The n = 1 fallacy is a common error in the analysis of epidemiologic studies, first defined in 2003.[1]
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Background
A public health intervention such as a vaccine is frequently evaluated in individually randomised trials. The unit of inference in individually randomised trials is the individual. The sample size calculation as well as the analysis should therefore be based on the individual. Problems arise when interventions have to be evaluated on a community level. Examples for such interventions include a) the herd immunity conferred by vaccines b) mass drug administrations c) transmission blocking vaccines against vector-borne diseases. If effects which apply to the community, or more abstractly a cluster of units, the unit of statistical inference has to be the community or the cluster and not the individual or the unit. A cluster-randomized trial is needed to evaluate such interventions. To compare communities or other clusters a larger number of individuals or units is needed than in an individually randomised trial[2][3] The additional sample in a cluster-randomised study compared to an individually randomised trial is sometimes called the design effect.[4]
Description
The n = 1 fallacy occurs when the units of randomisation are communities (or clusters) but the unit of inference for sample size calculation or analysis is the individual.
Here a less abstract way of describing this statistical error. Investigators want to evaluate an intervention e.g. a vaccine. People living in one community (or cluster) receive the vaccine (n = 1). This community is compared with one other community which did not receive the vaccine. The investigators make an error if they compare statistically the individuals living in the two communities. In reality they compare one unit with one other unit as the residents in each cluster or community are likely to be similar in their exposure to climate, disease vectors, access to health care etc.. If the investigators want to compare individuals they have to randomise the individuals to receive the intervention or a control agent. If investigators want to compare communities or clusters they have to randomise an appropriately large number of communities or clusters.
Example
Investigators want to evaluate the benefit of vaccination campaigns. Two communities A and B with an approximate population of 8000 each are selected and are under surveillance for the target disease (e.g. cholera). Members of community A but not of community B are vaccinated. During the surveillance period 8 cholera cases are detected in the vaccinated community A and 160 cholera cases are detected in the unvaccinated community B. There is an intuitive tendency to calculate a chi-square test comparing 8/8000 with 160/8000 which gives a highly statistically significant but wrong result. The investigators should compare 0.1% in community A with 2% in community B which does not allow any statistically meaningful interpretation. This misuse of statistics has been described 25 years ago and continues unabatedly.[5]
See also
References
- ^ von Seidlein L, Greenwood BM. "Mass administrations of antimalarial drugs". Trends in Parasitology 2003;19(10):452–60.doi:10.1016/j.pt.2003.08.003
- ^ Jaffar S, Leach A, Hall AJ, Obaro S, McAdam KP, Smith PG, et al. "Preparation for a pneumococcal vaccine trial in The Gambia: individual or community randomisation?" Vaccine 1999;18(7–8):633–40.
- ^ Smith PG, Morrow R. Field Trials of Health Interventions in Developing Countries: a Toolbox. London: Macmillan, 1996.
- ^ Donner A, Klar N. Design and Analysis of Cluster Randomization Trials in Health Research. London: Arnold, 2000.
- ^ Blum D, Feachem R. "Measuring the impact of water supply and sanitation investments on diarrheal diseases: problems of methodology". International Journal of Epidemiology 1983;12(3):357–65.
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