# Selecting the control group in a before-after study

I am interested in analyzing the effect of a specific change in traffic conditions on the amount of road accidents in a city.

I need to select a comparison group; my approach is to select from possible candidates, the city\district that was in the past most similar to the city being investigated .

Monthly data is available to me for all the cities.

However, I do not know if I should take as the comparison group the city most similar to mine comparing across the months, or rather sum the months, and use the city most similar to mine judging by the years.

I do not have access to a transportation expert whom I could ask for advice that would be relevant to the specific situation.

Are there statistical considerations to make the choice?

The way I judge the similarity between two cities:

For each city in the control group, there is a monthly amount of accidents, C(t). For the treatment group, I will denote the amount M(t). If the treatment is similar to the control group, then in the period before the treatment M(t+1)/M(t) = C(t+1) / C(t).

Which means that the rate of change is the same between the control and the treatment group. As far as I understand, this assumption allows me to use difference -in-differences to test for the effect of the treatment.

This is based on the procedure descirbed in the book "Observational Before-after Studies in Road Safety" \ Ezra Hauer.

However, he doesn't address there the question whether I should work with the monthly data, or sum it and select according to the yearly data.

• Is it not the case that a city closest to your city of interest by months will also be closest by years? Using months is clearly a more stringent requirement, which, if satisfied, would yield a more valid effect estimate, but it may be harder to find such a city. This is the classic issue of the bias-variance trade-off in observational studies. – Noah Jul 26 '18 at 17:48
• Thanks @Noah , you nailed it, it is indeed an issue of bias-variance trade-off. Precisely for that reason,using months is a "more stringent requirement", only if by stringent you mean having less bias. According to the trade-off, using months should result in less bias, but in more variance. Using years should result in more bias, but less variance. This is precisely what I see in the past data. (Btw, according to the data, the control group closest in term of years, is indeed not the closest one in terms of months.) I will present both, or will look at the synthetic group approach suggested. – Sam Jul 28 '18 at 9:02