ThrEEBoost: Thresholded Boosting for Variable Selection and Prediction via Estimating Equations

<p>Most variable selection techniques for high-dimensional models are designed to be used in settings, where observations are independent and completely observed. At the same time, there is a rich literature on approaches to estimation of low-dimensional parameters in the presence of correlation, missingness, measurement error, selection bias, and other characteristics of real data. In this article, we present ThrEEBoost (<i>Thr</i>esholded <i>EEBoost</i>), a general-purpose variable selection technique which can accommodate such problem characteristics by replacing the gradient of the loss by an estimating function. ThrEEBoost generalizes the previously proposed EEBoost algorithm (Wolfson <a href="#cit0026" target="_blank">2011</a>) by allowing the number of regression coefficients updated at each step to be controlled by a thresholding parameter. Different thresholding parameter values yield different variable selection paths, greatly diversifying the set of models that can be explored; the optimal degree of thresholding can be chosen by cross-validation. ThrEEBoost was evaluated using simulation studies to assess the effects of different threshold values on prediction error, sensitivity, specificity, and the number of iterations to identify minimum prediction error under both sparse and nonsparse true models with correlated continuous outcomes. We show that when the true model is sparse, ThrEEBoost achieves similar prediction error to EEBoost while requiring fewer iterations to locate the set of coefficients yielding the minimum error. When the true model is less sparse, ThrEEBoost has lower prediction error than EEBoost and also finds the point yielding the minimum error more quickly. The technique is illustrated by applying it to the problem of identifying predictors of weight change in a longitudinal nutrition study. Supplementary materials are available online.</p

MOESM1 of Decision trees in epidemiological research

Additional file 1. Regression tree representing the relationship between adjusted residuals for energy intake (adjusted for age, sex, and BMI) and 22 baseline covariate

Supplemental Material, Appendix_Tables - The Minne-Loppet Motivation Study: An Intervention to Increase Motivation for Outdoor Winter Physical Activity in Ethnically and Racially Diverse Elementary Schools

<p>Supplemental Material, Appendix_Tables for The Minne-Loppet Motivation Study: An Intervention to Increase Motivation for Outdoor Winter Physical Activity in Ethnically and Racially Diverse Elementary Schools by Jonathan M. Miller, Julian Wolfson, Melissa N. Laska, Toben F. Nelson, and Mark A. Pereira in American Journal of Health Promotion</p

Relevance of Interleukin-6 and D-Dimer for Serious Non-AIDS Morbidity and Death among HIV-Positive Adults on Suppressive Antiretroviral Therapy

<div><p>Background</p><p>Despite effective antiretroviral treatment (ART), HIV-positive individuals are at increased risk of serious non-AIDS conditions (cardiovascular, liver and renal disease, and cancers), perhaps due in part to ongoing inflammation and/or coagulation. To estimate the potential risk reduction in serious non-AIDS conditions or death from any cause that might be achieved with treatments that reduce inflammation and/or coagulation, we examined associations of interleukin-6 (IL-6), D-dimer, and high-sensitivity C-reactive protein (hsCRP) levels with serious non-AIDS conditions or death in 3 large cohorts.</p><p>Methods</p><p>In HIV-positive adults on suppressive ART, associations of IL-6, D-dimer, and hsCRP levels at study entry with serious non-AIDS conditions or death were studied using Cox regression. Hazard ratios (HR) adjusted for age, gender, study, and regression dilution bias (due to within-person biomarker variability) were used to predict risk reductions in serious non-AIDS conditions or death associated with lower “usual” levels of IL-6 and D-dimer.</p><p>Results</p><p>Over 4.9 years of mean follow-up, 260 of the 3766 participants experienced serious non-AIDS conditions or death. IL-6, D-dimer and hsCRP were each individually associated with risk of serious non-AIDS conditions or death, HR = 1.45 (95% CI: 1.30 to 1.63), 1.28 (95% CI: 1.14 to 1.44), and 1.17 (95% CI: 1.09 to 1.26) per 2x higher biomarker levels, respectively. In joint models, IL-6 and D-dimer were independently associated with serious non-AIDS conditions or death, with consistent results across the 3 cohorts and across serious non-AIDS event types. The association of IL-6 and D-dimer with serious non-AIDS conditions or death was graded and persisted throughout follow-up. For 25% lower “usual” IL-6 and D-dimer levels, the joint biomarker model estimates a 37% reduction (95% CI: 28 to 46%) in the risk of serious non-AIDS conditions or death if the relationship is causal.</p><p>Conclusions</p><p>Both IL-6 and D-dimer are independently associated with serious non-AIDS conditions or death among HIV-positive adults with suppressed virus. This suggests that treatments that reduce IL-6 and D-dimer levels might substantially decrease morbidity and mortality in patients on suppressive ART. Clinical trials are needed to test this hypothesis.</p></div

Baseline characteristics ^a.

<p>Baseline characteristics <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0155100#t001fn002" target="_blank">^a</a>.</p

Estimated risk reduction.

<p>Panel A: Contour plot of the estimated reduction in the risk of serious non-AIDS conditions or death (SNA/death) when “usual” (within-person long-term average) levels of IL-6 and/or D-dimer are decreased by 0–40%, possibly through an intervention. Solid lines show predicted risk reductions of 5%, 10%, etc. Panels B and C show the lower and upper 95% confidence limits, respectively. For a 25% reduction in IL-6 and D-dimer, the risk of SNA/death is predicted to decline by 37% (95% CI: 28 to 46%). <b><i>Footnotes</i>:</b> The reduction in the risk was estimated using Cox proportional hazards models, adjusted for regression dilution bias, and for age, sex, and study. Reliability coefficients for the regression dilution adjustment were estimated using longitudinal mixed models for biomarker data collected at baseline, years 1 and 3 for 235 participants on stable ART in the ESPRIT study. Abbreviations: CI = confidence interval; IL-6 = Interleukin-6.</p

Estimated hazard ratios (HR) for the composite endpoint of serious non-AIDS or death (SNA/death) and its components.

<p>Hazard ratios are estimated per 2x higher level of IL-6 and D-dimer, with 95% confidence intervals. Two times higher biomarker levels corresponds to 1 unit higher on the log₂ biomarker scale, and 0.49 units higher for the IL-6 & D-dimer score. Hazard ratios were estimated in proportional hazards models adjusted for age, sex and study. <b><i>Footnotes</i>:</b> Of the 144 deaths, 37 were due to non-AIDS cancer, 33 CVD, 11 non-cancer hepatic disease, 1 renal failure, 15 AIDS-related, 9 due to violence, accident or suicide, 38 due to other or unknown causes. Abbreviations: CI = confidence interval; CVD = cardiovascular disease (myocardial infarction, stroke, and death due to CVD); HR = hazard ratio.</p

Acute Log₁₀ Viral Load.

<p>The distribution of acute log₁₀ viral load values in vaccine and placebo groups. Solid lines correspond to observed means and dashed lines correspond to means estimated using the multiple imputation approach.</p

Post-Infection Magnitude of CD8+ T-Cell Response.

<p>Magnitude of the post-infection CD8+ T-cell response measured by ICS, as quantified by the percentage of CD8+ T-cells producing IFN or IL-2 when stimulated with the vaccine-insert-matched peptide pools (Gag, Pol, and Nef) and other non-vaccine-insert peptide pools, for vaccine and placebo groups. Positive responses are indicated using closed red circles and negative responses using open blue circles. The p-values refer to tests comparing response magnitudes between the vaccine and placebo positive responders.</p

Post-Infection Breadth of T-Cell Response.

<p>Breath of the post-infection T-cell response as measured by IFNγ ELISpot, as quantified by the number of reactive 15-mers, for the vaccine (grey) and placebo (black) groups. The distribution of breadth is shown for all proteins in aggregate; for Gag, Pol, and Nef combined; for other non-insert proteins; and for Gag, Pol, and Nef individually. The p-values refer to tests comparing breadth between vaccine and placebo groups.</p