Identifying Unobserved Hazard Functions in Discrete-Time Survival Mixture Analysis

Abstract

This Monte Carlo simulation adds to the growing body of enumeration index performance research in continuous response variable mixture models by addressing the issue of the performance of these indexes in discrete-time survival mixture analysis (DTSMA) models. Results showed that although all enumeration indexes performed very well in identifying a homogeneous DTSMA model (i.e., k = 1 hazard function in the sample data), the findings also showed that the enumeration indexes performed poorly in identifying the correct number of unobserved hazard functions present in a heterogeneous (i.e., k = 3) DTSMA model. More important, the performance of the enumeration indexes for the heterogeneous DTSMA models did not improve as the sample size, the effect of time-invariant covariates, or adjacent hazard function separation distance increased, which is inconsistent with some previous Monte Carlo simulation results. The limitations of this Monte Carlo simulation study and future empirical investigation possibilities are both discussed.

Keywords:

• Discrete time survival mixture analysis
• enumeration index
• hazard function mixture modeling
• Monte Carlo simulation

Notes

¹ Citations marked with an asterisk (*) in the References represent applied discrete time survival analysis studies consulted to inform the hazard function shape independent variable condition.

² The five data generation independent variable conditions, all involving nonproportional mixture hazard function shapes, which did not result in parameter estimation convergence for at least 95% of the 1,000 data set replications were:

• 1. Covariate effect: OR = 2; hazard mixture function separation: OR = 2; N = 250; equal mixture hazard allocation (k₁–k₃ each 33% of N): 80.2% convergence rate.

• 2. Covariate effect: OR = 3.5; hazard mixture function separation: OR = 2; N = 250; equal mixture hazard allocation (k₁–k₃ each 33% of N): 61.4% convergence rate.

• 3. Covariate effect: OR = 3.5; hazard mixture function separation: OR = 2, N = 500; equal mixture hazard allocation (k₁–k₃ each 33% of N): 91.3% convergence rate.

• 4. Covariate effect: OR = 3.5; hazard mixture function separation: OR = 2; N = 250; 50%, 33%, 17% allocation of N for k₁–k₃, respectively: 86.3% convergence rate.

• 5. Covariate effect: OR = 3.5; hazard mixture function separation: OR = 3.5; N = 250; equal mixture hazard allocation (k₁–k₃ each 33% of N): 86.1% convergence rate.

Correct data generation model identification percentages for those conditions were based on the total number of admissible analyses within their respective conditions.

³ Correct data generation model identification percentages for the nonproportional hazard function shape conditions are available from the first author on request.