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In competitive business, such as insurance and telecommunications, customers can easily replace one provider for another, which leads to customer attrition. Keeping customer attrition rate low is crucial for companies, since retaining a customer is more profitable than recruiting a new one. As a main statistical process control (SPC) method, the CUSUM scheme is able to detect small and persistent shifts in customer attrition. However, customer attrition summaries are typically available on an uneven time scale (e.g. 4-week and 5-week 'business month'), which may not satisfy the assumptions of traditional CUSUM designs. This paper mainly develops a latent CUSUM chart based on an exponential model for monitoring 'monthly' customer attrition, under varying time scales. Both maximum likelihood and least squares methods are studied, where the former mostly performs better and the latter is advantageous for quite small shifts. We apply a Markov chain algorithm to obtain the average run length (ARL), make calibrations for different combinations of parameters, and present reference tables of cutoffs. Three more complicated models are considered to test the robustness of deviations from the initial model. Furthermore, a real example of monitoring monthly customer attrition from a Chinese insurance company is used to illustrate the scheme.

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The check loss function is used to define quantile regression. In cross-validation, it is also employed as a validation function when the true distribution is unknown. However, our empirical study indicates that validation with the check loss often leads to overfitting the data. In this work, we suggest a modified or L2-adjusted check loss which rounds the sharp corner in the middle of check loss. This has the effect of guarding against overfitting to some extent. The adjustment is devised to shrink to zero as sample size grows. Through various simulation settings of linear and nonlinear regressions, the improvement due to modification of the check loss by quadratic adjustment is examined empirically.

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Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model (GLMM) by introducing latent random variables. The first approach is effective for parameter estimation, but leaves one without a formal model for the data with which to assess quality of fit or make individual-level predictions for future observations. The second approach overcomes these deficiencies, but leads to parameter estimates that must be interpreted conditional on the latent variables. To obtain marginal summaries, one needs to evaluate an analytically intractable integral or use attenuation factors as an approximation. Further, we note an unpalatable implication of the standard GLMM. To resolve these issues, we turn to a class of marginally interpretable GLMMs that lead to parameter estimates with a marginal interpretation while maintaining the desirable statistical properties of a conditionally specified model and avoiding problematic implications. We establish the form of these models under the most commonly used link functions and address computational issues. For logistic mixed effects models, we introduce an accurate and efficient method for evaluating the logistic-normal integral.

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OBJECTIVE: To determine the influence of surgical site infection (SSI) on the median disease-free interval (DFI) and median survival time (MST) in dogs after amputation in the curative-intent treatment of appendicular osteosarcoma (OSA). STUDY DESIGN: Multi-institutional retrospective cohort study. ANIMALS: Fifteen dogs with OSA and SSI, and 134 dogs with OSA and no SSI. METHODS: Medical records were reviewed, and dogs were included if the following criteria were met: histologic confirmation of OSA, no evidence of metastasis, ≥1 chemotherapy treatment, and available follow-up data. We used the definition of SSI from the Centers for Disease Control and Prevention. Kaplan-Meier estimates of median DFI and MST for the SSI and non-SSI groups were compared by log-rank test. Univariate and multivariate Cox proportional hazard regression analysis was evaluated for associations with DFI and survival. RESULTS: The median DFI and MST of all OSA dogs were 236 days (95% CI, 181-283) and 283 days (95% CI 237-355), respectively. The median DFI of dogs with SSI (292 days) did not differ from that of dogs without SSI (224 days, P = .156). The MST of dogs with SSI (292 days) did not differ from that of dogs without SSI (280 days, P = .417). Failure to complete chemotherapy was associated with decreased DFI and survival (P < .001). Adjustments for chemotherapy completion found no effect of SSI on survival. CONCLUSION: SSI did not influence the survival of dogs with appendicular OSA treated with amputation and curative-intent treatment. CLINICAL SIGNIFICANCE: The extended survival associated with SSI after limb-spare surgery for OSA does not appear to be present after amputation. Interactions between the canine immune system and OSA warrant additional study.

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We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

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BACKGROUND: The Amish have not been previously studied for cancer incidence, yet they have the potential to help in the understanding of its environmental and genetic contributions. The purpose of this study was to estimate the incidence of cancer among the largest Amish population. METHODS: Adults from randomly selected households were interviewed and a detailed cancer family history was taken. Using both the household interview data and a search of the Ohio cancer registry data, a total of 191 cancer cases were identified between the years 1996 and 2003. RESULTS: The age-adjusted cancer incidence rate for all cancers among the Amish adults was 60% of the age-adjusted adult rate in Ohio (389.5/10(5) vs. 646.9/10(5); p < 0.0001). The incidence rate for tobacco-related cancers in the Amish was 37% of the rate for Ohio adults (p < 0.0001). The incidence rate for non-tobacco-related cancers in the Amish was 72% of the age-adjusted adult rate in Ohio (p = 0.0001). CONCLUSION: Cancer incidence is low in the Ohio Amish. These data strongly support reduction of cancer incidence by tobacco abstinence but cannot be explained solely on this basis. Understanding these contributions may help to identify additional important factors to target to reduce cancer among the non-Amish.

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In many scientific studies, information that is not easily translated into covariates is ignored in the analysis. However, this type of information may significantly improve inference. In this research, we apply the idea of judgment post-stratification to utilize such information. Specifically, we consider experiments that are conducted under a completely randomized design. Sets of experimental units are formed, and the units in a set are ranked. Estimation is performed conditional on the sets and ranks. We propose a new estimator for a treatment contrast. We improve the new estimator by Rao-Blackwellization. Asymptotic distribution theory and corresponding inferential procedures for both estimators are developed. Simulation studies quantify the superiority of the new estimators and show their desirable properties for small and moderate sample sizes. The impact of the new techniques is illustrated with data from a clinical trial.

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Judgement post-stratification, which is based on ideas similar to those in ranked set sampling, relies on the ability of a ranker to forecast the ranks of potential observations on a set of units. In practice, the authors sometimes find it difficult to assign these ranks. This note shows how one can borrow techniques from the literature on finite population sampling to allow a probabilistic ranking of the units in a set, thus facilitating use of these sampling plans and improving estimation. The same techniques provide one approach to estimation using a judgement post-stratified sample with multiple rankers. The technique is illustrated on allometric data relating brain weight to body weight in different species of mammals, and on a study of student performance in graduate school.

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