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Measures of disease frequency: Use and misuse(proportions and rates, prevalence, cumulative incidence, incidence rate, intensity, age standardization)Statistics courses, especially for biologists, assume formulae = understanding and teach how to do statistics, but largely ignore what those procedures assume, and how their results mislead when those assumptions are unreasonable. The resulting misuse is, shall we say, predictable... Use and MisuseBe aware that the terminology for these measures in the literature is rich and varied! Medical researchers usually distinguish clearly between prevalence, cumulative incidence and incidence rate. Veterinarians and ecologists, on the other hand, tend to use the terms more 'loosely' and the terms infection rate or percentage parasitism may refer to any one of them. A common misuse of cumulative measures is to not define the time period involved  or allow it to vary. Often it is the incidence that one wishes to estimate, but it may only be possible to measure prevalence. One can try to infer incidence rates from age prevalence data, but this requires many assumptions. We look at two examples where somewhat questionable inferences are made from age prevalence curves. Estimates of prevalence are usually made from a sample with the aim of extrapolating to some larger population. If this is the case, one must use some form of random sampling! Unfortunately haphazard or convenience sampling is still extremely common, and we give several examples in all research areas. There are also problems with measurement error  a realistic evaluation of the various biases involved is essential for any study of disease frequency. Disease frequency is more difficult to study in wildlife populations than in human or veterinary studies, as it is not usually possible to continuously monitor disease status. In the wildlife examples we have given, researchers either use seroprevalence, or, in the case of parasitic infections, prevalence in faecal samples. Both may provide very biased measures of disease frequency. What the statisticians sayPfeiffer (2010) looks at quantifying disease occurrence in Chapter 3. Woodward (2004) covers incidence and prevalence in Chapter 1 (although not very well!). Rothman (1998) gives an authoritative and comprehensive account of measures of disease frequency in Chapter 3 aimed at medical epidemiologists. Thrusfield (2005) provides a fairly comprehensive coverage for veterinary epidemiologists in Chapter 4. Streiner & Norman (1998) provide an introduction to the topic, although beware  the distinction between rates and proportions is not made clear.Goldman & Brender (2000) compare the validity of standardized mortality ratios (indirect adjustment) with standardized rate ratios (direct adjustment). They conclude that either method of standardization can be used. Brockelman et al. (1987) compare two methods of measuring incidence: direct determination and estimation of incidence from agespecific prevalence data. Williams (2000) and Hallett (2008) describe more sophisticated methods for estimating incidence from age prevalence data. Rogers (1985) reviews definitions of the term challenge as applied to trypanosomosis and demonstrates a linear relationship between a simple index of challenge and disease incidence. RuizNarváez & CastroWebb (2003) suggest a novel approach for estimating generational percentage parasitism. Van Driesche et al. (1991) considers what ecologists mean by percent parasitism, and looks at three approaches to estimate losses from parasitism. Wikipedia provides sections on prevalence , seroprevalence and incidence. The term intensity is covered in a (rather prescriptive) section on quantitative parasitology . Coggon et al. (2003) provide a very basic introduction to cases, rates versus proportions, and incidence versus prevalence. A somewhat fuller treatment on line is given by Pfeiffer (2002).
