Not All in our Genes, The Sequel

Last November a WHO study "stated" there was evidence a genetic factor was at work in the susceptibility to H5N1 because it appeared an abnormally high number of reported clusters involved only blood relatives. At the time I expressed some polite skepticism (Not All in Our Genes). Whether the observed data actually had more blood relative cases than would be expected bdepends on what one would expect. What you "expect" is the so-called null-distribution, which in turn depends on a plausible underlying probability model. Now a doctoral student working with Marc Lipsitch and his collaborators at the Harvard School of Public Health have taken a harder look at this question in a paper published ahead of print in CDC's journal Emerging Infectious Diseases (Pitzer et al.).

At the time of writing, there were 261 confirmed cases in 36 family clusters, ranging in size from 2 to 8 infected persons each. Only 4 of these clusters had unrelated family members, such as a husband and wife, so on its face this seemed highly unlikely. But the paper by Pitzer et al. makes the case it is not at all unlikely. They describe a null model for no blood relationship that implies such a pattern would be seen with some frequency by chance alone. Moreover, other features of the data, such as the proportion of all cases that are part of a cluster and the average number of cases per cluster are consistent with the model.

What is a null model, anyway? Suppose you flip a coin you believe to be fair. Your null model is that the probability it will come up heads is the same as the probability it will come up tails. If you flip it four times and it comes up heads three times and tails once, that could easily happen under this null model, i.e., even with a fair coin. Thus those results are consistent with the null model of fairness. Of course it is also consistent with other models, such as heads are more likely to come up. You might test it further by flipping it more often, since the proportion that deviate a lot from the 50 - 50 expected outcome is much smaller if you flip the coin 1000 times rather than four times. You wouldn't expect a fair coin to come up 750 heads and 250 tails.

So what was the null model in this case? It's a very simple one. Each person is equally susceptible (i.e., everyone has the same risk of infection) and there is no human to human transmission. Neither of these assumptions affects the blood relative proposition, so this is a reasonable model. It is really a coin flip experiment where the chance of "heads" is now not 50% but the probability of infection. Clusters would be confined to blood relatives unless both parents were infected. Using fairly simple probability arguments, the authors construct a plausible null distribution for both nuclear and extended families and show that under these very simple conditions (and depending somewhat on the size of a family), the observed data would be quite common if the probability of infection is not too high (less than 30%). If the probability of infection is lower, say around 15% or less, than the model also predicts the observed proportion of cases in clusters, but not the average number of cases per cluster, which require higher infection probabilities or larger family sizes. On the other hand these discrepancies can be accounted for if the probability of infection varies between families, which it almost certainly does. For example, if the probability of infection is lower in families with fewer cases but higher in families with more cases, this would produce something like the observed pattern. This can easily be explained by differences in the virus, different intensities of exposure, environmental factors or many other explanations.

Does this mean that family clustering must be from non genetic causes? No, not necessarily. It just says that a non-genetic explanation is is quite consistent with the data. Genetic predispositions might well be involved to a greater or lesser extent. But at this point the observed data don't point to them, as was previously thought.

Meanwhile a graduate student has got herself a pretty nifty paper and the rest of us have learned something. Unfortunately what we've learned is that something we thought might be an answer isn't necessarily an answer any more.