Longitudinal Analysis of Hospital Evaluations: Do the Bad Get Worst?

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:

  1. Hospitals that perform well initially continue to receive more funds and improve further.
  2. 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 ?