Modern biomedical datasets are increasingly high-dimensional and exhibit complex correlation structures. Generalized linear mixed models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the fixed and random effects in GLMMs is increasingly difficult in high dimensions, and computational complexity grows with increasing dimension of the random effects. We present a novel reformulation of the GLMM using a factor model decomposition of the random effects, enabling scalable computation of GLMMs in high dimensions by reducing the latent space from a large number of random effects to a smaller set of latent factors. We also extend our prior work to estimate model parameters using a modified Monte Carlo Expectation Conditional Minimization algorithm, allowing us to perform variable selection on both the fixed and random effects simultaneously. We show through simulation that through this factor model decomposition, our method can fit high-dimensional penalized GLMMs faster than comparable methods and more easily scale to larger dimensions not previously seen in existing approaches.

PURPOSECALGB (Alliance)/SWOG 80405 was a randomized phase III trial that in first-line patients with metastatic colorectal cancer (mCRC) treated with bevacizumab or cetuximab with chemotherapy. We aimed to discover novel mutated genes associated with prognosis and differential response to therapy with the biologics.METHODSPrimary tumor DNA from 548 patients was sequenced using FoundationOne. The effect of mutated genes and mutations on overall survival (OS) was tested adjusting for microsatellite instability status, BRAF V600E, all RAS mutations, arm, sex, and age.RESULTSThe median number (lower-upper quartile) of mutated genes was 5 (3-7), 5 (3-6) in microsatellite stable and 12.5 (4.5-32) in microsatellite instability-high tumors. Mutated KRAS and APC were more frequent in Black (53% and 85%) than White (27% and 65%, respectively) patients while BRAF V600E was less frequent in Black (5%) than White (14%) patients. The median OS in patients with BRAF non-V600E (2.2% of patients) was 31.9 months (95% CI, 15.1 to not applicable [NA]) similar to that of BRAF wild-type (WT) patients (31.2 months [95% CI, 29.0 to 33.9]). Mutated LRP1B (10.7% of patients) was associated with improved OS compared with WT LRP1B (hazard ratio, 0.57 [95% CI, 0.40 to 0.80]). RNF43 (5.6% of patients) interacted with treatment arms as, in the cetuximab arm, patients with mutated RNF43 had a median OS of 11.5 (95% CI, 10.8 to NA) months compared with 30.1 (95% CI, 24.9 to 35.3) months in patients with WT RNF43, whereas in the bevacizumab arm, patients with mutated RNF43 had a median OS of 25.0 (95% CI, 14.2 to NA) months compared with 31.3 (95% CI, 29.0 to 34.3) months in patients with WT RNF43.CONCLUSIONThese results can provide new tools to predict patient outcome and improve therapeutic decisions and trial participation in patient minorities. The molecular alterations identified in this study may direct biomarker-driven studies.