Motivated by the study of singular values of random rectangular matrices, we define and study the rectangular additive convolution of polynomials with nonnegative real roots. Our definition directly generalizes the asymmetric additive convolution introduced by Marcus, Spielman and Srivastava (2015), and our main theorem gives the corresponding generalization of the bound on the largest root from that paper. The main tool used in the analysis is a differential operator derived from the "rectangular Cauchy transform" introduced by Benaych-Georges (2009). The proof is inductive, with the base case requiring a new nonasymptotic bound on the Cauchy transform of Gegenbauer polynomials which may be of independent interest.

Mathematics Subject Classifications: 26C10, 33C45

Background: Previous studies established that unemployment is associated with poorer self-reported physical health quality of life among people living with HIV/AIDS (PLHA). The present cross-sectional study tested a Social Action Theory model in which difficulties with self-regulation mediate the association of perceived barriers to employment with poorer physical health quality of life.

Methods: 108 PLHA from a vocational rehabilitation program in San Francisco were enrolled from December of 2011 to January of 2012. Hierarchical linear regression was applied to examine whether difficulties with self-regulation mediated the association between perceived barriers to employment and poorer physical health quality of life.

Results: PLHA with income less than $12,000 per year reported greater perceived barriers to employment. Perceived personal, career, and job barriers to employment were associated with self-regulation difficulties (e.g., lower coping self-efficacy). Perceived personal and career barriers were associated with poorer physical health quality of life. Lower coping self-efficacy partially mediated the associations of perceived personal barriers to employment (Sobel test Z = -2.25, p < .05) and perceived career barriers to employment (Sobel test Z = -2.33, p < .05) with poorer physical health quality of life.

Conclusion: PLHA with greater perceived barriers to employment report poorer physical health quality of life. Clinical research is needed to examine if vocational rehabilitation and interventions targeting self-regulation processes improve physical health quality of life among PLHA.

Introduction

To inform the optimal implementation of HIV pre-exposure prophylaxis (PrEP), we conducted three studies that evaluated serodisclosure, identified correlates of PrEP disengagement, and characterized the PrEP cascade of care.

Methods

Study 1 examined the association of PrEP use with participant non-disclosure and lack of knowledge of partner HIV status in the iPrEx Open Label Extension (OLE). Study 2 examined the effects of stimulant use and binge drinking (i.e., ≥5 drinks on one occasion) on PrEP disengagement in a nested case-cohort in OLE. PrEP disengagement was defined as failure to show for a follow-up visit or tenofovir drug levels <700fmol/punch. Study 3 characterized the PrEP cascade (i.e., seeking services, initiating PrEP, and retention in care) and identified predictors of non-retention among those who started PrEP in a clinic-based cohort of men who have sex with men in San Francisco.

Results

We analyzed data from 1,184 participants in Study 1. PrEP use was not significantly associated with non-disclosure or lack of knowledge of partner status in adjusted analyses (p-values≥.16). However, relationship characteristics were significantly associated with both outcomes. Of the 330 MSM and transgender women included in Study 2, 16% used stimulants and 22% reported binge drinking in the previous three months. Stimulant users had more than 5-fold greater odds of PrEP disengagement (adjusted odds ratio [aOR]=5.24, 95% CI [1.64-16.76]). Binge drinking was not significantly associated with PrEP disengagement after adjusting for stimulant use and baseline confounders (aOR=0.78 [0.33-1.88]). Of the 344 men who sought PrEP services in Study 3, 268 (78%) initiated PrEP. Cost was the most commonly cited reason for not starting. Among patients who initiated PrEP, cumulative incidence of non-retention at 13 months was 38%. Men with an STI diagnosis at enrollment had a 79% greater rate of non-retention (adjusted hazard ratio [aHR]=1.79 [1.06-3.01]).

Conclusion

We found no evidence to suggest that PrEP use is associated with non-disclosure or not knowing partner status. Comprehensive prevention approaches that enhance uptake, reduce stimulant use, and support PrEP adherence and persistence are needed to address the heightened risk of HIV infection of those who use stimulants and those with STI diagnoses.