Analysis of Lifetime Mortality Trajectories in Wildlife Disease Research: BaSTA and Beyond

Round 1

Reviewer 1 Report

As a biostatistician and epidemiologist in human studies, I cannot comment on the study from the wildlife disease research aspects. However, after my reading, I think the manuscript demonstrates a sound application of Bayesian approaches in inferential statistics, and the method can also be used in human studies.

The study was well design and the manuscript was well written. The results are interesting and the authors gave reasonable discussion.

But I do have some concerns below about the data analysis:

1.       In line 146-149, the authors said “… there is no gold standard diagnostic test available for bovine tuberculosis in live badgers.” Therefore, it leaves a problem, i.e. misclassification, in cub-positive and never-positive groups. It might involve in bias in parameter estimation. The authors should address this problem in a sensitivity analysis or discuss it in limitations.

2.       The authors should give likelihood function and posterior distribution for the Bayesian inferential analysis and 95% credible intervals for the parameters.

3.       The authors only give projected survival and mortality trajectories in the paper. However, to visually evaluate the goodness of fit of the models, it would be also necessary to give the observed survival and mortality trajectories at the same.

I do hope the see the authors may address above concerns in their major revision.

 Bets regards

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Review for diversity-573547

The paper analyses age-specific survival patterns in badgers in relation to their infected status with bovine tuberculosis, with the aim to parameterize epidemiological models where the demography of the badger reservoir is important to understand the dynamics of the epidemics. The authors report that infected badgers have impaired survival via an increase in actuarial senescence, which may reduce their rôle as a reservoir relative to what is currently considered to be the case based on models with age-constant survival. This is certainly a major message to convey given the management and political implications.

Major comments

I am aware of at least one previous study in which the interaction between infection status and age was investigated in badgers (Benton et al JAE 2018). This is at odd with the statement of anteriority in the abstract (line 22). The scientific purpose of that statement (and all similar « we are the first » statements) eludes me anyway. The authors should focus on the applied implications instead, and make their message easy to uptake by policy makers. The analytical procedures in this study are really subpar relative to what is broadly available in CMR software today. The authors chose to discard the majority of their data and focus on two specific subsets : animals that were caught as cubs and tested positive, and animals that were caught as adults and tested negative. The authors ignore 1) the dynamical nature of the infection (animals that tested negative may acquire the disease after their capture) 2) the potential for false negatives, and 3) the process of selective disappearance. Indeed, the control is made of individuals that were caught several times as adults, thus by construct the control is made of individuals with better performance on average, irrespective of their infection status. Thereby the protocol is potentially severely flawed I’m afraid, and the conclusion that the control survived better may be artificially constructed by the sampling design. In any case, this study is bound to be quickly replaced by an update with better analytical procedures, leaving me to question the relevance of the present effort as a stand-alone manuscript.

Minor comments

It is really odd to quote a specific software name in the title. Especially because Basta is to my knowledge not even the most used software for age-specific survival estimation. Reading the phrase « Basta and beyond » honestly sounded weird to me because it in effect put that software as the reference against the rest should be evaluated ? In line with the previous comment, the literature cited is really too much biased towards Dr Colchero -- at least a dozen papers that he authored. I obviously have nothing against him personally, but it is just weird given the wealth of literature on age-specific survival and biodemography, to cite only from the list of one author. The intro was on the too long side, with many sections that for me were beside the point and blurred the main take-home message. The abstract failed to convey the severe limitations introduced by the data selection procedure and sounded way too definitive relative to the actual content of the manuscript.

I hoped this was helpful in some way or another.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments for the authors

General comment

Overall, I think the paper may make a good contribution to the literature.  Although the paper clearly written, there are a number of places where discussion is inadequate.  A revision should fill in these missing details.  Some specific examples are below.

Specific comments

Line 63.  I disagree with the use of “biased” here.  I think conclusions based on crude age categories may be coarse, but not technically biased.  Explain.

Line 68.  What is meant by “ecological understanding?”  elaborate.

Line 74.  The Weibull distribution, while more flexible than the Gompertz because of its different parameterization, usually does not capture mortality experience for living things as well as the Gompertz because of early deceleration in mortality rates.

Line 84.  The absence of evidence vs. evidence of absence needs more explanation.  The real problem with mortality models that incorporate heterogeneity is that there is not enough information in real data to distinguish between shapes of true individual hazards and the extent of heterogeneity across a population in individual hazards.  For example, if everyone’s hazard is identically logistic in shape, the population hazard will be logistic in shape.  But, if everyone’s hazard is Gompertz in shape but heterogeneity in the baseline hazard is gamma distributed, the population hazard will still be logistic in shape.  Since individuals die once, we cannot know the latent hazard for any individual.

Line 160.  Equations 1-3 are not necessary.  These are commonly known and not specific enough to help with understanding your specific methods/analysis.

Line 202 (and earlier).  It is not clear what the “vector” of parameters is.  Typically, age is continuous and there is one parameter for it in the hazard.  Explain.

Lines 213-220.  Since DIC is your key measure for comparing models, it needs direct discussion/definition.  Furthermore, the paper needs more discussion regarding “overlap.”  The parameters have not been described, so it is not clear what is being examined for overlap.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

All of my previous comments were fully addressed. I have no more comments.