Parasite Prevalence and Sample Size

Parasite prevalence and sample size: misconceptions and solutions

Roger Jovani and Jose´ L. Tella

Department of Applied Biology, Estacio´ n Biolo´ gica de Don˜ ana, Consejo Superior de Investigaciones Cient ´ıficas, Avenid Maria Luisa s/n, 41013 Sevilla, Spain

Parasite prevalence (the proportion of infected hosts) is changes dramatically when we move from small to large a common measure used to describe parasitaemias and sample sizes. For instance, if we sample six adult to unravel ecological and evolutionary factors that lizards and find four to be infected (nZ6, iZ4) we influence host–parasite relationships. Prevalence esti- obtain pZ(4/6)*100Z67%, but if we found five infected, mates are often based on small sample sizes because of then pZ83%, a difference of 16%. However, for nZ100, either low abundance of the hosts or logistical problems iZ4 returns pZ4%, and iZ5 returns pZ5%, only a 1% associated with their capture or laboratory analysis. difference. This produces the effect that slight prevalence Because the accuracy of prevalence estimates is lower differences can be detected at high sample sizes but not at with small sample sizes, addressing sample size has low ones. In other words, our uncertainty about the real been a common problem when dealing with prevalence prevalence (i.e. population prevalence, P) is higher at low data. Different methods are currently being applied to sample sizes (Figure 2). overcome this statistical challenge, but far from being The accuracy with which we calculate the prevalence different correct ways of solving a same problem, some decreases not only at low sample sizes (as expected), but are clearly wrong, and others need improvement. also when the populational prevalence is close to 50% (Figure 2). At first, this property could seem counter- intuitive, because rare events (e.g. a parasitised individ- Introduction ual at PZ1% or an uninfected individual at PZ99%) are In a given population with N individuals, the prevalence difficult to observe, particularly at low sample sizes. (P) denotes the proportion of infected individuals by a However, when populational prevalence is close to zero or given parasite species or group of species (e.g. a parasite 100%, sample prevalence is also close to or equal to zero genus). The actual prevalence of a population, however, is or 100%, respectively, precisely because rare events are usually unknown because the number of sampled hosts (n; difficult to detect. At intermediate populational preva- the sample size) is generally lower than total population lences (e.g. PZ52%), the chance of finding parasitised or size (N). However, we can easily obtain an estimate (p) by non-parasitised individuals is similar, and sample preva- dividing the number of infected individuals (i) by the lence could then freely fluctuate from zero to 100%, number of sampled ones [pZ(i/n)*100], where iZ0,1,2.n, falling away from the actual populational prevalence and and nZ1,2,3.N. Nonetheless, the accuracy of this increasing the uncertainty in the prevalence estimate. estimate is known to be affected by sample size. This problem has long concerned researchers because the results of statistical analyses dealing with prevalence Minimum sample size data and the derived conclusions could depend greatly on The most intuitive method to overcome the high the number of sampled hosts [1]. Here, we review current statistical uncertainty of prevalences calculated from methods used to overcome this statistical problem, low sample sizes is to reject data obtained from small identify wrong approaches, improve others and suggest sample sizes. However, the threshold for establishing a more powerful practices. minimum sample size is highly variable because it depends on subjective decisions of the researchers. This leads to researchers either not considering a minimum Basic concepts sample size (e.g. [2]), or considering low minimum sample The low accuracy of prevalence estimates when using a sizes, such as three [3], five [4], or eight [5]; medium small sample size has a mathematical basis. Given that sample sizes, such as ten [6], 15 [7] or 20 [8]; and higher both the number of infected individuals and sample size ones up to 30 [9] or even 75 [10]. Obviously, more is are integers, sampling prevalence (i.e. the prevalence better, but rather than being a linear relationship, within a given sample of individuals) is constrained to a uncertainty rapidly decreases as sample size increases particular set of values for each sample size (Figure 1). up to 10–20 individuals, but not much more with further Moreover, the behaviour of prevalence estimates for increasing sample sizes (Figure 2). Thus, a sample size slight increases in the number of infected individuals around 15 could be used as a reasonable trade-off Corresponding author: Jovani, R. ( [email protected]. e s). between not losing too much data from analyses and maintaining acceptable levels of uncertainty (around 1/3 Avoiding zero prevalences (a) Gregory and Blackburn [13] claimed that the minimum 100 but not the maximum prevalence that could be achieved in a sample of a population is affected by sample size. This )

p influential paper caused several studies to reject zero (

75 e prevalences from their analyses or to question its previous c n

e use. These authors stated correctly [13] that large sample l a

v sizes (e.g. 1000 hosts) are needed to detect very low e

p prevalences (e.g. 0.1%), but that 100% prevalences could

i be detected with only one individual sampled if it is l p infected. They presented figures with both axes log- m

S transformed (similar to Figure 1b), but this hid the symmetric shape of the actual relationship between sample size and prevalence (Figure 1a,c). That is, as 0 happens with prevalences near zero, prevalences near 0 10 20 30 40 50 100% (e.g. 99.9%) could only be achieved with high sample Sample size (n)

) sizes (e.g. 1000 hosts). Thus, according to this symmetry p ( )

g p e n

(b) ( (c) i c 100 l 100 g and the suggestions of Gregory and Blackburn [13], we n e p n i c e l 10 l 75 m n p

a should also reject 100% prevalences from analyses. a e v l 50 m

1 S e a a

r Parasite prevalence differs widely both between and v 25 p S

e 0.1 r 0 within host species [14,15]. Therefore, when assessing p

1 10 100 1000 1 10 100 1000 sources of variability in parasite prevalences (e.g. between Sample size (n) Sample size (n) marine and freshwater habitats [16]), a prevalence value TRENDS in Parasitology of zero has the same ecological relevance as a prevalence of 0.1%; and the same happens between 100 and 99.9%. Figrue 1. All the possible values that prevalence could reach at different sample Thus, we are throwing out very relevant information by sizes. For instance, for a sample sizeZ1, prevalence could be either (0/1)*100Z0% or (1/1)*100Z100%; for a sample size of 2, there are three possibilities: (0/2)*100Z rejecting zero and 100% prevalences. Accordingly, zero 0%, (1/2)*100Z50%, and (2/2)*100Z100%, and so on. This is illustrated for sample (see Box 1) and 100% prevalences should be included in sizes (a) from 1 to 50 in lineal axes, (b) from 1 to 3500 in log-log axes, and (c) from 1 to 3500 with logarithmic x-axis and lineal y-axis. the analyses. of the sampling prevalence). An additional recommen- Residuals of prevalence on sample size dation is to test the robustness of the results of the Another method used to control for the potential effects of analyses using different minimum sample size cut-offs sample size is to obtain the residuals of a linear regression [11,12]. between sampling prevalence (the dependent variable) and sample size (the independent variable), and use them as the dependent variable for comparative studies [17,18]. A clear example of this rationale is a study [18] in which 50 residuals of parasite prevalence against sample size were used in an independent contrast analysis when a correlation was found among these variables, but not in 40 another analysis of the same study, in which such a relationship was not found [18]. This approach follows previous methods that aimed to remove the effect of body r

o size on body-size-related variables, such as home range

r 30 r

e area [19]. Moreover, it has been influenced by the need to

d r control for sample size when analysing parasite richness, a d

n because the more host individuals that are examined, the a

S more parasite species could be found [7,20]. Adding more support to this method, and using empirical log-log plots similar to Figure 1b, Gregory and 10 Blackburn [13] suggested that a negative relationship between sample size and prevalence is expected as a 100 mathematical artefact (and thus needed to be controlled 50

0 0 for). In addition, they stated that nothing but negative 10 20 30 40 50 60 70 80 90 100 slopes were found when simulating the effect of sample Sample size (n) size (from 1 to 3500) on prevalence estimates when zero

TRENDS in Parasitology values were deliberately avoided. Clearly, however, there is no mathematical relationship between prevalence and www.sciencedirect.com Figrue 2. Standard error of prevalence estimates at different sample sizes and sample size per se (Figure 1). We confirmed this by populational prevalences. Standard error (SE) is calculated using the formula: SEZ 100*[p*q/(n-1)] where p is the sample prevalence, qZ1-p, and n is the sample size. repeating the same simulation study done in Ref. [13]. We The white line shows results for nZ15. performed100 simulations in which 200 hypothetical

www.sciencedirect.com Opinion

Box 1. Zeros are also relevant prevalences

Non-parasitised individuals and populations are clearly not the real absence of parasites; or be the result of a low prevalence and scope of parasitologists. This has produced a parasitological intensity of parasites, leading to an apparent absence because of literature traditionally biased towards positive prevalence values. low sample size or low methodological sensitivity [29]. However, As an example, the world avian host–haemoparasite catalogues the relevant question here is whether the inclusion of zero [26,27] report, for a given bird species, all studies that found some prevalences improves the conclusions of the research. We feel parasites, but only one study example for species that were not that a full understanding of natural variation in parasite burdens parasitised. In 1982, the seminal paper by Hamilton and Zuk [28] should also consider why some populations and species have zero extended the interest in parasites among evolutionary ecologists by or very low parasite prevalences, whereas others have 100% or suggesting a role for parasites in the evolution of plumage very high prevalences. For comparative purposes, a zero prevalence colouration and song in birds. Moreover, this generated a plethora is as informative as a 1% prevalance (and similarly for 99% or of hypotheses that were also initially tested by making use of data 100%), if calculated using appropriated sample sizes (as for any previously published by parasitologists, thus suffering from their other prevalence data). However, by excluding zero prevalences, we biases [7]. are throwing out extreme values from analyses, and thus excluding These new hypotheses encouraged evolutionary ecologists to potential host populations or species with interesting ecological or initiate extensive parasite surveys, finding great variability in life-history traits that make them completely or almost completely parasite burdens among and within species and previously hidden free from parasites. zero prevalences. This led to new questions about the ecological Thus, we make here a plea that zero prevalences should be factors, host behaviours and life history traits shaping such a reported. As an alternative to scientific journals, we propose the variation in nature [2,5,15,23]. Perhaps recalling the parasitological creation of a website under scientific supervision for compiling data tradition, doubts arose about the effects of sample size on zero published in leading journals as well as ‘grey’ literature (such as prevalences and the accuracy of prevalence estimates, even non-international journals or conference proceedings), old data including suggestions that zero prevalences should be excluded never published submitted by researchers, and data coming from from analyses and journal reports [13]. This publication bias has future surveys of parasite prevalence, whether or not they are started to creep into ecological and zoological journals, enhanced finally published. This would allow an easily available source of by the fact that zero prevalences have already ceased to be permanently updated data for researches worldwide, becoming one surprising and thus generate less interest among journal editors. more of the invaluable virtual services provided by natural history Failure to find parasites in a sample could either be because of a museums in this century. species (or populations) took prevalence values varying (1–15), sampling prevalences and sample sizes were between zero and 100% and sample sizes between 1 and usually positively correlated at low populational preva- 3500 (R.J. And J.L.T., unpublished). Among the resulting lences, uncorrelated at intermediated populational pre- relationships, 49 were negative (Spearman rank corre- valences, and negatively correlated at high populational lations, r rangeZK0.0008 to K0.1714; meanZK0.0565) prevalences (Figure 3a). At higher sample sizes (15–100), and 51 positive (r rangeZ0.0045–0.2675; meanZ0.0598), however, significant correlations were fewer and were only two negative and four positive weak correlations evenly distributed (Figure 3b). This is because, at low being statistically significant. Moreover, the results were populational prevalence, the chances of finding an infected identical when zero prevalences were not allowed in the simulations. Our results differ greatly from those of Ref. [13], suggesting that the conclusions of Gregory and (a) (b) Blackburn were based on the visual examination of log- 0.6 log plots similar to Figure 1b. In a more recent but largely unnoticed study regarding the relationships between prevalence and sample size, 0.4 p Gregory and Woolhouse [21] simulated the effect of sample d n a

sizes ranging from 10 to 1280 on the mean and the

accuracy of prevalences estimated for a theoretical n e population with a prevalence of 80%. They concluded e w t that prevalence estimates were not biased under any e 0.0 b

r sample size, only causing greater inaccuracy at low - n sample sizes, being thus consistent with our own analysis a m

r –0.2

(Figure 3; see later). However, Gregory and Woolhouse a e

[21] did not link these challenging results with their p S previous work, and their first recommendations [13] have –0.4 prevailed among researchers so far. Curiously, however, although clearly there is not a relationship between prevalence and sample size –0.6 0 20 40 60 80 100 0 20 40 60 80 100 (Figure 1a), there have been reports not only of null simple simulations using different sample sizes and empirical correlations between prevalence and sample populational prevalences (Figure 3). At low sample sizes size [18], but also of negative [18] and positive [22] correlations. Why? Because of the effect of detecting rare events at low sample sizes. This point is illustrated by www.sciencedirect.com Opinion Populational prevalence (P) Populational prevalence (P)

TRENDS in Parasitology

Figrue 3. Simulation of the effect of sample size on the correlation between sample size and prevalence at different actual populational prevalences. Each point indicates the Spearman correlation coefficient (in red p value !0.05) between sample size and prevalence for 100 simulated species with sample sizes randomly varying (a) from 1 to 15 or (b) from 15 to 100.

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