Mixed-effect model analysis of ISTA GMO Proficiency Tests

Transcription

1 Mixed-effect model analysis of ISTA GMO Proficiency Tests ISTA GMO TF ISTA Statistics Committee Jean-Louis Laffont

2 Outline PT-Round Species Event spiking levels #samples PT01 PT0 PT03 PT04 PT05 PT06 PT07 PT08 Maize Maize Maize Soybean Soybean Canola Maize Soybean T5 MON810 MON810 T5 MON810 GTS40-3- GTS40 A704 GT73 MON863 NK603 GTS , ,.0, , 0.5, , 0.5, 1.0, , , 0.8, , 0.5, 1.0, Computation of measurement CV and quantification of flour sub-sampling variation Comparisonof different methods regarding precision PT09 Maize MON863 NK , 0.8, 90, usingmixed-effect modelling

3 About mixed-effect models Analysis of variance (ANOVA) Collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables Mixed-effect models is one class of such models Will be used here to quantify the different variations contributing to the total variation of a %GMO result.

4 The different sources of variation of a %GMO result from an ISTA PT Grinding Sample Sub-sampling and DNA extraction For some PTs, some laboratories kindly provided detailed information on their final result: Measuring Mixed-effect modelling

5 Mixed-effect model used to analyze laboratory detailed results Each dataset corresponding to the results from a particular laboratory is analyzed using a heteroscedastic linear mixed effects model. where:. μi is the mean for the i th spiking level Y = μ + A + B + E ijkl i j() i k ( ij) ijkl. Aji () is the random effect of the j th sample within spiking level i. The A ji () are i.i.d. N(0, σ sample ), where i.i.d. is used to indicate that the observations are independently and identically distributed. B is the random effect of the k th flour sub-sample from sample j and spiking level i.. k( ij) The k( ij) B are i.i.d. N(0, σ ). sample. E ijkl are the measurement errors: E are i.i.d. N(0, σ ) 1 jkl 1 E jkl are i.i.d. N(0, σ ) E Ijkl are i.i.d. N(0, σ I ) cov( E, E ) = 0for i different from i. ijkl i' j ' k ' l ' Measurement variability assumed to be different for each spiking level

6 Analysis of laboratory detailed results Output from mixed-effect model a lot of information! A portion of it will be mined in the following slides

7 Analysis of laboratory detailed results PT04 example Mean estimates and associated 95%CI A-Quant-10 A-Quant-1 A-Quant-17 A-Quant-18 A-Quant A-Quant- A-Quant-3 A-Quant-4 A-Quant-3 A-Quant A-Quant A-Quant A and A-Quant-4 B 0. A-Quant A-Quant A-Quant-9 B-Quant-15 B-Quant-7 B-Quant-33 B-Quant BMP-Quant-56 C-Quant-8 C-Quant-9 C-Quant-31 C-Quant-44b C-Quant C-Quant Results consistent with ISTA ratings

8 Analysis of laboratory detailed results Seedcalc Measurement CV and Flour Sub-sample Std Dev

9 Analysis of laboratory detailed results Measurement CV PT03 - Measurement CV (%) PT04 - Measurement CV (%) Measurement CV (%) Measurement CV (%) Average measurement CV: 0% quantile: 5% PT05 - Measurement CV (%) PT06 - Measurement CV (%) Measurement CV (%) Measurement CV (%) GTS GTS40 1-A704 1-GTS GTS

10 Analysis of laboratory detailed results Flour Sub-sample Std Dev PT03 - Flour sub-sample Std Dev PT04 - Flour sub-sample Std Dev Average: 0.06% quantile: 0.08% PT05 - Flour sub-sample Std Dev PT06 - Flour sub-sample Std Dev

11 Mixed-effect model used to analyze laboratory submitted results For PT07 and PT09, we have the information unit of measure (%DNA copies, %Mass, %Seed). For the other PTs, we have the information about the method used: Quantitative vs Semi-Quantitative. Each dataset corresponding to one type of unit of measure or one method and one PT (laboratories with BMP rating removed) is analyzed using an heteroscedastic mixed-effect model. ( ) Y = μ+ α + L + αl + E ijk i j ij ijk where:. μ is the intercept.. α i is the fixed effect of the i th spiking level.. B k( ij) is the random effect of the j th laboratory. The L j are i.i.d. N(0, σ lab ).. ( α L) ij is the random interaction effect between the i th spiking level and the j th laboratory. The ( α L) ij are i.i.d. N(0, σ spiking _ level lab ).. E ijk are the residuals: E 1 jk are i.i.d. N(0, σ 1 ) E Ijk are i.i.d. N(0, σ I ) cov( E, E ) = 0 for i different from i. ijk i' j ' k '

12 Analysis of laboratory submitted results Residual variation expressed as ˆ σ ( ˆ μ+ ˆ α ) i i Quant SemiQ PT05 PT06 PT Spiking level 4 PT0 PT03 PT CV(%)

13 Analysis of laboratory submitted results Residual variation expressed as ˆ σ ( ˆ μ+ ˆ α ) i i %DNA copies %Mass %Seed PT07 PT Spiking level CV(%)

14 Analysis of laboratory submitted results Spiking level x Lab interaction expressed as ˆspiking σ _ level lab PT05 PT06 PT08 SemiQ Quant PT0 PT03 PT04 SemiQ Quant Spiking_level x Lab standard-deviation

15 Analysis of laboratory submitted results Spiking level x Lab interaction expressed as ˆspiking σ _ level lab PT07 PT09 %Seed %Mass %DNA copies Spiking_level x Lab standard-deviation

16 Summary The mixed-effect model analysis of ISTA GMO PTs allowed us to estimate some parameters useful for Quantitative Test Plan design with Seedcalc. The mixed-effect model analysis of ISTA GMO PTs did not reveal differences in precision (not accuracy) when different methods or units of measure are used for estimating GMO%.