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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.17646 |
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| _version_ | 1866917506210332672 |
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| author | Sepehrifar, Mohammad |
| author_facet | Sepehrifar, Mohammad |
| contents | We develop a Starshaped Mean Residual Life (SMEL) framework for survival data with non-monotonic hazard patterns, where early-stage attrition is followed by mid-career stabilization. Unlike Cox proportional hazards models or standard mean residual life models requiring monotonicity, SMEL accommodates complex temporal dynamics by requiring only that $m(t)/t$ be nondecreasing, formalizing the transition from vulnerability to equilibrium. We extend SMEL to regression settings via proportional mean residual life (PMRL) models, $m(t\mid Z)=m_0(t)\exp(Z^\topγ)$, with adaptive Bayesian estimation using three-parameter Weibull--resilience distributions and the No-U-Turn Sampler. Monte Carlo simulations across 48,000 datasets show SMEL-PMRL maintains bias $\leq 0.02$ under 40\% right-censoring, reduces integrated Brier score by 19\% over Cox models ($2.34$ vs.\ $2.88\times10^{-2}$), and achieves 5.4\% AIC improvement. Joint longitudinal-survival extensions via shared frailty enable simultaneous modeling of correlated time-to-event and continuous outcomes. Application to 169 rural STEM teachers (2018--2023, NSF Noyce) confirms starshaped equilibrium ($Λ=12.47$, $p=0.002$), with 38\% early-career tenure decline (years 1--3). The joint model ($\hatθ=0.41$, 95\% CI: $[0.35,\,0.47]$) shows persistence beyond year~3 yields 31-point cumulative achievement gains (0.56~SD) over four years. SMEL-PMRL offers a flexible, theoretically grounded alternative to proportional hazards for workforce dynamics and high-attrition settings where equilibrium processes govern long-term stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Starshaped Mean Residual Life Models for Non-Monotonic Survival Data: A Bayesian PMRL Regression Framework with Applications to Teacher Retention Sepehrifar, Mohammad Methodology We develop a Starshaped Mean Residual Life (SMEL) framework for survival data with non-monotonic hazard patterns, where early-stage attrition is followed by mid-career stabilization. Unlike Cox proportional hazards models or standard mean residual life models requiring monotonicity, SMEL accommodates complex temporal dynamics by requiring only that $m(t)/t$ be nondecreasing, formalizing the transition from vulnerability to equilibrium. We extend SMEL to regression settings via proportional mean residual life (PMRL) models, $m(t\mid Z)=m_0(t)\exp(Z^\topγ)$, with adaptive Bayesian estimation using three-parameter Weibull--resilience distributions and the No-U-Turn Sampler. Monte Carlo simulations across 48,000 datasets show SMEL-PMRL maintains bias $\leq 0.02$ under 40\% right-censoring, reduces integrated Brier score by 19\% over Cox models ($2.34$ vs.\ $2.88\times10^{-2}$), and achieves 5.4\% AIC improvement. Joint longitudinal-survival extensions via shared frailty enable simultaneous modeling of correlated time-to-event and continuous outcomes. Application to 169 rural STEM teachers (2018--2023, NSF Noyce) confirms starshaped equilibrium ($Λ=12.47$, $p=0.002$), with 38\% early-career tenure decline (years 1--3). The joint model ($\hatθ=0.41$, 95\% CI: $[0.35,\,0.47]$) shows persistence beyond year~3 yields 31-point cumulative achievement gains (0.56~SD) over four years. SMEL-PMRL offers a flexible, theoretically grounded alternative to proportional hazards for workforce dynamics and high-attrition settings where equilibrium processes govern long-term stability. |
| title | Starshaped Mean Residual Life Models for Non-Monotonic Survival Data: A Bayesian PMRL Regression Framework with Applications to Teacher Retention |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.17646 |