A central limit theorem for the Benjamini-Hochberg false discovery proportion under a factor model

The Benjamini-Hochberg (BH) procedure remains widely popular despite having limited theoretical guarantees in the commonly encountered scenario of correlated test statistics. Of particular concern is the possibility that the method could exhibit bursty behavior, meaning that it might typically yield no false discoveries while occasionally yielding both a large number of false discoveries and a false discovery proportion (FDP) that far exceeds its own well controlled mean. In this paper, we investigate which test statistic correlation structures lead to bursty behavior and which ones lead to well controlled FDPs. To this end, we develop a central limit theorem for the FDP in a multiple testing setup where the test statistic correlations can be either short-range or long-range as well as either weak or strong. The theorem and our simulations from a data-driven factor model suggest that the BH procedure exhibits severe burstiness when the test statistics have many strong, long-range correlations, but does not otherwise.Comment: Main changes in version 2: i) restated Corollary 1 in a way that is clearer and easier to use, ii) removed a regularity condition for our theorems (in particular we removed Condition 2 from version 1), and iii) we added a couple of remarks (namely, Remark 1 and 6 in version 2). Throughout the text we also fixed typos, improved clarity, and added a some additional commentary and reference

Tie-breaker designs provide more efficient kernel estimates than regression discontinuity designs

Tie-breaker experimental designs are hybrids of Randomized Controlled Trials (RCTs) and Regression Discontinuity Designs (RDDs) in which subjects with moderate scores are placed in an RCT while subjects with extreme scores are deterministically assigned to the treatment or control group. The tie-breaker design (TBD) has practical advantages over the RCT in settings where it is unfair or uneconomical to deny the treatment to the most deserving recipients. Meanwhile, the TBD has statistical benefits due to randomization over the RDD. In this paper we discuss and quantify the statistical benefits of the TBD compared to the RDD. If the goal is estimation of the average treatment effect or the treatment at more than one score value, the statistical benefits of using a TBD over an RDD are apparent. If the goal is estimation of the average treatment effect at merely one score value, which is typically done by fitting local linear regressions, about 2.8 times more subjects are needed for an RDD in order to achieve the same asymptotic mean squared error. We further demonstrate using both theoretical results and simulations from the Angrist and Lavy (1999) classroom size dataset, that larger experimental radii choices for the TBD lead to greater statistical efficiency.Comment: This version is quite different than version 1. We have added an analysis when the bandwidth is shrinking with the sample size. We have also added a discussion of other statistical advantages of a TBD compared to an RD

Biases in estimates of air pollution impacts: the role of omitted variables and measurement errors

Observational studies often use linear regression to assess the effect of ambient air pollution on outcomes of interest, such as human health outcomes or crop yields. Yet pollution datasets are typically noisy and include only a subset of potentially relevant pollutants, giving rise to both measurement error bias (MEB) and omitted variable bias (OVB). While it is well understood that these biases exist, less is understood about whether these biases tend to be positive or negative, even though it is sometimes falsely claimed that measurement error simply biases regression coefficient estimates towards zero. In this paper, we show that more can be said about the direction of these biases under the realistic assumptions that the concentrations of different types of air pollutants are positively correlated with each other and that each type of pollutant has a nonpositive association with the outcome variable. In particular, we demonstrate both theoretically and using simulations that under these two assumptions, the OVB will typically be negative and that more often than not the MEB for null pollutants or for pollutants that are perfectly measured will be negative. We also provide precise conditions, which are consistent with the assumptions, under which we prove that the biases are guaranteed to be negative. While the discussion in this paper is motivated by studies assessing the effect of air pollutants on crop yields, the findings are also relevant to regression-based studies assessing the effect of air pollutants on human health outcomes

Season of Birth and Dopamine Receptor Gene Associations with Impulsivity, Sensation Seeking and Reproductive Behaviors

Season of birth (SOB) has been associated with many physiological and psychological traits including novelty seeking and sensation seeking. Similar traits have been associated with genetic polymorphisms in the dopamine system. SOB and dopamine receptor genetic polymorphisms may independently and interactively influence similar behaviors through their common effects on the dopaminergic system.Based on a sample of 195 subjects, we examined whether SOB was associated with impulsivity, sensation seeking and reproductive behaviors. Additionally we examined potential interactions of dopamine receptor genes with SOB for the same set of traits. Phenotypes were evaluated using the Sociosexual Orientation Inventory, the Barratt Impulsivity Scale, the Eysenck Impulsivity Questionnaire, the Sensation Seeking Scale, and the Delay Discounting Task. Subjects were also asked about their age at first sex as well as their desired age at the birth of their first child. The dopamine gene polymorphisms examined were Dopamine Receptor D2 (DRD2) TaqI A and D4 (DRD4) 48 bp VNTR. Primary analyses included factorial genderxSOB ANOVAs or binary logistic regression models for each dependent trait. Secondary analysis extended the factorial models by also including DRD2 and DRD4 genotypes as independent variables. Winter-born males were more sensation seeking than non-winter born males. In factorial models including both genotype and season of birth as variables, two previously unobserved effects were discovered: (1) a SOBxDRD4 interaction effect on venturesomeness and (2) a DRD2xDRD4 interaction effect on sensation seeking.These results are consistent with past findings that SOB is related to sensation seeking. Additionally, these results provide tentative support for the hypothesis that SOB modifies the behavioral expression of dopaminergic genetic polymorphism. These findings suggest that SOB should be included in future studies of risky behaviors and behavioral genetic studies of the dopamine system

31st Annual Meeting and Associated Programs of the Society for Immunotherapy of Cancer (SITC 2016) : part two

Background The immunological escape of tumors represents one of the main ob- stacles to the treatment of malignancies. The blockade of PD-1 or CTLA-4 receptors represented a milestone in the history of immunotherapy. However, immune checkpoint inhibitors seem to be effective in specific cohorts of patients. It has been proposed that their efficacy relies on the presence of an immunological response. Thus, we hypothesized that disruption of the PD-L1/PD-1 axis would synergize with our oncolytic vaccine platform PeptiCRAd. Methods We used murine B16OVA in vivo tumor models and flow cytometry analysis to investigate the immunological background. Results First, we found that high-burden B16OVA tumors were refractory to combination immunotherapy. However, with a more aggressive schedule, tumors with a lower burden were more susceptible to the combination of PeptiCRAd and PD-L1 blockade. The therapy signifi- cantly increased the median survival of mice (Fig. 7). Interestingly, the reduced growth of contralaterally injected B16F10 cells sug- gested the presence of a long lasting immunological memory also against non-targeted antigens. Concerning the functional state of tumor infiltrating lymphocytes (TILs), we found that all the immune therapies would enhance the percentage of activated (PD-1pos TIM- 3neg) T lymphocytes and reduce the amount of exhausted (PD-1pos TIM-3pos) cells compared to placebo. As expected, we found that PeptiCRAd monotherapy could increase the number of antigen spe- cific CD8+ T cells compared to other treatments. However, only the combination with PD-L1 blockade could significantly increase the ra- tio between activated and exhausted pentamer positive cells (p= 0.0058), suggesting that by disrupting the PD-1/PD-L1 axis we could decrease the amount of dysfunctional antigen specific T cells. We ob- served that the anatomical location deeply influenced the state of CD4+ and CD8+ T lymphocytes. In fact, TIM-3 expression was in- creased by 2 fold on TILs compared to splenic and lymphoid T cells. In the CD8+ compartment, the expression of PD-1 on the surface seemed to be restricted to the tumor micro-environment, while CD4 + T cells had a high expression of PD-1 also in lymphoid organs. Interestingly, we found that the levels of PD-1 were significantly higher on CD8+ T cells than on CD4+ T cells into the tumor micro- environment (p < 0.0001). Conclusions In conclusion, we demonstrated that the efficacy of immune check- point inhibitors might be strongly enhanced by their combination with cancer vaccines. PeptiCRAd was able to increase the number of antigen-specific T cells and PD-L1 blockade prevented their exhaus- tion, resulting in long-lasting immunological memory and increased median survival