Rajen Dinesh Shah

Variable selection with error control: another look at stability selection

Summary. Stability selection was recently introduced by Meinshausen and Buhlmann as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection procedure to subsamples of the data. We introduce a variant, called complementary pairs stability selection, and derive bounds both on the expected number of variables included by complementary pairs stability selection that have low selection probability under the original procedure, and on the expected number of high selection probability variables that are excluded. These results require no (e.g. exchangeability) assumptions on the underlying model or on the quality of the original selection procedure. Under reasonable shape restrictions, the bounds can be further tightened, yielding improved error control, and therefore increasing the applicability of the methodology.

Diffuse Large B-Cell Lymphoma Classification System That Associates Normal B-Cell Subset Phenotypes With Prognosis

PURPOSE Current diagnostic tests for diffuse large B-cell lymphoma use the updated WHO criteria based on biologic, morphologic, and clinical heterogeneity. We propose a refined classification system based on subset-specific B-cell-associated gene signatures (BAGS) in the normal B-cell hierarchy, hypothesizing that it can provide new biologic insight and diagnostic and prognostic value. PATIENTS AND METHODS We combined fluorescence-activated cell sorting, gene expression profiling, and statistical modeling to generate BAGS for naive, centrocyte, centroblast, memory, and plasmablast B cells from normal human tonsils. The impact of BAGS-assigned subtyping was analyzed using five clinical cohorts (treated with cyclophosphamide, doxorubicin, vincristine, and prednisone [CHOP], n = 270; treated with rituximab plus CHOP [R-CHOP], n = 869) gathered across geographic regions, time eras, and sampling methods. The analysis estimated subtype frequencies and drug-specific resistance and included a prognostic meta-analysis of patients treated with first-line R-CHOP therapy. RESULTS Similar BAGS subtype frequencies were assigned across 1,139 samples from five different cohorts. Among R-CHOP-treated patients, BAGS assignment was significantly associated with overall survival and progression-free survival within the germinal center B-cell-like subclass; the centrocyte subtype had a superior prognosis compared with the centroblast subtype. In agreement with the observed therapeutic outcome, centrocyte subtypes were estimated as being less resistant than the centroblast subtype to doxorubicin and vincristine. The centroblast subtype had a complex genotype, whereas the centrocyte subtype had high TP53 mutation and insertion/deletion frequencies and expressed LMO2, CD58, and stromal-1-signature and major histocompatibility complex class II-signature genes, which are known to have a positive impact on prognosis. CONCLUSION Further development of a diagnostic platform using BAGS-assigned subtypes may allow pathogenetic studies to improve disease management.

Goodness‐of‐fit tests for high dimensional linear models

In this work we propose a framework for constructing goodness of fit tests in both low and high-dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or Lasso fit to the data, and using some proxy for prediction error as the final test statistic. We call this family Residual Prediction (RP) tests. We show that simulation can be used to obtain the critical values for such tests in the low-dimensional setting, and demonstrate using both theoretical results and extensive numerical studies that some form of the parametric bootstrap can do the same when the high-dimensional linear model is under consideration. We show that RP tests can be used to test for significance of groups or individual variables as special cases, and here they compare favourably with state of the art methods, but we also argue that they can be designed to test for as diverse model misspecifications as heteroscedasticity and nonlinearity.