There are two major categories of observation data in studying time-dependent processes: one is the time-series data, and the other is the perhaps lesser-recognized but similarly prevalent time-to-event data (also known as survival or failure time). Examples in entomology include molting times and death times of insects, waiting times of predators before the next attack or the hiding times of preys. A particular challenge in analyzing time-to-event data is the observation censoring, or the incomplete observation of survival times, dealing which is a unique advantage of survival analysis statistics. Even with a perfectly designed experiment being conducted perfectly, such 'naturally' censoring may still be unavoidable due to the natural processes, including the premature death in the observation of insect development, the variability in instarship, or simply the continuous nature of time process and the discrete nature of sampling intervals. Here we propose to apply the classic Cox proportional hazards model for modeling both insect development and survival rates (probabilities) with a unified survival analysis approach. We demonstrated the advantages of the proposed approach with the development and survival datasets of 1800 Russian wheat aphids from their births to deaths, observed under 25 laboratory treatments of temperatures and plant growth stages.
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