3 Reju Beads > Dorans Shield
D Shield, it regens 0 to 30 based on % missing health over 10 seconds and not FOR. Needing so you practically need to be at half health to just regen 15 OVER 10 seconds and to also be hit on top of it. And because of the regen is based off of % missing health, it actually gets worse. Whats the opposite of scaling? Because the more health and defenses you get, the more % HP you have left after taking a hit. Thus, the less HP you will regen from D Shield. Not only that but the health regen adapts based on your current missing health. Because of this, after getting damaged once, the health regen will slowly decrease over the duration. Whereas starting with 3 Reju Beads, you're practically gaining the same regen value without the previous' condition, scales, and better resell value.
So lets say when you hit level 4 with 10hp regen, the 3 Reju Beads will now give a constant +15 making the total be 25hp per 5 seconds. Recovering 100 health in 20 seconds acting like a permanent mini health potion
However the most damning of all and deserves a repeat is that D Shield only recovers 0-30 "over 10 seconds". Its NOT a for statement like "**for **10 seconds", its an **over **statement. So if you want to look at the actual value for comparison, you would need to either cut Shield's regen value by half or double the Bead's Regen.
The outliers for Dorans Shield being better than the 3 Beads start is if the champion has low health regen to begin with. Which majority are ADCs and Mages. If you want an easy way to figure out which start would be better, if your champ has less than 10 base health regen at about level 4 then get D Shield. Otherwise 3 Beads is objectively better.