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Cross-validation, Direct plug-in method, Generalized information criterion, Kullback–Leibler information, Maximum penalized likelihood method, Penalized spline, Ridge regression, Tuning parameter estimation,

Objectives This study analyzed the risk of infection with Plasmodium vivax in local residents through a stochastic simulation in which an infected tourist, local resident, or immigrants from an endemic area would visit Himi-shi, Toyama prefecture, which is a formerly endemic area in Japan. Methods In Toyama, the habitats of Anopheles sinensis, which can transmit P. vivax, have been examined previously. We constructed a stochastic model of P. vivax transmission that can handle small numbers of infected persons and infected mosquitoes. The seasonal fluctuation in the numbers of captured An. sinensis was taken into account in the model. Results Ten thousand trial simulations were carried out stochastically with a range of human blood indexes (HBI) of 1-10% for a range of months (June-September). The simulation results for a realistic assumption of a 1% HBI showed that the risk of infection for local residents was low (below 1%) except for the immigrants scenario. Conclusions The risk of infection among local residents (second cycle) was estimated to be very low for all situations. Therefore, there is little possibility for P. vivax infection to become established in this area of Japan.

Abstract:In model selection, the most effective method requires much time.The analysis of the bivariate B-spline model with a penalized term has many difficulties.It has many factors and parameters such the number of the knots, the locations of those knots, number of B-spline functions and the value of the smoothing parameter of the penalized term.For the determination of the model we have to compare a large amount of the combinations of those parameters. Various information criteria are considered and the cross validation (CV) criterion is excellent but it requires a large amount of computational costs. The effect of the influence function and the techniques of the generalized cross validation (CV) are considered. The influence function is related to the first term of a Taylor expansion. Some alternative methods are tested and a new method is proposed. For the verification of this method theoretical proof and the computational results are shown.