Additional file 1 of Effects of influential points and sample size on the selection and replicability of multivariable fractional polynomial models
Creators: name: Sauerbrei, Willi
name: Kipruto, Edwin
name: Balmford, James
Publisher: name: figshare
Year: 2024
Subjects: subject: Medicine
subject: Ecology
subject: FOS: Biological sciences
subject: Mathematical Sciences not elsewhere classified
subject: Cancer

description: Additional file 1: Table A1. MethProf-simu profile giving an overview of the aims, data, estimand or target of analysis, methods and performance measures (ADEMP structure) in part A. All analyses are listed in part B, categorized into analysis (A), presentation (P) and description of data (D). Table A2. ART data (N = 5,000, R2=0.49). Contribution of each predictor to the model fit, expressed in terms of the percentage reduction in R2 when regressing the index on all predictors minus the one of interest. The last column shows the variables that was used to generate the outcome variable. Table A3. Data A250. Descriptive statistics for continuous (top) and categorical (bottom) variables. Table A4. Data A250. The entries above and below the main diagonal are Spearman correlation coefficients with absolute values larger than 0.25 and differences between Spearman and Pearson correlation coefficients greater than 0.05 for continuous variables. Figure A1. Data C250. Identification of influential points in univariable analysis using leave-one-out approach. Figure A2. Data C250, univariable analysis. Smoothed residuals with 95% pointwise confidence intervals for variable x5 and x6 before and after removal of IPs. Figure A3. Data C250. Functional form of variable x7 in full data (dashed line) and without observation 104 (solid line). Truncated at 600. Figure A4. Data A250. Identification of influential points using L-1 approach in the selected MFP model (see Table 3, all data). Figure A5. Data A250. Identification of influential points in multivariable analysis using leave-two-out approach. left panel: functional form for x5 when the pair (37, 175) was removed. Right panel: functional form for x5 when pair (151, 175) was removed. Figure A6. data B250. Identification of influential points in the selected MFP model (see Table 3). Multivariable analysis using L-1 approach. Figure A7. data C250. Identification of influential points of x10 in the selected MFP model using L-1approach. Table A5. Data A500, B500, C500 and D1000. Multivariable analysis for relatively large datasets. See Fig. 8, A8 and A9 for the related functions. Figure A8. data D1000. Identification of influential points in the selected MFP model (see Table A5). Multivariable analysis using L-1 approach. No IPs identified at 5% level, but 3 IPS identified at 1% in variable x5. Figure A9. Data D1000. Identification of influential points in multivariable analysis using L-1. left panel: functional form for x5 in full data. Right panel: functional form for x5 before (red solid line) and after (blue dashed line) removal of observations 379, 664 and 925. The green solid line is the true function. Table A6. Data body fat, univariable analysis. P-values for different model comparison are displayed in column 2-4. The last two columns show the FP powers or exclusion of a variable in the complete data set and after deleting influential points respectively. Table A7. Data body fat. Selected models from a MFP analysis with all data represented by MFP(0.05, 0.05) and after removal of IPs identified from univariable (IPBFu (k)) and multivariable (IPBFm(l)) diagnostic analyses where k and l represent the number of IPs identified in the corresponding analysis. MFP (1, 0.05) – no elimination of variables, FSP with significance level 0.05. Figure A10. Data body fat. Multivariable analysis of complete data. Functional forms for continuous predictors in MFP (0.05, 0.05) model. Deleting 3 IPs biceps is no longer significant.