Table 4.
Mean Difference in X Between Exposed and Unexposed Subjects When a Caliper Selected by Youden's Indexa is Applied, Using 5 Different Matching Methods
| Matching Method by Controls per Case | OR for Effect of X on Exposure |
|||
|---|---|---|---|---|
| 1.5 | 2 | 5 | 10 | |
| 2 | ||||
| Ascendingb | −0.0060 | −0.0107 | −0.0138 | −0.0124 |
| Descendingc | 0.0061 | 0.0119 | 0.0171 | 0.0164 |
| Random orderd | 0.0001 | 0.0004 | 0.0008 | 0.0014 |
| Best firste | 0.0001 | 0.0002 | 0.0003 | 0.0007 |
| 5-to-1-digitf | −0.0004 | −0.0007 | −0.0009 | −0.0005 |
| 5 | ||||
| Ascending | −0.0005 | −0.0012 | −0.0066 | −0.0078 |
| Descending | 0.0005 | 0.0012 | 0.0078 | 0.0096 |
| Random order | 0.0000 | 0.0000 | 0.0003 | 0.0005 |
| Best first | 0.0000 | 0.0000 | 0.0002 | 0.0002 |
| 5-to-1-digit | −0.0000 | −0.0001 | −0.0004 | −0.0004 |
| 10 | ||||
| Ascending | −0.00012 | −0.00026 | −0.00326 | −0.00536 |
| Descending | 0.00012 | 0.00026 | 0.00366 | 0.00640 |
| Random order | 0.00000 | 0.00000 | 0.00016 | 0.00032 |
| Best first | 0.00000 | 0.00001 | 0.00010 | 0.00014 |
| 5-to-1-digit | −0.00001 | −0.00002 | −0.00017 | −0.00030 |
| 20 | ||||
| Ascending | −0.00003 | −0.00006 | −0.00150 | −0.00343 |
| Descending | 0.00003 | 0.00006 | 0.00161 | 0.00397 |
| Random order | 0.00000 | 0.00000 | 0.00006 | 0.00019 |
| Best first | 0.00000 | 0.00000 | 0.00005 | 0.00009 |
| 5-to-1-digit | 0.00000 | 0.00000 | −0.00007 | −0.00019 |
Abbreviation: OR, odds ratio.
a For each point, Youden's index is the sum of the horizontal distance from the y-axis plus the vertical distance from the line y = 1.
b In the ascending method, each time a match is made, the exposed subject with the lowest propensity score is used.
c In the descending method, each time a match is made, the exposed subject with the highest propensity score is used.
d In the random order method, each time a match is made, the exposed subject is selected at random.
e In the best first method, each time a match is made, the exposed subject with the closest matching unexposed subject is used.
f n the 5-to-1-digit method, initially, matched pairs are selected at random from exposed-unexposed pairs for which propensity score is identical to 5 decimal places (on a log-odds scale). When no such pairs remain, pairs are selected at random from those with identical scores to 4 decimal places, then to 3 decimal places, and so forth.