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Rheumatology 2001; 40: 121-122
© 2001 British Society for Rheumatology
Editorial |
The ‘zero patient’ design to compare the prevalences of rare diseases
c
Division of Rheumatology, Department of Medicine, Cerrahpasa Medical Faculty, University of 
stanbul and
1 Departments of Medicine and
2 Methodology and Statistics, Maastricht University, Maastricht, The Netherlands
Ascertaining the population frequency of a rare disease is difficult and costly. Some rheumatic diseases show considerable geographical variation in prevalence. Behçet's syndrome (BS) and Takayasu arteritis are examples. These conditions seem to be rare in the north compared with the south of Europe. There seems to be a lack of population-based surveys [1], and studies comparing different geographical regions are needed in order to provide some insight into the aetiopathogenesis of such diseases.
We believe that comparative estimates of the frequencies of these conditions can be made relatively easily even though the true prevalences may remain unknown. The relative frequency of a disease can be estimated by not finding the disease in a population sample. Depending on the size of this sample, a 95% confidence interval can be computed which indicates that the frequency of this condition is less than a given value.
It is worth mentioning here that a previous estimate of the prevalence in a region with relatively high disease frequency, determined by traditional statistical methods, will be helpful in determining the size of the population that should be screened in a region with the hypothesized lesser prevalence.
Our aim with this design is to determine the size of a sample that can be expected to be free of a certain disease. First we use the approximation that loge(1-p)=-p, where p<0.02 is the prevalence of a rare disease. This approximation is true only for prevalences below 0.02.
If all people in our sample of n are free of disease, the 95% confidence upper bound for the prevalence p0 can be computed from the relationship 0.05=(1-p0)n, according to standard statistical theory. This corresponds to rejection of the null hypothesis that the true prevalence is p0 at a one-sided significance level of 0.05. Taking the natural logarithm yields n=-loge(0.05)/p0 or simply n=3/p0. This is the required sample size that yields the 95% confidence interval p<3/n.
We had previously shown that for BS, and for a certain geographical area in Turkey, this condition had a prevalence close to 4 per 1000 inhabitants (0.004) [1]. Thus, using the above formula, if one screens around 3/0.004(=750) individuals and does not find a case of BS in, say, The Netherlands, then one could be 95% confident that the prevalence of BS is less than 0.004 in this country. Or after screening 1500 people and still not coming across a single BS patient, one could conclude with 95% confidence that BS has a frequency of less than 0.002 in The Netherlands.
In the planning phase, the statistical power may be considered. In this setting it is the probability that all n people who will be screened are disease-free, assuming that the true prevalence is pA (alternative hypothesis) instead of p0 (null hypothesis), where pA is much smaller than p0. This may be expressed as: power=(1-pA)n. Taking the natural logarithm yields: loge(power)= -npA=-3pA/p0. So pA=-loge(power)xp0/3. Thus, a power of 0.80 is obtained for a true prevalence of pA=-loge (0.80)xp0/3=0.074xp0.
Assuming that the null prevalence (p0) of BS is 0.004 in Turkey, according to our design, the alternative prevalence (pA) in The Netherlands should be less than 0.074x0.004(
0.0003) for our method to have at least 80% power. This power increases with yet smaller prevalences.
The proposed formula for the zero-patient design is straightforward and is accurate for conditions with a prevalence less than 2%. We think that a one-tailed test is adequate, in that we propose to use this formula mainly to state more accurately what we strongly suspect is the case regarding the frequency of a rare condition at one place compared with another, better defined place with a suspected higher prevalence. As we say, the comparison of the prevalence of BS in The Netherlands and in Turkey would be a case in point.
The alternative question of what would be the likelihood of coming across a single patient in The Netherlands if we assume (i) that the prevalence in The Netherlands is indeed smaller than 0.004 and (ii) we screen 750 patients brings us to the issue of power—the likelihood of rejecting the null hypothesis when it is false, which in this case is the likelihood that all 750 patients are disease-free. We think that the power of our design is acceptable in that the real prevalence of BS in The Netherlands is probably even less than 0.0003. Thus, the probability of not coming across a single patient with BS among the 750 we screen, the power (which, as we saw above, is 80% with the projected frequencies) will be even higher with still lower prevalences.
In the event that one comes across even a single patient in the scheme we propose, a further study should be planned using standard epidemiological methods [2].
As an illustration, the data on childhood BS, as reported by Özen et al. [3], may be considered. In a field survey, these authors screened just over 45 000 children in Turkey and did not find any patients with BS. According to the formula, for the 95% confidence interval this puts the frequency of childhood BS in Turkey at less than 3/45 000(=0.00007). This observation supports and gives a numerical framework to our clinical observation that BS is indeed rare in children, while adults, according to one field survey, might have a prevalence as high as 0.004 [1].
Another application of our formula could be in the comparison of clinical or laboratory features of diseases. Let us assume that a certain feature of a disease is seen with a high frequency in one region and rather infrequently in another. Again using BS as an example, the frequency of intestinal disease among patients from the Far East ranges from 4 to 37% [4], but is very low (<1%?) among BS patients from Turkey [5]. According to our formula, one would need to screen 300 patients with BS in Turkey and not find a single patient with intestinal disease in order to obtain 95% confidence that the frequency of intestinal involvement among Turkish BS patients is indeed less than 1%.
We suggest that the use of our formula would make comparative studies of the prevalence of rare diseases or their infrequently seen features less time-consuming and less expensive.
The authors greatly appreciate the help of Professor H. Beker (Department of Physics, Bo
aziçi University) during the preparation of this paper and Professor . Dimitriyadis (Department of Mathematics, Boaziçi University) for critical review. The help of Dr . Fresko is also acknowledged.
Notes
Correspondence to: H. Yazc, Cerrahpasa Medical Faculty, Aksaray, stanbul 34303, Turkey. 
References
- Yurdakul S, Günaydn , Tüzün Y et al. The prevalence of Behçet's syndrome in a rural area in Northern Turkey. J Rheumatol1988;15:820–2.[ISI][Medline]
- Lemeshaw S, Hosmer DW Jr, Klar J, Lwanga SK. Statistical methods for sample size determination, In: Lemeshaw S, Hosmer DW Jr, Klar J, Lwanga SK, eds. Adequacy of sample size in health studies, Chichester: John Wiley and Sons, 1993:1–47.
- Özen S, Karaaslan Y, Özdemir O et al. Prevalence of chronic arthritis and familial Mediterranean fever in Turkey: a field survey. J Rheumatol1998;25:2445–9.[Medline]
- Bang D, Yoon KH, Chung HG, Choi EH, Lee A-S, Lee S. Epidemiological and clinical features of Behçet's disease in Korea. Yonsei Med J1997;38:248–36.
- Yurdakul S, Tüzüner N, Yurdakul , Hamuryudan V, Yazici H. Gastrointestinal involvement in Behçet's syndrome: a controlled study. Ann Rheum Dis1996;55:208–10.
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