Statistical aspects and sample sizes

1. Statistical aspects
The nature of epidemiological study is that the result of any estimate of exposure is considered only to be just that, an estimate of the true figure in a conceptual complete population. Assuming that a study population was randomly sampled from this conceptual whole population (be it selected either by exposure or disease status) then it is possible to calculate a 95% confidence interval around this estimate giving a range in which the likely true effect within the population as a whole lies. If this range excludes unity then a "statistically significant" association is said to exist. The problem with most studies in this field given small numbers, is that very rarely does the 95% confidence interval exclude unity. Indeed, for example, a 95% confidence interval of 0.2-2.8 would suggest that the study results would be compatible either with the implanted group having a risk a fifth of that to almost 3 times as that of an unexposed group. Clearly, such a result does not advance science, as it is neither possible to exclude a protective or harmful effect. In general, given the data, numerical value of the risk obtained is the best estimate. Results at the extreme of the 95% confidence interval are less likely given that data.

2. Appropriate sample size for studies

Type of study	How many to show 1.5 increase in relative risk	Notes
Cohort	80000 with 10 year follow up	background of 10 per million per year
Case control	5000 cases	based on 4 controls, nb ~500 cases per year in UK

The importance of what has been mentioned above might be illustrated in considering the appropriate sample size that would be necessary to undertake a study to be absolutely certain an important effect had not been missed. Using the cohort approach and assuming there is a desire to detect a 1.5-fold increased risk in an implanted group in a disease such as scleroderma where there is a background population incidence of approximately 10 per million per year then it would be necessary to follow-up 80,000 women for 10 years to have a sufficient power to detect an effect. Similarly, if a case control design was to be adopted and using the most efficient matching system of four non-diseased women to every women with connective tissue disease, similar calculations can be undertaken. Based on current studies, it seems likely that a 1% exposure to silicone breast implants might be expected in the control group. To detect an increased risk of 1.5 in the implanted group would require some 5000 cases of the disease under investigation. As an indication of the magnitude of this problem, there are unlikely to be enough women with scleroderma who would have been eligible to have been implanted in the United Kingdom.