Fig. 1

Framework of dualmarker. Dualmarker contains two parts: visualization of one specific marker pair and de novo identification of biomarker pairs for binary outcome (therapy response, upper left panels) and time-to-event outcome (survival, lower left panels). To facilitate visualization, both markers are dichotomized into positive/high and negative/low groups with four quadrants, labeled R1-R4 with dedicated colors. Both markers are shown in a scatter chart or Kaplan–Meier plot (KMplot, see detailed plots in Figs. 2 and 3), and all plots can be easily generated by a single function: dm_pair. For de novo identification of dual-marker pair, four logistic regression models or Cox regression models are built depending on whether response or survival analysis is performed: two single-marker models and two dual-marker models with interaction (M1*M2) or without interaction (M1 + M2). To control any covariates, ‘cov’ option can also be added in the model. Each candidate is evaluated by model comparison, which compares the dual-marker models with the single ones using the likelihood ratio test (LRT). The -log10 p values from model comparisons of dual-vs-marker1 and dual-vs-marker2 are shown as scatterplots, with each dot representing a candidate biomarker pair (see detailed plots in Fig. 4); The analysis is performed by the dm_searhM2_logit/cox and dm_combM_logit/cox functions to search marker2 to combine with specific marker1 or search among all combinations of marker pairs, respectively