Handout22 - Lecture 22 1. Mixed model example 2. Crossover...

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Lecture 22 1. Mixed model example 2. Crossover designs 3. The 2 x 2 Crossover: Wine Study Example 4. Modeling fxed eFFects: treatment, period, carryover 5. Mixed model 6. The 3 x 3 Crossover: ±ood Supplement Example 7. Carryover term 8. Planning crossover designs with R: crossdes 1 Mixed Model example: Rat Diets In Lectures 10 and 11, we ft a linear model to data From a study by Sabrina Peterson (±ood Science and Nutrition) which examined eFFects on MROD (liver enzyme) over time From diets containing: • cruciFerous (C) vegetables : broccoli, cabbage, and watercress • apiaceous (A) vegetables: parsnips and celery 2 × 2 Factorial in diets: Basal (control), A, C, A+C, with 30 rats assigned to each At three times (7, 30, 60 days), they sacrifced 10 rats From each diet group to measure MROD. 2 × 2 × 3 Factorial : A × C × times 2
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day diet Frequency|Control |A |C |AC | Total ---------+--------+--------+--------+--------+ 7| 10| 1 0| 1 4 0 ---------+--------+--------+--------+--------+ 30 | 10 | 10 | 10 | 10 | 40 ---------+--------+--------+--------+--------+ 60 | 10 | 10 | 9 | 9 | 38 ---------+--------+--------+--------+--------+ Total 30 30 29 29 118 Slightly unbalanced because 2 rats not measured. 3 Part of the data: Obs Plate animal Liver_wt MROD Api Cru day diet 107 15 109 11.32 4.1450 0 1 60 C 108 15 110 14.22 4.2353 0 1 60 C 109 11 112 14.63 3.5352 1 1 60 AC 110 12 113 19.91 2.5222 1 1 60 AC Two different ways to specify the 4 diets: • by diet (0, A, C, AC) — used to make interaction plot with time • by combinations of Cru and Api — used in model 4
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Fixed-effects model: Proc GLM Preliminary model: 2 × 2 × 3 factorial: A × C × times adjusted for weight of liver, which was strongly associated with MROD level Proc GLM data=ph6470.rat_diets; class day api cru ; model MROD = liver_wt api cru api*cru day day*api day*cru day*api*cru; lsmeans day*api*cru / slice=day; All 2-factor and 3-factor interactions between experimental factors. 5 Source DF Type III SS Mean Square F Value Pr > F Liver_wt 1 10.06110559 10.06110559 15.53 0.0001 Api 1 0.85420092 0.85420092 1.32 0.2536 Cru 1 12.90007396 12.90007396 19.91 <.0001 Api*Cru 1 0.75793715 0.75793715 1.17 0.2820 day 2 0.34908168 0.17454084 0.27 0.7644 day*Api 2 0.51629446 0.25814723 0.40 0.6724 day*Cru 2 0.43713415 0.21856708 0.34 0.7145 day*Api*Cru 2 1.07263533 0.53631766 0.83 0.4400 6
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LSmeans adjusted for liver weight: Least Squares Means Standard day Api Cru MROD LSMEAN Error Pr > |t| 7 0 0 3.19037736 0.26254278 <.0001 7 0 1 4.19380460 0.27126807 <.0001 7 1 0 3.94692888 0.27513287 <.0001 7 1 1 4.13322903 0.27041769 <.0001 30 0 0 3.47668375 0.25462926 <.0001 30 0 1 4.18853602 0.25462283 <.0001 30 1 0 3.77017422 0.25465618 <.0001 30 1 1 4.18165666 0.25457044 <.0001 60 0 0 3.35529699 0.27806812 <.0001 60 0 1 4.12976077 0.28882738 <.0001 60 1 0 3.31199757 0.26548906 <.0001 60 1 1 4.21805146 0.30036140 <.0001 7 Interaction plot shows combinations of two factors: ods graphics on; ods select lsmeans meanplot; proc glimmix data=ph6470.rat_diets; class diet day; model mrod = liver_wt diet day day*diet ; lsmeans day*diet/alph a = . 3 2 plots=(meanplot(cl join sliceby=diet)); run; ods graphics off; 8
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9 Fixed-effects model 2 In rat diet experiment, liver enzyme assayed in plates, 8 rats at a time. Values within a plate are correlated by “plate effect.” Problem: 10 rats per treatment group, 8 rats per plate To account for plate-to-plate variation, we should include this in model. proc glm data=flash.rat_diets; class day api cru plate ; model mrod = plate liver_wt api cru api*cru day day*api day*cru day*api*cru / solution; lsmeans day*api*cru / stderr slice=day; 10
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Source DF Type III SS Mean Square F Value Pr > F Plate 12 14.20216234 1.18351353 2.05 0.0284 Liver_wt 1 4.69052329 4.69052329 8.11 0.0054 Api 1 1.01404063 1.01404063 1.75 0.1887 Cru 1 12.58240943 12.58240943 21.76 <.0001 Api*Cru 1 0.76569779 0.76569779 1.32 0.2528 day 0 0.00000000 . . .
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This note was uploaded on 11/21/2011 for the course PUBH 6470 taught by Professor Williamthomas during the Fall '11 term at University of Florida.

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Handout22 - Lecture 22 1. Mixed model example 2. Crossover...

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