Typically "T"-optimality is used to obtain optimal designs to discriminate between homoscedastic models with normally distributed observations. Some extensions of this criterion have been made for the heteroscedastic case and binary response models in the literature. In this paper, a new criterion based on the Kullback-Leibler distance is proposed to discriminate between rival models with non-normally distributed observations. The criterion is coherent with the approaches mentioned above. An equivalence theorem is provided for this criterion and an algorithm to compute optimal designs is developed. The criterion is applied to discriminate between the popular Michaelis-Menten model and a typical extension of it under the log-normal and the gamma distributions. Copyright 2007 Royal Statistical Society.
Background
Ovarian cancer is a silent and largely asymptomatic cancer, leading to late diagnosis and worse prognosis. The late-stage detection and low survival rates, makes the study of the space-time evolution of ovarian cancer particularly relevant. In addition, research of this cancer in small areas (like provinces or counties) is still scarce.
Methods
The study presented here covers all ovarian cancer deaths for women over 50 years of age in the provinces of Spain during the period 1989-2015. Spatio-temporal models have been fitted to smooth ovarian cancer mortality rates in age groups [50,60), [60,70), [70,80), and [80,+), borrowing information from spatial and temporal neighbours. Model fitting and inference has been carried out using the Integrated Nested Laplace Approximation (INLA) technique.
Results
Large differences in ovarian cancer mortality among the age groups have been found, with higher mortality rates in the older age groups. Striking differences are observed between northern and southern Spain. The global temporal trends (by age group) reveal that the evolution of ovarian cancer over the whole of Spain has remained nearly constant since the early 2000s.
Conclusion
Differences in ovarian cancer mortality exist among the Spanish provinces, years, and age groups. As the exact causes of ovarian cancer remain unknown, spatio-temporal analyses by age groups are essential to discover inequalities in ovarian cancer mortality. Women over 60 years of age should be the focus of follow-up studies as the mortality rates remain constant since 2002. High-mortality provinces should also be monitored to look for specific risk factors.
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