1. Center for Biofilm Engineering Al Parker, Biostatistician Experimental design and statistical analysis of in vitro models of oral biofilms July, 2012

2. What is statistical thinking?  Data/Response  Experimental Design  Uncertainty assessment

3. What is statistical thinking?  Data/Response (pixel intensity in an image? log(cfu) from viable plate counts?)  Experimental Design - controls - randomization - replication (How many coupons? experiments? technicians? labs?)  Uncertainty and variability assessment

4. Why statistical thinking?  Anticipate criticism (design method and experiments accordingly)  Provide convincing results (establish statistical properties)  Increase efficiency (conduct the least number of experiments)  Improve communication

5. Why statistical thinking? in vitro testing

6. Attributes of an in vitro method: Seven R’s  Relevance  Reasonableness  Ruggedness  Responsiveness  Reproducibility (inter-laboratory)  Resemblance  Repeatability (intra-laboratory reproducibility) http://www.biofilm.montana.edu/content/ksa-sm-03

7. Attributes of an in vitro method: Seven R’s  Relevance  Reasonableness  Ruggedness  Responsiveness  Reproducibility (inter-laboratory)  Resemblance  Repeatability (intra-laboratory reproducibility)

8. Resemblance Independent repeats of the same experiment in the same laboratory produce nearly the same control data, as indicated by a small repeatability standard deviation, CS r = STDEV( Mean Controls for each experiment ) http://www.biofilm.montana.edu/content/ksa-sm-10

9. Resemblance Example Drip Flow Reactor Low shear Plug flow ASTM E2647

10. Resemblance Example 4 slides or coupons control treated (sterile saline) (Chlorhexidine digluconate 0.12%) Experimental Design: saliva collected from volunteers 4 day old supragingival biofilms Both saline and treatment applied for 1 minute 5 independent experimental runs

11. Resemblance Example Density LD Coupon cfu/cm 2 log(cfu/cm 2 ) 1 2.3 x 10 8 8.36 2 1.7 x 10 8 8.23 ControlLD= 8.29 Data: log 10 (cfu/cm 2 ) from viable plate counts

12. Resemblance Example Exp coupon LD Control LD Control SD 18.36 18.238.290.0871 27.62 27.497.550.0910 37.59 37.787.680.1376 47.84 48.087.960.1660 57.77 57.337.550.315

13. Resemblance from experiment to experiment 1. Mean ControlLD = 7.81 the best guess for the true mean control LD 2. CS r =STDEV(ControlLDs) =0.32 the typical distance between the ControlLD for a single experiment and the true mean control LD log 10 (cfu/cm 2 ) Summary Statistics: CS r is not STDEV(LDs)

14. Resemblance from experiment to experiment The variance CS r 2 can be partitioned: 84% due to among experiment sources 16% due to within experiment sources log 10 (cfu/cm 2 )

15. CS n c m c 2 + Estimating the true mean control LD with confidence 2. Calculate the SE of Mean ControlLD, using: CS 2 c = within-experiment variance of control coupon LD CS 2 E = among-experiments variance of control coupon LD n c = number of control coupons per experiment m = number of experiments CS m E 2 SE of Mean ControlLD = CS r / = 3. CI for the true mean control LD = Mean ControlLD ± t m-1 x SE 1. Start with your best guess: Mean ControlLD m

16. 2 5 Estimating the true mean control LD with confidence 1. Mean ControlLD = 7.81 2. Calculate the SE of Mean ControlLD: CS 2 c = 0.16 x (.32) 2 = 0.03211 CS 2 E = 0.84 x (.32) 2 = 0.08544 n c = 2 m = 5 5 SE of Mean ControlLD = 0.03211 + 0.08544 = 0.1425 3. A 95% CI for true mean control LD = 7.81 ± 2.78 x 0.1425 = 7.81 ± 0.33 = (7.41, 8.20)

17. We are 95% confident that the true mean of the control LDs is in this interval log 10 (cfu/cm 2 ) Estimating the true mean control LD with confidence

18. Attributes of an in vitro method: Seven R’s  Relevance  Reasonableness  Ruggedness  Responsiveness  Reproducibility (inter-laboratory)  Resemblance  Repeatability (intra-laboratory reproducibility)

19. Repeatability Independent repeats of the same experiment in the same laboratory produce nearly the same response, as indicated by a small repeatability standard deviation S r = STDEV( Mean response for each experiment ) http://www.biofilm.montana.edu/content/ksa-sm-10

20. Repeatability Example 4 slides or coupons control treated (saline) (Chlorhexidine digluconate 0.12%)

21. Repeatability Example Data/Response: log reduction (LR) LR = mean(control LDs) – mean(treated LDs)

22. Repeatability Example Exp coupon LD Control LD Control SD 18.36 18.238.290.0871 27.62 27.497.550.0910 37.59 37.787.680.1376 47.84 48.087.960.1660 57.77 57.337.550.315

23. Repeatability Example Mean LR = 1.87 Exp control coupon LD Control LD treated coupon LD Treated LDLR 18.366.60 18.238.294.975.792.51 27.625.61 27.497.555.475.542.08 37.595.25 37.787.685.205.222.46 47.847.37 48.087.965.636.501.46 57.777.46 57.337.555.876.660.89 Since there is no obvious pairing between the controls and treated coupons in each experiment, get 1 LR for each experiment

24. Repeatability Example 1. Mean LR = 1.87 the best guess for the true mean LR 2. S r = STDEV(LRs) = 0.69 the typical distance between the LR for a single experiment and the true mean LR Summary Statistics:

25. Estimating the true mean LR with confidence 2. Calculate the SE of Mean LR, using: S 2 c = within-experiment variance of control coupon LD S 2 d = within-experiment variance of treated coupon LD S 2 E = among-experiment variance of LR n c = number of control coupons per experiment n d = number of treated coupons per experiment m = number of experiments 1. Start with your best guess: Mean LR S n c m c 2 + S n d m d 2 + S m E 2 SE of mean LR = S r / = 3. CI for the true mean LR = Mean LR ± t m-1 x SE m

26. Estimating the true mean LR with confidence 1. Mean LR = 1.87 2. S c 2 = 0.03211 S d 2 = 0.82092 S E 2 = 0.06219 n c = 2, n d = 2, m = 5 SE of mean LR = 2 5 5 0.03211 + 0.06219 2 5 0.82092 + = 0.309 3. 95% CI for true mean LR= 1.87 ± 2.78 x 0.309 = 1.87 ± 0.8580 = (1.01, 2.73)

27. We are 95% confident that the true mean LR is in this interval Estimating the true mean LR with confidence

28. How many coupons? experiments? no. control coupons (n c ):112141 no. treated coupons (n d ):122347 no. experiments (m) 2 8.496.316.215.394.674.10 3 2.351.751.721.491.291.13 4 1.501.121.100.960.830.73 5 1.170.870.860.750.640.57 10 0.680.500.490.430.370.33 100 0.190.14 0.120.100.09 n c m m 0.03211 + 0.06219 n d m 0.82092 + margin of error= t m-1 x

29. Summary  Even though biofilms are complicated, it is feasible to develop in vitro methods that meet the “Seven R” criteria.  Good experiments use controls, randomization where possible, and sufficient replication.  Assess uncertainty by reporting CIs.  To reduce uncertainty, invest effort in conducting more experiments instead of using more coupons in a single experiment.  For additional statistical resources for biofilm methods, check out: http://www.biofilm.montana.edu/category/documents/ksa-sm

30. Any questions?