Hazard function estimators: a simulation study.

Kernel-based methods for the smooth, non-parametric estimation of the hazard function have received considerable attention in the statistical literature. Although the mathematical properties of the kernel-based hazard estimators have been carefully studied, their statistical properties have not. We reviewed various kernel-based methods for hazard function estimation from right-censored data and compared the statistical properties of these estimators through computer simulations. Our simulations covered seven distributions, three levels of random censoring, four types of bandwidth functions, two sample sizes and three types of boundary correction. We conducted a total of 504 simulation experiments with 500 independent samples each. Our results confirmed the advantages of two recent innovations in kernel estimation - boundary correction and locally optimal bandwidths. The median relative improvement (decrease) in mean square error over fixed-bandwidth estimators without boundary correction was 3 per cent for fixed-bandwidth estimators with left boundary correction, 52 per cent locally optimal bandwidths without boundary correction, and 66 per cent for locally optimal bandwidths with left boundary correction. The locally optimal bandwidth estimators with left boundary correction also outperformed three previously published and publicly available algorithms, with median relative improvements in mean square error of 31 per cent, 77 per cent and 80 per cent.

Genotype selection to rapidly breed congenic strains.

Congenic strains can now be constructed guided by the transmission of DNA markers. This allows not only selection for transmission of a desired, donor-derived differential region but also selection against the transmission of unwanted donor origin genomic material. The additional selection capacity should allow congenic strains to be produced in fewer generations than is possible with random backcrosses. Here, we consider modifications of a standard backcross breeding scheme to produce congenic mice by the inclusion of genotype-based selective breeding strategies. Simulation is used to evaluate the consequences of each strategy on the number of chromosomes that contain unwanted, donor-derived genetic material and the average length of this unwanted donor DNA for each backcross generation. Our prototypic strategy was to choose a single mouse to sire each generation using criteria designed to select against the transmission of chromosomes, other than the one containing the replacement genomic region, that contain any donor origin sequence at all. This chromosome elimination strategy resulted in an average of 16.4 chromosomes free of donor DNA in mice of the third backcross (N3) generation. A strategy based solely on positive selection for the replacement region required six backcross generations to achieve the same results.