To assess the prevalence of DUX4-expressing human malignancies, we performed a large-scale analysis of publicly available RNA-seq data across diverse cancer types (Fig. 1A, Fig. S1A). We found that DUX4 expression is a particularly common feature across advanced-stage cancers, with 10-50% of cancer samples (depending upon cancer type) displaying DUX4 expression levels comparable to or greater than those observed in the early embryo, which result in expression of the highly stereotyped, DUX4-induced gene expression program (Chew et al., 2019; Hendrickson et al., 2017). A markedly higher proportion of metastatic cancers express DUX4—and tend to have higher absolute DUX4 expression levels—than do their primary cancer counterparts (Fig. 1B-C).

We sought to determine if the DUX4 transcripts in metastatic cancers express the entire coding sequence or only a portion thereof, as expressed DUX4 truncations due to genomic rearrangements are frequent oncogenic drivers in specific cancer types, most notably undifferentiated round cell sarcomas (CIC-DUX4 oncoprotein) (Antonescu et al., 2017; Choi et al., 2013; Graham et al., 2012; Italiano et al., 2012; Kawamura-Saito et al., 2006; Yoshida et al., 2016; Yoshimoto et al., 2009) and adolescent B-cell acute lymphoblastic leukemia (ALL) (Lilljebjörn et al., 2016; Liu et al., 2016; Qian et al., 2017; Yasuda et al., 2016). We aligned RNA-seq reads to the DUX4 cDNA sequence and examined read coverage over the open reading frame. Resembling the cleavage stage embryo and DUX4-expressing primary cancers, DUX4-positive metastatic tumors transcribe the full-length coding region. In contrast, B-cell ALL exhibited the expected C-terminal truncation due to DUX4 fusion with the IGH locus (Fig. 1D).

Since DUX4 is typically silent in most healthy tissue contexts outside the cleavage-stage embryo (Das & Chadwick, 2016; Snider et al., 2010), we investigated if artifacts related to sequencing and sample processing could account for the observed high rates of DUX4 expression in metastatic versus primary cancers. We were particularly interested in determining whether the method of RNA recovery influenced DUX4 detection rate, as the analyzed metastatic cohorts frequently relied upon formalin-fixed samples rather than the frozen samples frequently used by TCGA. We took advantage of a cohort of patients with diverse metastatic tumor types for which patient-matched flash-frozen and formalin-fixed metastatic tumor samples were analyzed by RNA-seq (via poly(A)-selection and hybrid probe capture sequencing library preparations, respectively) (D. Robinson et al., 2015). Our re-analysis revealed that DUX4 expression is readily detectable and quantifiable for both sample and library preparation methods. DUX4 transcript levels in the majority of the sequenced samples were higher in poly(A)-selected sequencing than were the analogous measurements obtained from hybrid capture (Fig. S1B-C). These data demonstrate that the high rates of DUX4 expression that we observed across metastatic cancer cohorts reflect true DUX4 expression rather than technical biases introduced by studying formalin-fixed tissues and are consistent with expression of a polyadenylated DUX4 transcript in both primary and metastatic cancers.

We next sought to assess the downstream consequences of DUX4 expression in metastatic cancers. We focused on urothelial cancers for two reasons. First, urothelial cancers exhibited one of the highest frequencies of DUX4 expression (54% of patients) in any of the five metastatic cancer cohorts that we analyzed, suggesting that DUX4 could be particularly important in that tumor type. Second, pretreatment samples from 347 patients enrolled in the IMvigor210 trial, a phase 2 trial of anti-PD-L1 (atezolizumab) therapy with advanced urothelial carcinoma, were subject to transcriptome profiling by RNA-seq as well as immunohistochemical analysis, enabling us to conduct comprehensive studies of the association between DUX4 expression, the global transcriptome, and immunophenotypes in a well-powered cohort (Balar et al., 2017; Mariathasan et al., 2018; Rosenberg et al., 2016).

We examined associations between global gene expression profiles and DUX4 expression in this advanced urothelial carcinoma cohort. We performed differential gene expression analyses on the individuals stratified according to tumor DUX4 expression status. Gene Ontology (GO) network analyses on the upregulated genes in DUX4-positive cancers identified multiple clusters of development-associated terms, consistent with the known role of DUX4 in early embryogenesis (Fig. S2A; de Iaco et al., 2017; Hendrickson et al., 2017; Sugie et al., 2020; Whiddon et al., 2017). By contrast, we found a single network associated with downregulated genes: GO terms corresponding to humoral or cell-mediated immunity (Fig. 2A). Using an IFN-γ gene signature predictive of response to blockade of the PD-1/PD-L1 axis, we found that DUX4-expressing cancers have statistically lower levels of IFN-γ activity (Fig. S2B; Ayers et al., 2017). Consistent with IFN-γ suppression, we observed extensive downregulation of genes involved in anti-tumor immunity such as those involved in MHC class I-dependent antigen presentation and T cell activation, checkpoint proteins, and chemokines involved in effector T cell recruitment. DUX4-expression was also correlated with suppression of genes critical for MHC class II-mediated antigen presentation, namely: MHC class II isotypes (HLA–DP/DQ/DR), HLA-DM and HLA-DO, and the invariant chain (CD74) (Roche & Furuta, 2015). MHC class II gene expression is regulated by the transactivator CIITA via a conserved SXY-module present in the promoter regions of these genes. CIITA is induced by IFN-γ and is also conspicuously downregulated in DUX4-expressing tumors (Fig. 2B; (Glimcher & Kara, 1992; Masternak et al., 2000; Steimle et al., 1993, 1994). MHC class II-mediated antigen presentation can regulate T cell abundance in the tumor microenvironment and patient response to PD-1 blockade (Johnson et al., 2020). These analyses suggest that DUX4 expression in the metastatic context induces an immunosuppressive gene expression program, concordant with its established function in inhibiting JAK-STAT signaling in primary cancers (Chew et al., 2019).

We hypothesized that DUX4 expression in these cancers will generate related transcriptomic signals consistent with CD8⁺ T cell exclusion from the tumor. We assessed this using an effector CD8⁺ T cell transcriptomic signature developed from initial studies of the IMvigor210 phase 2 trial (Balar et al., 2017; Rosenberg et al., 2016). DUX4-expressing cancers had lower measures of the gene signature, consistent with decreased CD8⁺ T cell infiltration into the tumor (Fig. 2C). We also investigated the possible effects of DUX4 expression on the exclusion of other immune cell types using gene signatures developed from The Cancer Genome Atlas (Danaher et al., 2017). In these analyses, we recapitulated the observation of lower CD8⁺ T cell signature associated with DUX4 positivity (Fig. S2C). In addition, we observed patterns consistent with widespread immune cell exclusion from the tumor microenvironment (Fig. S2D). Defects in chemokine signaling could partially account for the observed DUX4-associated decrease in immune gene signature measurements. To test this hypothesis, we examined expression of chemokines involved in immune cell recruitment. In DUX4-expressing cancers, we observed lower mRNA levels of CXCL9 and CXCL10, chemokines which recruit T cells to the tumor site (Fig. 2D-E; Nagarsheth et al., 2017). Utilizing a chemokine signature associated with host immune response to solid tumors, we observed that DUX4 expression was correlated with broad reduction in the expression of chemokine signaling genes, beyond T cell-associated signals (Fig. S2E; Coppola et al., 2011).

We directly assessed the correlation of DUX4 expression to immune cell exclusion by examining CD8⁺ T cell abundance in the tumor microenvironment, measured by immunohistochemistry (IHC) on formalin fixed paraffin embedded (FFPE) patient tumor sections. We verified that DUX4 expression in the advanced urothelial carcinoma tumors was associated with an immune exclusion phenotype: a higher proportion of DUX4+ tumors exhibit either an immune-excluded or immune-desert phenotype compared to malignancies where DUX4 is silent (Fig. 2F, Fig. S2F). We similarly examined the correlation of DUX4 expression status with PD-L1 levels in the tumor and immune compartments quantified via IHC. We determined that DUX4 expression was associated with a significant decrease in PD-L1 levels on both tumor and host immune cells, consistent with DUX4-induced suppression of IFN-γ signaling (Fig. 2G, Fig. S2G, Fig. 2H, Fig. S2H). PD-L1 expression on immune cells such as dendritic cells and macrophages modulate anti-tumor immune suppression and response to ICI in in vivo mouse models (Lau et al., 2017; Lin et al., 2018; Noguchi et al., 2017). Importantly, PD-L1 levels on immune cells are correlated with response to ICI in clinical trials (Powles et al., 2014; Rosenberg et al., 2016).

Given the association between tumor DUX4 expression and suppression of anti-tumor immune response, we next sought to understand if tumor DUX4 expression conferred changes to patient overall survival during PD-L1 inhibition. DUX4 expression was associated with a significant decrease in objective response rates, assessed using the Response Evaluation Criteria in Solid Tumors (RECIST) (Fig. 3A). As expected, higher tumor mutational burden (TMB) was associated with improved survival outcomes in this cohort (Fig. 3B). In contrast, DUX4 expression was correlated with a significant reduction in median overall survival (Fig. S3A). We attempted to control for the possible confounding effects of TMB on the DUX4 signal by removing the bottom quartile of patients, those with the lowest number of missense mutations in their tumors. DUX4 expression was associated with statistically lower survival rates in this cohort, even after controlling for TMB in this crude manner (Fig. 3C).

We next determined whether DUX4 expression was a significant predictor of survival for ICI-treated patients even after controlling for TMB and other potentially relevant variables in a statistically rigorous manner. We used Cox Proportional Hazards (PH) regression to quantify the effects of multiple clinical, demographic, and molecular features on risk of death during ICI. In the context of multivariate Cox PH regression, which controls for the confounding effects of all other covariates simultaneously, we observed that TMB was positively associated with survival [hazard ratio (HR) = 0.14], as expected. Conversely, DUX4 expression, Eastern Cooperative Oncology Group Performance Status (ECOG PS) > 0, and previous administration of platinum chemotherapy were correlated with increased risk (or shorter survival), while other features that have previously been reported as associated with reduced survival [e.g., TGFB1 expression (Mariathasan et al., 2018)] did not remain significant after controlling for TMB and other variables. In particular, DUX4 positivity was associated with dramatically worse survival, with a 3.2-fold increase in risk of death at any point in time compared to DUX4-negative status (Fig. 4A, Table 1, Table S1).

We next investigated if DUX4 expression status carried added value as a predictor over routinely collected clinical and molecular information. We focused on the variables with significant hazard ratios under both the univariate and multivariate regression settings: DUX4 expression status, TMB, ECOG PS, and history of platinum chemotherapy. We employed goodness of fit measurements, which compare the observed data to expectations from Cox PH models created using various combinations of the covariates. In these analyses, we observed a quantifiable improvement in data-model congruence with the addition of DUX4 expression status (Fig. 4B, Fig. S4A-B). Additionally, we measured statistically significant differences in the likelihoods of the reduced models (without DUX4 expression as a predictor) when compared to the full model (employs all covariates) (Table 2). Taken together, these analyses indicate that DUX4 expression status is an informative predictor of risk under ICI treatment.

We evaluated the utility of DUX4 expression status for pre-treatment risk assignment in predicting patient response to ICI. We trained full and reduced Cox PH models on randomly sampled patients (training set, 70% of the cohort) and quantified their respective risk scores. A reference risk score per model was computed as the median score across the training set and was used to ascribe patients into low- vs. high-risk groups. Using these models, we quantified risk scores on the individuals excluded from model construction (test set, 30% of the patients), and similarly assigned patients into low- or high-risk groups based on the training set reference score. By empirically quantifying survival of the two risk groups using KM (Kaplan-Meier) estimation, we found that the full model stratifies patients in an informative manner, appropriately discriminating patients with longer vs. shorter survival times (Fig. 4C, Fig. S4C-D). Further, the addition of DUX4 expression status improves model performance as illustrated by the time-dependent Brier score, a measure of survival prediction accuracy at specific timepoints (Fig. S4E).

We used a Random Survival Forest (RSF) model to quantify the effect of DUX4 expression on survival in ICI-treated advanced urothelial carcinoma patients (Ishwaran et al., 2008). The Random Survival Forest (RSF) is a machine learning ensemble, an extension of the Random Forest algorithm for right-censored data (Breiman, 2001). It can provide accurate estimates of risk and survival probability at definite times by aggregating predictions from a multitude of base learners (survival trees) (Ishwaran et al., 2008). RSFs have been successfully used to study time-to-event problems in medicine, including measurement of variable importance (Dietrich et al., 2016; Hsich et al., 2019; Ishwaran et al., 2009; O’Brien et al., 2021; Semeraro et al., 2011). We utilized the RSF model to address potential limitations of our Cox PH analyses. First, the RSF model is fully non-parametric and as such does not operate under the Cox PH assumptions: a constant relative hazard between strata over time (proportional hazards), a linear relationship between the predictors and the log hazard, and the unspecified baseline hazard function. Second, the RSF model can compute estimates of absolute risk and survival probability over time independent of a reference, unlike relative risk models such as Cox PH (Ishwaran et al., 2008).

We used all available molecular, clinical, and demographic covariates to grow an RSF. We randomly selected 70% of the patients to grow the forest, with the resulting model having an Out-of-Bag (OOB) error of 38.4%. The OOB error stabilizes with increasing number of trees and converges to the leave-one-out cross-validation error estimate. Thus, OOB error is characterized as an unbiased estimate of the model’s true prediction error (Breiman, 2001; Hastie et al., 2009). In some instances, the OOB error provides overestimates and some reports have recommended treating it as an upper bound (Bylander, 2002; Janitza & Hornung, 2018; Mitchell, 2011). Thus, we measured the RSF model’s test error using a holdout set (the remaining 30% of the cohort) excluded from training. The RSF model recorded a test error of 32.6% illustrating an appropriate fit (Fig. S5A). Our error measurements are comparable to Ishwaran, et al. (2008), suggesting our model can be used for inference purposes. Further, the time-dependent Brier score of the RSF model on the training and test sets confirms informative survival prediction (Fig. S5B).

The RSF model predicted worse survival outcomes in patients with DUX4-expressing cancers compared to their DUX4-silent counterparts. These predictions were mirrored in the test dataset, illustrating robustness of the model (Fig. 5A). Using time-dependent Receiver Operating Characteristic (ROC) curve analyses, we identified the time range for which the RSF predictive performance is statistically divergent from random guessing: approximately 6 to 20 months (Fig. S5C). In this window we observed significant survival differences between patients with DUX4+ and DUX4-tumors. We highlighted the model’s performance at predicting 1-year and 1.5-year survival, typical timepoints of clinical interest. For these times, the RSF appropriately discriminates patient death and survival (Fig. S5D). Examining the absolute effects of DUX4 expression on survival, the RSF model predicted an approximately 20% decrease in both 1-year and 1.5-year survival probabilities in patients with DUX4-expressing cancers (Fig. 5B).

We sought to determine the importance of DUX4 expression status relative to the other covariates in the RSF model. We measured feature importance using estimated Shapley values, which quantify the marginal contribution of each variable to the RSF prediction (Lundberg & Lee, 2017; Maksymiuk et al., 2020; Shapley, 1953; Štrumbelj & Kononenko, 2014). Specifically, Shapley values measure variable contributions to predictions at the level of each patient. Contributions to the overall performance of the RSF model can be assessed by examining the aggregated summary: the average of the absolute Shapley values for a predictor across the patient cohort. We estimated Shapley values associated with predicting ensemble mortality, the RSF risk estimate. In these analyses, ECOG PS had the largest contribution, followed by TMB and DUX4 expression (Fig. S5E). We validated these feature rankings using two independent metrics. The first metric was permutation importance, which quantifies the change in prediction error associated with permutation of a variable’s data; important covariates will record large deviations from the original predictions (Breiman, 2001; Ishwaran, 2007). The second measure employed was minimal depth, a measure of the variable-node-to-root-node distance within the survival trees of the RSF; important variables tend to have smaller minimal depth values as they are typically used for earlier decision splits (Ishwaran et al., 2010, 2011). Feature contributions measured using permutation importance and minimal depth were consistent with the Shapley-based assignments, notably identifying DUX4 expression as an important contributor to patient survival outcomes (Fig. S5E). We investigated time-dependent changes in variable importance by estimating Shapley values associated with predicting survival probability at distinct time points along the observation window. Interestingly, we observed the strong dependence on ECOG PS for predicting survival at early timepoints under this paradigm. The importance of DUX4 expression for survival prediction is most prominent at later times (Fig. 5C). Altogether, we found that diverse variable importance measures converge on identifying DUX4 as a major contributor to patient survival prediction.

We sought to quantify the effect of DUX4 expression on survival predictions after controlling for the effects of the other covariates. With Shapley dependence plots, which allows visualization of the marginal effects of a variable on the predicted outcome, we measured the expected negative correlation between TMB and mortality (Fig. S5F; Lundberg et al., 2020). We performed a similar dependence analysis on DUX4 expression and observed a clear separation of positive and negative Shapley values based on DUX4-positive and -negative status, respectively. These results signify an increase in predicted risk of death associated with DUX4 expression (Fig. S5E). To quantify the effects of TMB and DUX4 expression in the appropriate risk units (expected number of deaths), we utilized partial dependence as an alternative way to represent mortality predictions as a function of these variables, marginalized over the other predictors in the data (Friedman, 2001). Specifically, the average model predictions across the individuals in the cohort are calculated over the unique predictor values. The marginal effects of TMB and DUX4 expression measured via partial dependence mirror the results of the Shapley dependence analyses. Patients with the lowest mutational burden exceed the individuals with the highest TMB by approximately 20 expected deaths on average. Further, we measured an increase in the number of predicted deaths associated with DUX4-positivity by approximately 16, over DUX4-negative status (Fig. S5F-G). We then extended the partial dependence analyses to survival probability predictions over time. In this paradigm, we similarly observed that higher TMB was correlated with increased survival probability, more pronounced at later times (Fig. 5D). DUX4 expression was correlated with poorer survival outcomes, with a 1-year and 1.5-year survival difference of 20.7% and 19.2% between patients with DUX4+ and DUX4-tumors, respectively. Strikingly, our analyses measure a difference of at least 12.5 months in median survival between the DUX4+ and DUX4-strata (Fig. 5E). Overall, our analyses demonstrate a significant and robust decrease in survival attributable to DUX4 expression in advanced cancers.

A genome annotation was created through merging of the UCSC knownGene (Meyer et al., 2013), Ensembl 71 (Flicek et al., 2013), and MISO v2.0 (Katz et al., 2010) annotations for the hg19/GRCh37 assembly. Further, this annotation was expanded by generating all possible combinations of annotated 5’ and 3’ splice sites within each gene. RNA-seq reads were mapped to the transcriptome using RSEM v1.2.4 (B. Li & Dewey, 2011) calling Bowtie v1.0.0 (Langmead et al., 2009), with the option “-v 2.” TopHat v.2.0.8b (Trapnell et al., 2009) was used to map the unaligned reads to the genome and to the database of splice junctions obtained from the annotation merging described previously. Gene expression estimates (TPM, transcripts per million) obtained were normalized using the trimmed mean of M values (TMM) method (M. D. Robinson & Oshlack, 2010). In the differential gene expression analyses for the DUX4-positive vs. -negative comparison, gene expression values per sample group were compared using a two-sided Mann-Whitney U test. Differentially expressed genes illustrated in Figure 2B were identified as those with an absolute log₂(fold-change) ≥ log₂(1.25) and a p-value < 0.05. GO enrichment analyses, using the clusterProfiler package (Wu et al., 2021; Yu et al., 2012), were performed on DUX4-upregulated or -downregulated genes [absolute log₂(fold-change) ≥ log₂(1.5) and a p-value < 0.05] compared against the set of coding genes. Significant GO terms were defined as “Biological Process” terms with a Benjamini-Hochberg FDR-adjusted p-value < 0.05. The top 25 significant GO terms were illustrated (Fig. 2A and Fig. S2A). To investigate DUX4 RNA-seq coverage patterns, a fasta file containing the DUX4 cDNA sequence was assembled, indexed using samtools (H. Li et al., 2009), and used as a reference for read pseudoalignment by kallisto v.0.46.1 (Bray et al., 2016). The following kallisto parameters were used: kmer size of 31, estimated fragment length of 200, and estimated fragment length standard deviation of 80. Usage of the single-end option (“--single”) and bias correction (“--bias”) were also specified. DUX4 read coverage was visualized using the Integrative Genomics Viewer (IGV, Thorvaldsdóttir et al., 2013).

For a given gene set, z-score normalization of the expression values per gene was performed across the patient cohort. The signature score was defined as the mean of the normalized values across the genes of the set.

Kaplan-Meier (KM) estimation, p-value estimates from the log-rank test, and Cox Proportional Hazards (PH) regression in the univariate and multivariate contexts were performed using the survival package (T. Therneau, 2022; T. M. Therneau & Grambsch, 2000). Goodness of fit evaluations of the Cox PH models were done by measuring the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). AIC and BIC metrics balance model complexity with maximized likelihood, penalizing feature number increases without a concomitant improvement in performance. The likelihood ratio test was also used to compare goodness of fit of full (all variables) vs. reduced (subset of variables) Cox PH models. Specifically, the null hypothesis that the simple model provides as good as a fit as the more complex model was evaluated. The AIC, BIC, and likelihood ratio test p-values were computed using R’s stats package (R Core Team, 2022). For the Cox PH risk modeling, the patients were randomly assigned into training (70%) and test (30%) datasets. The createDataPartition() function from the caret package (Kuhn, 2022) was used to preserve the DUX4 status class distribution after splitting. Full and reduced Cox PH models were created using the training data and the risk scores for each respective model were calculated using caret’s predict.coxph() function. For a given patient, the calculated risk score is equal to the hazard ratio relative to a “reference patient” (an individual whose covariate values are set to the respective means, from the training set). Specifically, the risk score is the quotient of the patient’s and the reference’s exponentiated linear predictors (the sum of the covariates in the model, weighted by the model’s regression coefficients). A “reference risk score” for each model was defined as the median risk score in the training data. Patients were assigned into low- or high-risk groups if their risk scores were lower or higher than the reference, respectively. The trained models were used to calculate risk scores and assign risk labels (based on the training set risk score reference) in the test set. The survival difference between low- and high-risk patients were empirically assessed via KM estimation and the log-rank test. Visualizations were created using the ggplot2 (Wickham, 2016), dplyr (Wickham et al., 2022), and survminer (Kassambara et al., 2021) packages.

We implemented a Random Survival Forest (RSF) model, an ensemble of multiple base learners (survival trees), using the randomForestSRC package (Ishwaran et al., 2008). The RSF algorithm is an extension of the Random Forest Algorithm (Breiman, 2001) for usage with right-censored data. Here, B bootstrap datasets are created from the original data, used to grow B concomitant survival trees (usually constrained by membership size in the terminal nodes) constructed using a randomly selected subset of the variables. Terminal node statistics are obtained for each tree: the survival function (via the Kaplan-Meier estimator), the cumulative hazard function (CHF, via the Nelson-Aalen estimator), and mortality (expected number of deaths; sum of the CHF over time). The RSF prediction is the average across the forest. Of note, each bootstrap dataset excludes 36.8% of the original data on average, the out-of-bag (OOB) samples. Thus, predictions for a particular sample can be made using the subset of the trees for which it was excluded from training (OOB predictions). Similarly, the associated OOB error for the RSF model can calculated, representing an unbiased estimate of the test error. We randomly assigned patients into training (70%) and test (30%) datasets. Since the DUX4-positive status was a minority class, we utilized the createDataPartition() function from the caret package (Kuhn, 2022) to preserve the class distribution within the splits. To determine optimal hyperparameters, we evaluated 5,616 RSF models representing different combinations of ntree (number of trees), nodesize (minimum terminal node size), mtry (number of randomly selected splitting variables), na.action (handling of missing data), splitrule (splitting rule), and samptype (type of bootstrap). We selected the model with hyperparameters which minimized both the OOB training and the test errors (defined as 1 – concordance index), namely: ntree = 1500, nodesize = 15, mtry = 3, na.action = “na.impute”, splitrule = “bs.gradient”, and samptype = “swr.” We specified the use of an nsplit (number of random splits) value of 0 to indicate evaluation of all possible split points and usage of the optimum. For test set predictions, patients with missing data were omitted (na.action = “na.omit”).

Feature importance in the final RSF model was evaluated using 3 metrics. First, permutation importance was measured using randomForestSRC’s subsample() function. RSF permutation importance utilizes OOB values: a variable’s OOB data is permuted and the change in the new vs. original OOB prediction error is quantified. The RSF permutation importance values were standardized by dividing by the variance and multiplying by 100, and the variance and confidence regions were obtained via the delete-d jackknife estimator (Ishwaran & Lu, 2019). Second, the tree-based feature importance metric minimal depth was calculated using randomForestSRC’s var.select() function. The minimal depth threshold (mean minimal depth) is the tree-averaged threshold (conservative = “medium”). Last, Shapley values were estimated using the fastshap package (Greenwell, 2021), using 1000 Monte Carlo repetitions. For each prediction, the sum of the estimated Shapley values was corrected (adjust = TRUE) to satisfy the efficiency (or local accuracy) property: for an individual i, the sum of i’s feature contributions equal the difference between the prediction for i and the average prediction across the entire cohort. For the overall measure of importance, the Shapley values were estimated from the mortality predictions from the RSF model (Fig S5E). Mortality is defined as the number of expected deaths. That is, if all patients in the cohort shared the same covariate values as patient i who has mortality m_i, then an average of m deaths is expected (Ishwaran et al., 2008). For the time-dependent implementation, we estimated Shapley values associated with the per timepoint RSF survival probability predictions along the observation window (Fig 5C).

The relationships of DUX4 expression and TMB to mortality or survival probability (marginal contributions) were assessed via Shapley dependence plots and partial dependence plots. Partial dependence values were obtained using randomForestSRC’s partial() function and OOB predictions for mortality and survival probability were used as input. Visualizations were created in the R programming environment using the dplyr (Wickham et al., 2022), ggplot2 (Wickham, 2016), pammtools (Bender & Scheipl, 2018), and plotly (Sievert, 2020) packages.

The time-dependent Receiver Operating Characteristic (ROC) curve analyses were done to evaluate the RSF model’s accuracy in differentiating patients who die before a particular time t, from those who survive past t (Heagerty & Zheng, 2005). Specifically, for each timepoint, the cumulative/dynamic Area Under the ROC curve (AUC^C/D) was calculated by computing the sensitivity (true positive rate) and specificity (1 – false positive rate) associated with using RSF-predicted mortality as the prognostic marker. The time-dependent AUC^C/D and 95% confidence interval per time point were estimated using the timeROC package, which adds the inverse-probability-of-censoring weights (IPCW) to the sensitivity calculation to correct for selection bias due to right-censoring (Blanche et al., 2013). The out-of-bag (training) or the test mortality predictions were used as input. The time-dependent Brier score and the Continuous Ranked Probability Score (CRPS, integrated Brier score divided by time) for the Cox PH models were computed using the pec package (Mogensen et al., 2012). The time-dependent Brier score and the CRPS for the RSF model was calculated using the randomForestSRC package (Ishwaran et al., 2008). The Kaplan-Meier estimator for the censoring times was used to estimate the IPCW (cens.model = “marginal”). Harrell’s concordance index for the Cox PH and RSF models were calculated using the survival (T. Therneau, 2022; T. M. Therneau & Grambsch, 2000) and randomForestSRC packages, respectively. Visualizations were created in the R programming environment using the dplyr (Wickham et al., 2022) and ggplot2 (Wickham, 2016) packages.