Question

c. suppose you have 80 patients in your sample, and you think the drug may be affected by the 4 stages of cancer. set up a block design experiment.

Explanation:

Step1: Identify blocking factor

The blocking factor here is the 4 stages of cancer. We need to group (block) patients by their cancer stage.

Step2: Determine number of blocks and treatments (assuming a common drug testing setup with, say, 2 treatments: drug and placebo)

Number of blocks (b) = 4 (stages). Let's assume number of treatments (k) = 2 (drug, placebo). Total patients (N) = 80.

Step3: Calculate patients per block - treatment combination

First, find patients per block: $\frac{80}{4} = 20$ patients per block (stage). Then, per treatment within a block: $\frac{20}{2} = 10$ patients. So each block (stage) has 10 patients for drug and 10 for placebo.

Step4: Outline the block design

• Block 1: Stage 1 cancer patients, 10 get drug, 10 get placebo.
• Block 2: Stage 2 cancer patients, 10 get drug, 10 get placebo.
• Block 3: Stage 3 cancer patients, 10 get drug, 10 get placebo.
• Block 4: Stage 4 cancer patients, 10 get drug, 10 get placebo.
• Randomize treatment assignment within each block to reduce bias.

Answer:

1. Blocks: Divide 80 patients into 4 blocks (one per cancer stage), with 20 patients per block.
2. Treatments (e.g., drug vs. placebo): Assign 10 patients in each block to the drug and 10 to the placebo (or other treatments), randomizing within blocks.
3. Analysis: Compare treatment effects within each block (stage) and across blocks to assess drug efficacy by cancer stage.

(Note: Treatment count can adjust; the key is blocking by cancer stage to control for its effect on the drug’s impact.)