I’m currently analyzing hospital performance data spanning approximately 5 to 8 years, where hospitals:
- Contribute funds based on their insurance size.
- Are evaluated annually on eight performance criteria: the outcome is an annual score from 0 to 8.
- Receive a portion of the pooled funds if they meet all the criteria (i.e. if they have 8/8) and no money otherwise.
Our goal is to model how these performance scores evolve over time and investigate whether:
- Hospitals that perform well initially continue to receive more funds and improve further.
- Hospitals that perform poorly initially receive less money and deteriorate over time.
We plan to use mixed models to account for:
- Fixed effects: Representing the evolution of scores over time.
- Random intercepts: Capturing hospital-specific baseline performance levels.
- Random slopes: Representing hospital-specific trends over time.
And evaluate the correlation between the random slopes and the random intercepts to see if a low intercept (i.e. hospital doing bad initially) lead to a high negative random slope (i.e. hospital getting worse over time). One concern is that hospitals starting at a maximum score may exhibit no change over time, leading to a random slope close to zero. This could affect the interpretation of slope variability across hospitals.
I would love to hear your thoughts on this approach:
- Have you encountered similar issues with performance plateaus in mixed models?
- Any suggestions on modeling hospitals with perfect initial scores?
- Any literature about this kind of models ?