Re: st: Using SAMPSI for repeated observations

[Ron�n Conroy <rconroy@rcsi.ie>]

On 22 Feabh 2006, at 22:59, Matt G wrote:

> However, there's a gap - no apparent way of
> calculating the sample size for a two-group comparison
> of PROPORTIONS where there are repeated observations
> in time.
Your outcome variable here is change over time in a binary variable.  
For this reason, people who don't change are uninformative. Your  
hypothesis is that the proportion of the changers who change in one  
direction (say from 0 to 1) is greater in population 1 than in  
population 2.

1. What proportion of changers in the control or reference population  
will change in the direction of interest?
2. What is the smallest difference in this proportion that would be  
of practical significance?
3. Calculate the sample size for two independent proportions.

Now is the awful bit!

4. What proportion of the population will change (in any direction)?
5. Divide the sample size by this proportion (essentially, multiply  
by 1/proportion)

Example
We want to see if getting an alternative medicine practicioner to  
give the lecture on alternative medicine will have a more beneficial  
effect on student attitudes than getting a doctor to do it.

1. We suspect that 60%  of those who change their view of alternative  
medicine following a lecture from a doctor will improve their view
2. We would regard a change of 75% as bigger than this in real life  
terms.
3. Sample size needed for 0.6 versus 0.75 in two groups is

. sampsi 0.6 0.75, pow(.9)

Estimated sample size for two-sample comparison of proportions

Test Ho: p1 = p2, where p1 is the proportion in population 1
                    and p2 is the proportion in population 2
Assumptions:

         alpha =   0.0500  (two-sided)
         power =   0.9000
            p1 =   0.6000
            p2 =   0.7500
         n2/n1 =   1.00

Estimated required sample sizes:

            n1 =      216
            n2 =      216

So we need to get two groups of 216 students (= 432) who change their  
opinions.

4. What proportion of students will change their opinions after the  
lecture? We might guess that as few as 40% will - people tend to have  
made their minds up about alternative medicine before you give your  
lecture!
5. So to recruit 432 students who change their opinions, we will need

. di 432/.4
1080

1080 students.

That's a lot.

Note that participants who do not change status from one follow-up to  
the next are uninformative. You have to inflate the sample size you  
get from Stata to account for these uninformative cases.

Note: -sampsi-  routinely gives 90% power. I needn't have included it  
in the command. I was being slightly pedagogical in making a decision  
about the power I needed as part of the calculation process.

Ron�n Conroy
rconroy@rcsi.ie




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