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Researchers derived analytical solutions for Royston/Parmar restricted cubic spline models, significantly speeding up discrete event simulation (DES) by enabling precise event time estimation. This analytical inversion method in Microsoft Excel is substantially faster than numerical approximations.

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Area of Science:

  • Biostatistics
  • Computational Statistics
  • Survival Analysis

Background:

  • Discrete event simulation (DES) models require event times, often derived from survival functions.
  • Parametric survival models typically provide cumulative survival probabilities, necessitating survival function inversion for event times.
  • Numerical methods for inversion can be computationally expensive, especially in large-scale simulations.

Purpose of the Study:

  • To derive an analytical solution for inverting Royston/Parmar restricted cubic spline survival models.
  • To compare the computational speed of this analytical solution against numerical methods (Goal Seek, Brent's algorithm) in Microsoft Excel.
  • To assess the impact on discrete event simulation speed for event time generation.

Main Methods:

  • Developed analytical solutions for Royston/Parmar restricted cubic spline inverse functions, handling different cases based on survival estimate positioning relative to model knots.
  • Implemented the analytical solution as a Visual Basic for Applications (VBA) user-defined function in Microsoft Excel.
  • Compared execution speeds against Goal Seek (default and high precision) and a hybrid Brent method over 100 replications using colon cancer data.

Main Results:

  • The analytical solution VBA function achieved a mean execution time of 0.612 seconds.
  • This was substantially faster than Goal Seek (10.567s and 12.230s) and the hybrid Brent method (1.140s).
  • The analytical solution demonstrated average execution time reductions of 94.2% (vs. default Goal Seek), 95.0% (vs. high precision Goal Seek), and 46.3% (vs. Brent method).

Conclusions:

  • Analytical inversion of Royston/Parmar restricted cubic spline models provides precise event time estimation and significantly accelerates discrete event simulation in Excel.
  • The derived analytical solution also facilitates the creation of a quantile function.
  • Further research is recommended to evaluate performance in other software (e.g., R) and extend to time-varying covariates.