Model Validation

1 downloads 0 Views 1MB Size Report
Nov 18, 2016 - one concentration. More confidence to those data points. WEIGHTING. Homoscedastic. Heteroscedastic. (More weight on those data points in.
An analyst-independent, unbiased procedure for selection and validation of a calibration model Brigitte Desharnais, Félix Camirand-Lemyre, Pascal Mireault, Cameron D. Skinner CBGRC 2016 Montréal, Québec, Canada Friday, November 18th 2016

Data treatment software offer different calibration models to fit data Cocaine Order Weighting

Linear

Quadratic

No weight

1/x 1/x2

2

Traditional methods are biased and perform poorly

Linear, No Weight

QC Identification

Accuracy

QC Low

15%

QC Middle

11%

QC High

8%

3

Traditional methods are biased and perform poorly

Linear, No Weight

Linear, 1/x

QC Identification

Accuracy

QC Low

30%

QC Middle

26%

QC High

19%

QC Identification

Accuracy

QC Low

27%

QC Middle

23%

QC High

17%

4

Traditional methods are biased and perform poorly

Linear, 1/x

2

Quadratic, No Weight

QC Identification

Accuracy

QC Low

26%

QC Middle

23%

QC High

18%

QC Identification

Accuracy

QC Low

17%

QC Middle

15%

QC High

12%

4

Traditional methods are biased and perform poorly Success Rate of “Fit and Check” method

Model

Weight

Order

Linear, No Weight

100%

100%

Linear, 1/x

2%

83%

Linear, 1/x2

32%

67%

Quadratic, No Weight

33%

44%

Quadratic, 1/x

79%

24%

Quadratic, 1/x2

34%

48%

5

Choosing the correct calibration model is important for QC accuracy Data is quadratic: Improvement provided by using a quadratic model rather than a linear model 1

1/x

1/x2

Minimum:

-155%

-20.1%

-18.5%

Maximum:

-2.40%

-0.26%

-0.03%

“It was found that for analytical data with heteroscedastic proportional error, neglecting the weightings could result in as high as one order of magnitude of precision loss in the low concentration region.” Gu et al. Analytical Chemistry, 2014-86-8959. 6

A defined method is required for the selection and validation of the correct calibration model

Weight Selection - Residuals graph - F-test - Cochran test

Order Selection - Residuals graph - ANOVA-LOF - Partial F-test - Significance of the second order term

Model Validation

- Residuals graph - ANOVA-LOF - Normality testing of the residuals

7

A defined method is required for the selection and validation of the correct calibration model Is weighting required? Heteroscedasticity testing through F-test

Which weight? Variance evaluation

Which order? Partial F-test

Model validated? Normality testing of the residuals

8

A defined method is required for the selection and validation of the correct calibration model

8

Heteroscedasticity testing through the F-test Heteroscedastic

Homoscedastic

Error smaller at one concentration

More confidence to those data points

WEIGHTING (More weight on those data points in regression calculation)

Heteroscedasticity testing through the F-test

Comparison of Fcalc with the F Distribution Table.

Cocaine p-value 6.896x10-9 Weighting required.

p>0.05 : Homoscedastic data No weighting p0.05 : Model Validated p