Baseline participant characteristics were presented using descriptive statistics: mean ± SD for continuous variables and percentages for categorical variables. All statistical analyses were conducted using SAS statistical software (version 9.3, SAS Institute, Cary, USA). Two-sided tests were used and p-values < 0.05 were considered statistically significant.

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.

A network meta-regression using IPD is recommended as the “gold standard” method to adjust for treatment effect modifiers when IPD are available for all considered studies [29, 30]; this method was implemented here in accordance with relevant methodological guidelines [29].

Two series of analyses were performed, using two definitions of the treatment variable: treatment variable with three levels (CT-P13 SC, CT-P13 IV, reference infliximab IV) and treatment variable with two levels (CT-P13 SC, infliximab IV [pooled data for CT-P13 IV and reference infliximab IV]).

Multivariate mixed models, with normal distribution and identity link function for continuous outcomes and binomial distribution and logit link function for binary outcomes, were fitted at weeks 30 and 54. Dependent variables were the outcomes of interest, as listed above. Model covariates were selected among variables listed in Additional file 1, Table S1. The same 3-step approach as described for the imputation model above was used for the models for DAS28-CRP, CDAI and SDAI change from baseline, EULAR good response (CRP criteria), ACR20, ACR50, ACR70, Boolean remission and HAQ-DI MCID (≥ 0.22) at week 30. For binary outcomes based on DAS28-CRP, CDAI and SDAI, the same covariates as in the model for corresponding continuous outcomes were used. For outcomes at week 54, the same covariates as for the corresponding outcomes at week 30 were used. In addition, a variable representing study 3.1 or 3.5 was entered in all regression models as a random effect.

Analysis outputs included treatment differences with associated 95% CIs for continuous outcomes, and odd ratios (OR) with associated 95% CIs for binary outcomes.

The treatment effect at week 54, for each continuous outcome (DAS28-CRP, CDAI and SDAI), was obtained as the mean of treatment effects estimated from the 10 simulated datasets, and the associated variance coefficient was calculated as the sum of the variance of estimated treatment effect within simulations and variance between simulations [28, 31]. p-value and 95% CI calculations considered a normal distribution of finally obtained coefficients.

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