Measuring Parallelism and Relative Potency In Well-Behaved and Ill-Behaved Cell-Based Bioassays

Transcription

1 IIR Third Annual Cell Based Assays Measuring Parallelism and Relative Potency In Well-Behaved and Ill-Behaved Cell-Based Bioassays Workshop Instructor: John R. Dunn, Ph.D. Chief Technical Officer Brendan Technologies ext. 4 jdunn@brendan.com

2 Curve Fitting Linear Regression Requires: Weight individual points Least squares regression algorithm Nonlinear Curve Fitting Requires: Weight individual points Numeric processes to find the global minimum - the one set of coefficients that results in the lowest residual sum of squared error (RSSE)

3 Residual Sum of Squared Errors {(, ), } D= x y i = K N i i Data Points w = i variance i Weighting RSSE = N i= w i y i Y Fit Measure χ Prob = Dist, N - P Fit Probability χ ( RSSE ) 3

4 Nonlinear Regression Fitting R e s p o n s e wsse Weights w Δ w Σ Δ w 3 Δ w 4 w 5 Δ w 6 Residuals (Errors) Dose Δ Δ Logistic Curve Being Fitted 4

5 3PL, 4PL and 5PL Logistic y = a* x b + c 3PL y y ( a d) = d + ( ) b + x c ( a d) = d + ( ) b + xc g 4PL 5PL The logistic model is a mathematical shape function only, its parameters do not correlate with any physical properties of the bioassay or immunoassay reaction. 5

6 5PL Regression Fitting wsse 4 g c 6

7 7 5PL Coefs b vs g g b 3 4 SSE g b 3 4 SSE

8 Evaluating Curve Models Compute Assays With Pooled Weighting Model Fit using highest parameter curve model (e.g. 5PL) Fit lower parameter model, if desired, and compare Examine Assay Fit Metrics RSSE is a χ distributed number having (Number of Points Number of Parameters) degrees of unconstdom The χ probability (Fit Probability) is uniformly distributed from Fit Probability Average From All Assays A good curve fit model and good weighting model average in range of.3.7 (bioassays) and.4.6 (immunoassays) Higher fit probabilities caused by estimated variances too large Lower fit probabilities caused by inadequate curve models or estimated variances too small for some or all residuals 8

9 Asymmetric Curve (High Knee) PL (a>d) 3 5PL (d>a) SSE: DF: 3 Res Var:.9995 Fit Prob: SSE: DF: 3 Res Var:.48 Fit Prob: PL 4 3 3PL SSE: DF: 4 Res Var:.69 Fit Prob: SSE: DF: 5 Res Var: 5.49 Fit Prob: <. 9

10 Asymmetric Curve (Low Knee) PL (a>d) PL (d>a) SSE: DF: 3 Res Var: Fit Prob:.793 SSE:.7958 DF: 3 Res Var: Fit Prob: PL 4 3PL SSE: DF: 4 Res Var:.499 Fit Prob: < SSE: DF: 5 Res Var: Fit Prob: <.

11 Symmetric Curve 4 5PL (a>d) 4 5PL (d>a) SSE:.46 DF:3 Res Var: Fit Prob: SSE:.366 DF:3 Res Var: Fit Prob: PL 5 3PL SSE:.4384 DF:4 Res Var:.6596 Fit Prob: SSE: DF:5 Res Var: 5.46 Fit Prob: <.

12 No Upper Plateau 5 5PL (a>d) 5 5PL (d>a) SSE: DF:3 Res Var:.366 Fit Prob:.3469 SSE: DF:3 Res Var:.393 Fit Prob: PL 5 3PL SSE: DF:4 Res Var:.8883 Fit Prob: SSE: DF:5 Res Var: Fit Prob:.6579

13 EEG Curve Metrics Method Controls: Reference Set Assay Coef a Coef b Coef c Coef d Coef g SSE Res Var Fit Prob EEG-43.6E EEG-44.4E EEG-45.E EEG-46.6E EEG-47.3E EEG-48.4E EEG-49.6E EEG-5.6E EEG-5.E EEG-5.3E E EEG-53.5E EEG-54.3E EEG-67.7E EEG-68.3E EEG-69.E EEG EEG EEG EEG-74.6E EEG-76.7E EEG-77.9E EEG-78.E EEG-79.E EEG EEG-8.8E EEG EEG-87.7E EEG-86.6E EEG-85.5E EEG-84.7E Assays Average Minimum Maximum

14 4PL & 5PL Curves (VUT-9) VUT-9 (Current Assay) 4 Parameter Logistic Curve 4PL VUT-9 (Current Assay) 5 Parameter Logistic Curve 5PL 4

15 5PL Curve Metrics (VUT) Method Controls: Reference Set Assay Coef a Coef b Coef c Coef d Coef g SSE Res Var Fit Prob VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT E-.95E-.889 VUT VUT VUT VUT VUT VUT E VUT E-.5E-.874 VUT VUT VUT VUT Assays Average Minimum Maximum

16 4PL Curve Metrics (VUT) Method Controls: Reference Set Assay Coef a Coef b Coef c Coef d Coef g SSE Res Var Fit Prob VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT VUT Assays Average Minimum Maximum

17 VUT Residuals (4 Assays) VUT 4PL Weighted Residuals Fit Prob =.3 (4 Assays) VUT 5PL Weighted Residuals Fit Prob =.35 (4 Assays) Squared Residuals Squared Residuals

18 5PL DEF-73 8

19 5PL Curve Metrics (DEF) Method Controls: Reference Set Assay Coef a Coef b Coef c Coef d Coef g SSE Res Var Fit Prob DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF E-.998 DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF Assays Average Minimum Maximum

20 4PL Curve Metrics (DEF) Method Controls: Reference Set Assay Coef a Coef b Coef c Coef d Coef g SSE Res Var Fit Prob DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF DEF Count Average Minimum Maximum

21 DEF Standard Response Residuals DEF 5PL Weighted Residuals Fit Prob =.485 (9 Assays) DEF 4PL Weighted Residuals Fit Prob =.5 (9 Assays) 6 6 Squared Residuals Squared Residuals Residuals - Residuals Mean Response Mean Response

22 ABC Standard Curve

23 5PL Curve Metrics (ABC) Method Controls: Reference Set Assay Coef a Coef b Coef c Coef d Coef g SSE Res Var Fit Prob ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC Assays Average Minimum Maximum

24 4PL Curve Metrics (ABC) Method Controls: Reference Set Assay Coef a Coef b Coef c Coef d Coef g SSE Res Var Fit Prob ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC Assays Average Minimum Maximum

25 ABC Standard Response Residuals ABC 5PL Weighted Residuals Fit Prob =.333 ( Assays) ABC 4PL Weighted Residuals Fit Prob =.379 ( Assays) 6 6 Squared Residuals Squared Residuals Residuals - Residuals Mean Response Mean Response 5

26 Logistic Curve Fits PL 5PL a > d 5PL d > a Assay a b c d SSE Fit Prob a b c d g SSE Fit Prob a b c d g SSE Fit Prob FCD FCD FCD FCD FCD FCD FCD FCD FCD FCD Average 6.99 <

27 FCD Standard Response Residuals Squared Residuals FCD 4PL Weighted Residuals Fit Prob =. ( Assays) Squared Residuals FCD 5PL a>d Weighted Residuals Fit Prob =.9 ( Assays) Squared Residuals FCD 5PL d>a Weighted Residuals Fit Prob =.443 ( Assays) Residuals - Residuals - Residuals Mean Response Mean Response Mean Response 7