Comparison of time to the event and nonlinear regression models in the analysis of germination data

Numerous studies are being carried out to reveal the effects of different treatments on the germination of seeds from various plants. The most commonly used method of analysis is the nonlinear regression which estimates germination parameters. Although the nonlinear regression has been performed based on different models, some serious problems in its structure and results motivated researchers to investigate alternative approaches with higher accuracy and precision. The main purpose of the present research is to introduce the alternative parametric time to event model and comparing its reliability to the nonlinear regression in experiments carried out under different conditions.

  The results of four different experiments were used here including the effect of Potassium cyanide on walnut seed germination, the effect of salinity on wheat seed germination, the effect of water potential on corn seed germination and the effect of temperature on cotton seed germination. The nonlinear regression and time to event methods were applied based on the Gompertz model. The obtained standard errors from the two models were further assessed using the Monte-Carlo method.

Both methods provided well-fitting models according to the MSE and R2   criteria. Although the germination parameters were approximately identical in both models, the standard error of parameters in nonlinear regression was significantly less than those of time to event method except for the experiments in which all tested seeds germinated within the time frame of study so that in the latter case the estimated standard errors in both models were identical. The Monte-Carlo method confirmed the results of the time to event model and reveals the underestimation of the nonlinear regression method in estimating the standard error of parameters.

Generally, the results of this research showed that the time to event model can be trustfully utilized in seed germination studies under different conditions and treatments. This model, not only provides precise estimates of the germination parameters but also provides the precise standard error of parameters that have important roles in making inferences for parameters. The drc package in R software enables researchers to fit the different time to event models.