PhEur Two-dose multiple assay with completely randomised design An assay of corticotrophin by subcutaneous injection in rats

Átírás

1 PhEur... Two-dose multiple assay with completely randomised design An assay of corticotrophin by subcutaneous injection in rats catterplot of multiple variables against dose PhEur_.sta v*0c *x T *x U *x két dózis, tehát a linearitás nem vizsgálható dose T U Parallel_példák 7 00 catterplot of multiple variables against PhEur.sta 6v*0c *x T -7.67*x U 0-.7*x T U Parallel_példák 8

2 * treatment treatment Total Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization Type I decomposition; td. of Estimate: Degr. of M F p Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: Degr. of M F p párhuzamosság Univariate Results for Each DV (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition Degr. of y y y y M F p Parallel_példák 9 Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization Type I decomposition; td. of Estimate: Degr. of M F p * Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: Degr. of M F p treatment treatment Total Univariate Results for Each DV (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition Degr. of y y y y M F p csak és T Parallel_példák 0

3 Raw Residuals Predicted vs. Residual Values Dependent variable: y (Analysis sample) Predicted Values 0. Expected Normal Value Normal Prob. Plot; Raw Residuals Dependent variable: y (Analysis sample) Residual Parallel_példák Parameter Estimates (PhEur.sta) (*Zeroed predictors failed tolerance check) Level of umn Comment y y y y (B/Z/P) Param. td.err t p T Biased Zeroed* catterplot of y against PhEur.sta v*0c Function *x-6. Function *x y Include '' Include 'T' Other Parallel_példák

4 a minta a std 6. ln xminta ln xstd b xminta exp x std potency ( 0.060) Parallel_példák Konfidencia-intervallum CM [ V ] + ( C ) C( M ) T ± T C tα sr M T ln x minta ln x std V d a dózisok száma, n az ismétlések száma b dn C tα s r V b dn ( 8.97) Parallel_példák

5 M T CM ln xminta ln xstd [ + ] ( C ) C( M ) ± V T T [ ] ± ± 0.0 c c 0 minta 0std ( 0.8,.) ( 0.9, 0.) Parallel_példák PhEur... Three-dose Latin square design Antibiotic agar diffusion assay using a rectangular tray 6 Row Row Row Row 6 Row T T T T T T T T T T T T T T T 6 T T T 7 Row6 6 Row Row Row Row 6 Row 7 Row y: inhibiciós zóna (mm) *0 Parallel_példák 6

6 Row Treatment higszer 6 dilution 7 8 y T T T T T T T T T T T T T T dilution.^higszer log(/dilution) a Treatment egy szintje egy készítmény*dózis kombináció Parallel_példák 7 0 catterplot of y against PhEur.sta 8v*6c y Include '' Include 'T' Other Parallel_példák 8

7 Main effects ANOVA Row Treatment Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate:.70 Degr. of M F p A sorok közötti különbség szignifikáns, megérte! Az előnye ennek a vizsgálatnak, hogy nem az illesztett egyenesekhez képest nézi az eltéréseket, tehát azok hibája nem a reziduumba (az sorba) kerül. Parallel_példák 9.0 Normal Prob. Plot; Raw Residuals Dependent variable: y (Analysis sample) Expected Normal Value Residual Parallel_példák 60

8 General linear models> General linear models Parallel_példák 6 Row * Univariate Tests of ignificance for y (PhEur.sta) Type I decomposition; td. of Estimate:.70 Degr. of M F p Type III, részben mások az eredmények! * Row Univariate Tests of ignificance for y (PhEur.sta) Type III decomposition; td. of Estimate:.70 Degr. of M F p Type I: ebben a sorrendben építjük föl a modellt a párhuzamosság teljesül Type III: ha már az összes többi tag benne van, mennyit hoz, ha ezt is bevesszük Parallel_példák 6

9 Parallel_példák 6 a linearitás teljesül, a másodfokú tag nem szignifikáns Row * *^ Univariate Tests of ignificance for y (PhEur.sta) Type I decomposition; td. of Estimate:.70 Degr. of M F p Parallel_példák 6

10 Row Treatment Row * nonlin Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate:.70 Degr. of M F p Univariate Tests of ignificance for y (PhEur.sta) Type I decomposition; td. of Estimate:.70 Degr. of M F p treatment * másik módszer a linearitás ellenőrzésére ν--- Parallel_példák 6 Analysis of covariance, mert a párhuzamosság teljesült meredekség Row Row Row Row Row Row Parameter Estimates (PhEur.sta) (*Zeroed predictors failed tolerance check) Level of umn Comment y y (B/Z/P) Param. td.err Biased Biased Biased Biased Biased Zeroed* Biased Biased Biased Biased Biased Zeroed* Biased..687 T Zeroed* Parallel_példák 66

11 ln x minta ln x std a minta a b std xminta exp x std ( 0.0) Parallel_példák 67 Konfidencia-intervallum CM [ V ] + ( C ) C( M ) T ± T C tα sr M T ln x minta ln x std V d a dózisok száma, n az ismétlések száma b dn C tα s r V b dn 87.0 ( 6.6) Parallel_példák 68

12 M T ln x ln x minta std 0.0 CM [ + ] ( C ) C( M ) ± V T T [ + 0. ] ( 0.0) ± ( 0.0) ± c c 0 minta 0std ( 0.9,.08) ( 0.098, 0.08) a különbség oka az eltérő modell Parallel_példák 69 y Row; Weighted Means Current effect: F(, )., p.0067 Type III decomposition Vertical bars denote 0.9 confidence intervals 6 Row Parallel_példák 70

13 Kérdezhetjük, hogy a sor és oszlop hatása mint ingadozás, mekkora: Row Components of Variance (PhEur.sta) Type III decomposition y Row Univariate Tests of ignificance for y (PhEur.sta) Type III decomposition; td. of Estimate: Degr. of M Den.yn. Den.yn. F p (F/R) df M Fixed Random Random Fixed Fixed Parallel_példák 7 Ha nem törődnénk a sorokkal és oszlopokkal: Univariate Tests of ignificance for y (PhEur.sta) Type III decomposition; td. of Estimate:.698 Degr. of M F p Összehasonlításul a helyes földolgozás: Row * df nagyobb ugyan, de az M-be bekerül a sor és oszlop okozta különbség is, p nagyobb Univariate Tests of ignificance for y (PhEur.sta) Type I decomposition; td. of Estimate:.70 Degr. of M F p Parallel_példák 7

14 Parameter Estimates (PhEur.sta) (*Zeroed predictors failed tolerance check) Level of umn Comment y y (B/Z/P) Param. td.err Row Biased Parameter Estimates (PhEur.sta) Row Biased (*Zeroed predictors failed tolerance Rowcheck) Biased Row Biased Level of umn Comment Row y y 6 Biased (B/Z/P) Row Param. td.err6 7 Zeroed* Biased Biased Biased Biased T Zeroed* Biased Biased Zeroed* Biased..687 T Zeroed* a becsült paraméterek nem különböznek Parallel_példák 7 Konfidencia-intervallum CM [ V ] + ( C ) C( M ) T ± T C tα sr M T ln x minta ln x std V d a dózisok száma, n az ismétlések száma b dn C tα s r az.008 helyett V b dn 87.0 ( 6.6) Parallel_példák 7

15 ln x ln x M T minta std ( ) ( T ± C C M T ) + CM 0.0 [ ] V [ + 0. ] ( 0.0) ± ( 0.0) ( 0.098, 0.08) ± c c 0 minta 0std ( 0.0) ± ( 0.0) ( 0.898,.06) [ + 0. ] ± ( 0.07, 0.060) ( 0.9,.08) helyett Parallel_példák 7 PhEur... Four-dose randomised block design Antibiotic turbidimetric assay A csöveket vízfürdőbe teszik, nyolcasával, az egy blokk. Block 6 T 7 T 8 T 9 T Parallel_példák 76

16 Block higszer dozis_no dilution 6 Treatment 7 8 y Parallel_példák catterplot of multiple variables against PhEur.sta 8v*0c T Parallel_példák 78

17 Main effects ANOVA Block Treatment Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: 7.76 Degr. of M F p A blokk hatása szignifikáns. Parallel_példák 79 0 Predicted vs. Residual Values Dependent variable: y (Analysis sample) 0 Raw Residuals Normal Prob. Plot; Raw Residuals Dependent variable: y (Analysis sample) Predicted Values Expected Normal Value Residual Parallel_példák 80

18 General linear models> General linear models a párhuzamosság teljesül Block * Univariate Tests of ignificance for y (PhEur.sta) Type I decomposition; td. of Estimate: 7.69 Degr. of M F p Parallel_példák 8 Block Treatment Block * Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: 7.76 Degr. of M F p Univariate Tests of ignificance for y (PhEur.sta) Type I decomposition; td. of Estimate: 7.69 Degr. of M F p nonlin treatment * ν7--- Parallel_példák 8

19 Block * *^ *^ Univariate Tests of ignificance for y (PhEur.sta Type I decomposition; td. of Estimate: 7.76 Degr. of M F p a görbeség nem szignifikáns, sem másodfokú, sem harmadfokú tag nem kell Parallel_példák 8 Analysis of covariance Block Block Block Block Block Parameter Estimates (PhEur.sta) (*Zeroed predictors failed tolerance check) Level of umn Comment y y (B/Z/P) Param. td.err Biased Biased Biased Biased Zeroed* Biased T 8 Zeroed* a minta a std 7.9 ln xminta ln xstd 0.07 b. xminta exp x std ( 0.07). 07 Parallel_példák 8

20 Konfidencia-intervallum CM [ V ] + ( C ) C( M ) T ± T C tα sr M T ln x minta ln x std V d a dózisok száma, n az ismétlések száma b dn C tα s r V b dn 07.6 (.) 0. Parallel_példák 8 M T CM ln xminta ln xstd 0.07 [ + ] ( C ) C( M ) ± V T T [ ] ± ± 0.07 c c 0 minta 0std (.09,.) ( 0.088, 0.) Parallel_példák 86

21 A blokk figyelembe vétele nélkül Treatment Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: Degr. of M F p Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: Degr. of M F p Parallel_példák 87 C tα s r CM [ + ] ( C ) C( M ) ± V T T [ ] ± ± 0.00 ( 0.0, 0.) c c 0 minta 0std (.0,.0) (.09,.) helyett Parallel_példák 88

22 PhEur... Five-dose multiple assay with completely randomised design: An in-vitro assay of three hepatitis B vaccines against a standard dilution : : : : : : : : : : : : : : : T U V mindegyik készítményből független hígítási sor, abszorbanciát mérnek Föltételezzük, hogy a hígítás hibamentes! Parallel_példák 89.6 catterplot of multiple variables against PhEur.sta v*c *x T *x U *x V.8+0.9*x T U V Parallel_példák 90

23 Treatment Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate:.0 Degr. of M F p * Univariate Tests of ignificance for y (PhEur.sta Type I decomposition; td. of Estimate:.0 Degr. of M F p nem párhuzamosak, de nem is lineárisak Parallel_példák 9 ha logaritmáljuk az adatokat, párhuzamosak lesznek a vonalak 0. catterplot of multiple variables against PhEur.sta v*c ln *x lnt *x lnu *x lnv *x ln lnt lnu lnv Parallel_példák 9

24 * Univariate Tests of ignificance for lny (PhEur.sta Type I decomposition; td. of Estimate: Degr. of M F p Treatment nonlin Univariate Tests of ignificance for lny (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: Degr. of M F p treatment * ν9--- Parallel_példák 9 Tests of Homogeneity of Variances (PhEur.sta) : "Treatment" Hartley F-max Cochran C Bartlett Chi-qr. df p lny Levene's Test for Homogeneity of Variances (PhEur.sta : "Treatment" Degrees of freedom for all F's: 9, 0 M M F p lny nem megnyugtató Test of Lack of Fit (PhEur.sta) Dependent Variable Pure Err df Pure Err M Pure Err Lack of Fit df Lack of Fit M Lack of Fit F p lny Parallel_példák 9

25 ANCOVA Univariate Tests of ignificance for lny (PhEur.sta Type I decomposition; td. of Estimate: Degr. of M F p Parameter Estimates (PhEur.sta) (*Zeroed predictors failed tolerance check) Level of umn Comment lny lny (B/Z/P) Param. td.err Biased T Biased U Biased V 6 Zeroed* a T a ln xt ln x 0.77 b xt exp x Parallel_példák 9 ( 0.77). 7 xt exp x ( 0.77). 7 P-Plot: lny: log(y) : "Treatment" (Plot of within-cell residuals) All Groups Expected Normal Value Predicted vs. Residual Values Dependent variable: lny (Analysis sample) Observed Value Raw Residuals Predicted Values Parallel_példák 96

26 PhEur... A completely randomised (0,,) design An assay of factor VIII B T T T abszorbancia a jel slope ratio assay Parallel_példák 97 nem jó a lineáris függvény a blank-re Test of Lack of Fit (PhEur.sta) Dependent Variable Pure Err df Pure Err M Pure Err Lack of Fit df Lack of Fit M Lack of Fit F p y Parallel_példák 98

27 Blank nélkül Test of Lack of Fit (PhEur.sta) Exclude condition: 0 Dependent Variable Pure Err df Pure Err M Pure Err Lack of Fit df Lack of Fit M Lack of Fit F p y dose doset Treatment Univariate Tests of ignificance for y (PhEur.sta) Type III decomposition; td. of Estimate: Exclude condition: 0 Degr. of M F p Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate: Exclude condition: 0 Degr. of M F p Parallel_példák 99 dose doset Parameter Estimates (PhEur.sta) Exclude condition: 0 y y Param. td.err R Parallel_példák 00

28 PhEur... A completely randomised (0,,,) design An in vitro assay of influenza vaccines conc (ug/ml) I II TI TII 6 UI 7 UII haemagglutinin antigen content by radial immunodiffusion, zone of precipitation area mm Parallel_példák 0 Treatment Univariate Tests of ignificance for y (PhEur.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate:.000 Degr. of M F p Test of Lack of Fit (PhEur.sta) Dependent Variable Pure Err df Pure Err M Pure Err Lack of Fit df Lack of Fit M Lack of Fit F p y Parallel_példák 0

29 PhEur... Four-parameter logistic curve analysis A serological assay of tetanus sera dose Dilution P 6 P N0 A guinea-pig antiserum is assayed against a standard serum (0. IU/ml) using an enzyme-linked immunosorbent assay technique (ELIA). 0 two-fold dilutions of each serum were applied on a 96-well ELIA plate. Each dilution was applied twice. Parallel_példák 0 α δ y δ + + e α δ δ + dose + EC0 β ( x γ ) β x bx a e a > 0, b ln a y lépések: variancia konstans? normális eloszlás? jó-e a függvény illeszkedése? párhuzamosak-e a görbék? RP konf. intervallum Parallel_példák 0

30 . catterplot of multiple variables against PhEur.sta 6v*0c y yp Parallel_példák Dilution e Pe 6 y P P P P P P P P P P P P P P P P P P P P 0 0. Parallel_példák 06

31 külön P Predicted vs. Residual Values Dependent variable: y (Analysis sample) Include condition: 'P' s e s e Raw Residuals treatment Univariate Tests of ignificance for y (PhEur kulon.sta) igma-restricted parameterization ive hypothesis decomposition; td. of Estimate:.09 Include condition: 'P'.0 Degr. of M F p Tests of Homogeneity of Variances : "treatment" Include condition: 'P' Hartley F-max Cochran C Bartlett Chi-qr. df p y Expected Normal Value P-Plot: y All Groups : Predicted "treatment" Values (Plot of within-cell residuals) Include condition: 'P' Observed Value Parallel_példák 07 Model: yd+(a-d)/(+exp(-bp*pe*(-gp))) (PhEur kulon.sta Dep. var: y Loss: (OB-PRED)** Final loss: R Variance explained: 99.9% Include condition: 'P' N0 d a bp gp 0.0 Estimate td.err t(6) %CL %CL p-value s e s r F s r 0 se ( 6,0). F Residual Values Predicted versus Residual Values Include condition: 'P' Expected Normal Value Predicted Values Normal Probability Plot of Residuals Include condition: 'P' Residuals Parallel_példák 08

32 külön treatment Univariate Tests of ignificance for y (PhEur kulon.sta).0 igma-restricted parameterization. ive hypothesis decomposition; td. of Estimate:.069 Include condition: ''.0 Degr. of M F p Tests of Homogeneity of Variances : "treatment" Include condition: '' Hartley F-max Cochran C Bartlett Chi-qr. df p y Levene's Test for Homogeneity of Variances : "treatment" Degrees of freedom for all F's: 9, 0 Include condition: '' M M F p y E re nem megy! s e s e Expected Normal Value Raw Residuals P-Plot: y : "treatment" (Plot of within-cell residuals) Include condition: '' Predicted Observed vs. Residual Value Values Dependent variable: y (Analysis sample) Include condition: '' Parallel_példák 09 All Groups Predicted Values Model: yd+(a-d)/(+exp(-b*e*(-g))) (PhEur kulon.sta) Dep. var: y Loss: (OB-PRED)** Final loss: R.9998 Variance explained: 99.86% Include condition: '' N0 d a b g Estimate td.err. t(6) -9%CL +9%CL p-value Normal Probability Plot of Residuals Include condition: '' 0.08 Predicted versus Residual Values Include condition: '' 0.00 s e s r sr.79 0 F.8 s. 0 0 e ( 6,0). F 0 Expected Normal Value Residual Values Residuals Predicted Values Parallel_példák 0

33 eddig: variancia konstans? normális eloszlás? jó-e a függvény illeszkedése? következik: párhuzamosak-e a görbék (a közös meredekség és aszimptoták feltétele teljesül)? RP konf. intervallum Parallel_példák yd+((a-d)/(+exp(-b*(pe*(-gp)+e*(-g))))) α δ step: 0. y δ + β ( x γ j ) + e Model: yd+((a-d)/(+exp(-b*(pe*(-gp)+e*(-g)... (PhEur.sta) Dep. var: y Loss: (OB-PRED)** Final loss:.09 R.999 Variance explained: 99.90% N0 d a b gp g Estimate td.err. t() -9%CL +9%CL p-value közös meredekség Correlation Matrix of Parameter Estimates (PhEur.sta) Parameter d a b gp g d a b gp g Parallel_példák

34 Parallel_példák yd+((a-d)/(+exp(-(pe*bp*(-gp)+e*b*(-g))))) Model: yd+((a-d)/(+exp(-(pe*bp*(-gp)+e*b*(... (PhEur.sta) Dep. var: y Loss: (OB-PRED)** Final loss: R.999 Variance explained: 99.90% N0 d a bp gp b g Estimate td.err. t() -9%CL +9%CL p-value Correlation Matrix of Parameter Estimates (PhEur.sta) Parameter d a bp gp b g d a bp gp b g α δ y δ + β j ( x γ j ) + e külön meredekség F Parallel_példák

35 Parallel_példák eddig: variancia konstans? normális eloszlás? jó-e a függvény illeszkedése? párhuzamosak-e a görbék? következik: RP konf. intervallum ln xt ln x lnγ ln γ T x x T e Parallel_példák 6

36 Model: y(pe*dp+e*d)+(((pe*ap+e*a)-(pe*dp+e*d))/(+e... (PhEur kieg.sta) Dep. var: y Loss: (OB-PRED)** Final loss: R.999 Variance explained: % N0 dp d ap a bp gp b g Estimate td.err. t() -9%CL +9%CL p-value F Parallel_példák 7 catterplot of multiple variables against PhEur.sta v*0c ky kyp Parallel_példák 8