Global food security is a major driver of population health, and food system collapse may have complex and long-lasting effects on health outcomes. We examined the effect of prenatal exposure to the Great Chinese Famine (1958–1962)—the largest famine in human history—on pulmonary tuberculosis (PTB) across consecutive generations in a major center of ongoing transmission in China. We analyzed >1 million PTB cases diagnosed between 2005 and 2018 in Sichuan Province using age–period–cohort analysis and mixed-effects metaregression to estimate the effect of the famine on PTB risk in the directly affected birth cohort (F1) and their likely offspring (F2). The analysis was repeated on certain sexually transmitted and blood-borne infections (STBBI) to explore potential mechanisms of the intergenerational effects. A substantial burden of active PTB in the exposed F1 cohort and their offspring was attributable to the Great Chinese Famine, with more than 12,000 famine-attributable active PTB cases (>1.23% of all cases reported between 2005 and 2018). An interquartile range increase in famine intensity resulted in a 6.53% (95% confidence interval [CI]: 1.19–12.14%) increase in the ratio of observed to expected incidence rate (incidence rate ratio, IRR) in the absence of famine in F1, and an 8.32% (95% CI: 0.59–16.6%) increase in F2 IRR. Increased risk of STBBI was also observed in F2. Prenatal and early-life exposure to malnutrition may increase the risk of active PTB in the exposed generation and their offspring, with the intergenerational effect potentially due to both within-household transmission and increases in host susceptibility.

When summarizing a Bayesian analysis, it is important to quantify the contribution of the prior distribution to the final posterior inference because this informs other researchers whether the prior information needs to be carefully scrutinized, and whether alternative priors are likely to substantially alter the conclusions drawn. One appealing and interpretable way to do this is to report an effective prior sample size (EPSS), which captures how many observations the information in the prior distribution corresponds to. However, typically the most important aspect of the prior distribution is its location relative to the data, and therefore traditional information measures are somewhat deficit for the purpose of quantifying EPSS, because they concentrate on the variance or spread of the prior distribution (in isolation from the data). To partially address this difficulty, Reimherr et al. ( 2014) introduced a class of EPSS measures based on prior-likelihood discordance. In this paper, we take this idea further by proposing a new measure of EPSS that not only incorporates the general mathematical form of the likelihood (as proposed by Reimherr et al., 2014) but also the specific data at hand. Thus, our measure considers the location of the prior relative to the current observed data, rather than relative to the average of multiple datasets from the working model, the latter being the approach taken by Reimherr et al. (2014). Consequently, our measure can be highly variable, but we demonstrate that this is because the impact of a prior on a Bayesian analysis can intrinsically be highly variable. Our measure is called the (posterior) mean Observed Prior Effective Sample Size (mOPESS), and is a Bayes estimate of a meaningful quantity. The mOPESS well communicates the extent to which inference is determined by the prior, or framed differently, the amount of sampling effort saved due to having relevant prior information. We illustrate our ideas through a number of examples including Gaussian conjugate and non-conjugate models (continuous observations), a Beta-Binomial model (discrete observations), and a linear regression model (two unknown parameters).

We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et al. [2008]. However, these measures typically ignore the likelihood for the inference currently at hand, and therefore address (i) rather than (ii). Since in practice (ii) is of great concern, Reimherr et al. [2014] introduced a new class of effective prior sample size measures based on prior-likelihood discordance. We take this idea further towards its natural Bayesian conclusion by proposing measures of effective prior sample size that not only incorporate the general mathematical form of the likelihood but also the specific data at hand. Thus, our measures do not average across datasets from the working model, but condition on the current observed data. Consequently, our measures can be highly variable, but we demonstrate that this is because the impact of a prior can be highly variable. Our measures are Bayes estimates of meaningful quantities and well communicate the extent to which inference is determined by the prior, or framed differently, the amount of effort saved due to having prior information. We illustrate our ideas through a number of examples including a Gaussian conjugate model (continuous observations), a Beta-Binomial model (discrete observations), and a linear regression model (two unknown parameters). Future work on further developments of the methodology and an application to astronomy are discussed at the end.