Estimation of a partially linear additive model for data from an outcome-dependent sampling design with a continuous outcome

Outcome-dependent sampling (ODS) designs have been well recognized as a cost-effective way to enhance study efficiency in both statistical literature and biomedical and epidemiologic studies. A partially linear additive model (PLAM) is widely applied in real problems because it allows for a flexible specification of the dependence of the response on some covariates in a linear fashion and other covariates in a nonlinear non-parametric fashion. Motivated by an epidemiological study investigating the effect of prenatal polychlorinated biphenyls exposure on children's intelligence quotient (IQ) at age 7 years, we propose a PLAM in this article to investigate a more flexible non-parametric inference on the relationships among the response and covariates under the ODS scheme. We propose the estimation method and establish the asymptotic properties of the proposed estimator. Simulation studies are conducted to show the improved efficiency of the proposed ODS estimator for PLAM compared with that from a traditional simple random sampling design with the same sample size. The data of the above-mentioned study is analyzed to illustrate the proposed method

A Direct Approach to Simultaneous Tests of Superiority and Noninferiority with Multiple Endpoints

Simultaneous tests of superiority and non-inferiority hypotheses on multiple endpoints are often performed in clinical trials to demonstrate that a new treatment is superior over a control on at least one endpoint and non-inferior on the remaining endpoints. Existing methods tackle this problem by testing the superiority and non-inferiority hypotheses separately and control the Type I error rate each at $\alpha$ level. In this paper we propose a unified approach to testing the superiority and non-inferiority hypotheses simultaneously. The proposed approach is based on the UI-IU test and the least favorable configurations of the combined superiority and non-inferiority hypotheses, which leads to the solution of an adjusted significance level $\alpha'$ for marginal tests that controls the overall Type I error rate at pre-defined $\alpha$. Simulations show that the proposed approach maintains a higher power than existing methods in the settings under investigation. Since the adjusted significance level $\alpha'$ is obtained by controlling the Type I error rate at $\alpha$, one can easily construct the exact $(1 - \alpha)\%$ simultaneous confidence intervals for treatment effects on all endpoints. The proposed approach is illustrated with two real examples

Partial linear inference for a 2-stage outcome-dependent sampling design with a continuous outcome

The outcome-dependent sampling (ODS) design, which allows observation of exposure variable to depend on the outcome, has been shown to be cost efficient. In this article, we propose a new statistical inference method, an estimated penalized likelihood method, for a partial linear model in the setting of a 2-stage ODS with a continuous outcome. We develop the asymptotic properties and conduct simulation studies to demonstrate the performance of the proposed estimator. A real environmental study data set is used to illustrate the proposed method

Robust empirical likelihood inference for generalized partial linear models with longitudinal data

AbstractIn this paper, we propose a robust empirical likelihood (REL) inference for the parametric component in a generalized partial linear model (GPLM) with longitudinal data. We make use of bounded scores and leverage-based weights in the auxiliary random vectors to achieve robustness against outliers in both the response and covariates. Simulation studies demonstrate the good performance of our proposed REL method, which is more accurate and efficient than the robust generalized estimating equation (GEE) method (X. He, W.K. Fung, Z.Y. Zhu, Robust estimation in generalized partial linear models for clustered data, Journal of the American Statistical Association 100 (2005) 1176–1184). The proposed robust method is also illustrated by analyzing a real data set

A Partial Linear Model in the Outcome-Dependent Sampling Setting to Evaluate the Effect of Prenatal PCB Exposure on Cognitive Function in Children

Outcome-dependent sampling (ODS) has been widely used in biomedical studies because it is a cost effective way to improve study efficiency. However, in the setting of a continuous outcome, the representation of the exposure variable has been limited to the framework of linear models, due to the challenge in terms of both theory and computation. Partial linear models (PLM) are a powerful inference tool to nonparametrically model the relation between an outcome and the exposure variable. In this article, we consider a case study of a partial linear model for data from an ODS design. We propose a semiparametric maximum likelihood method to make inferences with a PLM. We develop the asymptotic properties and conduct simulation studies to show that the proposed ODS estimator can produce a more efficient estimate than that from a traditional simple random sampling design with the same sample size. Using this newly developed method, we were able to explore an open question in epidemiology: whether in utero exposure to background levels of PCBs is associated with children’s intellectual impairment. Our model provides further insights into the relation between low-level PCB exposure and children’s cognitive function. The results shed new light on a body of inconsistent epidemiologic findings

A partially linear regression model for data from an outcome-dependent sampling design: Model for Data from an Outcome-dependent Sampling Design

The outcome dependent sampling scheme has been gaining attention in both the statistical literature and applied fields. Epidemiological and environmental researchers have been using it to select the observations for more powerful and cost-effective studies. Motivated by a study of the effect of in utero exposure to polychlorinated biphenyls on children’s IQ at age 7, in which the effect of an important confounding variable is nonlinear, we consider a semi-parametric regression model for data from an outcome-dependent sampling scheme where the relationship between the response and covariates is only partially parameterized. We propose a penalized spline maximum likelihood estimation (PSMLE) for inference on both the parametric and the nonparametric components and develop their asymptotic properties. Through simulation studies and an analysis of the IQ study, we compare the proposed estimator with several competing estimators. Practical considerations of implementing those estimators are discussed

Common Statistical Methods and Reporting of Results in Medical Research

Statistical analysis is critical in medical research. The objective of this article is to summarize the appropriate use and reporting of commonly used statistical methods in medical research, on the basis of existing statistical guidelines and the authors’ experience in reviewing manuscripts, to provide recommendations for statistical applications and reporting. </p

Risk Prediction of Second Primary Malignancies in Primary Early-Stage Ovarian Cancer Survivors: A SEER-Based National Population-Based Cohort Study

Purpose: This study aimed to characterize the clinical features of early-stage ovarian cancer (OC) survivors with second primary malignancies (SPMs) and provided a prediction tool for individualized risk of developing SPMs. Methods: Data were obtained from the Surveillance, Epidemiology and End Results (SEER) database during 1998–2013. Considering non-SPM death as a competing event, the Fine and Gray model and the corresponding nomogram were used to identify the risk factors for SPMs and predict the SPM probabilities after the initial OC diagnosis. The decision curve analysis (DCA) was performed to evaluate the clinical utility of our proposed model. Results: A total of 14,314 qualified patients were enrolled. The diagnosis rate and the cumulative incidence of SPMs were 7.9% and 13.6% [95% confidence interval (CI) = 13.5% to 13.6%], respectively, during the median follow-up of 8.6 years. The multivariable competing risk analysis suggested that older age at initial cancer diagnosis, white race, epithelial histologic subtypes of OC (serous, endometrioid, mucinous, and Brenner tumor), number of lymph nodes examined (<12), and radiotherapy were significantly associated with an elevated SPM risk. The DCA revealed that the net benefit obtained by our proposed model was higher than the all-screening or no-screening scenarios within a wide range of risk thresholds (1% to 23%). Conclusion: The competing risk nomogram can be potentially helpful for assisting physicians in identifying patients with different risks of SPMs and scheduling risk-adapted clinical management. More comprehensive data on treatment regimens and patient characteristics may help improve the predictability of the risk model for SPMs

Derivation and validation of a prognostic model for predicting in-hospital mortality in patients admitted with COVID-19 in Wuhan, China:the PLANS (platelet lymphocyte age neutrophil sex) model

Background Previous published prognostic models for COVID-19 patients have been suggested to be prone to bias due to unrepresentativeness of patient population, lack of external validation, inappropriate statistical analyses, or poor reporting. A high-quality and easy-to-use prognostic model to predict in-hospital mortality for COVID-19 patients could support physicians to make better clinical decisions. Methods Fine-Gray models were used to derive a prognostic model to predict in-hospital mortality (treating discharged alive from hospital as the competing event) in COVID-19 patients using two retrospective cohorts (n = 1008) in Wuhan, China from January 1 to February 10, 2020. The proposed model was internally evaluated by bootstrap approach and externally evaluated in an external cohort (n = 1031). Results The derivation cohort was a case-mix of mild-to-severe hospitalized COVID-19 patients (43.6% females, median age 55). The final model (PLANS), including five predictor variables of platelet count, lymphocyte count, age, neutrophil count, and sex, had an excellent predictive performance (optimism-adjusted C-index: 0.85, 95% CI: 0.83 to 0.87; averaged calibration slope: 0.95, 95% CI: 0.82 to 1.08). Internal validation showed little overfitting. External validation using an independent cohort (47.8% female, median age 63) demonstrated excellent predictive performance (C-index: 0.87, 95% CI: 0.85 to 0.89; calibration slope: 1.02, 95% CI: 0.92 to 1.12). The averaged predicted cumulative incidence curves were close to the observed cumulative incidence curves in patients with different risk profiles. Conclusions The PLANS model based on five routinely collected predictors would assist clinicians in better triaging patients and allocating healthcare resources to reduce COVID-19 fatality