ROC curves of cross-validated prediction for the super learner (SL) and the logistic step-wise regression (SW), for different time intervals.

<p>ROC curves of cross-validated prediction for the super learner (SL) and the logistic step-wise regression (SW), for different time intervals.</p

Directed acyclic graph, the arrows in blue and red denote the relations that confound the causal effect of <i>L</i>₂₁ on <i>Y</i>₂.

<p>Directed acyclic graph, the arrows in blue and red denote the relations that confound the causal effect of <i>L</i>₂₁ on <i>Y</i>₂.</p

Variable Importance and Prediction Methods for Longitudinal Problems with Missing Variables

<div><p>We present prediction and variable importance (VIM) methods for longitudinal data sets containing continuous and binary exposures subject to missingness. We demonstrate the use of these methods for prognosis of medical outcomes of severe trauma patients, a field in which current medical practice involves rules of thumb and scoring methods that only use a few variables and ignore the dynamic and high-dimensional nature of trauma recovery. Well-principled prediction and VIM methods can provide a tool to make care decisions informed by the high-dimensional patient’s physiological and clinical history. Our VIM parameters are analogous to slope coefficients in adjusted regressions, but are not dependent on a specific statistical model, nor require a certain functional form of the prediction regression to be estimated. In addition, they can be causally interpreted under causal and statistical assumptions as the expected outcome under time-specific clinical interventions, related to changes in the mean of the outcome if each individual experiences a specified change in the variable (keeping other variables in the model fixed). Better yet, the targeted MLE used is doubly robust and locally efficient. Because the proposed VIM does not constrain the prediction model fit, we use a very flexible ensemble learner (the SuperLearner), which returns a linear combination of a list of user-given algorithms. Not only is such a prediction algorithm intuitive appealing, it has theoretical justification as being asymptotically equivalent to the oracle selector. The results of the analysis show effects whose size and significance would have been not been found using a parametric approach (such as stepwise regression or LASSO). In addition, the procedure is even more compelling as the predictor on which it is based showed significant improvements in cross-validated fit, for instance area under the curve (AUC) for a receiver-operator curve (ROC). Thus, given that 1) our VIM applies to any model fitting procedure, 2) under assumptions has meaningful clinical (causal) interpretations and 3) has asymptotic (influence-curve) based robust inference, it provides a compelling alternative to existing methods for estimating variable importance in high-dimensional clinical (or other) data.</p></div

Additional file 1: Table S1. of Risk of cardiovascular events from current, recent, and cumulative exposure to abacavir among persons living with HIV who were receiving antiretroviral therapy in the United States: a cohort study

ICD-9-CM and CPT codes for defining various covariates and outcomes. Table S2. Age-specific incidence rate (IR) of acute myocardial infarction (AMI) among persons living with HIV receiving antiretroviral therapy. Table S3. Factors associated with initiation of abacavir among persons living with HIV, by pooled logistic regression. Table S4 The influence of various risk factors on the development of CVD among persons living with HIV receiving anti-retroviral therapy. Table S5 Risk of CVD from current exposure to abacavir in sub-groups of variables at baseline (test of interactions). Table S6 Risk of cardiovascular disease from exposure to abacavir among persons living with HIV free of heart diseasea or substance or alcohol abuse at baseline. Appendix 1. Detailed approach to developing marginal structural models. (DOCX 58 kb

Repeated <em>Schistosoma japonicum</em> Infection Following Treatment in Two Cohorts: Evidence for Host Susceptibility to Helminthiasis?

<div><p>Background</p><p>In light of multinational efforts to reduce helminthiasis, we evaluated whether there exist high-risk subpopulations for helminth infection. Such individuals are not only at risk of morbidity, but may be important parasite reservoirs and appropriate targets for disease control interventions.</p> <p>Methods/Principal Findings</p><p>We followed two longitudinal cohorts in Sichuan, China to determine whether there exist persistent human reservoirs for the water-borne helminth, <i>Schistosoma japonicum</i>, in areas where treatment is ongoing. Participants were tested for <i>S. japonicum</i> infection at enrollment and two follow-up points. All infections were promptly treated with praziquantel. We estimated the ratio of the observed to expected proportion of the population with two consecutive infections at follow-up. The expected proportion was estimated using a prevalence-based model and, as highly exposed individuals may be most likely to be repeatedly infected, a second model that accounted for exposure using a data adaptive, machine learning algorithm. Using the prevalence-based model, there were 1.5 and 5.8 times more individuals with two consecutive infections than expected in cohorts 1 and 2, respectively (p<0.001 in both cohorts). When we accounted for exposure, the ratio was 1.3 (p = 0.013) and 2.1 (p<0.001) in cohorts 1 and 2, respectively.</p> <p>Conclusions/Significance</p><p>We found clustering of infections within a limited number of hosts that was not fully explained by host exposure. This suggests some hosts may be particularly susceptible to <i>S. japonicum</i> infection, or that uncured infections persist despite treatment. We propose an explanatory model that suggests that as cercarial exposure declines, so too does the size of the vulnerable subpopulation. In low-prevalence settings, interventions targeting individuals with a history of <i>S. japonicum</i> infection may efficiently advance disease control efforts.</p> </div

Coefficients in the Super Learner.

<p>Coefficients in the Super Learner.</p

The marginal distributions of exposure and host susceptibility, together with contours of their joint distribution.

<p>The y-axis shows exposure, <i>E</i>, and the x-axis shows host susceptibility, <i>α</i>. The line <i>w_T = αE</i> describes the threshold of detectable infections: the minimum worm burden in an individual detectable by currently available assays. The shaded area depicts those combinations of <i>α</i> and <i>E</i> producing infection intensities above this lower limit of detection, w_t. The fraction of the population susceptible to infection at or above this threshold is that lying to the right of the line <i>α</i> = <i>α</i>*.</p

Description of the two cohorts at enrollment (<i>T₀</i>).

*<p>Cohort 1 is composed of 424 residents from 10 villages in Xichang County, Sichuan, China where schistosomiasis was endemic, monitored from 2000 to 2006.</p>†<p>Cohort 2 is composed of 400 residents from 27 villages in two counties in Sichuan, China where schistosomiasis reemerged following reduction of <i>S. japonicum</i> infection prevalence below 1%, monitored from 2007 to 2010.</p>‡<p>Prevalence and infection intensity estimates include all participants in village-wide infection surveys conducted at cohort enrollment: 1,801 individuals in 10 villages in cohort 1, 1,608 individuals in 27 villages in cohort 2.</p>**<p>Participants were asked about water contact behaviors from the start of the rice planting season. In Xichang County (from which cohort 1 participants were drawn) rice planting begins in April, whereas in the two reemerging counties (from which cohort 2 participants were drawn) rice planting begins in May.</p

Distribution of incident <i>S. japonicum</i> infections by age in cohorts 1 (top) and 2 (bottom).

<p>Incident <i>S. japonicum</i> infections were measured at two follow-up points (2002 and 2006 in cohort 1, 2008 and 2010 in cohort 2). All participants were tested for <i>S. japonicum</i> at enrollment (2000 in cohort 1, 2007 in cohort 2) and all infections were promptly treated with praziquantel.</p

<i>S. japonicum</i> infection prevalence and intensity at follow-up.

*<p>Cohort 1 is composed of people from 10 villages where schistosomiasis is endemic. Participants were tested for <i>S. japonicum</i> infection in 2000 (<i>T₀</i>), 2002 (<i>T₁</i>) and 2006 (<i>T₂</i>).</p>†<p>Cohort 2 is composed of people from 27 villages in two counties where schistosomiasis reemerged following reduction of <i>S. japonicum</i> infection prevalence below 1%. Participants were tested for <i>S. japonicum</i> infection in 2007 (<i>T₀</i>), 2008 (<i>T₁</i>) and 2010 (<i>T₂</i>).</p>‡<p>Infection prevalence and intensity were estimated for the source population, accounting for the stratified sampling used in enrolling cohort participants. Each individual in the cohort was assigned a weight equal to the inverse probability of being sampled.</p