Survival probabilities with time-dependent treatment indicator: quantities and non-parametric estimators

Area of Science:

• Biostatistics
• Survival Analysis
• Clinical Research

Background:

• Landmark and Simon and Makuch estimators are used for time-dependent treatment group survival comparisons.
• Previous literature lacked clear definitions for Simon and Makuch theoretical survival functions, leading to criticism.

Purpose of the Study:

• To review and clarify the landmark approach in survival analysis.
• To define the counterfactual survival probabilities estimated by the Simon and Makuch approach.
• To introduce a novel time rescaling method for improved counterfactual probability estimation.

Main Methods:

• Review of the landmark survival analysis approach.
• Theoretical analysis of the Simon and Makuch estimator and its Markov assumption.
• Development of a novel time rescaling method for semi-Markov processes.

Main Results:

• The landmark approach estimates conditional survival based on landmark time treatment status.
• The Simon and Makuch approach estimates counterfactual survival assuming fixed treatment, valid only under the Markov assumption.
• The novel time rescaling method provides valid counterfactual probability estimates in semi-Markov processes.

Conclusions:

• The landmark approach focuses on conditional survival at a specific time point.
• The Simon and Makuch estimator has limitations due to its reliance on the Markov assumption.
• The proposed time rescaling method offers a more robust approach for estimating counterfactual survival probabilities in complex treatment scenarios.