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Design and Analysis of Augmented Designs in Screening Trials Kathleen Yeater USDA-ARS-SPA 3 rd Curators Workshop February 3, 2010

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5 Basic Steps of Experiment 1. Research Planning 2. Experimental Design 3. Summarize Observations 4. Analysis – Statistical Inference 5. Document / Present study results

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Research Planning - What is the Question? Is the focus on development? Are you trying to find something better? Is it discovery research? Not necessarily a specific hypothesis

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Remember the Basics, the 3 R’s ? Replication Valid estimation of error variance Reduction of variation among plots Controls (reduces) error variance Use blocking to control heterogeneity present in experiment; Block at scale of variability Randomization Unbiased estimates of means and variances

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Impractical, prohibitively expensive, impossible Not enough material (seed, -icides) Not enough space Not enough time Too many entries What if replication is ?

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What leads to unreplicated design in field trials? 3 R’s, making cause and effect statements In screening, making a cut based on good/bad in testing …What is the Research Question again? Design for the experiment under consideration; DO NOT experiment for design

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Augmented Design Introduced by various publications of W.T. Federer Developed for plant breeding research Genotypes Yield Disease Insecticides All are excellent subject Herbicides variables in a Screening Fertilizers Trial

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Augmented Design as Experimental Design Utilizes experimental designs principles for arrangement of checks New treatments (n) are not replicated and checks are replicated as points of reference Usually want between 4-6 checks n can be large

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Augmented Design - Implementation I – Select any experiment design for the check(s) II – Enlarge the blocks or increase number of rows and/or columns to accommodate the new test entries (treatments, n) III – New test entries are randomly distributed among blocks/rows/columns

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Design Set-up - RCB ABCD moisture gradient CADB DCBA BDAC

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Design Set-up – Augmented RCB moisture gradient AB 14 C 1912 D CA D 16 B DCB3A6 B 10 2D 15 AC

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Advantages of Augmented Design More than one check included 4 to 6 optimal Allows for estimate of experimental error and is efficient Less physical space needed

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How to select a check Checks are units of experimentation [varieties/genotypes/cultivars/entries] with known ranges of various measurement characteristics that you want to evaluate What are good checks for your objective? Yield CHO content Seed characteristics A quantitative measurement that holds constant

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Variability of Checks The test entries (n) range of measurement will be 5.0 – The mean of the overall test entries ~ What do you think about these checks? Did I do a good job of selecting appropriate checks?

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Consistent Checks that cover the range of our test data. The test entries (n) range of measurement will be 5.0 – The mean of the overall test entries ~ 12.6.

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Augmented RCBD Goal: Screen 300 new entries for response X. This is an Early Generation Screening Trial. 4 additional genotypes are CHECK entries (A, B, C, D) 6 Blocks (field plots, time placement for lab assay, location in growth chamber) Randomize location of A, B, C, D within each block (replicate the check genotypes within block for spatial variation) 300/6 = 50 new entries randomly selected and placed within each block

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How many repeats of each check for optimal design? Design Resources Server Indian Agricultural Statistics Research Institute (ICAR), New Delhi, India. Online Design Generation-I Augmented Design

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Construction of Augmented Designs via IASRI site Augmented Designs Home (Augmented designs) Outline of Analysis Welcome to construction of Augmented Designs. Use this to generate augmented design. Fill in the number of test treatments, control treatments and number of blocks etc. Number of Test treatments (w): Number of Control Treatments (u) Number of Blocks (b) Number of replication of control Requires Javascript to be enabled; Runs in Microsoft(R) Internet Explorer(R) 5.0 and above and Mozilla(R) Firefox (R) 2.0 & above Kindly send us your comments, problems to V.K. Gupta / Rajender Parsad / A. Dhandapani.V.K. GuptaRajender ParsadA. Dhandapani Home (Augmented designs)Home (Augmented designs) Design ResourcesDesign Resources CopyrightCopyright Disclaimer How to Quote this page Report Error Comments/suggestions DisclaimerHow to Quote this pageReport ErrorComments/suggestions Inserted from

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Cells filled out, Enter block sizes

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Generated Design Generated Design Block 1: (T132, T1, T214, T159, T15, T55, T69, T197, C3, T31, T88, T124, T134, T245, T165, C1, T290, T163, T291, T101, T238, T298, T74, T282, C2, T35, C3, T135, T185, T181, T8, T72, T166, T217, T3, T260, T156, T270, T7, T220, T84, T207, T170, C4, T20, T240, C1, T51, T210, T138, T112, T68, T5, C2, C4, T108, T258, T118) Block 2: (T295, C4, T208, T152, T39, T91, T178, T219, T215, T52, T237, T82, T248, C1, T62, T133, T29, T53, T162, C3, T60, T66, T172, T198, T231, T271, T269, T183, T106, C2, T253, T80, T235, C4, T199, T257, C1, T232, T289, T125, T204, T78, T43, T119, T9, T97, T16, T115, C3, T102, T294, T192, T85, C2, T300, T143, T160, T223) Block 3: (T107, T184, T280, T42, T200, T131, T17, T21, T46, T276, T100, T169, T93, T180, C1, T267, T283, C1, T4, T239, T275, T120, T262, T236, T233, T193, T70, T277, T56, T168, T110, T105, T287, T38, T171, T27, T18, C2, T274, T136, T265, C3, T293, T281, C2, T175, T59, T79, T128, C4, T158, T146, C4, T252, T161, C3, T225, T89) Block 4: ( C2, T41, T234, T14, T10, T86, T206, T145, T230, T249, T196, T114, T209, T90, T205, C2, C3, T13, C3, T244, T142, T48, T76, C1, T2, C4, T261, T12, T36, T23, T109, T113, T255, T213, T191, T202, T218, T58, C1, T285, T96, T67, T188, T45, T150, T137, T164, T259, T221, T273, T73, T144, T226, T155, T40, T194, C4, T167) Block 5: (T266, T71, C2, T157, T179, T222, T123, C1, T104, T278, T111, T272, T22, T47, T148, T182, T212, T81, T195, T247, T216, T174, T25, C3, T130, T251, T203, T28, T228, T263, T297, C4, T246, T92, T64, T117, C1, T61, C4, T32, T19, T147, T288, T94, T99, T189, T34, T98, T243, C3, T57, T254, T126, T6, T122, C2, T242, T121) Block 6: (T54, T139, T151, T77, T49, C4, C2, T201, T284, T129, T241, T227, C2, T65, T95, T264, T11, T211, T268, T296, T75, T154, T141, T33, T149, C3, T173, T176, T286, T224, T250, T37, C1, T256, T87, T177, C3, T44, T116, T103, C4, T187, C1, T190, T299, T26, T140, T50, T127, T30, T279, T229, T63, T292, T24, T83, T153, T186)

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RCB Model - Augmented Y = u + check + block + test entry + error checks are fixed effects (source of experimental error) block, test entry, and error are random effects Recall: Fixed effects = parameter estimation (mean and experimental error) Random effects = sources of variability

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Data Structure – Summarize Observations Data data-set; input BLOCK ENTRY $ CHECK $ Response ; datalines; _3C _1A _3C _2B _4D

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Analysis of Augmented RCB proc mixed; class CHECK BLOCK ENTRY; model response = CHECK / solution; random BLOCK ENTRY / solution; lsmeans CHECK; run;

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Covariance Parameters Covariance Parameter Estimates Cov ParmEstimate BLOCK0.0646variance component of block ENTRY variance component of entry Residual2.8793error variance

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LSMEANS – Checks Least Squares Means Standard Effect CHECK Estimate Error CHECK CHECK A CHECK B CHECK C CHECK D

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SOLUTION option in MODEL statement presents estimates of the fixed effect parameters Solution for Fixed Effects Standard Effect CHECK Estimate Error Intercept CHECK CHECK A CHECK B CHECK C CHECK D 0.

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Estimated BLUPs Best Linear Unbiased Predictors Random effects – estimate the variance Estimate “realized values of random variables” (test entries) Augmented designs – use SOLUTION option in RANDOM statement random BLOCK ENTRY / solution;

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Solution for Random Effects Std Err EffectENTRY BLOCK Estimate Pred DF t Value Pr > |t| BLOCK BLOCK BLOCK ENTRY ENTRY ENTRY ENTRY ENTRY ENTRY ENTRY <.0001 ENTRY ENTRY ENTRY ENTRY ENTRY ENTRY <.0001 ENTRY <.0001 ENTRY

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“Realized values” Rearrange estimates of entries from highest to lowest proc sort data=data-set; by DESCENDING estimate; run; Add Intercept to Estimate values – calculate predicted adjusted mean values data data-set; pred_adjmean = estimate ; run;

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Predicted Adjusted Mean Values StdErr pred_ ObsEffect BLOCK ENTRY Estimate Pred DF tValue Probt adjmean 1 ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ < ENTRY _ <

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Augmented Designs - Recap Screening – Discovery Driven Select 4-6 meaningful checks Select appropriate experimental design and increase rows and columns to include unreplicated test entries in each block RCB is simplest case, split-plots, factorials are also possibilities (can look at interactions and autocorrelations) Mixed model analyses Phase II begins – Select entries to do pilot study to elicit better estimate of true response; generate hypotheses

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Augmented Designs - References To get started: Google! Federer et al (2001) Agron. J. 93: Federer, W.T. (2005) Agron. J. 97: Burgueño and Crossa (2000) SAS Macro for Analysing Unreplicated Designs CIMMYT CRIL (crop research informatics laboratory) IASRI, Augmented Design tool

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