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## Statistics from Altmetric.com

Editor,—Carpenter has written an important study on prevalence and distribution of bruising in babies.1 However, there are problems with the terms relating to measures of disease frequency in epidemiology which, arguably, make this descriptive paper misleading.

The terms *point prevalence*,*prevalence proportion*,*prevalence ratio*, and*prevalence rate* are sometimes used to mean the same thing.2 However, the word*rate* is used more specifically in the context of the number of events per unit time and intuitively suggests a survival rate or an incidence rate. This is strongly purported by the use of the term *rate parameter *to describe the unknown and estimated value associated with a Poisson probability model.3 The distinction is often not explicit, even in the best textbooks of epidemiology, but I think that it is worth making.

Carpenter's study included infants aged between 6 and 12 months who were opportunistically screened for bruising at the time of routine surveillance checks. It is implied that each child was examined on only one occasion. Bruises were found in 22 infants, and seven had more than one bruise. However, a bruise would be expected to be visible for fewer than 28 days. If we take even this liberal estimate of duration, the infants were observed for approximately 1/6th of the period during which they might be found to have one or more bruises.

Hence, use of the term *point prevalence *in place of *prevalence rate *would have made things clearer, as it emphasises the fact that measurements were made at a single time between the ages of 6 and 12 months—the stated age range of study participants. The appropriate measure of risk depends on the question being asked. If we want to know the probability of a bruise being present at a single, random visit during the second 6 month period after birth, the point prevalence of 12% (0.12) is a useful measure of risk. If, however, we are asking for the probability that a child will develop one or more bruises with regular surveillance during the second 6 month period after birth, the appropriate risk is a*cumulative rate*, which can be derived from an *incidence rate*.

We can use the point prevalence presented in Carpenter's paper and our assumptions about duration to calculate a cumulative incidence from the relation: incidence rate = (point prevalence)/(duration).

The cumulative incidence is obtained from the formula: cumulative incidence = (1 − exp(−(incidence rate) × (number of periods))).

Assuming that bruising occurs at a constant rate and that the probability of a child having a bruise at one age is independent of the probability of it having a bruise at another age—assumptions that are probably not justified but which excuse a simpler model—the cumulative rate is (1 − exp (−0.12 × 6)) = 0.51 (that is, approximately 1 in 2). If we assume that a bruise lasts only two weeks and calculate the risk from the 12% point prevalence and 12 time periods, the risk becomes 0.76. It is worth being clear about which risk figure we are going to carry around in our heads and for which purpose: 1 in 8, or 1 in 2, or 3 out of 4.

As bruising is more common in infants who are more mobile, the incidence rate of bruising will increase with age. The age distribution of the sample would thus be important in the calculation of even a summary “average” measure of risk, and mention of risk estimates in appropriate age strata would provide useful information.

Carpenter suggests in the abstract that his study “tested out the methodology which might be used in future research”. I hope that these aspects of terminology and study design will be considered in such future studies.

## References

Dr Carpenter comments:

First, I thank Dr Lux for pointing out that I should have used the term *point prevalence* rather than*prevalence rate*.

Second, my figure (12.4% or 1 in 8) is the one “to carry in our heads”. Although it is possible to calculate the cumulate index over a 6 month period, as he suggests, this is not relevant for the clinical situation at presentation when abuse could be considered.

Finally, the study showed that age was barely significant when looking at bruises (p = 0.05) whereas mobility was significant (p < 0.001, see also table 1). Therefore, age cannot be used as a proxy for mobility and so risk estimates for age would not be helpful.

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