Semiparametric minimax rates

We consider the minimax rate of testing (or estimation) of nonlinear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular, if the semiparametric model is indexed by several infinite-dimensional parameters. To cover these examples we extend the approach of [1], which is based on comparing a “true distribution” to a convex mixture of perturbed distributions to a comparison of two convex mixtures. The first mixture is obtained by perturbing a first parameter of the model, and the second by perturbing in addition a second parameter. We apply the new result to two examples of semiparametric functionals:the estimation of a mean response when response data are missing at random, and the estimation of an expected conditional covariance functional

Instrumental variable approaches to identifying the causal effect of educational attainment on dementia risk

PURPOSE: Education is an established correlate of cognitive status in older adulthood, but whether expanding educational opportunities would improve cognitive functioning remains unclear given limitations of prior studies for causal inference. Therefore, we conducted instrumental variable (IV) analyses of the association between education and dementia risk, using for the first time in this area, genetic variants as instruments as well as state-level school policies. METHODS: IV analyses in the Health and Retirement Study cohort (1998-2010) used two sets of instruments: (1) a genetic risk score constructed from three single-nucleotide polymorphisms (SNPs; n = 7981); and (2) compulsory schooling laws (CSLs) and state school characteristics (term length, student teacher ratios, and expenditures; n = 10,955). RESULTS: Using the genetic risk score as an IV, there was a 1.1% reduction in dementia risk per year of schooling (95% confidence interval, -2.4 to 0.02). Leveraging compulsory schooling laws and state school characteristics as IVs, there was a substantially larger protective effect (-9.5%; 95% confidence interval, -14.8 to -4.2). Analyses evaluating the plausibility of the IV assumptions indicated estimates derived from analyses relying on CSLs provide the best estimates of the causal effect of education. CONCLUSIONS: IV analyses suggest education is protective against risk of dementia in older adulthood

Minimax estimation of a functional on a structured high-dimensional model

Analysis and Stochastic

Bachelors, Divorcees, and Widowers: Does Marriage Protect Men from Type 2 Diabetes?

While research has suggested that being married may confer a health advantage, few studies to date have investigated the role of marital status in the development of type 2 diabetes. We examined whether men who are not married have increased risk of incident type 2 diabetes in the Health Professionals Follow-up Study. Men (n = 41,378) who were free of T2D in 1986, were followed for ≤22 years with biennial reports of T2D, marital status and covariates. Cox proportional hazard models were used to compare risk of incident T2D by marital status (married vs unmarried and married vs never married, divorced/separated, or widowed). There were 2,952 cases of incident T2D. Compared to married men, unmarried men had a 16% higher risk of developing T2D (95%CI:1.04,1.30), adjusting for age, family history of diabetes, ethnicity, lifestyle and body mass index (BMI). Relative risks (RR) for developing T2D differed for divorced/separated (1.09 [95%CI: 0.94,1.27]), widowed (1.29 [95%CI:1.06,1.57]), and never married (1.17 [95%CI:0.91,1.52]) after adjusting for age, family history of diabetes and ethnicity. Adjusting for lifestyle and BMI, the RR for T2D associated with widowhood was no longer significant (RR:1.16 [95%CI:0.95,1.41]). When allowing for a 2-year lag period between marital status and disease, RRs of T2D for widowers were augmented and borderline significant (RR:1.24 [95%CI:1.00,1.54]) after full adjustment. In conclusion, not being married, and more specifically, widowhood was more consistently associated with an increased risk of type 2 diabetes in men and this may be mediated, in part, through unfavorable changes in lifestyle, diet and adiposity

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

Superior Effectiveness of Zidovudine Compared With Tenofovir When Combined With Nevirapine-based Antiretroviral Therapy in a Large Nigerian Cohort

Background. Despite sparse efficacy data, tenofovir–emtricitabine or tenofovir–lamivudine plus nevirapine is used in many resource-constrained settings. Methods. This retrospective cohort study included patients initiating nevirapine-based antiretroviral therapy (ART) with either tenofovir–emtricitabine or lamivudine (tenofovir group) or zidovudine–lamivudine (zidovudine group). Clinical, virologic, and immunologic evaluations were performed at baseline and every 6 months. Virologic failure was defined as 2 consecutive human immunodeficiency virus (HIV)-RNA values >1000 copies/mL. Patients were included from ART initiation until time of failure, regimen switch, discontinuation, or last HIV-RNA measurement. Cox proportional hazards regression was used to model factors influencing time to failure. Bias due to dependent censoring was investigated via inverse probability weighted pooled logistic regression. Results. A total of 5547 patients were evaluated; 1484 (26.8%) were in the tenofovir group and 4063 (73.2%) were in the zidovudine group. In the adjusted model, tenofovir regimen (hazard ratio [HR], 1.47; 95% confidence interval [CI], 1.21–1.79) and higher baseline log10 HIV-RNA (HR, 1.15; 95% CI, 1.03–1.28) were associated with virologic failure. Higher baseline log10 CD4+ cell count (HR, 0.50; 95% CI, .40–.63) and increasing age (HR, 0.98; 95% CI, .97–.99) decreased the risk of virologic failure. Inverse probability weighting results were consistent with the primary analysis. Conclusions. Compared with zidovudine–lamivudine, the use of tenofovir–lamivudine or emtricitabine in combination with nevirapine was a strong predictor of virologic failure in our cohort, which was not explained by other risk factors or criteria for regimen selection

Prostate involvement during sexually transmitted infections as measured by prostate-specific antigen concentration

Background:We investigated prostate involvement during sexually transmitted infections by measuring serum prostate-specific antigen (PSA) as a marker of prostate infection, inflammation, and/or cell damage in young, male US military members.Methods:We measured PSA before and during infection for 299 chlamydia, 112 gonorrhoea, and 59 non-chlamydial, non-gonococcal urethritis (NCNGU) cases, and 256 controls.Results:Chlamydia and gonorrhoea, but not NCNGU, cases were more likely to have a large rise (⩾40%) in PSA than controls (33.6%, 19.1%, and 8.2% vs 8.8%, P<0.0001, 0.021, and 0.92, respectively).Conclusion:Chlamydia and gonorrhoea may infect the prostate of some infected men

Modelling imperfect adherence to HIV induction therapy

Abstract Background Induction-maintenance therapy is a treatment regime where patients are prescribed an intense course of treatment for a short period of time (the induction phase), followed by a simplified long-term regimen (maintenance). Since induction therapy has a significantly higher chance of pill fatigue than maintenance therapy, patients might take drug holidays during this period. Without guidance, patients who choose to stop therapy will each be making individual decisions, with no scientific basis. Methods We use mathematical modelling to investigate the effect of imperfect adherence during the inductive phase. We address the following research questions: 1. Can we theoretically determine the maximal length of a possible drug holiday and the minimal number of doses that must subsequently be taken while still avoiding resistance? 2. How many drug holidays can be taken during the induction phase? Results For a 180 day therapeutic program, a patient can take several drug holidays, but then has to follow each drug holiday with a strict, but fairly straightforward, drug-taking regimen. Since the results are dependent upon the drug regimen, we calculated the length and number of drug holidays for all fifteen protease-sparing triple-drug cocktails that have been approved by the US Food and Drug Administration. Conclusions Induction therapy with partial adherence is tolerable, but the outcome depends on the drug cocktail. Our theoretical predictions are in line with recent results from pilot studies of short-cycle treatment interruption strategies and may be useful in guiding the design of future clinical trials

Proceedings of the second international molecular pathological epidemiology (MPE) meeting

Disease classification system increasingly incorporates information on pathogenic mechanisms to predict clinical outcomes and response to therapy and intervention. Technological advancements to interrogate omics (genomics, epigenomics, transcriptomics, proteomics, metabolomics, metagenomics, interactomics, etc.) provide widely-open opportunities in population-based research. Molecular pathological epidemiology (MPE) represents integrative science of molecular pathology and epidemiology. This unified paradigm requires multidisciplinary collaboration between pathology, epidemiology, biostatistics, bioinformatics, and computational biology. Integration of these fields enables better understanding of etiologic heterogeneity, disease continuum, causal inference, and the impact of environment, diet, lifestyle, host factors (including genetics and immunity), and their interactions on disease evolution. Hence, the Second International MPE Meeting was held in Boston in December 2014, with aims to: (1) develop conceptual and practical frameworks; (2) cultivate and expand opportunities; (3) address challenges; and (4) initiate the effort of specifying guidelines for MPE. The meeting mainly consisted of presentations of method developments and recent data in various malignant neoplasms and tumors (breast, prostate, ovarian and colorectal cancers, renal cell carcinoma, lymphoma, and leukemia), followed by open discussion sessions on challenges and future plans. In particular, we recognized need for efforts to further develop statistical methodologies. This meeting provided an unprecedented opportunity for interdisciplinary collaboration, consistent with the purposes of the BD2K (Big Data to Knowledge), GAME-ON (Genetic Associations and Mechanisms in Oncology), and Precision Medicine Initiatives of the U.S.A. National Institute of Health. The MPE Meeting Series can help advance transdisciplinary population science, and optimize training and education systems for 21st century medicine and public health

Informed Conditioning on Clinical Covariates Increases Power in Case-Control Association Studies

Genetic case-control association studies often include data on clinical covariates, such as body mass index (BMI), smoking status, or age, that may modify the underlying genetic risk of case or control samples. For example, in type 2 diabetes, odds ratios for established variants estimated from low–BMI cases are larger than those estimated from high–BMI cases. An unanswered question is how to use this information to maximize statistical power in case-control studies that ascertain individuals on the basis of phenotype (case-control ascertainment) or phenotype and clinical covariates (case-control-covariate ascertainment). While current approaches improve power in studies with random ascertainment, they often lose power under case-control ascertainment and fail to capture available power increases under case-control-covariate ascertainment. We show that an informed conditioning approach, based on the liability threshold model with parameters informed by external epidemiological information, fully accounts for disease prevalence and non-random ascertainment of phenotype as well as covariates and provides a substantial increase in power while maintaining a properly controlled false-positive rate. Our method outperforms standard case-control association tests with or without covariates, tests of gene x covariate interaction, and previously proposed tests for dealing with covariates in ascertained data, with especially large improvements in the case of case-control-covariate ascertainment. We investigate empirical case-control studies of type 2 diabetes, prostate cancer, lung cancer, breast cancer, rheumatoid arthritis, age-related macular degeneration, and end-stage kidney disease over a total of 89,726 samples. In these datasets, informed conditioning outperforms logistic regression for 115 of the 157 known associated variants investigated (P-value = 1×10−9). The improvement varied across diseases with a 16% median increase in χ2 test statistics and a commensurate increase in power. This suggests that applying our method to existing and future association studies of these diseases may identify novel disease loci