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.]

We conclude our section by section examination of the mathematical modeling paper by Lipsitch et al., published in PLoS Medicine. We have finally arrived at the final section, Discussion (starting on page 8 of the .pdf version). In the second post we said many scientists read only the Abstract, Introduction and Discussion sections of papers to see if they are sufficiently interested (or have enough specialist knowledge) to read the Methods and Results sections. This may shock you, as most people assume that when scientists read and cite a paper they have read the whole thing in detail. When it is in their own field, usually they have, but outside their own area of special knowledge there is neither the time nor ability to do this. And frankly, neither is it usually worth the effort. The scientific enterprise is a web of trust, credibility and credulity. The reputation and credentials of a scientist and his or her institution or laboratory, an unquestioned (and probably misplaced) faith in the peer review system, and simple necessity are the foundations of day to day practice. This is why allegations of scientific fraud are so deadly. But since we have been through the paper in detail, we don’t have to take the Discussion section on faith, except for one proviso. Online journals are now able to publish more and longer papers and to include details not possible when print space was limited. So this paper and many others now have online supplements with additional material, often important and valuable. We will find it necessary to refer to this as well, although we will not go through the mathematics because it uses methods that would require a graduate course to explain (although it’s not that complicated).

The first two paragraphs of the Discussion give the big picture, both the premise of the modeling effort and the overall result. It says the model confirms what common sense and other models have also shown, that a combination of an effective antiviral and non-drug measures, if applied sufficiently quickly and intensively, can reduce and stretch the duration of spread of epidemic influenza in a community. Increasing the duration allows additional time for preparation and eases the burden on health services. If resistance develops but the mutant is less genetically fit and transmits less effectively, then if measures are applied quickly, say within the first few thousand cases, spread can be aborted. This is the “Tamiflu blanket” scenario.

However the authors, and most expert observers, consider the required conditions improbable. There is currently not enough available Tamiflu nor the means to distribute it in a timely manner. The model examines two questions related to the ideal case: what happens when timely coverage of the population by antiviral use is much less than 40% of the population; and what happens if mutant resistant strains evolve that are just as fit or almost as fit as the sensitive strains? The model examines even very rare emergences of one mutant in 50,000 to 500,000 prophylaxed cases because we must assume assume that with mass antiviral use, tens or even hundreds of millions of people will be treated. Even rare occurrences would then happen with certainty. And since outbreaks will occur in many communities almost simultaneously, rare resistant mutants in one community can spread to others even when the others have been intensively treated with antivirals. In other words, you might conceivably have a local Tamiflu blanket but not a global one. The model shows that even for rare mutants will eventually spread rapidly and widely. So in this sense the model delivers bad news.

But there is less pessimistic news in the details, and it is summarized in paragraphs three and four of the Discussion. The third paragraph notes again that when antiviral and other measures are insufficient to stop spread completely (the likely case), the optimum benefit comes from intermediate use. Benefit does not ramp up continuously with population coverage. The authors argue for the reasonableness of this with a simple thought experiment. You are always better off using Tamiflu and less coverage is sometimes better than more coverage.

A second counter-intuitive (potential) outcome is revealed by the model. The more intense the non-drug interventions (e.g., social distancing), the higher the level of eventual resistance in the population. The reason relates to the speed with which the sensitive strain can spread in a population where transmissibility is high (less intervention), more sensitive spread occurring before a rarely emerging resistant strain can get going. Slowing the spread with non-drug interventions gives the needed time for the resistant strain to gain a foothold and start to spread before the sensitive strain has infected more people.

It is important to recognize that all of these results describe what might happen under very plausible conditions, not what would definitely happen in a pandemic. The model helps us understand why these things could happen and enlarges our intuition for the dynamics of influenza spread when antivirals are used on a population. In constructing this fairly simple model, a number of important assumptions had to be made. In the final posts we will ask to what extent these assumptions affect what we learn from the model.

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 M. Randolph Kruger
    April 3, 2007

    Revere-“The more intense the non-drug interventions (e.g., social distancing), the higher the level of eventual resistance in the population. The reason relates to the speed with which the sensitive strain can spread in a population where transmissibility is high (less intervention), more sensitive spread occurring before a rarely emerging resistant strain can get going. Slowing the spread with non-drug interventions gives the needed time for the resistant strain to gain a foothold and start to spread before the sensitive strain has infected more people.”

    Can you be a little more simplistic on this explanation? Is social distancing going to CAUSE a more undesireable result in a resistant strain or is it the other way around in the sensitive strain? Thats almost a quid pro quo for doing nothing, doing something, or state of equilibrium if all things are equal. Need just a bit more on this part. It sounds like the novel hairy virus will infect fewer, but eventually get its legs from what you are saying. If that is the case, isnt that what H5N1 is doing now in Indon and Egypt? But under that same assumption, it might be containable?

    Reason I ask is that to me the Indons have done a miserable job along with the Chinese of containment and surveillance. So if you have a tiger in the house, why wouldnt you try to do more unless what I consider to be the latter from above. More people get infected but the outcomes are better.

    You can see the confusion part.

  2. #2 revere
    April 3, 2007

    Randy: The more social distancing or other non-drug intervention, the more the resistant strain will have time to spread in the population. Fast spread for the senstive virus means that a greater proportion of people will be affected by sensitive virus and a smaller proportion by the resistant virus, but of course it means also that there will be more pressure on health care facilities and a greater overall attack rate. So it is a balancing act, but you win overall with the combination of antivirals and other interventions in terms of attack rate and spreading out the cases and delaying the peak, but you “lose” by having more of the circulating virus resistant.

    Using antivirals produces a lower overall attack rate (proportion of the population eventually affected) in every instance, and that effect is strongly helped by other interventions, so that is the way to go. But the cost is that a greater proportion of the circulating virus is resistant. Does that help?

  3. #3 M. Randolph Kruger
    April 4, 2007

    So its a win-win, lose-win, win-lose, or lose-lose.

    Its a helluva business you are in Revere. Not enough finality in it for me. Even lawyers get a full blown decision. Sounds to me though that if and when the big Panda bear comes blowing in that they are absolutely going to have to have their act together if its highly pathogenic.

    Sheyit, just identifying the modality of the stuff will take too long. IYO do you think they could contain it? If its like you say, I put our chances at no better than 55% and thats based upon immediate detection of the Pan 4 sliding to 5/6.


  4. #4 revere
    April 4, 2007

    Randy: One lesson from modeling is that there are many behaviors possible and it shows us how some of them might work. It is a very complicated system and doesn’t lend itself easily to exact prediction of what will or won’t happen, although we have some guides from past events. If it becomes easily transmissible (e.g., like seasonal influenza) IMO it is not containable and we will be in the mode of figuring out how to manage the consequences.

  5. #5 Melanie
    April 4, 2007

    If it is as transmissible as the norovirus, we are in a world of hurt. The last coupla days haven’t been a lot of fun around here.

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

    Okay so we have about five years of fun and games on the table and you are definitely qualified to make a guess even though you dont like to. What do you think is going to happen? Is it going to grab the patterns to start in on us, do you think its going to lose part of its ability to kill, or barring that do you think it comes in as a superpandemic with at least 40%?

    I respect your opinion more than the governments. I went to a meeting yesterday and listened to the usual song and dance about a mild pandemic. Ah, busting the people in charge is so much fun and they had an overhead projector when they were putting up their 5% estimations, the planning associated with it and etc. They finished up and thats when I pulled out my acetate sheet from the WHO slides that we get from WPRO. They were stunned. They asked me where I got that from? Pressing me hard and I said “Jeez, guys its on the internet on the WHO sites.” Treated me like I was spilling classified. They all dashed for their laptops. Only one guy and he is a biggie said he was aware of it. Now that make me nervous.

    The bottom line to this is that they are all locked in on this 5% stuff which is the product of a very neat model that some modeler produced at the behest of someone who wanted a model and was willing to produce one for a grade, money or both. One variable change such as adaptive mutation, lack of something, ineffective Relenza or Tamiflu, and all bets are off. Model to me goes into the trash and the new model starts.

    We could strengthen as you suggest the public health system. But like all variables too, this doesnt mean necessarily that there would be a cost effective outcome. I dont say that to be mean spirited either. I would like my government to blow the bank to keep me alive if I got sick, but its not reasonable to assume they will or would because the cost will be astronomical. Sooner or later someone would say thats all there is and then its over.

    Will modeling this beyond the first dozen or so cases produce any results in your opinion that will change outcomes? I dont care how we get there but let yourself flow here. Could or can we correctly model anything but the CFR’s?

    Your thoughts?

  7. #7 revere
    April 4, 2007

    Randy: I’m not completely clear on what you are asking. We can’t model CFRs, of course, because we have no way to do that. We can assume various values for it. Remember what the object of planning is. It isn’t to prevent a pandemic, it is to manage the consequences. Some of the consequences will be very hard to manage and we won’t be able to. Some will be manageable and we will do better than if we hadn’t tried. No matter what the CFR, it is still possible to do better than if we haven’t thought ahead.

    Regarding cost, strengthening the public health and social service infrastructure is almost always cost effective because it works for so many things, whether there is a pandemic or not and no matter what its severity. It doesn’t do everything, only some things. But it can do those things and much else besides and do them before, during and after a pandemic. Remember that even during a pandemic people will still get sick from other things: heart attacks, strokes, kidney stones, diabetes, etc. They will still have accidents and childhood illnesses. They will lose their jobs and be unable to buy food or pay rent. It will take a resilient community to get through a pandemic. We should be building the infrastructure to do that.

  8. #8 M. Randolph Kruger
    April 4, 2007

    That was it Revere, the CFR modeling is way off in my opinion and its based soley on the current facts of about 83% for the rolling one year average.

    All those other things though I think Revere will take a side seat and then out the door in the face of this because they wont get seen in my opinion by a doctor until the midway point or just a bit after. The things you describe are things that really only a doctor, a PA or maybe a smart nurse. Thats where I think we will lose so many to secondary cause rather than primary cause flu.

    They are going to definitely lose their jobs in a 8% effect. I havent got a clue other than to say that at least in Tennessee they are talking about a freeze in mortgage, utilities until 2-3 months after the all clear. Dont know what will happen post of that.

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