When someone says they need to have something done by tomorrow, they don't mean midnight today, or they would have said "today". If Dr. P meant that we would have the primary endpoints completed "before" Q1, he would have said "by the end of this year". When someone, especially in business, says they plan to complete something by "Q1", they're saying by March 31st. This is very common language.
Think of it this way, "by today" means "before tomorrow". By "Q1" means "before Q2" (Apr 1- June 30).
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