the antecedent of the clause "that adds no value to the patient care"

[GoodTaste]

Afflicted by studies with small sample sizes, tiny effects, invalid exploratory analyses, and flagrant conflicts of interest, together with an obsession for pursuing fashionable trends of dubious importance.’ 1 In this context, a tiny effect is an effect without a clinical impact for management that adds no value to the patient care.

Source (British Medical Journal)

The antecedent of the clause "that adds no value to the patient care" appears, logically, to be "an effect" rather than "management." But do you native speakers at once get what is the antecedent for the clause without hesitation?

 

[5jj]

If we are reading sentences like that, we read more slowly than if we were reading a light novel, and most of us will have no real problem.

 

[jutfrank]

Yes.

The final sentence is structured as a typical definition: A tiny effect is an effect ... that ...

From the sentence structure alone, the mind naturally interprets the part after that to be definitive of effect.