Nonidentifiability in the presence of factorization for truncated data

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Left truncation in time-to-event data can lead to biased estimates due to oversampling of large values.
• Standard risk-set estimators may require adjustments to handle left truncation, especially when variables are quasi-independent.

Purpose of the Study:

• To derive a weaker factorization condition for risk-set adjustment in the presence of left truncation.
• To investigate the conditions under which the distributions of time-to-event and truncation can be estimated.

Main Methods:

• Derivation of a weaker factorization condition for the conditional distribution of time-to-event given truncation.
• Application of risk-set adjustments to estimators under the derived condition.
• Simulation study to illustrate concepts with left-truncated and right-censored data.

Main Results:

• A weaker factorization condition permits risk-set adjustment for the time-to-event distribution, but not the truncation distribution.
• Quasi-independence allows estimation of both distributions, but requires the analogous factorization condition to hold.
• Testing for factorization does not distinguish between different conditions, necessitating an unverifiable assumption for full distribution estimation.

Conclusions:

• Estimating time-to-event distributions from left-truncated data may require unverifiable assumptions, contrary to common belief.
• The distinction between left truncation and censoring regarding unverifiable assumptions is highlighted.
• Careful consideration of factorization conditions is crucial for accurate estimation in survival analysis.