A New Method to Determine the Presence of Continuous Variation in Parameters of Biological Growth Curve Models

Quantitative assessment of the growth of biological organisms has produced many mathematical equations. Many efforts have been given on statistical identification of the correct growth model from experimental data. Every growth equation is unique in terms of mathematical structures; however, one model may serve as a close approximation of the other by appropriate choice of the parameter(s). It is still a challenging problem to select the best estimating model from a set of model equations whose shapes are similar in nature. Our aim in this manuscript is to develop methodology that will reduce the efforts in model selection. This is achieved by utilizing an existing model selection criterion in an innovative way that reduces the number of model fitting exercises substantially. In this manuscript, we have shown that one model can be obtained from the other by choosing a suitable continuous transformation of the parameters. This idea builds an interconnection between many equations which are scattered in the literature. We also get several new growth equations; out of them large number of equations can be obtained from a few key models. Given a set of training data points and the key models, we utilize the idea of interval specific rate parameter (ISRP) proposed by Bhowmick et al (2014) to obtain a suitable mathematical model for the data. The ISRP profile of the parameters of simpler models indicates the nature of variation in parameters with time, thus, enable the experimenter to extrapolate the inference to more complex models. Our proposed methodology significantly reduces the efforts involved in model fitting exercises. The proposed idea is verified by using simulated and real data sets. In addition, theoretical justifications have been provided by investigating the statistical properties of the estimators.