1 Introduction
2 Data structure and parameters for the before-after study with comparison sites
Treated site | Comparison site (or group of sites) | |
---|---|---|
Period I (Before) |
x
1
|
x
3
|
Period II (After) |
x
2
|
x
4
|
3 The Bayesian framework
4 Low-informative prior distributions
4.1 Case where regression to the mean bias is unlikely
4.2 Case where regression to the mean bias is likely
5 Posterior probabilities
5.1 Case where regression to the mean bias is unlikely
5.2 Case where regression to the mean bias is likely
5.3 Practical uses of the posterior cumulative distribution function of Θ
6 Particular cases
6.1 Group of comparison sites instead of a single comparison site
6.2 Multiple treated sites
7 Examples of application
7.1 Example 1: Safety effect of redesigning an urban road section
95% symmetrical credible interval: | 0.062 to 0.815 |
Median: | 0.259 |
Posterior probability that θ < 1: | 0.990 |
θ
ML
* = 0.249 | |
Woolf 95% confidence interval: | 0.068 to 0.904 |
7.2 Example 2: Safety effect of a rural crossroads modification
95% symmetrical credible interval: | 0.117 to 1.389 |
Median: | 0.439 |
Posterior probability that θ < 1: | 0.917 |
95% symmetrical credible interval: | 0.151 to 1.789 |
Median: | 0.566 |
Posterior probability that θ < 1: | 0.828 |
7.3 Example 3: Safety effect of resurfacing on main roads
95% symmetrical credible interval: | 0.794 to 1.537 |
Median: | 1.106 |
Posterior probability that θ < 1: | 0.275 |
θ
ML
* = 1.105 | |
Woolf 95% confidence interval: | 0.794 to 1.537 |