Statistics

Multi-Arm Multi-Stage (MAMS) platform trials are an efficient tool for the comparison of several treatments. Suppose we wish to add a treatment to a trial already in progress, to access the benefits of a MAMS design. How should this be done? The MAMS framework requires pre-planned options for how the trial proceeds at each stage in order to control the family-wise error rate. Thus, it is difficult to make both planned and unplanned design modifications. The conditional error approach is a tool that allows unplanned design modifications while maintaining the overall error rate. In this work, we use the conditional error approach to allow adding new arms to a MAMS trial in progress. We demonstrate the principles of incorporating additional hypotheses into the testing structure. Using this framework, we show how to update the testing procedure for a MAMS trial in progress to incorporate additional treatment arms. Simulations illustrate the possible operating characteristics of such procedures using a fixed rule for how and when the design modification is made.

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory Phase III studies.

Environmental epidemiologists are increasingly interested in establishing causality between exposures and health outcomes. A popular model for causal inference is the Rubin Causal Model (RCM), which typically seeks to estimate the average difference in study units' potential outcomes. An important assumption under RCM is no interference; that is, the potential outcomes of one unit are not affected by the exposure status of other units. The no interference assumption is violated if we expect spillover or diffusion of exposure effects based on units' proximity to other units and several other causal estimands arise. Air pollution epidemiology typically violates this assumption when we expect upwind events to affect downwind or nearby locations. This paper adapts causal assumptions from social network research to address interference and allow estimation of both direct and spillover causal effects. We use propensity score-based methods to estimate these effects when considering the effects of the Environmental Protection Agency's 2005 nonattainment designations for particulate matter with aerodynamic diameter less than 2.5 micrograms per cubic meter (PM2.5) on lung cancer incidence using county-level data obtained from the Surveillance, Epidemiology, and End Results (SEER) Program. We compare these methods in a rigorous simulation study that considers both spatially autocorrelated variables, interference, and missing confounders. We find that pruning and matching based on the propensity score produces the highest probability coverage of the true causal effects and lower mean squared error. When applied to the research question, we found protective direct and spillover causal effects.

Many epidemiologic studies forgo probability sampling and turn to nonprobability volunteer-based samples because of cost, response burden, and invasiveness of biological samples. However, finite population inference is difficult to make from the nonprobability samples due to the lack of population representativeness. Aiming for making inferences at the population level using nonprobability samples, various inverse propensity score weighting (IPSW) methods have been studied with the propensity defined by the participation rate of population units in the nonprobability sample. In this paper, we propose an adjusted logistic propensity weighting (ALP) method to estimate the participation rates for nonprobability sample units. Compared to existing IPSW methods, the proposed ALP method is easy to implement by ready-to-use software while producing approximately unbiased estimators for population quantities regardless of the nonprobability sample rate. The efficiency of the ALP estimator can be further improved by scaling the survey sample weights in propensity estimation. Taylor linearization variance estimators are proposed for ALP estimators of finite population means that account for all sources of variability. The proposed ALP methods are evaluated numerically via simulation studies and empirically using the naïve unweighted National Health and Nutrition Examination Survey III sample, while taking the 1997 National Health Interview Survey as the reference, to estimate the 15-year mortality rates.

In addition to objective indicators (e.g. laboratory values), clinical data often contain subjective evaluations by experts (e.g. disease severity assessments). While objective indicators are more transparent and robust, the subjective evaluation contains a wealth of expert knowledge and intuition. In this work, we demonstrate the potential of pairwise ranking methods to align the subjective evaluation with objective indicators, creating a new score that combines their advantages and facilitates diagnosis. In a case study on patients at risk for developing Psoriatic Arthritis, we illustrate that the resulting score (1) increases classification accuracy when detecting disease presence/absence, (2) is sparse and (3) provides a nuanced assessment of severity for subsequent analysis.

We describe a supply chain optimization model deployed in an online fashion e-commerce company in India called Myntra. Our model is simple, elegant and easy to put into service. The model utilizes historic data and predicts the quantity of Stock Keeping Units (SKUs) to hold so that the metrics "Fulfilment Index" and "Utilization Index" are optimized. We present the mathematics central to our model as well as compare the performance of our model with baseline regression based solutions.

Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations where the system output is measured in its complete form. In reality, however, it may not be feasible to obtain the complete output measurement of a system, which results in observations that contain missing values. This paper introduces a general framework that integrates tensor regression with tensor completion and proposes an efficient optimization framework that alternates between two steps for parameter estimation. Through multiple simulations and a case study, we evaluate the performance of the proposed method. The results indicate the superiority of the proposed method in comparison to a benchmark.

Non-pharmaceutical interventions (NPIs) have been crucial in curbing COVID-19 in the United States (US). Consequently, relaxing NPIs through a phased re-opening of the US amid still-high levels of COVID-19 susceptibility could lead to new epidemic waves. This calls for a COVID-19 early warning system. Here we evaluate multiple digital data streams as early warning indicators of increasing or decreasing state-level US COVID-19 activity between January and June 2020. We estimate the timing of sharp changes in each data stream using a simple Bayesian model that calculates in near real-time the probability of exponential growth or decay. Analysis of COVID-19-related activity on social network microblogs, Internet searches, point-of-care medical software, and a metapopulation mechanistic model, as well as fever anomalies captured by smart thermometer networks, shows exponential growth roughly 2-3 weeks prior to comparable growth in confirmed COVID-19 cases and 3-4 weeks prior to comparable growth in COVID-19 deaths across the US over the last 6 months. We further observe exponential decay in confirmed cases and deaths 5-6 weeks after implementation of NPIs, as measured by anonymized and aggregated human mobility data from mobile phones. Finally, we propose a combined indicator for exponential growth in multiple data streams that may aid in developing an early warning system for future COVID-19 outbreaks. These efforts represent an initial exploratory framework, and both continued study of the predictive power of digital indicators as well as further development of the statistical approach are needed.

This paper evaluates the heterogenous impacts of the America Invents Act of 2011 (AIA) on patent applications for small and large businesses. Using data collected from the United States Patent and Trademark Office and Google Patents, I compare how the probability of successfully overcoming an initial rejection is affected by the AIA for small- and large-business applicants, respectively. This comparison is achieved by analyzing the data using a difference-in-differences approach. Results suggest that after the enactment of the AIA, small-business applicants were relatively favored when compared against large-business applicants. This effect is statistically significant and also practically large.

We proposed a new generalized model based on the classical Hawkes process with environmental multipliers, which is called an environmentally-adaptive Hawkes (EAH) model. Compared to the classical self-exciting Hawkes process, the EAH model exhibits more flexibility in a macro environmentally temporal sense, and can model more complex processes by using dynamic branching matrix. We demonstrate the well-definedness of this EAH model. A more specified version of this new model is applied to model COVID-19 pandemic data through an efficient EM-like algorithm. Consequently, the proposed model consistently outperforms the classical Hawkes process.