Table 1.
Second order quadratic utility functions
| Country | 2-nd order quadratic line | Tool | Interpretation | Rank (equation 5D-5D-5L) | Rank (EQ-5D-3L) |
|---|---|---|---|---|---|
| Japan | Y = − 0.0000000550x2 + 0.0003563210x − 0.0742209093 | EQ-5D-5L | Concave | 1 | – |
| Japan | y = − 0.0000062x2 + 0.0045459x − 0.0090418 | EQ-5D-3L | Concave | – | 1 |
| Denmark | Y = − 0.0000000446x2 + 0.0004197915x − 0.1655666889 | EQ-5D-5L | Concave | 2 | – |
| Denmark | y = − 0.0000054x2 + 0.0057193x − 0.2949838 | EQ-5D-3L | Concave | – | 2 |
| France | Y = 0.0000000237x2 + 0.0001943942x − 0.2303118192 | EQ-5D-5L | Convex | 6 | – |
| Germany | Y = 0.0000000323x2 + 0.0001660183x + 0.0082592409 | EQ-5D-5L | Convex | 10 | – |
| Germany | y = 0.0000094x2 + 0.0014504x – 0.0378014 | EQ-5D-3L | Convex | – | 8 |
| Netherlands | Y = 0.0000000268x2 + 0.0001734792x − 0.0647394984 | EQ-5D-5L | Convex | 8 | – |
| Netherlands | y = 0.0000055x2 + 0.0021384x − 0.0380753 | EQ-5D-3L | Convex | – | 5 |
| Spain | Y = 0.0000000251x2 + 0.0002372594x − 0.2745223392 | EQ-5D-5L | Convex | 7 | – |
| Spain | y = 0.0000083x2 + 0.0025337x − 0.3504985 | EQ-5D-3L | Convex | – | 7 |
| Thailand | Y = − 0.0000000134x2 + 0.0002816214x − 0.1901163980 | EQ-5D-5L | Concave | 4 | – |
| Thailand | y = 0.0000015x2 + 0.0033337x − 0.2652283 | EQ-5D-3L | Convex | – | 4 |
| UK | Y = 0.0000000299x2 + 0.0002053902x − 0.2343214473 | EQ-5D-5L | Convex | 9 | – |
| UK | y = 0.0000079x2 + 0.0023519x − 0.3067348 | EQ-5D-3L | Convex | – | 6 |
| USA | Y = 0.0000000092x2 + 0.0001832790x + 0.0991735591 | EQ-5D-5L | Convex | 5 | – |
| Zimbabwe | Y = − 0.0000000189x2 + 0.0002390259x + 0.1619338051 | EQ-5D-5L | Concave | 3 | – |
| Zimbabwe | y = − 0.0000025x2 + 0.0034765x + 0.0751729 | EQ-5D-3L | Concave | – | 3 |
The ranking of concavity was based on the second derivative of each country. Lowest second derivative was ranked as the number 1 of the ranking