Adriëtte Oostvogels

Supplementary material Appendix – Predicting C-peptide in the ABCD-study with a survival analysis The C-peptide variable was left-censored: 63.6% of the assessed C-peptide concentrations in the entire ABCD-study population fell below the detection limit of 0.34 nmol/l. Data below the detection limit can be treated as missing, but that decreases the power of the analysis, although information of the variable is available: it is lower than the detection limit. Three other methods are broadly used: substituting data below the detection limit with 0 (biases your estimate downwards), substituting with the limit of detection (biases your estimate upwards) or using half of the detection limit (could average your bias). 1 We predicted the values of C-peptide using a survival analyses in the statistical package R using the survreg function from the library survival. Normally in survival analyses, a time-to-event is modelled, but what if the event does not occur during the study period? Then the time-to-event is greater than the study period, but not measurable, i.e. right-censored data. Survival analyses predicts the time to event in these cases. We used the same technique for left-censored data, as this was the case in our study. 1,2,3 We predicted the C-peptide levels of those children with a value below the detection limit of whom BMI, age and sex, as these variables are correlated with C-peptide. 4 A loglogistic distribution was applied because it was most fitting, based on loglikelihood (R 2.13.0, R foundation for statistical computing, Vienna, Austria). The use of survival analysis for predicting values below the detection limit is described more often in environmental sciences than in medicine. 1 Before imputation of C-peptide we had information 508 valid values of C-peptide with a mean of 0.4435, a median of 0.4100 and an standard deviation of 0.118. The range of C-peptide was from 0.34-1.53. After imputation of C-peptide we have information on 1426 values of C-peptide with a mean of 0.3464, a median of 0.3229 and a standard deviation of 0.105. The range of C-peptide now is 0.23-1.53 (Figure A.1a + A.1b) 1) Dennis R. Helsel, “Fabricating data: How substituting values for nondetects can ruin results, and what can be done about it,” Chemosphere 65 (2006) 2434-2439 http://waterlegacy.org/sites/default/files/PolyMet_SuppEIS/WLExpert/BranfireunReferences/ Helsel_2006.pdf 2) Dennis R. Helsel, Statistics for censored environmental data using minitab and R. 2nd edition ; pages 17-21; published by John Wiley & Sons, Inc., Hoboken, New Jersey in 2012 http://197.14.51.10:81/pmb/STATISTIQUES/0470479884Statistics.pdf 138 Chapter 5