Comparing estimation approaches for the illness-death model under left truncation and right censoring

Area of Science:

• Biostatistics
• Survival Analysis
• Medical Statistics

Background:

• Left-truncated data occur when observations are only available above a certain time threshold.
• This is common in cross-sectional studies, like observing patients only if they survive to the sampling day.
• Statistical inference for left-truncated data requires careful consideration of different estimation approaches.

Purpose of the Study:

• To compare three distinct statistical inference approaches for left-truncated data within the illness-death model.
• To evaluate the efficiency and robustness of unconditional, truncation-value-conditioned, and history-conditioned methods.
• To apply these methods to real-world intensive care unit data, specifically bloodstream infections.

Main Methods:

• Parametric regression framework applied to the illness-death model.
• Comparison of three estimation strategies: unconditional (i), conditioning on truncation value (ii), and conditioning on history (iii).
• Evaluation through theoretical examples, simulation studies, and application to intensive care unit data.

Main Results:

• Conditioning on the truncation value (ii) is more efficient than the standard history-conditioned approach (iii), despite higher computational demands.
• The unconditional approach (i) demonstrates the highest efficiency but is less robust due to its reliance on the truncation variable's distribution.
• Differences between approaches are highlighted, particularly in the multi-state framework.

Conclusions:

• The choice of statistical approach for left-truncated data impacts efficiency and robustness.
• Conditioning on truncation value offers a practical balance between efficiency and computational feasibility.
• Unconditional approaches provide maximum efficiency when distributional assumptions are met.