The rarity of the disease is not an issue, since you are interested in estimating the incidence of side effect due to treatment (i.e., the prevalence of disease in your sample is 100%). You never mentioned the follow-up time for your incidence measure of side effects. If the time point is fixed for all patients (e.g., say 10 days), then you would estimate an incidence proportion (number of eligible patients reporting side effects in 10 days divided by all eligible patients receiving treatment -- assuming no attrition). For this estimate, the approaches above are fine. Since you appear only interested in a point esitmate of side effects, I would compute the sample size based on the width of the 95% CI. Use 50% for the estimate since this will be conservative (tha is, for a given sample size, the CI will be narrower for a 30% estimate than for a 50% estimate).

If you can document follow-up time for each patients and record time-to-side effect, say a specific side effect of interest, You might be able to compute a more precise incidence rate (or incidence density). The formula for the incidence rate will be different from those for a proportion. Rothman has these formulas, as does Rosner. WinPEPI may do this computation, also

Paul

I could try WINPEPI program (free on internet and easy for use) and put the parameters you have mentioned above but you have along with theses parameters to feed the size of error you will accept . Good luck

Hi,Anthony:

Since the mild side effects occur at 30-50% of treated patients, I think your size (400 patients) is big enough. If you like to continue, 500 patients will be your target.

Hi, Anthony:

you can use this formula :

n= (〖(Zα)〗^2 (PQ))/d^2 =

if the side effects occur 50% then the sample size will be 400 with this

p=50% Q=1-p=50% d=0.1 p=0.05

n= 400

Thanks guys. @Maryam, we've used that formula, but it appears its meant for prevalence studies in the general population. When we applied the population prevalence of this rare disease, we just got a sample size

There are several online calculators that will give you a CI for a simple percentage like this. Try SISA statistics. With 400 observations, the 95% CI should be accurate to about 5%

Hi Anthony,

I think you need to consider the 30-50% as the prevalence you want to assess, the disease prevalence does not play a role for the number of patients you want to enroll. Assuming 95% confidence intervall, 30% side effects (conservative approach) you will need to recruit 323 individuals if you use OpenEpi (http://www.openepi.com/OE2.3/Menu/OpenEpiMenu.htm).

You will further have to consider drop out rates if you want to do a follow up, since side effects probably won't occur instantly.

Ignoring drop out rates for now and staying on the conservative side you could assume a disease prevalence of 1 / 1.000.000 giving you a target population of 323.000.000 individuals, which may be tricky. You can address this by extending your surveillance period.

Think this through, maybe I got it wrong. Take care.

Ben

The G*Power is another software that may help in decision making depending upon power, effect size, sample size, and many more parameters. It is open source and freely available online.

Hope this helps.

The rarity of the disease is not an issue, since you are interested in estimating the incidence of side effect due to treatment (i.e., the prevalence of disease in your sample is 100%). You never mentioned the follow-up time for your incidence measure of side effects. If the time point is fixed for all patients (e.g., say 10 days), then you would estimate an incidence proportion (number of eligible patients reporting side effects in 10 days divided by all eligible patients receiving treatment -- assuming no attrition). For this estimate, the approaches above are fine. Since you appear only interested in a point esitmate of side effects, I would compute the sample size based on the width of the 95% CI. Use 50% for the estimate since this will be conservative (tha is, for a given sample size, the CI will be narrower for a 30% estimate than for a 50% estimate).

If you can document follow-up time for each patients and record time-to-side effect, say a specific side effect of interest, You might be able to compute a more precise incidence rate (or incidence density). The formula for the incidence rate will be different from those for a proportion. Rothman has these formulas, as does Rosner. WinPEPI may do this computation, also

Paul

SAS or SPS has a sample size module. If you don't have either I would go with WinPepi ( its free)

Is it essential to calculate the sample size for a rare disease?

Is there a point in calculating the sample size after 400 have been recruited?

In observatinal study. Particular in rare disease is recommended to use case control study design and using lameshow formula to determine number of sample. But for single sample, is it important to calculate sampel? This study just for descriptive analysis.

Best Regard

For retrospective come prospective descriptive studies its better to calculate power at the end or even without it, its fine. If the disease is rare a case control design will take years to accumulate desired sample size..

please go through http://www.stattools.net/SSizRareInc_ExpTab.php site for your sample size calculations.

Prevalence of the disease being treated not really important. You're targeting a single proportion (frequency of a side effect to a particular drug) within those (hopefully) with the condition. You have an initial estimate of that incidence rate. You should consider using the acceptable WIDTH of that confidence interval to guide your calculation of the target sample size. If your sampling is straightforward, consider using the binomial in that calculation. I'm away from my office do unfortunately cannot send you any specific refs. I hope this is helpful. Be well, Howard

As our aim is to estimate the true incidence of side effects of the drug used, we use the following input data to calculate the needed sample size:

Expected incidence of side effects ( from apilot study it is around 40%), the maximum error in the estimate we are willing to tolerate ( say +- 2%), at confidence level 95% AND POWER EQUAL TO 80%.

The computational issues are pretty straight forward. Ignoring temporal aspects (which may not be ignorable as others have suggested...depends on how short times-to-side effects are):

I definitely agree to the use of 95% CI ...essentially increasing the denominator until the bounds fall within acceptable bounds. Make sure you're using a confidence interval that appropriately models the asymmetry of error for proportions (as you deviate from 50%...Wilson method should suffice...N is large enough and you're close enough to 50% to not need continuity correction). This means +/- X% won't work...each 1/2 width will have to be specified...or just specify the upper since that will be the larger when you're below 50%.

This is distinct from power, though. For power, of course you have to be testing a hypothesis. You may want to effectively rule out side effects of >= XX%, for example. If so, you could decide on this threshold and power based on a 1-tailed hypothesis.

These are related, but approach from different perspectives...and accomplish different real-world goals. I think you should consider doing both and take the larger sample size. but first...

In both cases, you have to decide on your parameters. These should be based on some sort of real-world anchor. The better you can match your real-world task at hand to your computations and design, the better.

For example,

Perhaps the disease has some symptoms that are effectively inhibited by the drug, but the side effects are roughly comparable in annoyance/cost. In that case you may consider playing these off one another in a cost-benefit scenario. e.g. Rate of symptom X is 65% in disease. Drug can reduce this rate to near-zero, but the cost is side-effect Y. We suspect a true rate of side effect between 30-50% and would like to effectively rule out that the drug creates an even exchange of side-effect for symptom.

This is just one scenario by way of example...whatever the justification for your parameters, they shoudl accomplish a goal that ties back to a real world goal.