In the aftermath of medical error : Caring for patients, family, and the healthcare workers involved

Medical errors, in particular those resulting in harm, pose a serious situation for patients ("first victims") and the healthcare workers involved ("second victims") and can have long-lasting and distressing consequences. To prevent a second traumatization, appropriate and empathic interaction with all persons involved is essential besides error analysis. Patients share a nearly universal, broad preference for a complete disclosure of incidents, regardless of age, gender, or education. This includes the personal, timely and unambiguous disclosure of the adverse event, information relating to the event, its causes and consequences, and an apology and sincere expression of regret. While the majority of healthcare professionals generally support and honest and open disclosure of adverse events, they also face various barriers which impede the disclosure (e.g., fear of legal consequences). Despite its essential importance, disclosure of adverse events in practice occurs in ways that are rarely acceptable to patients and their families. The staff involved often experiences acute distress and an intense emotional response to the event, which may become chronic and increase the risk of depression, burnout and post-traumatic stress disorders. Communication with peers is vital for people to be able to cope constructively and protectively with harmful errors. Survey studies among healthcare workers show, however, that they often do not receive sufficient individual and institutional support. Healthcare organizations should prepare for medical errors and harmful events and implement a communication plan and a support system that covers the requirements and different needs of patients and the staff involved.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

A Ladder Operator Solution to the Particle in a Box Problem

A ladder operator solution to the particle in a box problem of elementary quantum mechanics is presented, although the pedagogical use of this method for this problem is questioned.

Optimal Test for Parameter Instability When the Unstable Process and the Error Distribution are Unknown

This paper proposes asymptotically optimal tests for unstable parameter process under the feasible circumstance that the researcher has little information about the unstable parameter process and the error distribution, and suggests conditions under which the knowledge of those processes does not provide asymptotic power gains. I first derive a test under known error distribution, which is asymptotically equivalent to LR tests for correctly identified unstable parameter processes under suitable conditions. The conditions are weak enough to cover a wide range of unstable processes such as various types of structural breaks and time varying parameter processes. The test is then extended to semiparametric models in which the underlying distribution in unknown but treated as unknown infinite dimensional nuisance parameter. The semiparametric test is adaptive in the sense that its asymptotic power function is equivalent to the power envelope under known error distribution.

Second, do less harm: The state of states' medical error reporting programs

Statement of the problem and public health significance. Hospitals were designed to be a safe haven and respite from disease and illness. However, a large body of evidence points to preventable errors in hospitals as the eighth leading cause of death among Americans. Twelve percent of Americans, or over 33.8 million people, are hospitalized each year. This population represents a significant portion of at risk citizens exposed to hospital medical errors. Since the number of annual deaths due to hospital medical errors is estimated to exceed 44,000, the magnitude of this tragedy makes it a significant public health problem. ^ Specific aims. The specific aims of this study were threefold. First, this study aimed to analyze the state of the states' mandatory hospital medical error reporting six years after the release of the influential IOM report, "To Err is Human." The second aim was to identify barriers to reporting of medical errors by hospital personnel. The third aim was to identify hospital safety measures implemented to reduce medical errors and enhance patient safety. ^ Methods. A descriptive, longitudinal, retrospective design was used to address the first stated objective. The study data came from the twenty-one states with mandatory hospital reporting programs which report aggregate hospital error data that is accessible to the public by way of states' websites. The data analysis included calculations of expected number of medical errors for each state according to IOM rates. Where possible, a comparison was made between state reported data and the calculated IOM expected number of errors. A literature review was performed to achieve the second study aim, identifying barriers to reporting medical errors. The final aim was accomplished by telephone interviews of principal patient safety/quality officers from five Texas hospitals with more than 700 beds. ^ Results. The state medical error data suggests vast underreporting of hospital medical errors to the states. The telephone interviews suggest that hospitals are working at reducing medical errors and creating safer environments for patients. The literature review suggests the underreporting of medical errors at the state level stems from underreporting of errors at the delivery level. ^

Nursing-related medication errors: A review of factors that facilitate and hinder error reporting, and recommendations for improvement

Medication errors, one of the most frequent types of medical errors, are a common cause of patient harm in hospital systems today. Nurses at the bedside are in a position to encounter many of these errors since they are there at the start of the process (ordering/prescribing) and the end of the process (administration). One of the recommendations from the IOM (Institute of Medicine) report, "To Err is Human," was for organizations to identify and learn from medical errors through event reporting systems. While many organizations have reporting systems in place, research studies report a significant amount of underreporting by nurses. A systematic review of the literature was performed to identify contributing factors related to the reporting and not reporting of medication errors by nurses at the bedside.^ Articles included in the literature review were primary or secondary studies, dated January 1, 2000 – July 2009, related to nursing medication error reporting. All 634 articles were reviewed with an algorithm developed to standardize the review process and help filter out those that did not meet the study criteria. In addition, 142 article bibliographies were reviewed to find additional studies that were not found in the original literature search.^ After reviewing the 634 articles and the additional 108 articles discovered in the bibliography review, 41 articles met the study criteria and were used in the systematic literature review results.^ Fear of punitive reactions to medication errors was a frequent barrier to error reporting. Nurses fear reactions from their leadership, peers, patients and their families, nursing boards, and the media. Anonymous reporting systems and departments/organizations with a strong safety culture in place helped to encourage the reporting of medication errors by nursing staff.^ Many of the studies included in this literature review do not allow results that can be generalized. The majority of them took place in single institutions/organizations with limited sample sizes. Stronger studies with larger sample sizes need to be performed, utilizing data collection methods that have been validated, to determine stronger correlations between safety cultures and nurse error reporting.^