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Impacts of the 1918 flu on survivors' nutritional status: A double quasi-natural experiment

Robust empirical evidence supports the idea that embryonic and, more generally, intrauterine disruptions induced by the 1918-flu pandemic had long-term consequences on adult health status and other conditions. In this paper we assess the 1918-flu long-term effects not just of in utero exposure but also during infancy and early childhood. A unique set of events that took place in Puerto Rico during 1918–1919 generated conditions of a “double quasi-natural experiment”. We exploit these conditions to empirically identify effects of exposure to the 1918 flu pandemic and those of the devastation left by an earthquake-tsunami that struck the island in 1918. Because the earthquake-tsunami affected mostly the Western coast of the island whereas early (in utero and postnatal) exposure to the flu was restricted to those born in the interval 1917–1920, we use geographic variation to identify the effects of the quake and timing of birth variation to identify those of the flu. We benefit from availability of information on markers of nutritional status in a nationally representative sample of individuals aged 75 and older in 2002. We make two contributions. First, unlike most fetal-origins research that singles out early nutritional status as a determinant of adult health, we hypothesize that the 1918 flu damaged the nutritional status of adult survivors who, at the time of the flu, were in utero or infants. Second, we target markers of nutritional status largely set when the adult survivors were infants and young children. Estimates of effects of the pandemic are quite large mostly among females and those who were exposed to the earthquake-tsunami. Impacts of the flu in areas less affected by the earthquake are smaller but do vary by area flu severity. These findings constitute empirical evidence supporting the conjecture that effects of the 1918 flu and/or the earthquake are associated not just with disruption experienced during the fetal period but also postnatally.


The simplest case: population homogeneity
Let BE be the number of births in the exposed group, πE the probability of developing malnutrition if exposed and σ1 the probability of surviving from age 0 to age 70.
Similarly, let BNE be the number of births in the non-exposed group, πNE the probability of developing malnutrition and σ2 the probability of surviving from age 0 to 70 among those non exposed. A measure of the effects of exposure on risks of adult malnutrition is the ratio of the odds of developing malnutrition in the exposed group to the odds of developing malnutrition in the non-exposed group, ORT = (πE/(1 πE)/(πNE/(1 πNE)). Under the above conditions, the observed odds ratio will be ORO =ORT (σ1/σ2). It follows that the ORO is a biased estimate of ORT and the magnitude of the bias is a function of the ratio σ1/σ2. In general, σ1 < σ2 and the observed odd ratios will underestimate the true odds ratio.

Mortality homogeneity
To keep things simple, assume that excess mortality among those exposed is experienced mostly during the first year of life and much less there after. Furthermore, assume that morality risks are proportional along the entire age span. Then we can write the probability of surviving from age 0 to age 70 among non exposed as (exp(-M0) exp (-I[1,69]) and as (exp(-θM0)exp(-δI[1,69]) among the exposed. Here M0 is infant mortality, ,69] is the integrated m o r t a l i t y hazard between ages 1 and 70 exactly, and θ and δ are the ratios of infant and adult mortality hazard of the exposed to the non-exposed population. Thus, the ratio of survival probabilities σ1/σ2 is given by exp(-(Mo(θ-1) + I[1,69](δ-1)) which can be written exp (-I[0,69] ((Mo/I0,69])(θ-1) + (I[1,69]/I[0,69])(δ-1))) showing that the final bias depends also on the fraction of all mortality that occurs during infancy.
To get a sense for the magnitude of the bias in our case we assume the following:

Mortality heterogeneity
The above assumes that excess mortality only depends on exposure and not on the occurrence of the event of interest, e.g. malnutrition. To generalize the expression for the magnitude of the bias we assign different mortality levels to those who experience malnutrition and those who do not. We further assume that both infant and "adult" mortality are similarly affected and, finally, that excess mortality is the same irrespective of exposure status and only varies as a function of malnutrition status.
The expression for the bias is the following: where the first term after the equal sign is the ratio of probabilities of surviving from age 0 to age 70 among exposed individuals who experience malnutrition to those who do not, and the second term after the equal sign is the ratio of survival probabilities among non-exposed individuals who do not experience malnutrition to those who do.
Note that the first term is likely to be considerable smaller than 1 whereas the second term will, as a rule, be larger than 1. It follows that, as should be intuitively clear, the downward bias in the odds ratio is likely to be smaller than when mortality homogeneity prevails In summary, the estimates presented in this paper are surely biased downward but the bias is unlikely to exceed 15 to 20 percent.

Population heterogeneity
Similar expressions can be derived to represent cases when there is population heterogeneity. For example, we may want to consider the fact that populations are composed of different social classes with heterogeneous risks. E v e n i f e x p o s u r e i s r a n d o m b y s o c i a l c l a s s e s , individuals belonging to different social classes could have different propensities to malnutrition both when they are exposed and when they are not exposed, different probabilities of surviving if they become malnourished, and heterogeneus mortality differentials between those who become malnourished and those who do not.
These expressions are quite cumbersome and depend on a number of parameters we have little information about. Thus, computing even approximately the magnitude of associated biases is less meaningful than in the cases above where only a few parameters were needed.