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There is no formal goodness of fit test for cure models, since they rely on a good fit at the end of follow-up, and most of the data is at the beginning of follow-up.
Two stochastic models of carcinogenesis were tested with several sets of experimental and epidemiological data using a formal goodness of fit test specially designed to accommodate censored observations: these were the two-stage model allowing for clonal expansion of initiated cells and its simpler version with gamma distributed promotion time.
The predicted and actual number of survivors and nonsurvivors were compared statistically using formal goodness of fit testing to determine whether the discrepancy between predicted and actual values was statistically insignificant (P > 0.05).
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In this approach, the goodness-of-fit of the copula function may be assessed either graphically through the K K plot or statistically with the formal goodness-of-fit test statistics (Genest et al. 2009).
Since there can be more than one joint distribution fitted to the multivariate random variables, the best distribution is then selected from either visual goodness-of-fit plot (e.g. Q–Q plot) or formal goodness-of-fit test statistics (Genest et al. 2009).
Formal goodness-of-fit tests were not used because they can be unreliable with sparse data.
The remaining studies (n = 19) explicitly reported using a formal goodness-of-fit measure.
The predicted and actual number of survivors and non-survivors were compared statistically with the use of formal goodness-of-fit testing to determine whether or not the discrepancy was statistically insignificant (P > 0.05).
Formal goodness-of-fit analysis comparing the observed deviance to the relevant χ-distribution requires some care for these data based on a complete national population, as conventional significance levels are not necessarily helpful, as these analyses were developed for relatively small sample sizes.
The next phase of data analysis focused on more formal comparisons of goodness of fit.
Tower 2 planned for the World Trade Center site has an honest-to-goodness formal address: 200 Greenwich Street.
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