Because all participants randomised to CT-P13 IV in the 3.5 trial switched to CT-P13 SC at week 30, week 54 effects in the CT-P13 IV treatment arm were imputed using regression methods based on the effects observed in the CT-P13 IV treatment arm of the CT-P13 3.1 trial (Fig. 1). Linear regression models were fitted using IPD from the CT-P13 IV treatment arm of the CT-P13 3.1 trial. The dependent variables were the changes from baseline to week 54 in DAS28-CRP, CDAI and SDAI, respectively. The model covariates were the values of the modelled outcome at baseline and the change from baseline to week 30, as well as possible confounders selected from a list shown in Additional file 1, Table S1. The selection of potential confounders was performed in three steps: (1) the association of each variable listed in Table S1 with the change from baseline to week 54 in modelled outcome was tested; (2) if several variables were correlated (Pearson r ≥ 0.6 for continuous variables; see correlation coefficients in Additional file 1, Table S2), only the variable with the strongest association with the modelled outcomes was retained; and (3) all selected variables from step 2 were entered in the model and a backward selection procedure was applied to further reduce the list of variables.

Imputation of week-54 CT-P13 3.5 results based on CT-P13 regression model. EU, European Union; IV, intravenous; MTX, methotrexate; PD, pharmacodynamics; PK, pharmacokinetics

R2 was used to assess the quality of the models. R2 was 0.48 for the model predicting change from baseline in DAS28-CRP score and 0.61 for the models predicting the changes from baseline in CDAI and SDAI, demonstrating that the quality of models was acceptable. The models are presented in Additional file 1, Table S3.

The obtained regression models provided predictions of the mean changes from baseline to week 54 in DAS28-CRP, CDAI and SDAI and associated SDs. A multiple imputation method was used to account for the uncertainty around the predicted values [28]. For each patient, 10 values were generated randomly from the statistical distribution around the predicted scores, thus generating 10 datasets on which the meta-regression models were estimated. Imputation was not performed for binary outcomes because prediction of the outcome itself was surrounded with a large degree of uncertainty.

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