Dependent Competing Risks Driven by Markov-Modulated Gamma Degradation

Abstract

Markov-modulated gamma processes and, more generally, Markov additive subordinators are established tools for degradation and reliability analysis. This paper uses such a process in a different role: as a shared latent driver of multiple cause-specific hazards. Conditional on a finite-state continuous-time Markov environment and accumulated gamma degradation, the competing causes are specified through affine degradation loadings. We derive a killed transform system for overall survival and cause-specific subdensities, establish structural invariances of the unrestricted parameterization, and distinguish what can be learned from event-only competing-risks observations from what requires repeated degradation measurements. Event-only data may recover cause-specific degradation effects when the degradation dynamics are calibrated, but generally provide insufficient information for stable joint estimation of gamma dynamics and hazard loadings. Repeated degradation sequences yield a transition-emission hidden Markov representation with matrix-valued Laplace kernels and provide sufficient conditions for generic local recoverability under explicit rank and separation assumptions. Sparse matrix-exponential and deterministic FFT implementations are verified against analytic limiting cases and an independent particle filter. In 200-replication experiments at each of three sample sizes, calibrated-loading estimates had relative bias below 1.5%, 100% numerical convergence, and decreasing root mean squared error. The framework connects competing-risks inference with degradation calibration while making its identification restrictions explicit.