) can not be randomised so special care is needed to ensure comparability
Outbred TO (8-12 weeks commercial)
Inbred CBA (12-16 weeks Home bred)
Six cages of 7-9 mice of each strain: error bars are SEMs
"CBA mice showed greater variability in body weights than TO mice..."
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A well designed experiment Absence of bias
Experimental unit, randomisation, blinding High power
Low noise (uniform material, blocking, covariance) High signal (sensitive subjects, high dose) Large sample size
Wide range of applicability Replicate over other factors (e.g. sex, strain): factorial
designs Simplicity Amenable to a statistical analysis
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High power: (good chance of detecting the effect of a treatment, if there is one)
High Signal/Noise ratio= High Standardized effect size= High |1-2|/= HighDifference between means)/SD
Student’s t =( X1-X2)/Sqrt (2S2/n)
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Power Analysis for sample size and effects of variation
A mathematical relationship between six variables Needs subjective estimate of effect size to be detected
(signal) Has to be done separately for each character Not easy to apply to complex designs Essential for expensive, simple, large experiments
(clinical trials) Useful for exploring effect of variability
A second method “The Resource Equation” is described later
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Power analysis: the variables
Sample size
Signala) Effect size of scientific interest
or b) actual response
Chance of a false positive result.
Significance level (0.05)
Sidedness of statistical test (usually 2-sided)
Power of theExperiment (80-90%?)
NoiseVariability of the
experimental material
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Group size and Signal/noise ratio
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3
Effect size (Std. Devs.)
Gro
up
siz
e
90%
80%
Assuming 2-sample, 2 sided t-test and 5% significance level
Signal/noise ratio
Power
Neutral
Bad
Good
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Comparison of two anaesthetics for dogs under clinical conditions (Vet. Anaesthes. Analges.)
Unsexed healthy clinic dogs,• Weight 3.8 to 42.6 kg. • Systolic BP 141 (SD 36) mm Hg
Assume: • a 20 mmHg difference between anaesthetics is of clinical importance, • a significance level of =0.05• a power=90% • a 2-sided t-test
Signal/Noise ratio 20/36 = 0.56Required sample size 68/group
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Power and sample size calculations using nQuery Advisor
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A second paper described:
• Male Beagles weight 17-23 kg• mean BP 108 (SD 9) mm Hg.• Want to detect 20mm difference between groups (as before)With the same assumptions as previous slide:
Signal/noise ratio = 20/9 = 2.22
Required sample size 6/group
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Summary for two sources of dogs: aim is to be able to detect a 20mmHg change in blood pressure
Type of dog SDev Signal/noise Sample %Power (n=8)
size/gp(1) (2) Random dogs 36 0.56 68 18Male beagles 9 2.22 6 98
(1)Sample size: 90% power(2)Power, Sample size 8/group
Assumes =5%, 2-sided t-test and effect size 20mmHg
The scientific dilemma: With small sample sizes we can not detect an important effect in genetically heterogeneous animals.
We can detect the effect in genetically homogeneous animals, but are they representative?
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Variation in kidney weight in 58 groups of rats
0
10
20
30
40
50
60
70
80
90
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57
Sample number
Va
ria
bil
ity
Mycoplasma
Outbred
F1
F2
Gartner,K. (1990), Laboratory Animals, 24:71-77.
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Required sample sizes
Factor Type Std.Dev Signal/ noise*
Sample size
Power**
Genetics F1 hybrid 13.5 0.74 30 80
F2 hybrid 18.4 0.54 55 53
Outbred 20.1 0.49 67 46
Disease Mycoplasma free
18.6 0.54 55 53
With Mycoplasma
43.3 0.23 298 14
*signal is 10 units, two sided t-test,=0.05, power = 80%** Assuming fixed sample size of 30/group
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The randomised block design: another method of controlling noise
B C A
A C B
B A C
A C B
B C A B1
B2
B3
B4
B5
Treaments A, B & C
• Randomisation is within-block
• Can be multiple differences between blocks
• Heterogeneous age/weight
• Different shelves/rooms• Natural structure (litters)• Split experiment in time
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A randomised block experiment
050
100150200250300350400450500
1 2 3
Week
Ap
op
tosis
sco
re
Control
CGP
STAU
365 398 421 423 432 459 308 320 329
Treatment effect p=0.023(2-way ANOVA)
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Analysis of apoptosis data
Analysis of Variance for Score
Source DF SS MS F PBlock 2 21764.2 10882.1 114.82 0.000Treatmen 2 2129.6 1064.8 11.23 0.023Error 4 379.1 94.8Total 8 24272.9
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-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
0
1
2
3
Residual
Fre
quen
cy
Histogram of Residuals
0 1 2 3 4 5 6 7 8 9
-20
-10
0
10
20
Observation Number
Res
idua
l
I Chart of Residuals
Mean=3.16E-14
UCL=20.17
LCL=-20.17
300 350 400 450
-10
0
10
Fit
Res
idua
l
Residuals vs. Fits
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
-10
0
10
Normal Plot of Residuals
Normal Score
Re
sid
ual
Residual Model Diagnostics
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Another method of determining sample size: The Resource Equation
Depends on the law of diminishing returns Simple. No subjective parameters Useful for complex designs and/or multiple outcomes
(characters) Does not require estimate of Standard Deviation Crude compared with Power Analysis
E= (Total number of animals)-(number of groups)
10<E<20 (but give some tolerance)
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0 5 10 15 20 25 30 35
2.0
4.5
7.0
9.5
12.0
Degrees of freedom
Stu
dent
's t
, 5%
crit
ical
val
ue
E= (total numbers)-(number of groups)
10<E<20
The Resource Equation & Sample Size
But if experimental subjects are cheap (e.g. multi-well plates, E can be much higher
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A well designed experiment Absence of bias
Experimental unit, randomisation, blinding High power
Low noise (uniform material, blocking, covariance) High signal (sensitive subjects, high dose) Large sample size
Wide range of applicability Replicate over other factors to (e.g. sex, strain) to increase
generality: factorial designs Simplicity Amenable to a statistical analysis
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Factorial designs
Single factor design
Treated Control
E=16-2 = 14
One variable at a time (OVAT)
Treated ControlTreated Control
E=16-2 = 14 E=16-2 = 14
Factorial design
Treated Control
E=16-4 = 12
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Factorial designs
(By using a factorial design)”.... an experimental investigation, at the same time as it is made more comprehensive, may also be made more efficient if by more efficient we mean that more knowledge and a higher degree of precision are obtainable by the same number of observations.”
R.A. Fisher, 1960
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A 4x2 factorial design
Analysed with Student’s t-test: This is not appropriate because:1. Each test is based on too few animals (n=3-4), so lacks power2. It does not indicate whether there are strain differences in protein thiol status3. It does not indicate whether dose/response differs between strains4. A two-way design should be analysed using a 2-way ANOVA
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Incorrect statistical analysis leading to excessive numbers of animals
8 mice per group8 groups = 64 mice. E= 64-8 =56
Alternative3 mice per group:8 groupsE=24-8 = 16
Saving:40 miceFormal test of interaction
One experiment or4 separate experiments?
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2 (strains) x 4 (Animal units) factorial
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Effect of chloramphenicol (2000mg/kg) on RBC count
Strain Control TreatedC3H 7.85 7.81
8.77 7.218.48 6.968.22 7.10
CD-1 9.01 9.187.76 8.318.42 8.478.83 8.67
Tests: Use a two-way ANOVA with interaction
1. Do the treatment means averaged across strains differ?
2. Do the strains differ, averaged across treatments
3. Do the two strains respond to the same extent?
Should not be analysedusing two t-tests1. Each test lacks power due to small sample size2. Will not give a test of whether strains differ in response
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A 2x2 factorial design with interaction
Source DF SS MS F Pstrain 1 2.4414 2.4414 13.13 0.003Treatment 1 0.8236 0.8236 4.43 0.057strain*treat. 1 1.4702 1.4702 7.91 0.016Error 12 2.2308 0.1859Total 15 6.9659
6.5
7
7.5
8
8.5
9
Control Treated Control Treated
Strain and treatment
Red
blo
od
cell
cou
nt
C3H CD-1
Pooled variance
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Use of several inbred strains to reduce noise, increase signal and explore generality
500 1000 1500 2000 2500
CD-1 8 8 8 8 8 8
CBA 2 2 2 2 2
C3H 2 2 2 2 2
BALB/c
2
2 2 2 2
C57BL
2
2 2 2 2
2
2
2
2
Inbred
0 Outbred
Dose of chloramphenicol (mg/kg)
Festing et al (2001) Fd. Chem.Tox. 39:375
Effect of chloramphenicol on mouse haematology
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WBC Strain Control TreatedCBA 1.90 0.40CBA 2.60 0.20C3H 2.10 0.40C3H 2.20 0.40BALB/c 1.60 1.30BALB/c 0.50 1.40C57BL 2.30 0.80C57BL 2.20 1.10
CD-1 3.00 1.90CD-1 1.70 1.90CD-1 1.50 3.50CD-1 2.00 1.20CD-1 3.80 2.30CD-1 0.90 1.00CD-1 2.60 1.30CD-1 2.30 1.60
Example of a factorial compared with a single factor design
Four inbred strains
One outbred stock
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Signal NoiseStrain N 0 2500 (Difference) (SD) Signal/noise pCBA 4 2.25 0.30 1.95 0.34 5.73C3H 4 2.15 0.40 1.85 0.34 5.44BALB/c 4 1.05 1.35 (-0.30) 0.34 (-0.88)C57BL 4 2.25 0.95 1.30 0.34 3.82Mean 16 1.93 1.20 0.73 0.34 2.15 <0.001Dose * strain <0.001
WBC counts following chloramphenicol at 2500mg/kg
Signal NoiseStrain N 0 2500 (Difference) (SD) Signal/noise pCD-1 16 2.23 1.83 0.40 0.86 0.47 0.38
White blood cell counts
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Genetics is important: Twenty two Nobel Prizes since 1960 for work depending on inbred strains
CancermmTV
Transmissableencephalopathacies/prionsPruisner
Retroviruses, Oncogenes & growth factorsCohen, Levi-montalcini, Varmus, Bishop, Baltimore, Temin
Humoral immunity/antibodiesT-cell receptorTonegawa, Jerne
Cell mediated immunityImmunological toleranceH2 restriction, immune responsesMedawar, Burnet, Doherty, ZinkanagelBenacerraf (G.pigs)
GeneticsSnell C.C. Little, DBA, 1909
Inbred Strains and derivativesJackson Laboratory
monoclonal antibodiesBALB/c miceKohler and Millstein
SmellAxel & Buck
ES cells & “knockouts”Evans, Capecchi, Smithies
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18th Annual Short Course on Experimental
Models of Human Cancer
August 21-30, 2009
Bar Harbor, ME
courses.jax.org
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Conclusions
Five requirements for a good design Unbiased (randomisation, blinding) Powerful (signal/noise ratio: control variability) Wide range of applicability (factorial designs, common but
frequently analysed incorrectly) Simple Amenable to statistical analysis
Mistakes in design and analysis are common Better training in experimental design would improve
the quality of research, save money, time and animals
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