Prevalence of the disease is not a point here, since the study will be conducted only on a group of people with this condition. Please precise the aim of the study .

Dear jakub the aim of study is to evaluate patient knowledge about their disease and its treatment. So how we can calculate the sample size?

hi Ehab,

I will send you a document that can help you in sampling

For prevalence study in rare disease, of course, you need a large sample.  Calculating the sample size, in that case, relative precision is better than the absolute precision. 

Thank you all for your answers. Unfortunately no one answer my question (I want to know an equation or calculator) to measure sample size for rare disease especially if we do a research in the center of that rare disease

I cannot give any answers to your question because I don't know the question you are asking, just the prevalence of the disease.

What is the question, and what is the study design you plan on using?

See what you need to do isto take any random sample size either it be 100 or 500..That will be prevalence per 100 population n then u can calculate per 100000 by talking 100 random samples as marker of population..

Dear Ronan

I want to do a cross sectional study in a rare (very low prevalence) disease center (more than 50% of country cases in that center) so how can I calculate a sample size with statistical power of 95%?

Dear Ehab

You said the aim of the study is to evaluate patient knowledge about their disease and its treatment. You must give an anticipated proportion about this knowledge in your medical center  to calculate the sample size.

The prevalence of 4/100000 of this disease in this population is useless given the purpose of your study. If the objective was to measure the prevalence of the disease in the population, the sample size would be at risk 5% with an accuracy of 1/100000:

N = (1.96² * 4/100000 * 96/100000) / (1/100000) ² = 133150

(Calculation with the free OpenEpi calculator)

The following reference may help you to estimate your sample size in rare diseases. L. Naing, T. Winn, B.N. Rusli. Practical Issues in Calculating the Sample Size for Prevalence Studies.  Archives of Orofacial Sciences 2006; 1: 9-14. In this study you can find a formula for estimating the sample size, including rare diseases.

Please keep in mind that the sample size takes into account the estimated prevalence of the disease and the estimated precision.  Also as stated abve mentioned study, for example, if the prevalence is 1% (in a rare disease) the precision of 5% is obviously crude and it may cause problems. The obvious problem is that 95% CIs of the estimated prevalence will end up with irrelevant negative lower-bound values or larger than 1 upper bound values as seen in the Table 1. Therefore, we recommend d as a half of P if P is below 0.1 (10%) and if P is above 0.9 (90%), d can be {0.5(1-P)}

Dear professor Federico G De Cosio

Thank you for your reply. Actually I read that article and when I applied in equation using d as half p, the result is not acceptable (33100)!!! so that's why I made my question here

I have combined excerpts from three sources (articles listed below) to provide a general overview on what has been published about sample sizes for rare diseases. I hope the below information is useful.

…Recruitment to a rare disease clinical trial is frequently mentioned as the major problem. Some authors recommend putting more emphasis on observational studies, like self‐ controlled observational studies, case‐control studies and prospective inception cohort studies. Registries can also serve as a basis for a randomized controlled trial. Caution is necessary because it is argued that the high heterogeneity in phenotypic expression of many rare diseases may hinder optimal natural history and outcome studies based on registries. Case‐control studies are useful for studying rare disease. Applying this study type to rare disease registries matching techniques are found to minimize bias. Stepped-wedge studies typically have one time period in which observations are made while all clusters are unexposed to the intervention, and one time period in which all clusters are exposed to the intervention. So from the practical point of view it has to be evaluated how many patients must be included in the trial to gain efficiency. A comparison of interventional clinical trials in rare versus non-rare diseases, based on ClinicalTrials.gov data, found that rare disease trials enrolled a median of 29 patients (vs. 62 for non-rare disease trials) and fewer trials were actively pursuing enrolment (15.9% vs. 38.5%)… In rare disease clinical trials, the sample size must take into account data loss due to follow-up or patient drop-out.

For more information, you may want to review the papers listed below that I used to form the above section.

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0146465

http://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0146465&type=printable

http://www.irdirc.org/wp-content/uploads/2016/01/SPCT_DraftDocument.pdf

Perhaps the "epidemiological" lexic  is confounding :) the problem. The prevalence of a disease in a population is just its proportion in that population. If you want to know the level of knowledge of something in the patients attended in your service, it seems to me that your "disease" is that level of knowledge, and you wish to know its proportion in these patients, which is your population.

Thank you all professors for your helpful answers

Dear Ehab

The sample size of any study is determined by two major factors. The first is the scientific requirements which are tackled by statistical equations. The second is the economics of the study itself ( the resources available to carry out the study). In your case, the sample size and the sampling procedures depends on the type of study you like to conduct, the hypothesis to test and so on. If the condition you talk about is very rare (4/100000) as in case of most cancers for example, the sample size to estimate true prevalence, incidence or mortality is too big to handle. JUst to give you one example. We tried to estimate the annual incidence of all malignant disease in Basrah, the sample size required was huge (say more than 100000 persons). The smallest sample size we used was 41000 persons).

I guess you want to study some features of that disease ( fatality, response to treatment, risk factors...etc) rather than to estimate epidemiological parameter. In this case, the sample size might be within your capabilities.

The writer of this question is thinking that there is a specific number for a specific power output. Is Gpower an approprite tool?

very good information regarding sample size