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Table 2 Mean ± mean standard error of the parameters and criteria for model assessment using in fitting of fibrosarcoma Sa-37 tumor growth data with modified models of Gompertz (Eq. 3), Logistic (Eq. 4) and Kolmogorov-Johnson-Mehl-Avrami (mKJMA) (Eq. 6) from t ≥ 0 days

From: Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

  Modified models on normalized data
Gompertz Logistic mKJMA
X1 ± SD (0.473 ± 0.053) days−1 (0.953 ± 0.031) cm3 (0.052 ± 0.003) days−1
X 2 ± SD (0.233 ± 0.031) days−1 (0.425 ± 0.043) days−1 7.599 ± 1.247
X3 ± SD - - 2.271 ± 0.521
r2 ± SD 0.995 ± 0.004 0.989 ± 0.007 0.994 ± 0.004
r 2 a ± SD 0.995 ± 0.004 0.989 ± 0.007 0.994 ± 0.004
SE ± SD 0.022 ± 0.007 0.032 ± 0.009 0.023 ± 0.007
SSE ± SD 0.009 ± 0.006 0.019 ± 0.0115 0.010 ± 0.006
PRESS ± SD 0.0004 ± 0.0003 0.0008 ± 0.0004 0.0004 ± 0.0002
MPRESS1 ± SD 0.0006 ± 0.0004 0.0012 ± 0.0007 0.0006 ± 0.0004
MPRESS2 ± SD 0.0006 ± 0.0004 0.0013 ± 0.0007 0.0007 ± 0.0004
MPRESS3 ± SD 0.0007 ± 0.0004 0.0014 ± 0.0007 0.0007 ± 0.0004
Ko (days−1) - - 0.056 ± 0.004
Ea (J/mol) - - 187.331 ± 157.609
RT (J/mol) - - 2 568.85
  1. X1 and X 2 variables signify the parameters α and β in the modified Gompertz model whereas these two variables symbolize the parameters K* and r* in the modified Logistic model, respectively. X1 X 2 and X3 represent K, n and λ in mKJMA model, respectively. RT is the thermal energy calculated. T, Ko, Ea, SE, SSE, r 2 a , PRESS, MPRESS and SD are the temperature, pre-exponential factor, activation energy (activation enthalpy) of the transformation, standard error of the estimate, sum of squares of errors, adjusted r 2, predicted residual error sum of squares, multiple predicted residual sum error of squares and standard deviation, respectively. r 2 is the goodness-of-fit. Details of SE, SSE, r 2, r 2 a , PRESS and MPRESS are given in [2, 14]