Statistics 541: Randomization (How To)

Admistrivia

• no homework this week (yea!)

As treated vs intent to treat

• doesn't it make more sense to look at those who get the drugs?
• Called "as treated" (obviously named by the evil empire!)
• Average treated - average untreated is hopelessly biased
• Suppose you have three types:
  1. always takers
  2. never takers
  3. proper subjects (as assigned takers)
• Then we can try to estimate the third group

Controlled experiments/random sampling

• Chase down some goats
• 100 mice are in a cage, pick 50 for treatment, leave remaining 50 for control
• Slow goats/mice are sampled!
• Must use randomization device

Blocking

• JMP will generate random Bernulli trials
• Problem with Bernuilli trials is that they are independent.
• You might get everyone under treatment!
• Better is to use a multinomial (fancy word for pulling cards from a deck without replacement)

Stratification

• Blocking for treatment vs control, why not also block for male vs female?
• Called stratification.
• Good idea: but male/female, young/old, black/white, healthy/sick. Now we have one person per cell.
• Talk to doctor to see what is likely to be important and control for the single most important issue.

Non-stratification approaches

• What if you want to control for 10 things?
• You need at least 1024 subjects!
• If you use 11 subjects and regression you are fine. (Ok, 40 would be more realistic)
• So do a multiple regression on things you want to control for
• Just don't tell anyone! Call it "adjusted" or something else
• Note: Toxicity can't be used as a covariate. Why?

Some math on efficiency

• Controling ahead of time doesn't cost a degree of freedom
• Controling afterward costs a degree of freedom
• No bigee-if you have at least 50 observations. Bigee if you have only 10 observations.