Transcript slides - NCS2016 Non-Clinical Statistics Conference

Statistical aspects for the
quantification of learning behaviour
By Sarah Janssen
NCS 2014, Brugge
External supervisor: Dr. Tom Jacobs, Janssen Pharmaceuticals (J&J)
Internal supervisor: Dr. Herbert Thijs, Uhasselt
1
Introduction
• A new animal behaviour model is setup to asses cognitive
functioning in animals:
– Animals are injected with PCP (also known as “Angel Dust”)
– PCP has a degrading effect on learning behaviour
– A good understanding of the effect of PCP on cognitive functioning is
important
• Optimizing the data analysis
– That allows to quantify learning behaviour
– That allows answering the research question in an unambiguous and
efficient way
2
The objective
• To study and quantify the dose effect of PCP on learning
behavior
• To put it explicitly:
– How does PCP affects learning behavior?
– Which characteristics of learning behavior are sensitive to the dose
effect?
– How to quantify the dose effect on these characteristics?
– Which dose levels show a significant effect on learning behaviour?
3
Experimental setup
• Male wistar rats were trained to
perform an action: choosing the
correct image between two images
• Through reward mechanism
• By the use of an operant
conditioning chamber
• One training session ends after 48
trials or after 30 minutes maximally
• Variable of interest: the proportion
of correctly executed trials within
one training session
Figure Retrieved from www.campden-inst.com on
12/08/2012, URL: http://www.campdeninst.com/product_detail.asp?ItemID=1975&cat=2
4
Experimental setup
• Data available from two dose-response studies with
PCP in identical conditions:
–
–
–
–
96 animals
5 dose levels: 0mg, 0.25mg, 0.5mg, 0.75mg, 1mg
Daily injection with PCP before every session
Sessions were performed daily during a period of 14 days
Dose level PCP:
Total # of animals
0mg 0.25mg 0.5mg 0.75mg 1mg Total # of animals
24
12
24
12
24
96
5
Exploratory data analysis:
individual profiles per dose level
4
6
8
10
12
2
4
6
8
10
Dose level: 0.5
Dose level: 0.75
6
8
10
12
14
days
14
12
14
0.4
0.0
0.8
4
12
0.8
days
0.4
2
0.8
0
days
0.0
0
0.4
14
proportion
2
0.0
proportion
0.8
0.4
0
proportion
Dose level: 0.25
0.0
proportion
Dose level: 0
0
2
4
6
8
10
days
0.8
0.4
0.0
proportion
Dose level: 1
0
2
4
6
8
days
10
12
14
6
0.8
0.6
0.2
0.4
Dose 0
Dose 0.25
Dose 0.5
Dose 0.75
Dose 1
0.0
proportion
• Variability between and within
animals
• Profiles start around 0.5
• Increase up to a level 0.9
• Increase in a non-linear way
• Less steep increase of the
profiles at higher dose levels
1.0
Exploratory data analysis:
average profiles per dose level
0
2
4
6
8
10
12
14
days
7
Part 1: Traditional Multivariate Anova
model
8
The model
y ijk  μ  dose k  time j  (dose*time)kj  ε ijk
• Covariates: dose, time and dose*time
• Residual errors are assumed to follow a multivariate normal
distribution
• Pairwise comparisons of the 4 dose levels to the vehicle dose
at every time point
• Without and with adjustment for multiple testing via
Bonferroni correction
9
Results
10
Results
11
Conclusion
• Flexible model
• Easy to understand and apply, also for non-statisticians
• Inefficient way to analyze the data:
– Perform many test (59 comparisons)
– Analyses becomes conservative when adjusting for
multiple testing
• Does not answer the research question in a direct,
unambiguous way
12
Part 2: Non-linear mixed effects model
13
The model
1.0
• The response variable (proportion) is assumed to follow a
beta distribution
• The average proportions (μij) are modeled as a Weibull
learning curve (Gallistel et al, 2004):
0.8
1
0.6
3
0.2
0.4
4
0.0
proportion
2
2
4
6
8
10
12
14
days
14
The model
• The Weibull distribution is characterized by a scale (L) and
shape (S) parameter
• An intercept (I) and an asymptotic level (A) is added:
ij  I  ( A  I ) * (1  e
[( dayij / L ) S ]
)
(3)
• To get a more meaningful interpretation for the scale
parameter, L is reparameterized as T70:
• T70: time until proportion 0.7 was reached
ij  I  ( A  I ) * (1  e
where L 
[( dayij / L ) S ]
T 70

 A  0.847  
  ln 

A

I



1/ S 
)
(3)
(4)
15
The model
• This way, learning behavior is characterized by 4 parameters:
Intercept (I)
Asymptotic level (A)
Time to reach proportion 0.7 (T70)
Abruptness (S)
1.0
Panel A
0.8
A=0.90
0.6
S=3
0.2
0.4
I=0.50
0.0
proportion
–
–
–
–
T70=5 days
0
2
4
6
8
10
12
14
days
16
The model
• Dose effect is included in the model by allowing the
parameters to change in function of dose level
• To take the heterogeneity between animals into account,
random effects were included
T 70*  T 70 _ int  ti   T 70 _slope*dos ei
S *  S_ int  si   S_slope*do sei
(9)
(10)
I *  I_ int  ii 
(11)
A*  A_ int  A_slope*dosei
(12)
17
Results
0.8
0.6
0.4
Dose 0
Dose 0.25
Dose 0.5
Dose 0.75
Dose 1
0.2
95% CI
(0.50, 0.54)
(1.42, 1.94)
(0.92, 0.94)
(-0.13, 1.74)
(3.4, 4.6)
(0.86, 1.36)
0.0
Estimate
0.52
1.66
0.93
0.81
3.9
1.11
proportion
Parameter
I_int
S_int
A_int
A_slope
T70_int
T70_slope
1.0
Model_L_2
0
2
4
6
8
10
12
14
days
18
Results
Parameter
Estimate
98.75% CI
p-value
T700.25 / T700
1.14
(0.78, 1.67)
0.3883
T700.50 / T700
1.50
(1.10, 2.06)
0.0014
T700.75 / T700
1.61
(1.09, 2.36)
0.0022
T701 / T700
3.21
(2.29, 4.49)
<0.0001
19
Conclusion
• Weibull funtion was used to model the learning curves
• Parameters have a biological interpretation
• Direct, unambiguous answer to the research question:
– How does PCP affects learning behaviour?  via T70
– How strong is the dose effect 3 fold increase of T70 with a unit
increase of dose
– Which does level show a statistical significant effect  all, except dose
level 0.25
• Efficient way to analyze the data
• Rather complex analysis
20
Thank you for your attention!
Thanks to:
•Dr. Tom Jacobs, Janssen Pharmaceuticals (J&J)
•Dr. Herbert Thijs, Uhasselt
21