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

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

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

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

Why statistical thinking? in vitro testing

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

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

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 )

Resemblance Example Drip Flow Reactor Low shear Plug flow ASTM E2647

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

Resemblance Example Density LD Coupon cfu/cm 2 log(cfu/cm 2 ) x x ControlLD= 8.29 Data: log 10 (cfu/cm 2 ) from viable plate counts

Resemblance Example Exp coupon LD Control LD Control SD

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)

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 )

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

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

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

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

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 )

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

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

Repeatability Example Exp coupon LD Control LD Control SD

Repeatability Example Mean LR = 1.87 Exp control coupon LD Control LD treated coupon LD Treated LDLR Since there is no obvious pairing between the controls and treated coupons in each experiment, get 1 LR for each experiment

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:

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

Estimating the true mean LR with confidence 1. Mean LR = S c 2 = S d 2 = S E 2 = n c = 2, n d = 2, m = 5 SE of mean LR = = % CI for true mean LR= 1.87 ± 2.78 x = 1.87 ± = (1.01, 2.73)

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

How many coupons? experiments? no. control coupons (n c ): no. treated coupons (n d ): no. experiments (m) n c m m n d m margin of error= t m-1 x

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:

Any questions?