Fig 1.
Three-node network according to available trials, the distribution of age and presence of age-treatment interaction.
Upper panel represents the two configurations, and lower panel represents the three scenarios. For each configuration, the three scenarios were simulated. The total number of patients and trial are indicated over each arrow. The direction of the arrows indicates the direction (sign) of the comparison when estimating the treatment effect; therefore, X → Y indicates a X versus Y comparison and log(HR)(XY) denotes the log hazard ratio of the X versus Y comparison. Density plots are the distribution of age with the dashed line indicating age 60. For scenarios 1 and 2, the distribution of age was identical for A-C and B-C pairwise treatment comparisons, while the distribution is opposite in scenario 3: Mean age is higher in A-C trials and lower in B-C trials. Each configuration was simulated according to the three scenarios as represented in the lower panel. Solid arrows indicate trials available in all configurations and dashed arrows indicate trials only available in configuration 2. Black arrows indicate no age-treatment interaction, while red arrows indicate an age-treatment interaction.
Table 1.
Treatment coding in the one-step individual patient data (IPD) model and the aggregated data (AD) meta-regression.
Table 2.
Simulation parameters.
Table 3.
Simulation results for the A-C and B-C comparisons when treatment effect = -0.5, the between-trial heterogeneity for baseline risk was set at 0.01 and the between-trial heterogeneity of the treatment effect set at 0.01.
Fig 2.
Simulation results for A-B treatment comparison in different scenarios and configurations. The indirect (configuration 1, left part) and mixed (configuration 2, right part) are represented with the three scenarios (none, interaction, and both) as rows. Age was considered a continuous variable for a treatment effect = -0.5, a between-trial heterogeneity of the baseline risk set at σ = 0.01, and a between-trial heterogeneity of the treatment effect set at τ1 = τ2 = 0.01. Red-dashed lines represent the true value of A-B treatment effect (log[HR]) according to age. Blue shaded zone represents the 2.5–97.5% and 25–75% quantiles of the estimated treatment effect across the 1,000 replications. IPD: individual patient data, AD: aggregated data, TEage = 60: conditional treatment effect at age 60, the mean age of the simulation, vTEage+1: the conditional variation in treatment effect with age, B: bias, ESE: empirical standard error, ASE: average standard error.
Table 4.
Simulation results of the indirect and mixed A-B treatment comparisons in the different scenarios when the true treatment effect was -0.5, the between-trial heterogeneity for baseline risk was set at 0.01 and the between-trial heterogeneity of the treatment effect was set at 0.01.
Fig 3.
Estimation of regression coefficients (log[HR]) by the models in the MARCH/MACH-NC dataset.
log(HR): log(hazard ratio), MARCH/MACH-NC: Meta-analyses of Chemotherapy in Radiotherapy in Carcinomas of Head and Neck/Meta-analysis of Chemotherapy in Head and Neck Cancer, CoxME: mixed-effects Cox Model, Poisson ME1: mixed-effects Poisson without interaction decomposition, Poisson ME2: mixed-effects Poisson with interaction decomposition, mRT: modified radiotherapy, RT: radiotherapy, CTRT: chemoradiotherapy, age:(mRT vs RT) and age:(CTRT vs RT) are the interaction between age (entered as a continuous variable) and treatment effect, ind.: indirect estimation of the treatment effect since no trial comparing mRT to CTRT exist. Vertical dashed lines indicate no effect. Blue and green bars indicate the between- and within-trial decomposition of the interaction, respectively.
Table 5.
Analysis of the real data network meta-analysis MARCH/MACH-NC with IPD- and AD-based models.