The key word here is Spielraum because it leads to a clear interpretation of Eingrenzung as the thing, the lack of which, is causing this too much Spielraum or leeway - noch zu viel Spielraum.

"andere Krankheiten" and"die nicht mit dem Prüfpräparat oder Ihrer Erkrankung in Verbindung stehen" are things (Angaben - statements/details/specifications) that would potentially have been able to reduce the Spielraum or scope or leeway to an acceptable or manageable level. But unfortunately in this case these do not provide such help because they are not relevant enough as elements of demarcation or delimitation.

Let me know if you need more explanation.

..fails to/doesn't provide the appropriate specificity.

As pompous as the German. Maybe that's what's required here.

On another note:
Congratulations to all English football fans. They deserved to go through against Denmark. But I wish it hadn't happened because of a Schwalbe.

German term (edited): dies ist keine entsprechende Eingrenzung

If this is about a medical study, it may have to do with identifying/describing the symptoms to be studied as opposed to other symptoms that have nothing to do with the study itself and are to be disregarded.

In healthcare, a differential diagnosis ... involves distinguishing a particular disease or condition from others that present with similar clinical features. Differential diagnostic procedures are used by clinicians to diagnose the specific disease in a patient...
https://en.wikipedia.org/wiki/Differential_diagnosis

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Note added at 15 Stunden (2021-07-08 08:02:16 GMT)
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or
... this does not adequately distinguish this disease from other diseases...
... is no adequate differential diagnosis