Exercise
on data from article (or author of)
* Impact of Folic Acid Fortification of the US Food Supply on the Occurrence of Neural
Tube Defects
* Incidence of open neural tube defects in Nova Scotia after folic acid fortification
I  [USA data] Restrict your comparison to spina bifida.  
a  Formally compare the observed rates pre and post (exclude data from the transition period). Do the same but using the numbers of cases [and denominators] explicitly. What is your best estimate (and 95% CI) of the difference that might be attributed to the fortification?  
b  Delevop (and fit) a single incidence model that covers all 3 periods and that that allows you to estimate the changes in incidence over these 3 periods. In a deluxe model [not required for this exercise!] you would probably like to 'round the corners'. For this exercise, as a rough approximation consider a simpler one with 3 (connected) straight lines (or curves if you use a rateratio model). This is as much an exrecise in how to represent 3 connected straight lines as it is about rates and counts.  
c  Is there evidence of overdispersion (ie extrabinomial or extraPoisson variation)? [the difference between binomial and Poisson is trivial here, since the binomial approaches the Poisson in the limiting case when, as here, the probability of an event is low].  
d  Does it change your estimates very much whether you use an additive (rate difference)
or a multiplicative (rate ratio) model? Does it matter very much if you use monthly or quarterly data? 

e  If we had the corresponding data for Canada (1/10th the population and numbers of births, with say with same incidence and same source of data), how much wider would the CI's be?  
f  Estimate, for various size reductions in the incidence, the statistical power of a study that  with an alpha of 0.05 2sided  compares (in the absence of other time trends) Quebec incidence in the 5 years pre with the incidence in the 5 years post introduction of fortification. Do so (a) without considering overdispersion, so that a regular Binomial or Poisson model is appropriate and (b) with the same amount of overdispersion as is seen in the 'pre' series in the US. [of course if there is overdispersion, and it is ignored in the analysis, it tends to increase both the power and the probability of a type I error! [we won't know which!].  
II  [Nova Scotia data] The Results section of the paper gives several point estimates, confidence intervals, and pvalues. the authors did not have a statistical analysis paragraph so you will have to try to determine how they calculated these items  or come up with your own.  
a  Calculate these items by 'tabular' (i.e., calculator) methods. Should you/they worry about the appropriateness of Gaussianbased inferences? [Remember that the chisquare statistic with 1 df is the same as the square of a zstatistic.. so whatever is accurate or inaccurate about one is equally so about the other] 

b  Calculate these items by 'regression' methods. Again, is use of Gaussianbased inferences OK?  
III  Why do you think the estimates of impact differ so much between the USA and Nova Scotia? What soes this say about any concerns you had in in IIf above? 
jh 2002.10.08