A Finite-Horizon Mixture Cure Model with Application to Online Flea Market Data

TL;DR

This paper introduces a finite-horizon mixture cure model that improves interpretability and decision-making relevance over traditional infinite-horizon models, demonstrated through simulation and real online flea market data analysis.

Contribution

It develops a finite-horizon mixture cure model that reduces reliance on untestable assumptions, enhancing interpretability for finite-time decision contexts.

Findings

Simulation studies show the estimator has low bias and variance.

Finite-horizon models provide more accurate decision insights than infinite-horizon models.

Application to Mercari data reveals different significant variables and seasonal user behavior patterns.

Abstract

This study proposes a mixture cure model that latently divides a population based on event occurrence within a finite time horizon. Conventional models rely on event occurrence over an infinite horizon, introducing untestable assumptions that often lead to issues with identifiability and interpretability. By shifting the estimand to a specific period of interest, the proposed approach reduces reliance on these infinite-tail assumptions and aligns interpretations more closely with finite-horizon decision-making objectives. Through simulation studies, we first evaluate the statistical properties of the proposed estimator, including estimation bias and variance. We further show that relying on conventional infinite-horizon models for finite-horizon decision-making can lead to erroneous judgments. Finally, we apply the model to transaction data from Mercari, a Japanese online flea market platform. The empirical results reveal that the proposed model identifies different significant variables compared to the conventional model, offering interpretations that better reflect seasonal variation in user behavior.