My exposure is poverty and blindness from trachoma. Poverty is a huge risk factor for trachoma infection, but allied with poverty is the idea that hand sanitation and access to clean water is a mediator between poverty and increased risk for trachoma. I think it likely that accumulation is the most appropriate model, where total time in poverty increases your risk of blindness from trachoma later in life. There may be some arguments for critical periods however, as sanitation is in part a learned behavior, so it may be that there are critical periods for taking maximum advantage of the access to sanitation that is available, or alternatively children continuing to have friends who remain in poverty/without access to clean water and continue to be high sources of transmission. I think there is little evidence for mobility having a large impact upon the risk of blindness from trachoma, as it is not obvious that changing upwards or downwards in and of itself would create increased or reduced risk from trachoma.
Ideal data- poverty data from a cohort study in a trachoma endemic area following villagers over 30+ years, with reported blindness from trachoma. I suspect that such data does exist, but I’m not sure if I personally would have access to it. I would really need longitudinal data. I would be interested on having data of poverty status during infancy (0-2), early childhood (2-5), mid-childhood (5-10), late childhood (11-15).
Saturated model:
E(blindness) = b0 + b1*P1+b2*P2 + b3*P3 + b4*P4 + ∂12*P1*P2 + ∂23*P2P3 + ∂34*P3*P4 + ∂13*P1*P3 + ∂14*P1*P4 + ∂24*P2*P4 + ∂123*P1*p2*P3 + ∂134*P1*P3*P4 + ∂124*P1*P2*P4 + ∂234*P2*P3*P4 + ∂1234*P1*P2*P3*P4
Testing critical period model – Compare the critical period model to the saturated model of poverty in which each period matters and each interaction between each. The critical period model would assume being exposed in at least one time period is significant, but non-significant in zero. This would assume that at least one of b1, b2, b3 or b4 = 0, and at least one is non-zero. It also assume that all ∂’s = 0. You would use the F-statistic for n-16 degrees of freedom to compare the two models on consistency with the data.
Testing the accumulation model: Compare again to the saturated model. Here you would assume that all ∂’s were = 0 since there was no interaction over time between poverty exposure status, and instead you would also assume that b1=b2=b3=b4. Here you can use the partial F-test to compare the saturated model with 16 parameters to the simpler accumulation model with only two parameters.
Testing social mobility model - compare again to the saturated model, but easier to compare to the saturated model specified as a change in poverty status rather than the direct model specified above.