Data on the occurrence and timing of discrete events such as spore germination, disease onset, or propagule death are recorded commonly in epidemiological studies. When analyzing such “time-to-event” data, survival analysis is superior to conventional statistical techniques because it can accommodate censored observations, i.e., cases in which the event has not occurred by the end of the study. Central to survival analysis are two mathematical functions, the survivor function, which describes the probability that an individual will “survive” (i.e., that the event will not occur) until a given point in time, and the hazard function, which gives the instantaneous risk that the event will occur at that time, given that it has not occurred previously. These functions can be compared among two or more groups using chi-square-based test statistics. The effects of discrete or continuous covariates on survival times can be quantified with two types of models, the accelerated failure time model and the proportional hazards model. When applied to longitudinal data on the timing of defoliation of individual blueberry leaves in the field, analysis with the accelerated failure time model revealed a significantly (P < 0.0001) increased defoliation risk due to Septoria leaf spot, caused by Septoria albopunctata. Defoliation occurred earlier for lower leaves than for upper leaves, but this effect was confounded in part with increased disease severity on lower leaves.
Flexible extension of the accelerated failure time model to account for nonlinear and time-dependent effects of covariates on the hazard
