Use of uncertain external information in statistical estimation

A product’s life cycle hinges on its sales. Product sales are determined by a combination of market demand, industrial production, logistics, supply chains, labor hours, and countless other factors. Business-specific questions about sales are often formalized into questions relating to specific quantities in sales data. Statistical estimation of these quantities of interest is crucial but restricted availability of empirical data reduces the accuracy of such estimation. For example, under certain regularity conditions the variance of maximum likelihood estimators cannot be asymptotically lower than the Cramer-Rao lower bound. The presence of additional information from external sources therefore allows the improvement of statistical estimation. Two types of additional information are considered in this work: unbiased and possibly biased. In order to incorporate these two types of additional information in statistical estimation, this manuscript minimizes mean squared error and variance. Publicly available Walmart sales data from 45 stores across 2010-2012 is used to illustrate how these statistical methods can be applied to use additional information for estimating weekly sales. The holiday effect (sales spikes during holiday weeks) adjusted for overtime trends is estimated with the use of relevant external information

Statistical estimation with possibly incorrect model assumptions

We combine a consistent (base) estimator of a population parameter with one or several other possibly inconsistent estimators. Some or all assumptions used for calculating the latter estimators may be incorrect. The suggested in the manuscriptapproach is not restricted to parametric families and can be easily used for improvingefficiency of estimators built under nonparametric or semiparametricmodels. The combined estimator minimizes the mean squared error (MSE) in a family of linear combinations of considered estimators when all variances and covariancesused in its structure are known. In real life problems these variances and covariances are estimated generating an empirical version of the combined estimator.The combined estimator as well as its empirical version are consistent. The asymptotic properties of these estimators are presented. The combined estimator is applicable when analysts can use several different procedures for estimating the same population parameter. Different assumptions are associated with the use of each of non-base estimators. Our estimator is consistent in the presence of wrongassumptions for non-base estimating procedures. In addition to theoretical resultsof this manuscript, simulation studies describe properties of the estimator combiningthe Kaplan-Meier estimator with the censored data exponential estimator of a survival curve. Another set of simulation examples combine semi-parametricCox regression with exponential regression on right censored data

Use of uncertain additional information in newsvendor models

The newsvendor problem is a popular inventory management problem in supply chain management and logistics. Solutions to the newsvendor problem determine optimal inventory levels. This model is typically fully determined by a purchase and sale prices and a distribution of random market demand. From a statistical point of view, this problem is often considered as a quantile estimation of a critical fractile which maximizes anticipated profit. The distribution of demand is a random variable and is often estimated on historic data. In an ideal situation, when the probability distribution of demand is known, one can determine the quantile of a critical fractile minimizing a particular loss function. When a parametric family is known, maximum likelihood estimation is asymptotically efficient under certain regularity assumptions and the maximum likelihood estimators (MLEs) are used for estimating quantiles. Then, the Cramer-Rao lower bound determines the lowest possible asymptotic variance for the MLEs. Can one find a quantile estimator with a smaller variance then the Cramer-Rao lower bound? If a relevant additional information is available then the answer is yes. This manuscript considers minimum variance and mean squared error estimation which incorporate additional information for estimating optimal inventory levels

Accounting for deficit in ABC-XYZ analysis

This work proposes an ABC-XYZ-type analysis modified with observed merchandise deficit. The deficit is determined by right censoring. This manuscript proposes to account for right censoring in the ABC-XYZ analysis. The modified ABC-XYZ analysis updates many important quantities including projected income, the coefficient of variation, and the Kaplan-Meier estimator. An illustrative example shows that the classical ABC-XYZ algorithm underestimates a merchandise value when deficit was observed; magnitude of the coefficient of variation is also underestimated. The new method corrects this bias and recalculates overall profit and the coefficient of variation

Assessment of Kinematics and Electromyography Following Arthroscopic Single-Tendon Rotator Cuff Repair

Background The increasing demand for rotator cuff (RC) repair patients to return to work as soon as they are physically able has led to exploration of when this is feasible. Current guidelines from our orthopedic surgery clinic recommend a return to work at 9 weeks postoperation. To more fully define capacity to return to work, the current study was conducted using a unique series of quantitative tools. To date, no study has combined 3-dimensional (3D) motion analysis with electromyography (EMG) assessment during activities of daily living (ADLs), including desk tasks, and commonly prescribed rehabilitation exercise. Objective To apply a quantitative, validated upper extremity model to assess the kinematics and muscle activity of the shoulder following repair of the supraspinatus RC tendon compared to that in healthy shoulders. Design A prospective, cross-sectional comparison study. Setting All participants were evaluated during a single session at the Medical College of Wisconsin Department of Orthopaedic Surgery\u27s Motion Analysis Laboratory. Participants Ten participants who were 9-12 weeks post–operative repair of a supraspinatus RC tendon tear and 10 participants with healthy shoulders (HS) were evaluated. Methods All participants were evaluated with 3D motion analysis using a validated upper extremity model and synchronized EMG. Data from the 2 groups were compared using multivariate Hotelling T2 tests with post hoc analyses based on Welch t-tests. Main Outcome Measurements Participants\u27 thoracic and thoracohumeral joint kinematics, temporal-spatial parameters, and RC muscle activity were measured by applying a quantitative upper extremity model during 10 activities of daily living and 3 rehabilitation exercises. These included tasks of hair combing, drinking, writing, computer mouse use, typing, calling, reaching to back pocket, pushing a door open, pulling a door closed, external rotation, internal rotation, and rowing. Results There were significant differences of the thoracohumeral joint motion in only a few of the tested tasks: comb maximal flexion angle (P = .004), pull door internal/external rotation range of motion (P = .020), reach abduction/adduction range of motion (P = .001), reach flexion/extension range of motion (P = .001), reach extension minimal angle (P = .025), active external rotation maximal angle (P = .012), and active external rotation minimal angle (P = .004). The thorax showed significantly different kinematics of maximal flexion angle during the call (P = .011), mouse (P = .007), and drink tasks (P = .005) between the 2 groups. The EMG data analysis showed significantly increased subscapularis activity in the RC repair group during active external rotation. Conclusions Although limited abduction was expected due to repair of the supraspinatus tendon, only a single ADL (reaching to back pocket) had a significantly reduced abduction range of motion. Thoracic motion was shown to be used as a compensatory strategy during seated ADLs. Less flexion of the thorax may create passive shoulder flexion at the thoracohumeral joint in efforts to avoid active flexion. The RC repair group participants were able to accomplish the ADLs within the same time frame and through thoracohumeral joint kinematics similar to those in the healthy shoulder group participants. In summary, this study presents a quantification of the effects of RC repair and rehabilitation on the ability to perform ADLs. It may also point to a need for increased rehabilitation focus on either regaining external rotation strength or range of motion following RC repair to enhance recovery and return to the workforce

Quadratic regression analysis for gene discovery and pattern recognition for non-cyclic short time-course microarray experiments

BACKGROUND: Cluster analyses are used to analyze microarray time-course data for gene discovery and pattern recognition. However, in general, these methods do not take advantage of the fact that time is a continuous variable, and existing clustering methods often group biologically unrelated genes together. RESULTS: We propose a quadratic regression method for identification of differentially expressed genes and classification of genes based on their temporal expression profiles for non-cyclic short time-course microarray data. This method treats time as a continuous variable, therefore preserves actual time information. We applied this method to a microarray time-course study of gene expression at short time intervals following deafferentation of olfactory receptor neurons. Nine regression patterns have been identified and shown to fit gene expression profiles better than k-means clusters. EASE analysis identified over-represented functional groups in each regression pattern and each k-means cluster, which further demonstrated that the regression method provided more biologically meaningful classifications of gene expression profiles than the k-means clustering method. Comparison with Peddada et al.'s order-restricted inference method showed that our method provides a different perspective on the temporal gene profiles. Reliability study indicates that regression patterns have the highest reliabilities. CONCLUSION: Our results demonstrate that the proposed quadratic regression method improves gene discovery and pattern recognition for non-cyclic short time-course microarray data. With a freely accessible Excel macro, investigators can readily apply this method to their microarray data

Reliability and Repeatability of Cone Density Measurements in Patients With Stargardt Disease and RPGR-Associated Retinopathy

PURPOSE: To assess reliability and repeatability of cone density measurements by using confocal and (nonconfocal) split-detector adaptive optics scanning light ophthalmoscopy (AOSLO) imaging. It will be determined whether cone density values are significantly different between modalities in Stargardt disease (STGD) and retinitis pigmentosa GTPase regulator (RPGR)–associated retinopathy. METHODS: Twelve patients with STGD (aged 9–52 years) and eight with RPGR-associated retinopathy (aged 11–31 years) were imaged using both confocal and split-detector AOSLO simultaneously. Four graders manually identified cone locations in each image that were used to calculate local densities. Each imaging modality was evaluated independently. The data set consisted of 1584 assessments of 99 STGD images (each image in two modalities and four graders who graded each image twice) and 928 RPGR assessments of 58 images (each image in two modalities and four graders who graded each image twice). RESULTS: For STGD assessments the reliability for confocal and split-detector AOSLO was 67.9% and 95.9%, respectively, and the repeatability was 71.2% and 97.3%, respectively. The differences in the measured cone density values between modalities were statistically significant for one grader. For RPGR assessments the reliability for confocal and split-detector AOSLO was 22.1% and 88.5%, respectively, and repeatability was 63.2% and 94.5%, respectively. The differences in cone density between modalities were statistically significant for all graders. CONCLUSIONS: Split-detector AOSLO greatly improved the reliability and repeatability of cone density measurements in both disorders and will be valuable for natural history studies and clinical trials using AOSLO. However, it appears that these indices may be disease dependent, implying the need for similar investigations in other conditions

The Reliability of Parafoveal Cone Density Measurements

Background Adaptive optics scanning light ophthalmoscopy (AOSLO) enables direct visualisation of the cone mosaic, with metrics such as cone density and cell spacing used to assess the integrity or health of the mosaic. Here we examined the interobserver and inter-instrument reliability of cone density measurements. Methods For the interobserver reliability study, 30 subjects with no vision-limiting pathology were imaged. Three image sequences were acquired at a single parafoveal location and aligned to ensure that the three images were from the same retinal location. Ten observers used a semiautomated algorithm to identify the cones in each image, and this was repeated three times for each image. To assess inter-instrument reliability, 20 subjects were imaged at eight parafoveal locations on one AOSLO, followed by the same set of locations on the second AOSLO. A single observer manually aligned the pairs of images and used the semiautomated algorithm to identify the cones in each image. Results Based on a factorial study design model and a variance components model, the interobserver study\u27s largest contribution to variability was the subject (95.72%) while the observer\u27s contribution was only 1.03%. For the inter-instrument study, an average cone density intraclass correlation coefficient (ICC) of between 0.931 and 0.975 was calculated. Conclusions With the AOSLOs used here, reliable cone density measurements can be obtained between observers and between instruments. Additional work is needed to determine how these results vary with differences in image quality