Soru

A clinical research institute follows a dynamic cohort of patients with heart failure with preserved ejection fraction (HFpEF) to determine the incidence rate of new-onset atrial fibrillation (AF). The total observation period for the study is exactly $4$ years.

Enrollment occurs in three phases:
- $400$ patients are enrolled at the start of the study (Year $0$).
- $200$ patients are enrolled exactly $1$ year into the study.
- $150$ patients are enrolled exactly $2$ years into the study.

During the $4$-year observation period, the following events are recorded:
- $60$ patients from the Year $0$ cohort develop AF exactly $2$ years into the study.
- $30$ patients from the Year $1$ cohort die from non-cardiac causes exactly $2$ years into the study.
- $40$ patients from the Year $2$ cohort are lost to follow-up exactly $2.5$ years into the study.
- $50$ patients from the Year $0$ cohort develop AF exactly $3$ years into the study.

Assume no other patients develop AF, die, or are lost to follow-up, and all remaining patients are followed continuously until the end of the $4$-year study period.

Calculate the incidence rate of atrial fibrillation for this dynamic cohort in cases per $1,000$ person-years. Round your final answer to the nearest whole integer.