1. Statistical aspects for the quantification of learning behaviour By Sarah Janssen NCS 2014, Brugge 1 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 2

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? 3

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 4

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:0mg0.25mg0.5mg0.75mg1mgTotal # of animals 241224122496 5

6. Exploratory data analysis: individual profiles per dose level 6

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 7 Exploratory data analysis: average profiles per dose level

8. Part 1: Traditional Multivariate Anova model 8

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 9

10. Results 10

11. Results 11

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 12

13. Part 2: Non-linear mixed effects model 13

14. The model The response variable (proportion) is assumed to follow a beta distribution The average proportions (μ ij ) are modeled as a Weibull learning curve (Gallistel et al, 2004): 14

15. The model 15 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

16. This way, learning behavior is characterized by 4 parameters: – Intercept (I) – Asymptotic level (A) – Time to reach proportion 0.7 (T70) – Abruptness (S) 16 The model

17. 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 17

18. Results 18 ParameterEstimate95% CI I_int0.52(0.50, 0.54) S_int1.66(1.42, 1.94) A_int0.93(0.92, 0.94) A_slope0.81(-0.13, 1.74) T70_int3.9(3.4, 4.6) T70_slope1.11(0.86, 1.36)

19. Results 19 ParameterEstimate98.75% CIp-value T70 0.25 / T70 0 1.14(0.78, 1.67)0.3883 T70 0.50 / T70 0 1.50(1.10, 2.06)0.0014 T70 0.75 / T70 0 1.61(1.09, 2.36)0.0022 T70 1 / T70 0 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 20

21. Thank you for your attention! 21 Thanks to: Dr. Tom Jacobs, Janssen Pharmaceuticals (J&J) Dr. Herbert Thijs, Uhasselt