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Several methods used to examine differential item functioning (DIF) in Patient-Reported Outcomes Measurement Information System (PROMIS®) measures are presented, including effect size estimation. A summary of factors that may affect DIF detection and challenges encountered in PROMIS DIF analyses, e.g., anchor item selection, is provided. An issue in PROMIS was the potential for inadequately modeled multidimensionality to result in false DIF detection. Section 1 is a presentation of the unidimensional models used by most PROMIS investigators for DIF detection, as well as their multidimensional expansions. Section 2 is an illustration that builds on previous unidimensional analyses of depression and anxiety short-forms to examine DIF detection using a multidimensional item response theory (MIRT) model. The Item Response Theory-Log-likelihood Ratio Test (IRT-LRT) method was used for a real data illustration with gender as the grouping variable. The IRT-LRT DIF detection method is a flexible approach to handle group differences in trait distributions, known as impact in the DIF literature, and was studied with both real data and in simulations to compare the performance of the IRT-LRT method within the unidimensional IRT (UIRT) and MIRT contexts. Additionally, different effect size measures were compared for the data presented in Section 2. A finding from the real data illustration was that using the IRT-LRT method within a MIRT context resulted in more flagged items as compared to using the IRT-LRT method within a UIRT context. The simulations provided some evidence that while unidimensional and multidimensional approaches were similar in terms of Type I error rates, power for DIF detection was greater for the multidimensional approach. Effect size measures presented in Section 1 and applied in Section 2 varied in terms of estimation methods, choice of density function, methods of equating, and anchor item selection. Despite these differences, there was considerable consistency in results, especially for the items showing the largest values. Future work is needed to examine DIF detection in the context of polytomous, multidimensional data. PROMIS standards included incorporation of effect size measures in determining salient DIF. Integrated methods for examining effect size measures in the context of IRT-based DIF detection procedures are still in early stages of development.

Exposure-response (ER) modeling for fixed-dose combinations (FDC) has previously been found to have an inflated false positive rate (FP), i.e., observing a significant effect of FDC components when no true effect exists. Longitudinal exposure-response (LER)analysis utilizes the time course of the data and is valid for several clinical endpoints for FDCs. The aim of the study was to investigate if LER is applicable for the validation of FDCs by demonstrating the contribution of each component to the overall effect without inflation of FP rates. FP and FN rates associated with ER and LER analysis were investigated using stochastic simulation and estimation. Four hundred thirty-two scenarios with varying numbers of patients, duration, sampling frequency, dose distribution, design, and drug activity were analyzed using a range of linear, log-linear, and non-linear models to asses FP and FN rates. Lastly, the impact of the clinical trial parameters was investigated. LER analyses provided well-controlled FP rates of the expected 5% or less; however, in low information clinical trials consisting of 30 patients, 4 samples, and 20 days, LER analyses lead to inflated FN rates. Parameter investigation showed that when the clinical trial includes sufficient patients, duration, samples, and an appropriate trial design, the FN rates are in general below the expected 5% for LER analysis. Based on the results, LER analysis can be used for the validation of FDCs and fixed ratio drug combinations. The method constitutes anew avenue for providing evidence that demonstrates the contribution of each component to the overall clinical effect. Refereed/Peer-reviewed

Careless responding is one of the most fundamental challenges of survey research. We need our respondents to respond honestly and with effort, but when they don’t, we need to be able to detect and remove them from our datasets. A few years ago, Meade and Craig (2012) published an article in Psychological Methods exploring a significant number of techniques for doing exactly this, ultimately recommending a combination of three detection techniques for rigorous data cleaning, which, let’s face it, is a necessary step when analyzing any internet survey. These techniques are even-odd consistency, maximum longstring, and Mahalanobis D:The even-odd consistency index involves calculating the subscale means for each measure on your survey, split by even and odd items. For example, the mean of items 1, 3, 5, and 7 would become one subscale whereas the mean of items 2, 4, 6, and 8 would become the other. Next, you take all of the even subscales and pair them with all of the odd subscales across all of the measures in your survey, calculate a correlation, and then apply the Spearman-Brown prophecy formula to adjust the value up to a scale of -1 to 1.Maximum LongString is the largest value for LongString across all scales on your survey, where LongString is the number of identical response in a row. Meade and Craig recommended LongString would be most useful when the items were randomly ordered.Mahalnobis D is calculated from the regression of scale means onto all the scores that inform them. In a sense, you are trying to see if responses to individual items correspond with the scale mean they created consistently across individuals. Some conceptualizations of this index regress participant number onto scores, which conceptually accomplishes basically the same thing.In all three cases, the next step is to create a histogram of the values and see if you see any outliers.Calculating Careless Responding IndicesOf these three, Mahalanobis D is the most easily calculated, because saving Mahalanobis D values is a core feature in regression toolkits. It is done easily in SPSS, SAS, R, etc.The second, the even-odd consistency index, is a bit harder but still fundamentally not too tricky; you just need to really understand how your statistical software works. Each step, individually, is simple: calculate scale means, calculate a correlation, apply a formula.The third, Max LongString, is the most intuitively understandable but also, often unexpectedly, the most difficult to calculate. I imagine that the non-technically-inclined generally count by hand – “this person has a maximum of 5 identical answers in a row, the next person has 3…”An SPSS macro already exists to do this, although it’s not terribly intuitive. You need to manually change pieces of the code in order to customize the function to your own data.Given that, I decided to port the SPSS macro into Excel and make it a little easier to use.An Excel Macro to Calculate LongStringFunction LongString(cells As Range) Dim cell As Range Dim run As Integer Dim firstrow As Boolean Dim maxrun As Integer Dim lastvalue As String firstrow = True run = 1 maxrun = 1 For Each cell In cells If firstrow = True Then firstrow = False lastvalue = cell.Value Else If cell.Value = lastvalue Then run = run + 1 maxrun = Application.Max(run, maxrun) Else run = 1 End If lastvalue = cell.Value End If Next cell LongString = maxrun End Function To Use This Code YourselfWith Excel open, press Alt+F11 to open the VBA Editor.Copy/paste the code block above into the VBA Editor.Close the VBA Editor (return to Excel).In an empty cell, simply type =LONGSTRING() and put the cell range of your scale’s survey items inside. For example, if your first scale was between B2 and G2, you’d use =LONGSTRING(B2:G2)Repeat this for each scale you’ve used. For example, if you measured five personality dimensions, you’d have five longstrings calculated.Finally, in a new cell use the =MAX() function to determine the largest of that set. For example, if you put your five LongStrings in H2 to L2, you’d use =MAX(H2:L2)That’s it! Importantly, the cells needs to be in Excel in the order they were administered. If you used randomly ordered items, this adds an additional layer of complexity, because you’ll need to recreate the original order for each participant first before you can apply LongString. That takes a bit of Excel magic, but if you need to do this, I recommend you read up on =INDIRECT() and =OFFSET(), which will help you get that original order back, assuming you saved that item order somewhere.Final StepsOnce you have Max LongString calculated for each participant, create a histogram of those values to see if any strange outliers appear. If you see clear outliers (i.e., a cluster of very high Max LongString values off by itself, away from the main distribution), congratulations, because it’s obvious which cases you should drop. If you don’t see clear outliers, then it’s probably safer to ignore LongString for this analysis.Another potential issue with Max LongString is that if you have scales with varying numbers of items, shorter scales can be lost when you calculate the Max. To avoid that problem, try converting each of your longstrings into a proportion. For example, for a 4-item scale, try =LONGSTRING(H4:H7)/4 and then calculate MAX() on those results.ReferencesMeade AW, & Craig SB (2012). Identifying careless responses in survey data. Psychological Methods, 17 (3), 437-55.

Objectives The selection of sample times for a pharmacokinetic study is important when trapezoidal integration (e.g. non-compartmental analysis) is used to determine the area under the concentration–time curve (AUC). The aim of this study was to develop an algorithm that determines optimal times that provide the most accurate AUC by minimising trapezoidal integration error. Methods The algorithm required initial single individual or mean pooled concentration data but did not specifically require a prior pharmacokinetic model. Optimal sample intervals were determined by minimising trapezoidal error using a genetic algorithm followed by a quasi-Newton method. The method was evaluated against simulated and clinical datasets to determine the method's ability to estimate the AUC. Key findings The sample times produced by the algorithm were able to accurately estimate the AUC of pharmacokinetic profiles, with the relative AUC having 90% confidence intervals of 0.919–1.05 for profiles with two-compartment kinetics. When comparing the algorithm with rich sampling (e.g. phase I trial), the algorithm provided equivalent or superior sample times with fewer observations. Conclusions The creation of the algorithm and its companion web application allows users with limited pharmacometric or programming training can obtain optimal sampling times for pharmacokinetic studies.

Making sense of the external world is vital for multiple domains of cognition, and so it is crucial that object recognition is maintained across the lifespan. We investigated age differences in perceptual and conceptual processing of visual objects in a population-derived sample of 85 healthy adults (24-87 years old) by relating measures of object processing to cognition across the lifespan. Magnetoencephalography (MEG) was recorded during a picture naming task to provide a direct measure of neural activity, that is not confounded by age-related vascular changes. Multiple linear regression was used to estimate neural responsivity for each individual, namely the capacity to represent visual or semantic information relating to the pictures. We find that the capacity to represent semantic information is linked to higher naming accuracy, a measure of task-specific performance. In mature adults, the capacity to represent semantic information also correlated with higher levels of fluid intelligence, reflecting domain-general performance. In contrast, the latency of visual processing did not relate to measures of cognition. These results indicate that neural responsivity measures relate to naming accuracy and fluid intelligence. We propose that maintaining neural responsivity in older age confers benefits in task-related and domain-general cognitive processes, supporting the brain maintenance view of healthy cognitive ageing. ispartof: SCIENTIFIC REPORTS vol:9 issue:1 ispartof: location:England status: published

Several methods have been developed to measure dynamic functional connectivity (dFC) in fMRI data. These methods are often based on a sliding-window analysis, which aims to capture how the brain's functional organization varies over the course of a scan. The aim of many studies is to compare dFC across groups, such as younger versus older people. However, spurious group differences in measured dFC may be caused by other sources of heterogeneity between people. For example, the shape of the haemodynamic response function (HRF) and levels of measurement noise have been found to vary with age. We use a generic simulation framework for fMRI data to investigate the effect of such heterogeneity on estimates of dFC. Our findings show that, despite no differences in true dFC, individual differences in measured dFC can result from other (non-dynamic) features of the data, such as differences in neural autocorrelation, HRF shape, connectivity strength and measurement noise. We also find that common dFC methods such as k-means and multilayer modularity approaches can detect spurious group differences in dynamic connectivity due to inappropriate setting of their hyperparameters. fMRI studies therefore need to consider alternative sources of heterogeneity across individuals before concluding differences in dFC., Graphical abstract fx1, Highlights • Estimates of dFC may be affected by various sources of between-people heterogeneity. • We simulated fMRI data to investigate the effect of such heterogeneity on dFC. • Differences in estimated dFC resulted from non-dynamic features of the data. • Choice of parameters in common methods produced spurious group differences in dFC.

Background The nested case-control study (NCC) design within a prospective cohort study is used when outcome data are available for all subjects, but the exposure of interest has not been collected, and is difficult or prohibitively expensive to obtain for all subjects. A NCC analysis with good matching procedures yields estimates that are as efficient and unbiased as estimates from the full cohort study. We present methodological considerations in a matched NCC design and analysis, which include the choice of match algorithms, analysis methods to evaluate the association of exposures of interest with outcomes, and consideration of overmatching. Methods Matched, NCC design within a longitudinal observational prospective cohort study in the setting of two academic hospitals. Study participants are patients aged over 70 years who underwent scheduled major non-cardiac surgery. The primary outcome was postoperative delirium from in-hospital interviews and medical record review. The main exposure was IL-6 concentration (pg/ml) from blood sampled at three time points before delirium occurred. We used nonparametric signed ranked test to test for the median of the paired differences. We used conditional logistic regression to model the risk of IL-6 on delirium incidence. Simulation was used to generate a sample of cohort data on which unconditional multivariable logistic regression was used, and the results were compared to those of the conditional logistic regression. Partial R-square was used to assess the level of overmatching. Results We found that the optimal match algorithm yielded more matched pairs than the greedy algorithm. The choice of analytic strategy—whether to consider measured cytokine levels as the predictor or outcome-- yielded inferences that have different clinical interpretations but similar levels of statistical significance. Estimation results from NCC design using conditional logistic regression, and from simulated cohort design using unconditional logistic regression, were similar. We found minimal evidence for overmatching. Conclusions Using a matched NCC approach introduces methodological challenges into the study design and data analysis. Nonetheless, with careful selection of the match algorithm, match factors, and analysis methods, this design is cost effective and, for our study, yields estimates that are similar to those from a prospective cohort study design.

Despite wide use of regression-based regional flood frequency analysis (RFFA) methods, the majority are based on either ordinary least squares (OLS) or generalized least squares (GLS). This paper proposes ‘spatial proximity’ based RFFA methods using the spatial lagged model (SLM) and spatial error model (SEM). The proposed methods are represented by two frameworks: the quantile regression technique (QRT) and parameter regression technique (PRT). The QRT develops prediction equations for flooding quantiles in average recurrence intervals (ARIs) of 2, 5, 10, 20, and 100 years whereas the PRT provides prediction of three parameters for the selected distribution. The proposed methods are tested using data incorporating 30 basin characteristics from 237 basins in Northeastern United States. Results show that generalized extreme value (GEV) distribution properly represents flood frequencies in the study gages. Also, basin area, stream network, and precipitation seasonality are found to be the most effective explanatory variables in prediction modeling by the QRT and PRT. ‘Spatial proximity’ based RFFA methods provide reliable flood quantile estimates compared to simpler methods. Compared to the QRT, the PRT may be recommended due to its accuracy and computational simplicity. The results presented in this paper may serve as one possible guidepost for hydrologists interested in flood analysis at ungaged sites.

Non-compartmental analysis (NCA) is regarded as the standard for establishing bioequivalence, despite its limitations and the existence of alternative methods such as non-linear mixed effects modelling (NLMEM). Comparisons of NCA and NLMEM in bioequivalence testing have been limited to drugs with one-compartment kinetics and have included a large number of different approaches. A simulation tool was developed with the ability to rapidly compare NCA and NLMEM methods in determining bioequivalence using both R and NONMEM and applied to a drug with two-compartment pharmacokinetics. Concentration–time profiles were simulated where relative bioavailability, random unexplained variability (RUV) at the lower limit of quantification (LLOQ) differed between simulations. NLMEM analyses employed either the M1 or M3 methods for dealing with values below the LLOQ. It was used to elucidate the impact of changes in (i) RUV at the LLOQ, (ii) the extent of censoring data below the LLOQ and (iii) the concentration sampling times. The simulations showed NLMEM having a consistent 20–40% higher accuracy and sensitivity in identifying bioequivalent studies when compared to NCA, while NCA was found to have a 1–10% higher specificity than NLMEM. Increasing data censoring by increasing the LLOQ resulted in decreases of ~10% to the accuracy and sensitivity of NCA, with minimal effects on NLMEM. The tool provides a platform for comparing NCA and NLMEM methods and its use can be extended beyond the scenarios reported here. In the situations examined it is seen that NLMEM is more accurate than NCA and may offer some advantages in the determination of bioequivalence. Refereed/Peer-reviewed

Studies of brain-wide functional connectivity or structural covariance typically use measures like the Pearson correlation coefficient, applied to data that have been averaged across voxels within regions of interest (ROIs). However, averaging across voxels may result in biased connectivity estimates when there is inhomogeneity within those ROIs, e.g., sub-regions that exhibit different patterns of functional connectivity or structural covariance. Here, we propose a new measure based on “distance correlation”; a test of multivariate dependence of high dimensional vectors, which allows for both linear and non-linear dependencies. We used simulations to show how distance correlation out-performs Pearson correlation in the face of inhomogeneous ROIs. To evaluate this new measure on real data, we use resting-state fMRI scans and T1 structural scans from 2 sessions on each of 214 participants from the Cambridge Centre for Ageing & Neuroscience (Cam-CAN) project. Pearson correlation and distance correlation showed similar average connectivity patterns, for both functional connectivity and structural covariance. Nevertheless, distance correlation was shown to be 1) more reliable across sessions, 2) more similar across participants, and 3) more robust to different sets of ROIs. Moreover, we found that the similarity between functional connectivity and structural covariance estimates was higher for distance correlation compared to Pearson correlation. We also explored the relative effects of different preprocessing options and motion artefacts on functional connectivity. Because distance correlation is easy to implement and fast to compute, it is a promising alternative to Pearson correlations for investigating ROI-based brain-wide connectivity patterns, for functional as well as structural data., Highlights • We introduce distance correlation as a new measure of ROI-based connectivity. • It can be used for functional connectivity and structural covariance analyses. • Simulations show that distance correlation copes with inhomogeneous ROIs. • In real data, distance correlation is more reliable and robust than Pearson correlation. • Distance correlation improves correspondence between different ROI definitions.

This study addressed yam production in response to climate change in Cross River State using a co-integration model approach. The specific objectives of this paper are to analyze the trend in yam production, annual precipitation, and annual temperature, and to analyze the impact of climate variables on yam production. Time-series data from 1996 to 2017 was used. Based on the analysis, which constituted a linear trend analysis, co-integration test, and error correction model, the study came up with robust findings. The linear trend analysis for yam production revealed a steady increase in output between the years 2005 and 2016. The result of the rainfall trend analysis showed the presence of rainfall variability and irregularity. The trend line for temperature showed an overall downward trend for the period under study. However, the Error Correction Model result showed that temperature was statistically significant and negatively impacted yam production. The study recommends that policymakers should take appropriate steps to encourage the development of pest- and disease-tolerant yam varieties because an increase in temperature leads to the proliferation of insects, pests, and diseases.

Introduction The analytical solutions to compartmental pharmacokinetic models are well known, but have not been presented in a form that easily allows for complex dosing regimen and changes in covariate/parameter values that may occur at discrete times within and/or between dosing intervals. Methods Laplace transforms were used to derive ADVAN-style analytical solutions for 1, 2, and 3 compartment pharmacokinetic linear models of intravenous and first-order absorption drug administration. The equations calculate the change in drug amounts in each compartment of the model over a time interval (t; t = t2 − t1) accounting for any dose or covariate events acting in the time interval. The equations were coded in the R language and used to simulate the time-course of drug amounts in each compartment of the systems. The equations were validated against commercial software [NONMEM (Beal, Sheiner, Boeckmann, & Bauer, 2009)] output to assess their capability to handle both complex dosage regimens and the effect of changes in covariate/parameter values that may occur at discrete times within or between dosing intervals. Results For all tested pharmacokinetic models, the time-course of drug amounts using the ADVAN-style analytical solutions were identical to NONMEM outputs to at least four significant figures, confirming the validity of the presented equations. Discussion To our knowledge, this paper presents the ADVAN-style equations for common pharmacokinetic models in the literature for the first time. The presented ADVAN-style equations overcome obstacles to implementing the classical analytical solutions in software, and have speed advantages over solutions using differential equation solvers. The equations presented in this paper fill a gap in the pharmacokinetic literature, and it is expected that these equations will facilitate the investigation of useful open-source software for modelling pharmacokinetic data.

Polebitski, Austin S. and Richard N. Palmer, 2012. Analysis and Predictive Models of Single-Family Customer Response to Water Curtailments During Drought. Journal of the American Water Resources Association (JAWRA) 1-12. DOI: 10.1111/j.1752-1688.2012.00691.x Abstract: This research investigates customer response to demand management strategies during two drought periods in the City of Seattle. An analysis of customer response to voluntary water curtailments is conducted using k-means clustering to identify like groups of customers and behavior patterns. The clustering method identified important variables (household income, lot size, living space, and family size) useful in determining customer response to water curtailments. Ordinary least squares and spatial lag regression models are estimated using the first and second principal components of variables identified in the clustering analysis. Larger values of income, lot size, and living space enhanced water reductions whereas larger family size tended to reduce the effectiveness of curtailments. Projections of changes in Seattle’s built environment and demographics between 2000 and 2030 were obtained from an urban simulation model (UrbanSim) and were processed through the regression models to investigate changes in future curtailment effectiveness. This research found that increasing household size hardened demands (decreased curtailment effectiveness) whereas decreasing household size increased per-capita curtailment effectiveness. These results suggest that changes in the number of residents within a home is likely to be the most important factor in determining future curtailment effectiveness.

A large body of research has established that, under relatively simple task conditions, human observers integrate uncertain sensory information with learned prior knowledge in an approximately Bayes-optimal manner. However, in many natural tasks, observers must perform this sensory-plus-prior integration when the underlying generative model of the environment consists of multiple causes. Here we ask if the Bayes-optimal integration seen with simple tasks also applies to such natural tasks when the generative model is more complex, or whether observers rely instead on a less efficient set of heuristics that approximate ideal performance. Participants localized a "hidden" target whose position on a touch screen was sampled from a location-contingent bimodal generative model with different variances around each mode. Over repeated exposure to this task, participants learned the a priori locations of the target (i.e., the bimodal generative model), and integrated this learned knowledge with uncertain sensory information on a trial-by-trial basis in a manner consistent with the predictions of Bayes-optimal behavior. In particular, participants rapidly learned the locations of the two modes of the generative model, but the relative variances of the modes were learned much more slowly. Taken together, our results suggest that human performance in a more complex localization task, which requires the integration of sensory information with learned knowledge of a bimodal generative model, is consistent with the predictions of Bayes-optimal behavior, but involves a much longer time-course than in simpler tasks.

A stochastic simulation model was developed to examine the impact of risky economic variables on the profitability of a small-scale shrimp farm. Sources of risk included input and output prices, random-kill events, and hurricane damages. Success was measured using the probability distribution of the net present value (NPV). A baseline model that assumed capital costs of $493,993, a stocking density of 100 shrimp per m2, a harvest survival of 80%, and a discount rate of 8% failed to generate a positive NPV. Subsequently adding a $0.66 price premium also failed to establish a positive NPV. Further reducing initial capital costs by 50% resulted in a 2% probability of a positive NPV. Incrementally reducing the discount rate generated increasingly positive NPV probabilities ranging from a 9% probability of success (7% discount rate) to a 94% probability of success (3% discount rate). Additional analyses suggested that probabilities of financial success were also sensitive to random-kill and hurricane events.

This paper proposes a new control chart to effectively monitor the decrease in variance of a normal process when only individual observations are available. The idea of the new control chart, which is called the exponentially weighted mean squared inverse error (EWMSI) chart, stems from the exponentially weighted mean squared error (EWMS) chart of MacGregor and Harris (J. Qual. Technol. 1993; 25(2):106–118). Simulation studies and an example demonstrate that the lower-sided EWMSI chart is superior to the lower-sided EWMS chart and the lower-sided modified EWMS (M-EWMS) chart of Huwang et al. (Nav. Res. Logist. 2009; 56(7):659–668) in detecting a decrease in process variance. Furthermore, the combination of a lower-sided EWMSI chart and an upper-sided EWMS chart is shown to outperform the two-sided EWMS chart and the two-sided M-EWMS chart in monitoring the overall changes in process variance. Copyright © 2010 John Wiley & Sons, Ltd.

When addressing quality problems, quality teams are often given a quantifiable goal, requiring data to be assessed in order to determine if the goal has been met. A method is proposed for determining the sample sizes necessary for detecting relative qu..

We propose and study exponentially weighted moving average (EWMA) control charts for monitoring high-yield processes. The EWMA control charts are developed based on non-transformed geometric, binomial and Bernoulli counts. The proposed charts are evaluated based on the average number of items sampled before the first out-of-control signal is detected. By selecting small smoothing constants, the proposed EWMA control charts outperform in numerous cases the recently developed CUSUM control charts [Chang, T.C. and Gan, F.F., Cumulative sum charts for high yield processes. Statist. Sin., 2001, 11, 791–805], which are considered the most efficient control charting mechanisms in the existing literature for monitoring fraction non-conforming as small as 0.0001. Numerous simulations are included for performance comparisons. An example is also given to demonstrate the applicability of the proposed EWMA control charts.

The purpose of this research report is to highlight a unique set of issues that arise when considering the effects of range restriction in the context of estimating predictor intercorrelations. Three approaches are used to illustrate the issue: simulation, a concrete applied example, and a reanalysis of a meta-analysis of ability-interview correlations. The general conclusion is that a predictor intercorrelation can differ dramatically from the population value when both predictors are used in a composite that is used operationally for selection. The compensatory nature of a composite means that low scorers on one predictor can only obtain high scores on the composite if they obtain very high scores on the other predictor; this phenomenon distorts the correlation between the predictors.

In observational studies of treatment effects, matched samples have traditionally been constructed using two tools, namely close matches on one or two key covariates and close matches on the propensity score to stochastically balance large numbers of covariates. Here we propose a third tool, fine balance, obtained using the assignment algorithm in a new way. We use all three tools to construct a matched sample for an ongoing study of provider specialty in the treatment of ovarian cancer. Fine balance refers to exact balance of a nominal covariate, often one with many categories, but it does not require individually matched treated and control subjects for this variable. In the example the nominal variable has 72 = 9 × 8 categories formed from 9 possible years of diagnosis and 8 geographic locations or SEER sites. We obtain exact balance on the 72 categories and close individual matches on clinical stage, grade, year of diagnosis, and other variables using a distance, and stochastically balance a total of ...

Analysis of variance (ANOVA) is a type of general linear model suitable for factorial designs, in which one is interested in the main effects of, and interactions between, one or more factors. ANOVA assumes a spherical error covariance, and violations such as correlation induced by repeated measures from the same subjects, or inhomogeneous variance across conditions, require either post hoc corrections to the degrees of freedom, partitioning of the error into separate error terms, or explicit modeling of the error covariance.

In this paper, we review multivariate control charts designed for monitoring changes in a covariance matrix that have been developed in the last 15 years. The focus is on control charts developed for multivariate normal processes, assuming that independent subgroups of observations or independent individual observations are sampled as process monitoring proceeds. Control charts developed between 1990 and 2005 are reviewed according to the types of the control chart: multivariate Shewhart chart, multivariate CUSUM chart and multivariate EWMA chart. In addition to these developments, a new multivariate EWMA control chart is proposed. We also discuss comparisons of chart performance that have been carried out in the literature, as well as the issue of diagnostics. Some potential future research ideas are also given.

In casino blackjack, the odds fluctuate from round to round as cards are dealt from a randomly shuffled pack. A player who ‘counts cards’ can estimate the odds on the next round and so can vary his bet size accordingly: better-than-average odds warrant a larger bet. The optimal relationship of bet to count is derived here under the criterion of maximum expected increase in capital per round subject to a specified risk of ruin. The optimisation analysis is complicated by the need to impose lower and possibly upper bounds on the bet size. A family of optimal betting schemes is found, depending on the risk selected and other parameters; among this family is the one found by Harris, Janecek and Yamashita using a different optimisation criterion. Representative computational results are displayed for a typical set of blackjack conditions. Some commentary is given on the choice of a bet scheme from the optimal family, depending on the player’s style and objectives. Remarks are also made about Kelly bet...

Background: Phase angle is an indicator based on reactance and resistance obtained from bioelectrical impedance analysis (BIA). Although its biological meaning is still not clear, phase angle appears to have an important prognostic role. Objective: The aim of this study was to estimate population averages and SDs of phase angle that can be used as reference values. Design: BIA and other methods used to evaluate body composition, including hydrodensitometry and total body water, were completed in 1967 healthy adults aged 18-94 y. Phase angle was calculated directly from body resistance and reactance, and fat mass (FM) was estimated from the combination of weight, hydrodensitometry, and total body water by using the 3-compartment Siri equation. Phase angle values were compared across categories of sex, age, body mass index (BMI), and percentage FM. Results: Phase angle was significantly (P < 0.001) smaller in women than in men and was lower with greater age (P < 0.001). Phase angle increased with an increase in BMI and was significantly inversely associated with percentage fat in men. Phase angle was significantly predicted from sex, age, BMI, and percentage FM in multiple regression models. Conclusions: Phase angle differs across categories of sex, age, BMI, and percentage fat. These reference values can serve as a basis for phase angle evaluations in the clinical setting.

The common “F test” for testing the equality of two population variances is very sensitive to the normality assumption, yet many introductory statistics books do not stress this sensitivity. Several alternative dispersion tests have been developed that do not assume normality, but these are rarely discussed other than in nonparametric statistics texts. Additionally, these tests generally require tables of critical values or software to calculate p values. We propose a simple graphical procedure, requiring no tables or software, that compares absolute deviations of one sample to another. With equal sample sizes, if one sample has the five largest absolute deviations, we conclude that its population has greater dispersion. We believe the simplicity of this test makes it a viable alternative to the often misleading F test and to other tests.

We explore the impact of dispersion effects on location effect estimation and derive approximate joint confidence regions for pairs of correlated location effect estimates. A procedure for estimating location effects in the presence of a single dispersion effect is recommended.

Fractional factorial designs are often used in industry to screen potentially important factors of their impact on the mean response or location effect. These experiments are often unreplicated in order to save resources, and so only one observation ..

A consistent product/process will have little variability, i.e. dispersion. The widely-used unreplicated two-level fractional factorial designs can play an important role in detecting dispersion effects with a minimum expenditure of resources. In this paper we develop a nonparametric dispersion test for unreplicated two-level fractional factorial designs. The test statistic is defined, critical values are provided, and large sample approximations are given. Through simulations and examples from the literature, the test is compared to general nonparametric dispersion tests and a parametric test based on a normality assumption. These comparisons show the test to be the most robust of those studied and even superior to the normality-based test under normality in some situations. An example is given where this new test is the only one of those studied that does not incorrectly detect a spurious dispersion effect.

Purpose To establish if a positive impingement sign in femoroacetabular impingement (FAI) may result from entrapment of the fat pad located at the anterior head-neck junction of the upper femur. This fat pad is routinely removed before any cam lesion excision. Methods We report a prospective study of 142 consecutive hip arthroscopies for symptomatic FAI where the aim was to remove the arthroscopically identified area of impingement, not necessarily to create a spherical femoral head. Patients were divided into two groups. Group 1 (n = 92; 34 females, 58 males), where a cam-type bony FAI lesion was identified and excised in addition to the fat pad which overlay it, and Group 2 (n = 50; 29 females, 21 males) where the only identified point of impingement was a prominent fat pad. In this situation the fat pad was excised in isolation and the underlying bone preserved. Patients were assessed preoperatively, at six weeks, six months, one year and two years with a modified Harris hip score (mHHS). Results Both groups were comparable preoperatively for mean age, mean alpha angle and mean anterior offset ratio. Both groups improved significantly after surgery at all time points. However, Group 1 (fat pad and bone resection) demonstrated 16.0% improvement in mHHS by two years while for Group 2 (fat pad resection only) the improvement was 18.9% (p = 0.628). Conclusions The fat pad found at the anterior head/neck junction of the hip joint can be a source of pain and we propose fat pad entrapment as a new, previously undescribed diagnosis. Our findings also suggest that a large number of cam lesions are being excised unnecessarily and that further efforts should be made to understand the role of the fat pad as a source of groin discomfort. Level of Evidence Level IV, case series.

In unreplicated 2k−p designs, the assumption of constant variance is commonly made. When the variance of the response differs between the two levels of a column in the effect matrix, that column produces a dispersion effect. In this article we show that two active dispersion effects may create a spurious dispersion effect in their interaction column. Most existing methods for dispersion-effect testing in unreplicated fractional factorial designs are subject to these spurious effects. We propose a method of dispersion-effect testing based on geometric means of residual sample variances. We show through examples from the literature and simulations that the proposed test has many desirable properties that are lacking in other tests.

When studying both location and dispersion effects in unreplicated fractional factorial designs, a “standard” procedure is to identify location effects using ordinary least squares analysis, fit a ...

Article-at-a-Glance Introduction It has been proposed that a ratio of the discordant cells from a McNemar's Chi-square table be used as a measure of quality improvement, and that this measure be called the Quality Improvement Ratio (QuIR). As proposed, patients enrolled in only one year of a two-year study are excluded from the McNemar's table of the QuIR. Since the original proposal of the McNemar's Chi-square in 1947 included application to matched pair data, a more comprehensive analysis would be possible if the single-year enrollees were matched into pairs. Methods Patients enrolled in only the first study year are matched and paired with patients enrolled in only the second study year. The pairs are matched on variables important to the disease or process being evaluated. The matched pairs are combined with the repeatedly measured subjects to increase the statistical power of the analysis. The Combined Quality Improvement Ratio (CQuIR) is demonstrated with parameters from the original articles, in a–Markov chain Monte-Carlo simulation, so a direct comparison can be made. Results CQuIR improved statistical power, especially in simulations of small populations. In some simulations the statistical power was double that of the QuIR alone. Discussion Although the QuIR provides important information, the CQuIR allows more of the data to be used to evaluate the effect of interventions in policy, delivery, and practice. The increase in statistical power of the CQuIR over the QuIR can facilitate successful evaluation of health care services.