Time-to-event endpoints are often used in clinical and epidemiological studies to evaluate disease association with hazardous exposures. In the statistical literature of time-to-event analysis, such association is usually measured by the hazard ratio in the proportional hazards model. In public health, it is also of important interest to assess the excess risk attributable to an exposure in a given population. In this article, we extend the notion of ‘population attributable fraction’ for the binary outcomes to the attributable risk function for the event times in prospective studies. A simple estimator of the time-varying attributable risk function is proposed under the proportional hazards model. Its inference procedures are established. Monte-Carlo simulation studies are conducted to evaluate its validity and performance. The proposed methodology is motivated and demonstrated by the data collected in a multicenter acquired immunodeficiency syndrome (AIDS) cohort study to estimate the attributable risk of human immunodeficiency virus type 1 (HIV-1) infections due to several potential risk factors.

Background: In sub-Saharan Africa (SSA), adolescent girls and young women (AGYW) ages 15 to 24 years represent <10% of the population yet account for 1 in 5 new HIV infections. Although oral pre-exposure prophylaxis (PrEP) with tenofovir disoproxil fumarate/emtricitabine (TDF/FTC) can be highly effective, low persistence in PrEP programs and poor adherence have limited its ability to reduce HIV incidence among women. Methods and findings: A total of 336 AGYW participating in the PEPFAR-funded DREAMS PrEP program in western Kenya were enrolled into a study of PrEP use conducted between 6/2019 to 1/2020. AGYW, who used daily oral TDF/FTC, completed interviews and provided dried blood spots (DBS) for measurement of tenofovir-diphosphate (TFV-DP) concentrations at enrollment and 3 months later, and 176/302 (58.3%, 95% confidence interval [95% CI 52.3 to 63.8]) met our definition of PrEP persistence: having expressed intention to use PrEP and attended both the second interview and an interim refill visit. Among AGYW with DBS taken at the second interview, only 9/197 (4.6%, [95% CI 1.6 to 7.5]) had protective TFV-DP levels (≥700 fmol/punch) and 163/197 (82.7%, [95% CI 77.5 to 88]) had levels consistent with no recent PrEP use (<10 fmol/punch). Perception of being at moderate-to-high risk for HIV if not taking PrEP was associated with persistence (adjusted odds ratio, 10.17 [95% CI 5.14 to 20.13], p < 0.001) in a model accounting for county of residence and variables that had p-value 90% indicated they were using PrEP to prevent HIV, although almost all had non-protective TFV-DP levels. Limitations included short study duration and inclusion of only DREAMS participants. Conclusions: Many AGYW persisted in the PrEP program without taking PrEP frequently enough to receive benefit. Notably, AGYW who persisted had a higher self-perceived risk of HIV infection. These AGYW may be optimal candidates for long-acting PrEP.

Regression is a useful tool for studying association between an outcome variable and its covariates. In a classical linear regression model, the outcome's expectation is usually a function of the covariates and some regression parameters, and the underlying distribution is often normal. In this article we propose a new class of additive expectancy regression models in which the outcomes tend to be positively skewed. In the new regression models, regression parameters are practically meaningful and also useful with inferences on the means of skewed outcomes. Parametric and semiparametric methods are developed for model estimation and inferences. Model-based prediction and model adequacy assessment are discussed. The proposed methodologies are demonstrated by two real data analyses.