PubMed · 15968772
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P M Preux, P Odermatt, A Perna, B Marin, A Vergnenègre. 2005. [Logistic regression].. https://doi.org/10.1016/s0761-8425(05)85450-6
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Mixed-type outcome data occur when the outcome variable's distribution is a mixture of both continuous and discrete ordinal variables. Such mixed-type outcomes are common in biomedical, psychological, and the health sciences, particularly for variables having either a detection or quantitation limit. When interest lies in identifying a combination of genomic features associated with a mixed-type outcome, any method used would require a variable selection strategy for high-dimensional data. Unfortunately, few variable selection methods exist for modeling a mixed-type outcome when the covariate space is high dimensional. This study develops a high-dimensional penalized cumulative probability model (CPM), to allow for the identification of genomic features associated with mixed-type outcome of interest. We demonstrated how such model may be estimated using the iterative penalization procedure-the generalized monotone incremental forward stagewise (GMIFS) algorithm. The Model-X knockoffs procedure was combined with the estimation algorithm to control the false discovery rates (FDR) when performing variable selection. Through extensive simulation studies, our penalized CPM was shown to outperform alternative methods in terms of controlled variable selection performance by achieving high statistical power with the FDR being controlled at the target level. We demonstrate the utility of our method by applying it to predict estimated glomeruli filtration rate (eGFR) in kidney transplant recipients at 24 months post-transplant using baseline gene expression data as predictors. Our CPM model identified five genes associated with this mixed-type outcome which have important links to renal disease, which may provide prognostic guidance for kidney transplantation recipients.
In multilevel modeling, researchers often encounter data with a relatively small number of units at the higher levels. As a result, of this and/or non-normality of the residuals, model parameter estimates, particularly the variance components and standard errors of parameter estimates at the group level, may be biased, thus the corresponding statistical inferences may not be trustworthy. This problem can be addressed by using bootstrap methods to estimate the standard errors of the parameter estimates for significance testing. This study illustrates how to use statistical analysis system (SAS) to conduct nonparametric residual bootstrap multilevel modeling. Specific SAS programs for such modeling are provided.
A simple and finite-termed analytical function for the finite size pencil beam kernel was constructed. The dose cross-profile of a semi-infinite field with field edge at x = 0 can be well fitted by the Boltzmann function. The pencil beam cross-profile of width 2x(0) can be obtained as the difference between two semi-infinite fields shifted by 2x(0). If the profile is centred about x = 0, it can derive from P(x + x(0)) - P(x - x(0)). The penumbra influence can be taken by the penumbra tuning factor f. The parameters A(1), A(2), A(3), A(4), f can be obtained by fitting depth-dose curves and cross-profiles for a set of square fields. The two-dimensional dose distribution F(x, y, x(0), y(0), A(1), A(2), A(3), A(4), f(1), f(2)) of a pencil beam of width (2x(0), 2y(0)) is defined by multiplication of two independent one-dimensional profiles.