FED

Factorial experimental design for assay development with Excel tool

Zhongming Yang

90 60

70 100

- A +

-

B

+

- A +

B: -

B: +

• Benefits of FED:1. Good coverage of experiment space

and locates solution with high efficiency

2. Lots of good statistic properties

How to estimate factor effect?

• Main effect: 1. Main effect of A (average of A+ - average

of A-):(100+60)/2 – (70+90)/2 = 0

2. Main effect of B (average of B+ - average of B-): (90+60)/2 – (70+100)/2 = -10

• Interaction effect: 1. Interaction effect of AB

((A+B+ - A+B-) – (A-B+ - A-B-))/2: ((60-100)-(90-70))/2 = -30

• Statistic model

How to optimize by experimental design?

• One factor at a time (OFAT) design:1. set A at -

1) compare B between + and -2) pick + for B

2. set B at +1) compare A between + and –2) pick – for A

3. Pick (A–B+) as final setting -> miss best setting at (A+B–)

• Factorial experimental design (FED):1. run experiment at all four conditions2. pick (A+B-) as final setting

Basic statistics: factorial experimental design basic

dose response modeling

BAABBAAB xxCBxAxy

Data from the pilot plant filtration rate experiment

Factor Effect Estimates and Sums of Squares

significant effects

negligible effects

• 4 factors (A, B, C, D)• 4 main effects: A, B, C, D• 6 2-factor interactions: AB, AC, AD, BC, BD, CD• 4 3-factor interactions: ABC, ABD, BCD• 1 4-factor interaction: ABCD

• typically, most high order interaction effects (>2) are negligible, and behave as random noise

• find statistically important factor by:• F test if have replicates• Half normal plot (assume most high order

interaction effects behave as random noise)• field specific insights are much more important!

Basic statistics: factorial experimental design example

Factorial experimental design example (Cont.)

best condition: • A +• C –• D +

FED Excel tool for assay development A pure excel tool for assay development includes following functions:

• Automatically design plate layout with factors alternate by rows or columns; But can handle ANY design (factors alternate by blocks, partial plate layout) by reading in predesigned plate layout.

• Visualize row data in plate and sorted column wise format to enable • outlier detection• decision making

• Report descriptive statistics for all main and 2-way interaction effects by table and figures

• Provide ANOVA table for all main and 2-way interaction effects (therefore should only be used as a tool to rank effects rather a statistically rigorous ANOVA analysis)

• An GUI driven tool to created a matrix of interaction plots to allow study 5 factors simultaneously.

• Well organized and comprehensive excel worksheets enable to locate essential information quickly. Excel report workbook has following sheets

• FactorialDesign• PlateMap• DataSheet• StatisticTables• StatisticFigures• ANOVATable• MatrixInteractionTables• MatrixInteractionFigures

FED Excel tool: main menu

Need enable macro first

FED Excel tool: Design page

Front factors alternate faster

design parameters provided by users

FED Excel tool: Basic data analysis - outlier detection

Outlier?delete it and redo data analysis

data are sorted by group mean colored by response level

FED Excel tool: Basic data analysis – which factors are important?

BSA NaCl MgCl DTT

Lowest response (top) Yes 150 10

Highest response (bottom ) No 0 10 1

In order to have maximum response• probably should fix following conditions: BSA -> No,

NaCl ->0, MgCl -> 10, DTT -> 1• use matrix of interaction plots and problem specific

knowledge to pick other conditions

FED Excel tool: matrix of interaction plots

FED Excel tool: partial plate design