My grandmother attributes her good health to active living.
There are four problems.
生き方のせいた is an obvious typo. It should be 生き方のせいだ. せいた is spelled as 急いた, meaning “too rush”.
生き方のせいだ sounds very rude. せいだ suggests that “I” (the speaker) wants my grandmother to die as soon as possible, but she leads a healthy life due to her active lifestyle. There is no nuance of “thanks to” in せいだ. The speaker wants to blame.
積極的な生き方 is understandable, but it is closer to “proactive life” rather than “active life”. I don’t say it’s wrong but I don’t say that in this context.
The particle は for the subject is grammatically incorrect. The original Japanese sentence means “My grandmother thinks that someone (not mentioned) is health due to the person’s proactive life. However, I don’t think so.” The particle は functions only as a subject, not an object in this sentence structure. And は is used when comparing the different situations/facts implicitly, and highlighting the gap.
My alternative translation is;
The word-for-word translation in English is “An active life environment is the secret of my grandmother’s health”. 秘訣 is a “secret for success”, so the speaker is happy with my grandmother’s healthy active lifestyle. And 健康の秘訣 is a frequent set phrase.