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.]

This is the last in a long series attempting to explain a recent paper by Lipsitch et al. on mathematical modeling of the effects on influenza control of antiviral resistance, published in PLoS Medicine in January 2007. Modeling is a valuable technique but for most readers, even most scientists in the flu community, the model itself is a black box. We wanted to look into the box to see its contents. Along the way we have tried to convey the flavor of mathematical modeling and locate this tool among the many other tools available to scientists to understand influenza. For a summary of what we learn from this paper we can do no better than quote the authors (from their Discussion section, internal literature citations omitted):

The simple model used here enables evaluation in a general way of the potential impact of resistance on an influenza control program, to assess the relative contributions of different factors (parameters) contributing to the epidemic. It uses a simplified, exponentially distributed natural history; however, since most of the conclusions (except for those about the magnitude of delays) are about the final state of the population, and all terms in the equations can be nondimensionalized by dividing by the generation time, this simplification does not have a major effect on outcomes. This model does not account for saturation of contacts due to transmission within families and other small groups, and therefore predicts higher attack rates than more complex, agent-based models for a given value of R0. Given the simplifications inherent in any model and the large uncertainties about the properties of a potential pandemic strain and its resistant variants, we emphasize the qualitative predictions of the model . . . rather than the exact quantitative predictions. Important predictions that we believe to be robust to model structure are that (1) antiviral use will favor the spread of resistance even if such use rarely generates de novo [spontaneously arising] resistant strains; (2) despite the spread of resistance, prophylaxis and treatment can both delay and reduce the size of the epidemic; (3) nondrug interventions (if effective) and antiviral use – which will likely be used together in the response to a pandemic – generally have synergistic benefits, despite the fact that nondrug interventions may promote resistance; and (4) relatively minor differences in fitness cost may make large differences in outcomes, even when emergence probabilities are low (Figure 4). These results extend those of previous models, which showed (like our model) that the fitness cost of resistance strongly influences the ability of resistant strains to spread during an epidemic. [our emphasis]

Notice the bolded sentence:

Given the simplifications inherent in any model and the large uncertainties about the properties of a potential pandemic strain and its resistant variants, we emphasize the qualitative predictions of the model . . . rather than the exact quantitative predictions.

The Lipsitch team are accomplished modelers with a solid understanding of their subject matter. One of the (many) things I like about this paper is it does not over interpret the results but extracts what is useful and potentially important. Many scientific papers are made to bear more interpretative weight than they should in press reports, but authors are often complicit. (I think of this every time I see a paper on a new vaccine technology that “works in mice.”) Modeling requires a variety of skills foreign to biologists and biology is also foreign to many modelers. So it is not surprising some modelers have an exaggerated or false impression of how generalizable their work is. Fortunately there is a cadre of flu modelers both expert in modeling and their subject matter. The Lipsitch team are among them. There are a number of others.

We close, then, with the bottom line of the Lipsitch paper (literally, the last paragraph) about the role of antivirals in controlling influenza after taking the emergence of resistance into account:

Optimism about the benefits of antivirals in an influenza pandemic should be tempered by the knowledge that transmissible, pathogenic resistant strains are a real possibility and could reduce the benefits of antiviral use in pandemic control. Successful implementation of nondrug interventions to control resistance will, in most circumstances, amplify the benefits of antiviral use in controlling the pandemic, although such interventions may increase the proportion of resistant cases. Because the impact of resistance is relatively insensitive to the rate at which resistant strains emerge de novo in antiviral recipients, efforts to control influenza transmission overall may be of greater benefit than efforts to reduce the de novo rate of emergence of resistance. Despite these caveats, we do not believe that concerns about resistance should preclude the widespread deployment of antivirals as part of the response to a pandemic. If these drugs, used prophylactically or for treatment, are effective in reducing transmission of the next pandemic strain, they should provide benefits by reducing the number of infected patients and delaying transmission, even if resistant strains ultimately become widespread.

Whether you agree or not, we hope at least you now have some idea how this judgment was arrived at.

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 Ann
    April 5, 2007

    Thank you for taking the time to help us(me)understand this. I really appreciate it.

  2. #2 JimV
    April 5, 2007

    Thanks very much. With this as a base and reference, I hope you see fit to give expanded discussions of more good papers in the future. They need not take quite as much time and effort on your part, since you can refer back to these posts for explanations of general concepts.

    (This is the first time a scienceblog article has given me enough detail to allow me to do a Runge-Kutta numerical integration and check the paper’s results.)

  3. #3 revere
    April 5, 2007

    JimV: Thanks for the “thanks” and to all others who have thanked me for this. I’ll never do it again, but you can expect shorter efforts. I had to laugh when you said there was enough to do a R-K run on it. Yes, you could. It’s even easier to download the free trial version of Berkeley Madonna and paste in the code from the Supplement.

  4. #4 M. Randolph Kruger
    April 6, 2007

    So Revere are we to assume that the modelers are sitting back and sharpening their knives for the pandemic if and when it comes? All of the factors you posted up were pretty much medical and I know, I know, its the limited explanation you put up. But what good is a model thats being produced as it happens? To me whats more needed is the predictive. We can make all sorts of assumptions (McKibbins-Australia) but its not much more from where I sit. I can safely say now I know how you guys get to where you are. Feel like I did a semester with you. Can the models help if this stuff is multiplying in a high path way in time to come up with real treatment processes? Obviously my, “You cant get it, if you dont put yourself in harms way” would work. But a certain number of even those will fall. Giving everyone Tamiflu in the US might work as its happening and likely would slow it, but wouldnt stop it as you said. So is it just slowing the spread and creating a longer pandemic? The longer its there, the more chance that anarchy and at the least chaos would break out.

    Man this goes so round robin back and forth it makes my head hurt. But it comes back to really two or three basic things. High path or not, Antivirals work or wont, Vaccine available or not, social distancing works or not. Everything pretty much keys off of this and someone is going to have to be inputing information into a computer fast to get a real result that we can use to determine what works and what doesnt. How long does it really take to come up with and I use the term loosely “an answer”.

  5. #5 Torbjörn Larsson
    April 6, 2007

    An enjoyable read.

    And now I will understand some idiosyncrasies of medical models next time. (Integrating up to the first infection, instead of randomly introduce it from some probability distribution, for example.)

  6. #6 Torbjörn Larsson
    April 6, 2007

    Uups, sorry, I guess I meant first resistance case above. Oh no, now I have to check the whole series of posts for that detail again. 🙂

  7. #7 revere
    April 6, 2007

    Randy: I don’t understand your question. A modeler is just a scientist. They aren’t sitting back and sharpening knives, they are practicing science. Maybe you’d like them to do something else or do it differently, I’m not sure. But this paper has produced results which are important and useful for other scientists (e.g., the paper on influenza B I posted on yesterday). Meanwhile other scientists are writing about the polymerase complex or lectins or any of a lot of things. You are writing here. Etc. It was work that started years ago and was just published in January. You know about it because I wrote about it. Nothing more, nothing less. If you don’t find it useful for your particular interests, that’s fair enough. But that’s not the fault of the scientists. At least now you know something about modeling, which was my objective.

    T. Larsson: Yes, but that’s this kind of deterministic model. You can also do stochastic models or agent based models or combinations. I was more trying to give the flavor o modeling and where it fits into other scientific techniques, like wet bench experiments or epidemiology.

  8. #8 M. Randolph Kruger
    April 6, 2007

    Revere, The simplest question is whether the modeling will be useful in the BF dilemma? Sharpening their knives to come up with an answer in the middle of the pandemic was my reference. Will they post up something that we can all use quickly enough to tell everyone what to do. I must hear it five or ten times a day, What do I do? Other than social distancing, maybe a mask, and for sure preparedness supplies, nothing seems to change the suggested outcome. We already know that two of these work to a large extent….. Thats my reference and question. What else can anyone do?

    Great stuff on modeling though it was indeed interseting.

  9. #9 revere
    April 6, 2007

    Randy: The model (strongly) suggests that if we use antivirals we will be better off than if we didn’t, even if resistance develops in the course of the pandemic wave, and that non drug interventions synergize with this effect, although they also produce more resistance over time. This is significant information for people doing influenza control, the main audience here. It is not directed at you or your neighbors. Most modeling, being about populations and not individuals, is like that. For the answers to your individual questions you need to look elsewhere, for example, to industrial hygienists who design and test masks.

  10. #10 Torbjörn Larsson
    April 6, 2007

    Yes, but that’s this kind of deterministic model.

    Oh, I understand – and it will be easier, perhaps even necessary, to compare results. But off hand it was tempting to use a simple probability to make the model closer to observations.

    (And in case of robust models it would probably make little difference. Of course, now one has to look at a couple of simulations outputs. More work. Ouch!)

  11. #11 revere
    April 7, 2007

    Torbrjorn: You really need stochastic models for small populations, but for larger ones, the expected values and the deterministic proportions should make them almost the same. In this case, there is the “hack” (as Prof. Lipsitch called it) to take care of it for nanocases.

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