Effect Measure

[A series of posts explaining a paper on the mathematical modeling of the spread of antiviral resistance. Links to other posts in the series by clicking tags, “Math model series” or “Antiviral model series” under Categories, left sidebar. Preliminary post here. Table of contents at end of this post.]

As promised, this post will start a detailed examination of the paper by Lipsitch et al., “Antiviral resistance and the control of pandemic influenza,” published in PLoS Medicine, section by section. We hope you have your own copy, available here (see previous post for more details). We’ll start with the Introduction (p. 2 of the .pdf version), the first of four main sections.

Parsing the Introduction:

The reason scientists often only read the Introduction and Discussion sections is that they set the stage (Introduction) and sum up the authors’ view of the meaning and significance of the paper (Discussion). In addition there are usually valuable citations to the literature you can use to follow up on points of interest. Many non-specialist readers don’t go beyond these two sections unless they have special reasons to look into the methodology (e.g., they don’t believe the results!) or want more details on what was found. Ideally scientists would subject every paper they read to a probing critique. The truth is there isn’t enough time, so we take shortcuts. We’re not going to take any shortcuts here, but we’ll still start with the Introduction because it tells the reader what was done and why.

The Introduction of this paper is typical, occupying about a page of text and consisting of five paragraphs, the last of which is a guide to the rest of the paper. The first paragraph orients the reader to the subject matter (neuraminidase inhibitor [NI] use for prophylaxis and treatment in a pandemic), why it is important (antivirals are a major part of national plans), and, in a few sentences, reviews previous work similar to this one modeling antiviral use in influenza (antivirals alone won’t have a significant impact but might be important in combination with other measures). You can learn a lot in a single paragraph of a well-written Introduction.

Paragraph two introduces the main problem, the possible development of resistance to NIs by a pandemic strain of influenza. We know the influenza virus can develop resistance to NIs. In some published series of clinical antiviral use, resistance to the main NI antiviral, Tamiflu, can amount to several percent of treated individuals. Models predict resistant strains would spread rapidly if they are fully or nearly fully as fit as the non resistant strain. If the virus is less fit, then the extent to which it spreads depends on how impaired it is and whether the effectiveness of antivirals against the unmutated sensitive virus (the “wildtype”) is sufficiently strong that even a somewhat defective resistant virus is better off. Most Tamiflu resistant viruses are believed impaired to some extent. So far. Previous modeling work suggests that the probability of resistance affects when in the epidemic resistant strains appear. Once they appear, how much they spread depends on how transmission-capable they are compared to the sensitive strain.

Paragraph three sets up a contrast between previous modeling results and the focus of clinicians and uses the contrast to introduce the concerns of the paper. Previous models, the authors say, suggest that the “overall course” of the epidemic is independent of the rate of emergence of resistance. We interpret “overall course” to mean impact on the number of infected people (attack rate), since the previous paragraph has just said that when resistant strains appear is related to the rarity (or not) of resistance (which makes sense). On the other hand, Litpsitch et al. note that clinical discussions of resistance focus on slowing the appearance of resistance by using appropriate dosing or combinations of antivirals. The authors suggest this difference in emphasis might be related to an assumption by clinicians and modelers that resistant strains are not transmissible (have high transmission fitness costs) and thus won’t spread beyond the patient. With this assumption, resistance appears almost entirely from spontaneous (“de novo”) mutation, not by spread.

The authors use this contrast to set up their main question: if there is widespread antiviral use (in the tens to hundreds of millions of doses), could very rare resistant strains with little or no transmission fitness cost arise and spread widely, or, alternatively, could selection pressure be sufficient to allow a less transmissible virus to spread easily. Paragraph four provides some citations to support the idea it is plausible there are resistant strains that might be as transmissible as the sensitive strain. The authors conclude that “it is prudent in pandemic planning to consider the possibilty that resistant strains with modest or no fitness cost might emerge at some point during the pandemic, even if most strains observed to date have shown substantial fitness costs [cite omitted].” In addition, they wonder if selection pressure (a strong effect on the sensitive virus) could allow a resistant virus with moderate fitness cost to spread widely.

Questions addressed by the paper:

The final paragraph sets out the four questions addressed by the paper:

  • Suppose resistant strains that were as fit, or almost as fit, as the sensitive strain developed, but only very rarely. Could they still spread in the population and if so, how fast?
  • Treatment generates resistant strains better than prophylaxis but prophylaxis blocks the spread of the sensitive strain. What are the relative roles of each of these tendencies in allowing the spread of resistance?
  • How does antiviral use interact with non-drug measures, like social distancing, to inhibit the spread of disease?
  • Suppose antiviral resistance emerges and spreads widely. How does that affect the overall course of the epidemic? Are we better off or worse off?

In the next series of posts we examine the mathematical model used to address these questions.

Table of contents for posts in the series:

What is a model?

A modeling paper

The Introduction. What’s the paper about?

The essential assumption.

Sidebar: thinking mathematically

The model variables

The rule book

More on the rule book

Finishing the rule book

The rule book in equation form

Ready to run the model

Effects of treatment and prophylaxis on resistance

Effects of Tamiflu use and non drug interventions

Effects of fitness costs of resistance


A few words about model assumptions

Conclusion and take home messages


  1. #1 cervantes
    March 23, 2007

    I’m curious as to how much empirical information we have about spread of resistant virus in other contexts, e.g. HIV. Certainly we have plenty of experience with drug resistant bacteria, although bacteria are a different matter because of their ability to exchange genes. To what extent does this real world information inform the modeling process, or permit us to assess its credibility?

  2. #2 revere
    March 23, 2007

    cervantes: There’s a huge literature on drug resistance in HIV which I am not very familiar with. Someone else want to weigh in? HIV is a retrovirus, so not biologically the same, but the population dynamics of spread of HIV or bacterial resistance formally should be similar. However the parameters of the models will change and along with it the qualitative behavior, so that isn’t an answer to your question.

  3. #3 Tim
    March 23, 2007

    Substitute vaccination for anti-virals, and you should have an immense amount of data available, at least as far as the prophylaxis rate functions of the model.

  4. #4 Racter
    March 23, 2007

    One thing I’m getting out of this is that treating a single patient appears to involve a different set of priorities than does treating a population. When infection occurs, prophylaxis may be considered to have failed, and further treatment with the drug incurs a greater risk of generating resistance — but it may still be the best hope as far as the individual patient is concerned. Tough choices for somebody. I still like the idea of using one class of antiviral for prophylaxis, switching to the other on the onset of symptoms.

  5. #5 revere
    March 23, 2007

    Racter: So far you haven’t seen any of the modeling. That comes in the next many posts.

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