Fitting semi-Markov models to interval-censored data with unknown initiation times.

Area of Science:

• Biostatistics
• Survival Analysis
• Stochastic Processes

Background:

• Semi-Markov models describe systems where transitions depend on time spent in the current state.
• Challenges arise with interval-censored data and unknown initiation times, hindering accurate analysis.
• Existing methods may not adequately address these data complexities.

Purpose of the Study:

• To develop methods for fitting semi-Markov models with interval-censored transition times and missing initiation times.
• To provide estimators for waiting-time distributions in specific semi-Markov model structures.
• To enhance the applicability of semi-Markov models in real-world scenarios with incomplete data.

Main Methods:

• Utilized semi-Markov models to account for time-dependent transition hazards.
• Developed techniques to handle interval-censored transition time data.
• Proposed nonparametric maximum likelihood estimators for discrete-time waiting-time distributions.

Main Results:

• Demonstrated the feasibility of fitting semi-Markov models despite missing initiation times and interval-censored data.
• Provided specific estimators for waiting-time distributions in sequential stage models.
• The proposed methods allow for robust analysis of complex event data.

Conclusions:

• Semi-Markov models can be effectively applied to interval-censored data with missing initiation times.
• The developed estimators offer a valuable tool for analyzing waiting times in specific model structures.
• This research expands the utility of semi-Markov models in biostatistical and survival analysis.