More Like this

1. Variance Estimation in the Analysis of Microarray Data

   https://doi.org/10.1111/j.1467-9868.2008.00690.x  

   Wang, Yuedong ; Ma, Yanyuan ; Carroll, Raymond J. ( December 2008 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Microarrays are one of the most widely used high throughput technologies. One of the main problems in the area is that conventional estimates of the variances that are required in the t-statistic and other statistics are unreliable owing to the small number of replications. Various methods have been proposed in the literature to overcome this lack of degrees of freedom problem. In this context, it is commonly observed that the variance increases proportionally with the intensity level, which has led many researchers to assume that the variance is a function of the mean. Here we concentrate on estimation of the variance as a function of an unknown mean in two models: the constant coefficient of variation model and the quadratic variance–mean model. Because the means are unknown and estimated with few degrees of freedom, naive methods that use the sample mean in place of the true mean are generally biased because of the errors-in-variables phenomenon. We propose three methods for overcoming this bias. The first two are variations on the theme of the so-called heteroscedastic simulation–extrapolation estimator, modified to estimate the variance function consistently. The third class of estimators is entirely different, being based on semiparametric information calculations. Simulations show the power of our methods and their lack of bias compared with the naive method that ignores the measurement error. The methodology is illustrated by using microarray data from leukaemia patients.

    

   more » « less
2. Florida mangrove saltmarsh reference surface soils

   https://doi.org/10.6073/pasta/0e08cbe07c84488cb7b9dd16669946d0  

   Lewis, David Bruce ( January 2021 , Environmental Data Initiative)

   Site description. This data package consists of data obtained from sampling surface soil (the 0-7.6 cm depth profile) in black mangrove (Avicennia germinans) dominated forest and black needlerush (Juncus roemerianus) saltmarsh along the Gulf of Mexico coastline in peninsular west-central Florida, USA. This location has a subtropical climate with mean daily temperatures ranging from 15.4 °C in January to 27.8 °C in August, and annual precipitation of 1336 mm. Precipitation falls as rain primarily between June and September. Tides are semi-diurnal, with 0.57 m median amplitudes during the year preceding sampling (U.S. NOAA National Ocean Service, Clearwater Beach, Florida, station 8726724). Sea-level rise is 4.0 ± 0.6 mm per year (1973-2020 trend, mean ± 95 % confidence interval, NOAA NOS Clearwater Beach station). The A. germinans mangrove zone is either adjacent to water or fringed on the seaward side by a narrow band of red mangrove (Rhizophora mangle). A near-monoculture of J. roemerianus is often adjacent to and immediately landward of the A. germinans zone. The transition from the mangrove to the J. roemerianus zone is variable in our study area. An abrupt edge between closed-canopy mangrove and J. roemerianus monoculture may extend for up to several hundred meters in some locations, while other stretches of ecotone present a gradual transition where smaller, widely spaced trees are interspersed into the herbaceous marsh. Juncus roemerianus then extends landward to a high marsh patchwork of succulent halophytes (including Salicornia bigellovi, Sesuvium sp., and Batis maritima), scattered dwarf mangrove, and salt pans, followed in turn by upland vegetation that includes Pinus sp. and Serenoa repens. Field design and sample collection. We established three study sites spaced at approximately 5 km intervals along the western coastline of the central Florida peninsula. The sites consisted of the Salt Springs (28.3298°, -82.7274°), Energy Marine Center (28.2903°, -82.7278°), and Green Key (28.2530°, -82.7496°) sites on the Gulf of Mexico coastline in Pasco County, Florida, USA. At each site, we established three plot pairs, each consisting of one saltmarsh plot and one mangrove plot. Plots were 50 m^2 in size. Plots pairs within a site were separated by 230-1070 m, and the mangrove and saltmarsh plots composing a pair were 70-170 m apart. All plot pairs consisted of directly adjacent patches of mangrove forest and J. roemerianus saltmarsh, with the mangrove forests exhibiting a closed canopy and a tree architecture (height 4-6 m, crown width 1.5-3 m). Mangrove plots were located at approximately the midpoint between the seaward edge (water-mangrove interface) and landward edge (mangrove-marsh interface) of the mangrove zone. Saltmarsh plots were located 20-25 m away from any mangrove trees and into the J. roemerianus zone (i.e., landward from the mangrove-marsh interface). Plot pairs were coarsely similar in geomorphic setting, as all were located on the Gulf of Mexico coastline, rather than within major sheltering formations like Tampa Bay, and all plot pairs fit the tide-dominated domain of the Woodroffe classification (Woodroffe, 2002, "Coasts: Form, Process and Evolution", Cambridge University Press), given their conspicuous semi-diurnal tides. There was nevertheless some geomorphic variation, as some plot pairs were directly open to the Gulf of Mexico while others sat behind keys and spits or along small tidal creeks. Our use of a plot-pair approach is intended to control for this geomorphic variation. Plot center elevations (cm above mean sea level, NAVD 88) were estimated by overlaying the plot locations determined with a global positioning system (Garmin GPS 60, Olathe, KS, USA) on a LiDAR-derived bare-earth digital elevation model (Dewberry, Inc., 2019). The digital elevation model had a vertical accuracy of ± 10 cm (95 % CI) and a horizontal accuracy of ± 116 cm (95 % CI). Soil samples were collected via coring at low tide in June 2011. From each plot, we collected a composite soil sample consisting of three discrete 5.1 cm diameter soil cores taken at equidistant points to 7.6 cm depth. Cores were taken by tapping a sleeve into the soil until its top was flush with the soil surface, sliding a hand under the core, and lifting it up. Cores were then capped and transferred on ice to our laboratory at the University of South Florida (Tampa, Florida, USA), where they were combined in plastic zipper bags, and homogenized by hand into plot-level composite samples on the day they were collected. A damp soil subsample was immediately taken from each composite sample to initiate 1 y incubations for determination of active C and N (see below). The remainder of each composite sample was then placed in a drying oven (60 °C) for 1 week with frequent mixing of the soil to prevent aggregation and liberate water. Organic wetland soils are sometimes dried at 70 °C, however high drying temperatures can volatilize non-water liquids and oxidize and decompose organic matter, so 50 °C is also a common drying temperature for organic soils (Gardner 1986, "Methods of Soil Analysis: Part 1", Soil Science Society of America); we accordingly chose 60 °C as a compromise between sufficient water removal and avoidance of non-water mass loss. Bulk density was determined as soil dry mass per core volume (adding back the dry mass equivalent of the damp subsample removed prior to drying). Dried subsamples were obtained for determination of soil organic matter (SOM), mineral texture composition, and extractable and total carbon (C) and nitrogen (N) within the following week. Sample analyses. A dried subsample was apportioned from each composite sample to determine SOM as mass loss on ignition at 550 °C for 4 h. After organic matter was removed from soil via ignition, mineral particle size composition was determined using a combination of wet sieving and density separation in 49 mM (3 %) sodium hexametaphosphate ((NaPO_3)_6) following procedures in Kettler et al. (2001, Soil Science Society of America Journal 65, 849-852). The percentage of dry soil mass composed of silt and clay particles (hereafter, fines) was calculated as the mass lost from dispersed mineral soil after sieving (0.053 mm mesh sieve). Fines could have been slightly underestimated if any clay particles were burned off during the preceding ignition of soil. An additional subsample was taken from each composite sample to determine extractable N and organic C concentrations via 0.5 M potassium sulfate (K_2SO_4) extractions. We combined soil and extractant (ratio of 1 g dry soil:5 mL extractant) in plastic bottles, reciprocally shook the slurry for 1 h at 120 rpm, and then gravity filtered it through Fisher G6 (1.6 μm pore size) glass fiber filters, followed by colorimetric detection of nitrite (NO_2^-) + nitrate (NO_3^-) and ammonium (NH_4^+) in the filtrate (Hood Nowotny et al., 2010,Soil Science Society of America Journal 74, 1018-1027) using a microplate spectrophotometer (Biotek Epoch, Winooski, VT, USA). Filtrate was also analyzed for dissolved organic C (referred to hereafter as extractable organic C) and total dissolved N via combustion and oxidation followed by detection of the evolved CO_2 and N oxide gases on a Formacs HT TOC/TN analyzer (Skalar, Breda, The Netherlands). Extractable organic N was then computed as total dissolved N in filtrate minus extractable mineral N (itself the sum of extractable NH_4-N and NO_2-N + NO_3-N). We determined soil total C and N from dried, milled subsamples subjected to elemental analysis (ECS 4010, Costech, Inc., Valencia, CA, USA) at the University of South Florida Stable Isotope Laboratory. Median concentration of inorganic C in unvegetated surface soil at our sites is 0.5 % of soil mass (Anderson, 2019, Univ. of South Florida M.S. thesis via methods in Wang et al., 2011, Environmental Monitoring and Assessment 174, 241-257). Inorganic C concentrations are likely even lower in our samples from under vegetation, where organic matter would dilute the contribution of inorganic C to soil mass. Nevertheless, the presence of a small inorganic C pool in our soils may be counted in the total C values we report. Extractable organic C is necessarily of organic C origin given the method (sparging with HCl) used in detection. Active C and N represent the fractions of organic C and N that are mineralizable by soil microorganisms under aerobic conditions in long-term soil incubations. To quantify active C and N, 60 g of field-moist soil were apportioned from each composite sample, placed in a filtration apparatus, and incubated in the dark at 25 °C and field capacity moisture for 365 d (as in Lewis et al., 2014, Ecosphere 5, art59). Moisture levels were maintained by frequently weighing incubated soil and wetting them up to target mass. Daily CO_2 flux was quantified on 29 occasions at 0.5-3 week intervals during the incubation period (with shorter intervals earlier in the incubation), and these per day flux rates were integrated over the 365 d period to compute an estimate of active C. Observations of per day flux were made by sealing samples overnight in airtight chambers fitted with septa and quantifying headspace CO_2 accumulation by injecting headspace samples (obtained through the septa via needle and syringe) into an infrared gas analyzer (PP Systems EGM 4, Amesbury, MA, USA). To estimate active N, each incubated sample was leached with a C and N free, 35 psu solution containing micronutrients (Nadelhoffer, 1990, Soil Science Society of America Journal 54, 411-415) on 19 occasions at increasing 1-6 week intervals during the 365 d incubation, and then extracted in 0.5 M K_2SO_4 at the end of the incubation in order to remove any residual mineral N. Active N was then quantified as the total mass of mineral N leached and extracted. Mineral N in leached and extracted solutions was detected as NH_4-N and NO_2-N + NO_3-N via colorimetry as above. This incubation technique precludes new C and N inputs and persistently leaches mineral N, forcing microorganisms to meet demand by mineralizing existing pools, and thereby directly assays the potential activity of soil organic C and N pools present at the time of soil sampling. Because this analysis commences with disrupting soil physical structure, it is biased toward higher estimates of active fractions. Calculations. Non-mobile C and N fractions were computed as total C and N concentrations minus the extractable and active fractions of each element. This data package reports surface-soil constituents (moisture, fines, SOM, and C and N pools and fractions) in both gravimetric units (mass constituent / mass soil) and areal units (mass constituent / soil surface area integrated through 7.6 cm soil depth, the depth of sampling). Areal concentrations were computed as X × D × 7.6, where X is the gravimetric concentration of a soil constituent, D is soil bulk density (g dry soil / cm^3), and 7.6 is the sampling depth in cm. 

   more » « less
3. Robust Small Area Estimation: An Overview

   https://doi.org/10.1146/annurev-statistics-031219-041212  

   Jiang, J. ; Rao, J.S. ( April 2020 , Annual review of statistics and its application)

   A small area typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain. While traditional small area methods and models are widely used nowadays, there have also been much work and interest in robust statistical inference for small area estimation (SAE). We survey this work and provide a comprehensive review here.We begin with a brief review of the traditional SAE methods. We then discuss SAEmethods that are developed under weaker assumptions and SAE methods that are robust in certain ways, such as in terms of outliers or model failure. Our discussion also includes topics such as nonparametric SAE methods, Bayesian approaches, model selection and diagnostics, and missing data. A brief review of software packages available for implementing robust SAE methods is also given. 

   more » « less
4. Min-Max Optimal Design of Two-Armed Trials with Side Information

   https://doi.org/10.1287/ijoc.2021.1068  

   Zhang, Qiong ; Khademi, Amin ; Song, Yongjia ( January 2022 , INFORMS Journal on Computing)

   In this work, we study the optimal design of two-armed clinical trials to maximize the accuracy of parameter estimation in a statistical model, where the interaction between patient covariates and treatment are explicitly incorporated to enable precision medication decisions. Such a modeling extension leads to significant complexities for the produced optimization problems because they include optimization over design and covariates concurrently. We take a min-max optimization model and minimize (over design) the maximum (over population) variance of the estimated interaction effect between treatment and patient covariates. This results in a min-max bilevel mixed integer nonlinear programming problem, which is notably challenging to solve. To address this challenge, we introduce a surrogate optimization model by approximating the objective function, for which we propose two solution approaches. The first approach provides an exact solution based on reformulation and decomposition techniques. In the second approach, we provide a lower bound for the inner optimization problem and solve the outer optimization problem over the lower bound. We test our proposed algorithms with synthetic and real-world data sets and compare them with standard (re)randomization methods. Our numerical analysis suggests that the proposed approaches provide higher-quality solutions in terms of the variance of estimators and probability of correct selection. We also show the value of covariate information in precision medicine clinical trials by comparing our proposed approaches to an alternative optimal design approach that does not consider the interaction terms between covariates and treatment. Summary of Contribution: Precision medicine is the future of healthcare where treatment is prescribed based on each patient information. Designing precision medicine clinical trials, which are the cornerstone of precision medicine, is extremely challenging because sample size is limited and patient information may be multidimensional. This work proposes a novel approach to optimally estimate the treatment effect for each patient type in a two-armed clinical trial by reducing the largest variance of personalized treatment effect. We use several statistical and optimization techniques to produce efficient solution methodologies. Results have the potential to save countless lives by transforming the design and implementation of future clinical trials to ensure the right treatments for the right patients. Doing so will reduce patient risks and reduce costs in the healthcare system. 

   more » « less
5. Modeling and tracking Covid-19 cases using Big Data analytics on HPCC system platform

   https://doi.org/10.1186/s40537-021-00423-z  

   Villanustre, Flavio ; Chala, Arjuna ; Dev, Roger ; Xu, Lili ; LexisNexis, Jesse Shaw ; Furht, Borko ; Khoshgoftaar, Taghi ( December 2021 , Journal of Big Data)

   Abstract This project is funded by the US National Science Foundation (NSF) through their NSF RAPID program under the title “Modeling Corona Spread Using Big Data Analytics.” The project is a joint effort between the Department of Computer & Electrical Engineering and Computer Science at FAU and a research group from LexisNexis Risk Solutions. The novel coronavirus Covid-19 originated in China in early December 2019 and has rapidly spread to many countries around the globe, with the number of confirmed cases increasing every day. Covid-19 is officially a pandemic. It is a novel infection with serious clinical manifestations, including death, and it has reached at least 124 countries and territories. Although the ultimate course and impact of Covid-19 are uncertain, it is not merely possible but likely that the disease will produce enough severe illness to overwhelm the worldwide health care infrastructure. Emerging viral pandemics can place extraordinary and sustained demands on public health and health systems and on providers of essential community services. Modeling the Covid-19 pandemic spread is challenging. But there are data that can be used to project resource demands. Estimates of the reproductive number (R) of SARS-CoV-2 show that at the beginning of the epidemic, each infected person spreads the virus to at least two others, on average (Emanuel et al. in N Engl J Med. 2020, Livingston and Bucher in JAMA 323(14):1335, 2020). A conservatively low estimate is that 5 % of the population could become infected within 3 months. Preliminary data from China and Italy regarding the distribution of case severity and fatality vary widely (Wu and McGoogan in JAMA 323(13):1239–42, 2020). A recent large-scale analysis from China suggests that 80 % of those infected either are asymptomatic or have mild symptoms; a finding that implies that demand for advanced medical services might apply to only 20 % of the total infected. Of patients infected with Covid-19, about 15 % have severe illness and 5 % have critical illness (Emanuel et al. in N Engl J Med. 2020). Overall, mortality ranges from 0.25 % to as high as 3.0 % (Emanuel et al. in N Engl J Med. 2020, Wilson et al. in Emerg Infect Dis 26(6):1339, 2020). Case fatality rates are much higher for vulnerable populations, such as persons over the age of 80 years (> 14 %) and those with coexisting conditions (10 % for those with cardiovascular disease and 7 % for those with diabetes) (Emanuel et al. in N Engl J Med. 2020). Overall, Covid-19 is substantially deadlier than seasonal influenza, which has a mortality of roughly 0.1 %. Public health efforts depend heavily on predicting how diseases such as those caused by Covid-19 spread across the globe. During the early days of a new outbreak, when reliable data are still scarce, researchers turn to mathematical models that can predict where people who could be infected are going and how likely they are to bring the disease with them. These computational methods use known statistical equations that calculate the probability of individuals transmitting the illness. Modern computational power allows these models to quickly incorporate multiple inputs, such as a given disease’s ability to pass from person to person and the movement patterns of potentially infected people traveling by air and land. This process sometimes involves making assumptions about unknown factors, such as an individual’s exact travel pattern. By plugging in different possible versions of each input, however, researchers can update the models as new information becomes available and compare their results to observed patterns for the illness. In this paper we describe the development a model of Corona spread by using innovative big data analytics techniques and tools. We leveraged our experience from research in modeling Ebola spread (Shaw et al. Modeling Ebola Spread and Using HPCC/KEL System. In: Big Data Technologies and Applications 2016 (pp. 347-385). Springer, Cham) to successfully model Corona spread, we will obtain new results, and help in reducing the number of Corona patients. We closely collaborated with LexisNexis, which is a leading US data analytics company and a member of our NSF I/UCRC for Advanced Knowledge Enablement. The lack of a comprehensive view and informative analysis of the status of the pandemic can also cause panic and instability within society. Our work proposes the HPCC Systems Covid-19 tracker, which provides a multi-level view of the pandemic with the informative virus spreading indicators in a timely manner. The system embeds a classical epidemiological model known as SIR and spreading indicators based on causal model. The data solution of the tracker is built on top of the Big Data processing platform HPCC Systems, from ingesting and tracking of various data sources to fast delivery of the data to the public. The HPCC Systems Covid-19 tracker presents the Covid-19 data on a daily, weekly, and cumulative basis up to global-level and down to the county-level. It also provides statistical analysis for each level such as new cases per 100,000 population. The primary analysis such as Contagion Risk and Infection State is based on causal model with a seven-day sliding window. Our work has been released as a publicly available website to the world and attracted a great volume of traffic. The project is open-sourced and available on GitHub. The system was developed on the LexisNexis HPCC Systems, which is briefly described in the paper. 

   more » « less