Report of reviewer 1

[pneuvial]

Associate Editor: Pierre Neuvial
Reviewer: (chose to remain anonymous)

Reviewing history

• Paper submitted 2023-02-15
• Decision: major revision 2023-07-23
• Paper revised 2023-09-20
• Decision: minor revision 2023-11-17
• Paper revised 2023-11-29
• Paper accepted 2023-12-21

General comments

In the manuscript 'A hierarchical model to evaluate pest treatments from prevalence and intensity data', Favrot & Makovski present a new and welcome (Bayesian) method for the (meta-)analysis of countable 'infection' units on individual hosts, where the recorded variable may be either the proportion of 'infected' hosts (prevalence) or the mean number of infection units per individual host (intensity), or both quantities. Then, a simulation study is used to demonstrate that intensity data provide more accurate estimates than prevalence data (especially for abundant 'infections'), and to assess the accuracy of the estimates depending on the number of trials. The provided code and convergence seems good.

A general comment : the article focusses on aphid abundance on plants sampled during field trials designed to compare the efficacy of various pest control options, but the framework is more generic (and might be used e.g. in animal/human epidemiology) and the authors may highlight this point in the abstract, introduction and/or discussion.

We added the following sentence in the conclusion : "Although our framework was illustrated to compare the efficacy of plant pest treatments, it could be applied to other areas of research in the future, in particular for optimizing designs used in animal and human epidemiology.". See lines 391-393.

Major comments

My only methodological comment relates to the choice of a Poisson distribution for W, which is the number of aphids on each plant. Because aphids land and initiate exponentially growing clonal populations at different times on different plants of the same trial x treatment x block x time combination, W should have an overdispersed Poisson distribution (e.g., negative binomial), instead of a Poisson distribution (eq. 1). Thus, Y (the sum of N independent W variables) should not have a Poisson distribution (eq. 3). It would be interesting to test whether an overdispersed Poisson distribution is better than a Poisson distribution for fitting the unaggregated data on the number of aphids on each of the $N_i$ (i.e. 10 here) sampled plants (gaining statistical power from the multiple trials). Although the authors state (in part 2.1) that such data are not available to the authors, these raw data are classically recorded and might be provided by the unspecified colleagues who conducted the field trials (by the way, the institutions that performed the field trials should be mentioned more explicitly).

Our Poisson log linear model includes an additive random dispersion term added to each individual observation. This is a standard and well-recognized approach to deal with over-dispersion (Xavier A. Harrison, "Using observation-level random effects to model overdispersion in count data in ecology and evolution", PeerJ. 2014; 2: e616). However, in order to address the reviewer's comment, we have performed two new analyses:

• We performed a posterior predictive check of our model to check that the data were compatible with the model assumptions. To do so, we computed the probability of exceeding each individual data with the fitted model (2). Note that the number of pest individuals per plant are not available in practice; the data correspond to observed numbers of pest individuals for groups of $N_i$ plants. Based on the posterior probability check, the computed probabilities were all falling in the range 0.22-0.93 (except for the observations equal to 0, for which the probability of being greater was equal to 1), and were thus not extreme. This result indicates that the model specified is not incompatible with the observed data and that the over-dispersion was correctly taken into account.
• We fitted a new model including a negative binomial distribution instead of a Poisson distribution. The results were almost identical between both types of model. See the figure below.

These new results are reported below, and were added in the supplementary material of the paper.

Moreover, we added the following sentences in the Material and method section of the revised paper (see lines 119-131) : "Our Poisson log linear model includes an additive random dispersion term added to each individual observation ($\epsilon_{ijkt}$ in Equation 2). This is a standard and well-recognized approach to deal with over-dispersion (Xavier A. Harrison (2014)). In order to check the model assumptions, we performed a posterior predictive check of our model to check that the data were compatible with the model assumptions. To do so, we computed the probability of exceeding each individual data with the fitted model (2). The computed probabilities were all falling in the range 0.22-0.93 (except for the observations equal to 0, for which the probability of being greater was equal to 1), and were thus not extreme. This result indicates that the model specified is not incompatible with the observed data and that the over-dispersion was correctly taken into account. In addition, we fitted another model including a negative binomial distribution instead of a Poisson distribution. The results were almost identical between the two models."

Figure 1: Posterior predictive check, The X-axis is on a logarithmic scale and represents the number of aphids increased by 1.

Figure 2: Observed vs predicted values