1

Statistical aspects for the quantification of learning behaviour

By Sarah JanssenNCS 2014, Brugge

External supervisor: Dr. Tom Jacobs, Janssen Pharmaceuticals (J&J)Internal supervisor: Dr. Herbert Thijs, Uhasselt

2

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

3

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?

4

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.campden-inst.com/product_detail.asp?ItemID=1975&cat=2

5

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: 0mg 0.25mg 0.5mg 0.75mg 1mg Total # of animalsTotal # of animals 24 12 24 12 24 96

6

Exploratory data analysis: individual profiles per dose level

0 2 4 6 8 10 12 14

0.0

0.4

0.8

Dose level: 0

days

prop

ortio

n

0 2 4 6 8 10 12 14

0.0

0.4

0.8

Dose level: 0.25

days

prop

ortio

n0 2 4 6 8 10 12 14

0.0

0.4

0.8

Dose level: 0.5

days

prop

ortio

n

0 2 4 6 8 10 12 14

0.0

0.4

0.8

Dose level: 0.75

dayspr

opor

tion

0 2 4 6 8 10 12 14

0.0

0.4

0.8

Dose level: 1

days

prop

ortio

n

7

• 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

0 2 4 6 8 10 12 140

.00

.20

.40

.60

.81

.0

days

prop

ortio

n

Dose 0Dose 0.25Dose 0.5Dose 0.75Dose 1

Exploratory data analysis: average profiles per dose level

8

Part 1: Traditional Multivariate Anova model

9

The model

• 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

ijkkjjkijk ε)(dose*timetimedoseμy

10

Results

11

Results

12

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

13

Part 2: Non-linear mixed effects model

14

The model

• 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):

2 4 6 8 10 12 14

0.0

0.2

0.4

0.6

0.8

1.0

days

prop

ortio

n

1

2

3 4

15

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:

• To get a more meaningful interpretation for the scale parameter, L is reparameterized as T70:

• T70: time until proportion 0.7 was reached

(3) eIAI ]Ldayij

Sij )1(*)( )/[(

(4)

IAA

TL where

(3) eIAI

S

]Ldayij

Sij

/1

)/[(

847.0ln

70

)1(*)(

16

• This way, learning behavior is characterized by 4 parameters: – Intercept (I)– Asymptotic level (A)– Time to reach proportion 0.7 (T70)– Abruptness (S)

0 2 4 6 8 10 12 140

.00

.20

.40

.60

.81

.0

Panel A

days

prop

ortio

n

A=0.90

I=0.50

T70=5 days

S=3

The model

17

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

(12) seA_slope*doA_A

(11) iI_I

(10) seS_slope*dosS_S

(9) e_slope*dosTt_TT

i*

i*

ii*

ii*

int

int

int

70int7070

18

Results

Parameter Estimate 95% CII_int 0.52 (0.50, 0.54)S_int 1.66 (1.42, 1.94)A_int 0.93 (0.92, 0.94)A_slope 0.81 (-0.13, 1.74)T70_int 3.9 (3.4, 4.6)T70_slope 1.11 (0.86, 1.36)

0 2 4 6 8 10 12 14

0.0

0.2

0.4

0.6

0.8

1.0

Model_L_2

days

prop

ortio

n

Dose 0Dose 0.25Dose 0.5Dose 0.75Dose 1

19

Results

Parameter Estimate 98.75% CI p-value

T700.25 / T700 1.14 (0.78, 1.67) 0.3883T700.50 / T700 1.50 (1.10, 2.06) 0.0014T700.75 / T700 1.61 (1.09, 2.36) 0.0022T701 / T700 3.21 (2.29, 4.49) <0.0001

20

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

21

Thank you for your attention!

Thanks to:•Dr. Tom Jacobs, Janssen Pharmaceuticals (J&J)•Dr. Herbert Thijs, Uhasselt