Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model with other desirable properties from a possibly very large set of candidate statistical models. Over the last 5–10 years the literature on model selection in linear mixed models has grown extremely rapidly. The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices. To obtain a better understanding of the available methods, their properties and the relationships between them, we review a large body of literature on linear mixed model selection. We arrange, implement, discuss and compare model selection methods based on four major approaches: information criteria such as AIC or BIC, shrinkage methods based on penalized loss functions such as LASSO, the Fence procedure and Bayesian techniques.

PURPOSE: To determine the efficacy and tolerability of combining oxaliplatin with capecitabine in the treatment of advanced nonpretreated and pretreated colorectal cancer. PATIENTS AND METHODS: Forty-three nonpretreated patients and 26 patients who had experienced one fluoropyrimidine-containing regimen for advanced colorectal cancer were treated with oxaliplatin 130 mg/m² on day 1 and capecitabine 1,250 mg/m² bid on days 1 to 14 every 3 weeks. Patients with good performance status (World Health Organization grade 0 to 1) were accrued onto two nonrandomized parallel arms of a phase II study. RESULTS: The objective response rate was 49% (95% confidence interval [CI], 33% to 65%) for nonpretreated and 15% (95% CI, 4% to 35%) for pretreated patients. The main toxicity of this combination was diarrhea, which occurred at grade 3 or 4 in 35% of the nonpretreated and 50% of the pretreated patients. Grade 3 or 4 sensory neuropathy, including laryngopharyngeal dysesthesia, occurred in 16% of patients on both cohorts. Capecitabine dose reductions were necessary in 26% of the nonpretreated and 45% of the pretreated patients in the second treatment cycle. The median overall survival was 17.1 months and 11.5 months, respectively. CONCLUSION: Combining capecitabine and oxaliplatin yields promising activity in advanced colorectal cancer. The main toxicity is diarrhea, which is manageable with appropriate dose reductions. On the basis of our toxicity experience, we recommend use of capecitabine in combination with oxaliplatin 130 mg/m² at an initial dose of 1,250 mg/m² bid in nonpretreated patients and at a dose of 1,000 mg/m² bid in pretreated patients.

In metastatic melanoma, it is vital to identify and validate biomarkers of prognosis. Previous studies have systematically evaluated protein biomarkers or mRNA-based expression signatures. No such analyses have been applied to microRNA (miRNA)-based prognostic signatures. As a first step, we identified two prognostic miRNA signatures from publicly available data sets (Gene Expression Omnibus/The Cancer Genome Atlas) of global miRNA expression profiling information. A 12-miRNA signature predicted longer survival after surgery for resection of American Joint Committee on Cancer stage III disease (>4 years, no sign of relapse) and outperformed American Joint Committee on Cancer standard-of-care prognostic markers in leave-one-out cross-validation analysis (error rates 34% and 38%, respectively). A similar 15-miRNA biomarker derived from The Cancer Genome Atlas miRNA-seq data performed slightly worse (39%) than these current biomarkers. Both signatures were then assessed for replication in two independent data sets and subjected to systematic cross-validation together with the three other miRNA-based prognostic signatures proposed in the literature to date. Five miRNAs (miR-142-5p, miR-150-5p, miR-342-3p, miR-155-5p, and miR-146b-5p) were reproducibly associated with patient outcome and have the greatest potential for application in the clinic. Our extensive validation approach highlighted among multiple independent cohorts the translational potential and limitations of miRNA signatures, and pointed to future directions in the analysis of this emerging class of markers.

We develop methodology and theory for a mean field variational Bayes approximation to a linear model with a spike and slab prior on the regression coefficients. In particular we show how our method forces a subset of regression coefficients to be numerically indistinguishable from zero; under mild regularity conditions estimators based on our method consistently estimate the model parameters with easily obtainable and (asymptotically) appropriately sized standard error estimates; and select the true model at an exponential rate in the sample size. We also develop a practical method for simultaneously choosing reasonable initial parameter values and tuning the main tuning parameter of our algorithms which is both computationally efficient and empirically performs as well or better than some popular variable selection approaches. Our method is also faster and highly accurate when compared to MCMC.

In patients with metastatic melanoma, the identification and validation of accurate prognostic biomarkers will assist rational treatment planning. Studies based on “‐omics” technologies have focussed on a single high‐throughput data type such as gene or microRNA transcripts. Occasionally, these features have been evaluated in conjunction with limited clinico‐pathologic data. With the increased availability of multiple data types, there is a pressing need to tease apart which of these sources contain the most valuable prognostic information. We evaluated and integrated several data types derived from the same tumor specimens in AJCC stage III melanoma patients—gene, protein, and microRNA expression as well as clinical, pathologic and mutation information—to determine their relative impact on prognosis. We used classification frameworks based on pre‐validation and bootstrap multiple imputation to compare the prognostic power of each data source, both individually as well as integratively. We found that the prognostic utility of clinico‐pathologic information was not out‐performed by any of the various “‐omics” platforms. Rather, a combination of clinico‐pathologic variables and mRNA expression data performed best. Furthermore, a patient‐based classification analysis revealed that the prognostic accuracy of various data types was not the same for different patients. This indicates that ongoing development in the individualized evaluation of melanoma patients must take account of the value of both traditional and novel “‐omics” measurements.