The risk factors with p values < 0.1 in the univariate analysis were placed in a multivariate analysis using the multiple logistic regression package in the SAS System for Windows V8.
Missing values for duration of caregiving (missing value in 7 cases) and income (missing value in 342 cases) were supplemented in the multivariate analysis using the multiple imputation by chained equations (MICE) command in Stata [ 56, 57].
Second, in our multivariate models, we used the multiple imputation method (MI) to handle missing values.
In this paper for all of the descriptive statistics (tables 1 2) only those with complete data are in included, of inferential analyses (tables 3 5) the results are those obtained using the multivariate multiple imputation methods.
Indeed, the sensitivity analysis using multiple multivariate imputation techniques did not alter the effect sizes reported; thus, bias resulting from the missing data was unlikely.
When crosschecking the significant variables from both models, it was found that both risk factors identified by the forward-entry BRT model were significantly associated with disease occurrence when analyzed using the multivariate logistic multiple regression, but yielded a lower AUC than the variable selected directly by the multivariate logistic regression.
We used multiple multivariate imputation, using all variables included in any analyses, the censoring indicator and the log of survival time for Cox models, to impute missing values for those variables with some missing data [17].
We implemented multiple imputation using the sequential regression multivariate imputation approach (SRMI), also referred to as Fully Conditional Specification (FCS) and Multiple Imputation by Chained Equations (MICE): this method allows for efficient imputation by fitting a model to each variable, conditional on all others, and imputing one variable at a time [ 50, 51].
Thirdly, to further explore the impact of selection bias resulting from missing data, we used multiple multivariate imputation and repeated the analyses on the basis of an imputed sample of all participants who were alive during the whole study period (n=9775) (see web appendix) The figure shows the selection of the sample.
In this paper, by extending the concept of "area metric" and the "u-pooling method" developed for validating a single response, we propose new model validation metrics for validating correlated multiple responses using the multivariate probability integral transformation (PIT).
