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This study introduces a statistical framework to evaluate interventions on systems with latent processes. It models intervention effects by estimating parameter changes and analyzing time intervals before and after intervention.

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Area of Science:

  • Statistics
  • Stochastic Processes
  • Survival Analysis

Background:

  • Latent internal processes drive system events (e.g., component failure, death).
  • Interventions aim to alter these processes before event occurrence.
  • Evaluating intervention effectiveness requires robust statistical methods.

Purpose of the Study:

  • To develop a statistical framework for evaluating interventions on latent processes.
  • To determine the joint distribution of time intervals before and after intervention (S and R).
  • To estimate model parameters and statistically compare interventions.

Main Methods:

  • Modeling intervention effects via parameter changes in the governing law of the internal process.
  • Deriving theoretical expressions for the joint distribution of (S,R).
  • Utilizing maximum likelihood estimators (MLEs) on simulated data, assuming Brownian motion with differing parameters before and after intervention.
  • Incorporating covariates and handling censored observations.

Main Results:

  • Established theoretical expressions for the joint distribution of time intervals (S,R).
  • Demonstrated the ability to estimate model parameters from observed (S,R) data.
  • Successfully applied the method to simulated data and illustrated its use on lung cancer data.

Conclusions:

  • The proposed statistical method effectively evaluates interventions on systems with latent processes.
  • The framework allows for parameter estimation and statistical comparison of intervention effects.
  • The approach is versatile, accommodating covariates and censored data, with practical applications in fields like medicine.