Estimating Sample Size for Grant Application

[GWestphal]

I just got my reviews back for a grant and they harped on that I didn't have any statistical analysis for how many animals I'll need. I'm super rusty on stats, could anyone point me in the direction I need.

Basically, a drug I'm testing will reduce the duration of an event by 75% relative to the control. So basically, in each event I will either achieve 75% reduction or not, meaning there is a 50% chance of success. How many samples do I need to ensure a confidence level of 99%?

 

[TrackSmart]

I just got my reviews back for a grant and they harped on that I didn't have any statistical analysis for how many animals I'll need. I'm super rusty on stats, could anyone point me in the direction I need.

Basically, a drug I'm testing will reduce the duration of an event by 75% relative to the control. So basically, in each event I will either achieve 75% reduction or not, meaning there is a 50% chance of success. How many samples do I need to ensure a confidence level of 99%?

You have to do a power analysis. I wish I could be more helpful, but my stats (particularly related to power analyses) are rusty, too! Check out the bottom of the page for an example.
http://en.wikipedia.org/wiki/Statistical_power

Your situation is more complicated, however. You are defining a binary outcome (success or failure based on a threshold of 75% improvement).

If you want to test the actual change in event duration (difference between mean event length) then you can use more ordinary statistical techniques. The number of animals you'd need to test will depend on the standard error (variation) between individual treatments. If you have no idea how high this variation will be, you'll need to make some educated guesses for your power calculation.

 

[Hacp]

I just got my reviews back for a grant and they harped on that I didn't have any statistical analysis for how many animals I'll need. I'm super rusty on stats, could anyone point me in the direction I need.

Basically, a drug I'm testing will reduce the duration of an event by 75% relative to the control. So basically, in each event I will either achieve 75% reduction or not, meaning there is a 50% chance of success. How many samples do I need to ensure a confidence level of 99%?

Are you sure the chance of success is 50%?

 

[GWestphal]

I found a random pdf describing what I need. A matched pairs t-test was what was in order. A simplification can be found to be

n=2+10.5(s/d)^2. Where s is the estimated standard deviation and d is the minimum size of effect you'd like to resolve, and 10.5 is a assuming a power of .9 and p=0.05.

 

[Hacp]

I found a random pdf describing what I need. A matched pairs t-test was what was in order. A simplification can be found to be

n=2+10.5(s/d)^2. Where s is the estimated standard deviation and d is the minimum size of effect you'd like to resolve, and 10.5 is a assuming a power of .9 and p=0.05.

The binomial confidence interval stuff is actually a highly studied topic right now, especially concerning medical research. It is hard to determine, since you need to assume a power. I think the most modern and well accepted method uses Bayesian inference. I found a PDF that might help you get what you want.

http://ba.stat.cmu.edu/journal/2008/vol03/issue02/mlan.pdf

This lecture slide explains it more clearly I guess.
http://www.stat.washington.edu/tsr/s481/lecture9f02/lecture9f02up2.pdf

 

[CycloWizard]

If you already know how often and how well the drug works, what are you proposing exactly? Sounds like a homework problem rather than an actual research question, so I'll give hints rather than an exact solution.

Since you already know everything about your distribution, it should be pretty easy to determine this. See here. You can simply compute the t-statistic necessary to achieve significance for a given number of samples in each population (n) and iteratively guess n to achieve that t-statistic. Since you want 99% confidence, your t-distribution inversion should use a p value of 0.01. All of this can easily be done in Excel. You could also use Monte Carlo simulations.

 

[Fallen Kell]

Cyclo, I was about to say the same thing about him knowing % of successes and the fact that it either fully works at that % or it doesn't work at all (which most drugs will affect the condition in a fairly large range, not either it works at 75% or it doesn't work at all....)