The cure model: an improved way to describe seed germination?

Traditional methods of data analysis (anova and linear/non-linear regression) may often not be appropriate for datasets resulting from seed germination/emergence assays. One major problem is that they take the form of ‘time to event’ data with censoring, i.e. the event is only known to have occurred within an interval of time. Parametric survival models have, therefore, been proposed as appropriate alternatives. These, in turn, have the disadvantage that they assume that all the seeds will germinate at some future time, conflicting with the fact that a proportion of ungerminated viable seeds is frequently observed at the end of an experiment. The ‘cure’ model, which we present here, has been used in cancer research as an extension to parametric survival models, to account for a final fraction of individuals that is cured from the disease under study and will not die because of that cause. We show that the ‘cure’ model holds the potential to be used successfully in germination assays, as an extension to non-linear regression and conventional accelerated failure time (AFT) models, with several logical improvements in terms of distributional assumptions and censoring. By way of selected examples, it is shown that the ‘cure’ model can separate the effect of factors/covariates on germination capacity (final germination percentage) from that on germination velocity (germination rate) and uniformity (synchrony of germination), which may represent an advantage from a biological point of view.