Kolassa, J.E., and McCullagh, P. (1990), Edgeworth Series for Lattice Distributions, Annals of Statistics
This paper investigates the use of Edgeworth expansions for approximating the distribution function of the normalized sum of n independent and identically distributed lattice-valued random variables. We prove that the continuity-corrected Edgeworth series, using Sheppard-adjusted cumulants, is accurate to the same order in n as the usual Edgeworth approximation for continuous random variables. Finally, as a partial justification of the Sheppard adjustments, it is shown that if a continuous random variable Y is rounded into a discrete part D and a truncation error U, such that Y=D+U, then under suitable limiting conditions the truncation error is approximately uniformly distributed and independent of Y, but not independent of D.
Kolassa, J.E. (1991) Saddlepoint Approximations in the Case of Intractable Cumulant Generating Functions, Selected Proceedings of the Sheffield Symposium on Applied Probability. Statistics, 236--255.
Saddlepoint Approximations have long been used to approximate densities and distribution functions of random variables with known cumulant generating function defined on an open interval about the origin. This approximation has very desirable asymptotic properties when approximating densities and tail probabilities for sums of random variables, and also often performs remarkably well for small sample sizes, including samples of one.
Calculating the saddlepoint approximation requires calculating the Legendre transform of the log of the cumulant generating function. In some cases this cumulant generating function may be unavailable; in other cases the Legendre transform is difficult to calculate analytically. This paper discusses modifications to the saddlepoint approximation necessary when the cumulant generating function is replaced by a similar but more tractable function whose Legendre transform can be given explicitly. Calculations for the logistic distribution are presented to illustrate the case of a known but intractable cumulant generating function, and an example involving an overdispersed binomial model is presented to illustrate the case of an unavailable cumulant generating function. An application to a random effects logistic linear model is discussed.
Handcock, M.S., and Kolassa, J.E. (1992), Statistical Review of the Henhouse experiments: The Effects of a Pulsed Magnetic Field on Chick Embryos, Bioelectromagnetics.
This paper analyzes data from a study conducted by the United States Office of Naval Research on the effects of pulsed magnetic fields on chick embryos. The experiment involved incubation of eggs under carefully controlled conditions in six different laboratories. The original analysis included inappropriate statistical methodology for analyzing the experimental results. Since the conclusions from this study rest so heavily on the results of statistical analyses, choosing the proper methodology is imperative. The major aim of this paper then is to introduce more appropriate analytic tools and illustrate their use in the present context. Qualitatively our results agree with those of the original analysis; our findings about interactions between effects, however, makes interpretation of these effects more subtle. We apply linear logistic modeling to counts of damaged embryos, using as covariates factors corresponding to exposure, laboratory, incubator, run, and measurements of background radiation. This facilitates estimation of the size of the effects. The effects of laboratory, incubator, and run are explored both as fixed and random effects. We find statistically significant exposure and laboratory effects, in accordance with the original study. However, we also find that the inter-laboratory variation in exposure effect is at least as large as the exposure effect itself. The presence of such effects fundamentally alters the interpretation of the fitted model, as is graphically presented.
Kolassa, J.E. (1992), Confidence Intervals for Thermodynamic Constants, Geochimica et Cosmochimica Acta
Phase equilibrium experiments using the same reactants and run at different temperatures and pressures give rise to linear constraints on thermodynamic variables, such as entropies, enthalpies, and volume changes of reaction. Linear programming has been applied to this problem to determine maxima and minima for these parameters separately. Since these temperatures and pressures are measured or set with uncertainty, their nominal values as reported by the experimenter need not define the same feasible region as that defined by their true values. Clearly, then, the ranges resulting from the linear programming procedure will not represent the reasonable ranges of parameter values. This paper explores the problem of inference on these parameters when a normal error distribution is postulated for temperature and pressure. Current methodologies and their relation to the field of statistical inference are discussed. Two algorithms for generating bounds on the entropies and enthalpies are presented. The first uses a normal approximation to the location of feasible region vertices and makes allowances for variations in the constraints contributing to this vertex to construct confidence intervals for the extrema in random linear programs in order to generate bounds holding for one parameter at a time. The second generates bounds holding simultaneously for all parameters. A comparison of these confidence intervals with those generated by conventional methods demonstrates that estimates of thermodynamic variables have far less variability than commonly believed.
Handcock, M.S., and Kolassa, J.E. (1992), Statistical Review of the Henhouse experiments: The Effects of a Pulsed Magnetic Field on Chick Embryos, Bioelectromagnetics
This paper analyzes data from a study conducted by the United States Office of Naval Research on the effects of pulsed magnetic fields on chick embryos. The experiment involved incubation of eggs under carefully controlled conditions in six different laboratories. The original analysis included inappropriate statistical methodology for analyzing the experimental results. Since the conclusions from this study rest so heavily on the results of statistical analyses, choosing the proper methodology is imperative. The major aim of this paper then is to introduce more appropriate analytic tools and illustrate their use in the present context. Qualitatively our results agree with those of the original analysis; our findings about interactions between effects, however, makes interpretation of these effects more subtle. We apply linear logistic modeling to counts of damaged embryos, using as covariates factors corresponding to exposure, laboratory, incubator, run, and measurements of background radiation. This facilitates estimation of the size of the effects. The effects of laboratory, incubator, and run are explored both as fixed and random effects. We find statistically significant exposure and laboratory effects, in accordance with the original study. However, we also find that the inter‐laboratory variation in exposure effect is at least as large as the exposure effect itself. The presence of such effects fundamentally alters the interpretation of the fitted model, as is graphically presented.
Kolassa, J.E., and Tanner, M.A. (1994), Approximate Conditional Inference in Exponential Families Via the Gibbs Sampler, Journal of the American Statistical Association
This article presents the Gibbs-Skovgaard algorithm for approximate frequentist inference. The method makes use of the double saddlepoint approximation of Skovgaard to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics. This approximation is then used in the Gibbs sampler to generate a Markov chain. The equilibrium distribution of this chain approximates the joint distribution of the sufficient statistics associated with the parameters of interest conditional on the observed values of the sufficient statistics associated with the nuisance parameters. This Gibbs-Skovgaard algorithm is applied to the cases of logistic and Poisson regression.
Tariot, P.N., Erb, R., Leibovici, A., Podgorski, C.A., Cox, C., Asnis, J., Irvine, C., and Kolassa, J.E. (1994), Carbamazepine Treatment of Agitation in Nursing Home Patients with Dementia: A Preliminary Study, Journal of the American Geriatrics Society
Objective: To determine the effects of carbamazepine versus placebo on ratings of behavior in agitated nursing home patients with dementia. Design: Nonrandomized, placebo-controlled, crossover trial conducted in 25 patients in two nursing homes. Intervention: Carbamazepine and placebo were administered during two 5-week periods separated by a 2-week washout. The carbamazepine dose was determined for each patient by a nonblinded physician who did not participate in ratings (modal dose 300 mg/day). Measurements: The primary outcome measures were Brief Psychiatric Rating Scale scores and Clinical Global Impression of Change, rated by blind observers. Secondary measures of behavior, adversity, cognition, and functional status were also included. Main results: Median total Brief Psychiatric Rating Scale score decreased 7 points on carbamazepine versus 3 on placebo (P = 0.03). Sixteen subjects were rated as improved globally on carbamazepine versus four on placebo (P = 0.001). Secondary measures of behavior showed similar changes at significant or suggestive (P < 0.10) levels. One subject developed carbamazepine-induced tics, and one died with a pneumonia. There was minimal other adversity. Conclusion: This preliminary study suggests that carbamazepine in low doses can reduce agitated behaviors in some patients, with limited adversity resulting. Further research is required to confirm and extend this finding before it can be considered routine clinical practice.
Kolassa, J.E. (1995), A Comparison of Size and Power Calculations for the Wilcoxon Statistic for Ordered Categorical Data, Statistics in Medicine
This paper compares the accuracy of approximations to test size and power based on the score and the Fisher information, with calculations using Edgeworth and Cornish Fisher approximations, and demonstrates that in some cases one must exercise much care in using the simpler approximations.
Falsey, A.R., McCann, R.M., Hall, W.J., Tanner, M.A., Criddle, M.M., Formica, M.A., Treanor, J.J., Irvine, C., and Kolassa, J.E. (1995), Acute Respiratory Tract Infection in Daycare Centers for the Older Persons, Journal of the American Geriatrics Society
Objective: To evaluate the rate of specific pathogens and clinical syndromes associated with acute respiratory tract infections (ARTI) in frail older persons attending daycare. Design: Prospective descriptive study, without intervention. Setting: Two sites of a senior daycare program providing all-inclusive care for the older persons in Rochester, New York. Participants: Staff members and participants of the day-care. Measurements: Demographic, medical, and physical findings were collected from older subjects at baseline and while ill with respiratory illnesses. Nasopharyngeal specimens for viral and Chlamydia culture and sputum for bacterial culture were obtained from subjects when ill. Acute and convalescent sera were also collected with each illness and examined for viral, chlamydial, and mycoplasma infection. Main results: One hundred sixty-five illnesses were documented in 165 older daycare participants as well as 113 illnesses among 67 staff members during the 15-month study. The rate of ARTI in the elderly group was 10.8 per 100 person months. The most common etiologies in both the staff and elderly participants were respiratory syncytial virus (RSV), Influenza A, and coronavirus. The etiologies of illnesses in the staff compared with those in elderly group were similar except that bacterial infections were significantly more common among the elderly (7% vs. 0, P = 0.05). Multiple pathogens were found to cocirculate within centers, and no clear outbreak of a predominant organism was noted. Cough and nasal congestion characterized most illnesses. The elderly experienced significantly more cough, dyspnea, and sputum production than did the staff. There were 10 hospitalizations related to respiratory infections and four deaths during the acute illness among the elderly group and none in staff.
Kolassa, J.E. (1995), Edgeworth Approximations for Rank Sum Test Statistics, Statistics and Probability Letters
Hettmansperger (1984) quotes a result showing that the distribution function of the Wilcoxon signed rank statistic is approximated by the usual Edgeworth series using the first four cumulants, to 0(1/n). In light of standard Edgeworth series results for random variables confined to a lattice, this result is counterintuitive. One expects correction terms to be necessary because of the lattice nature of the Wilcoxon statistic. This paper explains this apparent paradox, provides an alternative proof relying on basic Edgeworth series results, and provides a sharper result. Interesting features in this problem highlighting limitations of expansions for random variables on a lattice are discussed.
Kolassa, J.E. (1996), Higher-Order Approximations to Conditional Distribution Functions, Annals of Statistics
This paper derives higher-order terms in the double-saddlepoint expansion of Skovgaard for a unidimensional conditional cumulative distribution function. Expansions for continuous and lattice random variables are derived. Results are applied to the sufficient statistic in logistic regression.
Wahlberg, K.-E., Wynne, L.C., Oja, H., Keskitalo, P., Pykäläinen, L., Lahti, I., Moring, J., Naarala, M., Sorri, A., Markku Seitamaa, M., Läksy, K., Kolassa, J., and Tienari, P. (1997), Gene--Environment Interaction in Vulnerability to Schizophrenia: Findings from the Finish Adoptive Family Study, American Journal of Psychiatry
Kolassa, J.E. (1997), Infinite Parameter Estimates in Logistic Regression, with Application to Approximate Conditional Inference, Scandinavian Journal of Statistics
This paper discusses recovery of information regarding logistic regression parameters in cases when maximum likelihood estimates of some parameters are infinite. An algorithm for detecting such cases and characterizing the divergence of the parameter estimates is presented. A method for fitting the remaining parameters is also presented. All of these methods rely only on sufficient statistics rather than less aggregated quantities, as required for inference according to the method of Kolassa and Tanner (1994). These results are applied to approximate conditional inference via saddlepoint methods. Specifically, the double saddlepoint method of Skovgaard (1987( is adapted to the case when the solution to the saddlepoint equations exist as a point at infinity.
Katz, P.R., Karuza, J., Kolassa, J.E., and Hutson, A. (1997), Medical Practice with Nursing Home Residents: Results from the National Physician Activities Census, Journal of the American Geriatrics Society
Objective: The study describes the prevalence of medical nursing home practice. Further, it examines the extent to which physician characteristics and local county health care resources predict nursing home involvement. This information is relevant to evaluating and devising strategies that address the future provision of medical care in institutionalized long-term care.
Design: A cross-sectional survey.
Setting: A national sample of all licensed practicing physicians was obtained from a special Professional Activities (PPA) survey conducted by the American Medical Association (AMA) in 1991.
Participants: Respondents were 21,578 physicians involved in direct patient care.
Measures: The typical number of hours spent weekly caring for nursing home patients was obtained from the PPA survey, and physician demographics were obtained from the AMA Masterfile. County health care resources were obtained from the National Institutes of Health Area Resources File.
Results: Most (77%) physicians reported spending no measurable time caring for nursing home patients. In all disciplines, a majority of physicians with a nursing home practice spent less than 2 hours per week with patients. Logistic regressions indicted that family practitioners and internists were most likely to have a nursing home practice, but general practitioners were most likely to spend more time in practice. Only 15% of specialists reported having a nursing home practice. Prevalence of practice was greatest among solo practitioners and physicians in partnerships and least among academic and hospital-based physicians and physicians in group practice or employed by the government. Most county of practice resources were not associated or were modestly associated with nursing home practice, but having a nursing home practice became much more likely as the number of nursing home residents increased and hospital beds decreased. A pattern was found for nursing home practice to be slightly less likely as the county's per capita income and the proportion of proprietary nursing facilities increased.
Conclusions: With increasing numbers of older and frailer residents, nursing homes will continue to be integral components of the future healthcare system. However, physicians currently spend minimal time caring for nursing home patients, with physician characteristics best predicting involvement. Questions remain about the future of nursing home medical practice and how to best recruit, staff, and train future cadres of physicians to provide sufficient quality care for nursing home patients in an evolving health care system.
Falsey, A.R., McCann, R.M., Hall, W.J., Criddle, M.M., Formica, M.A., Wycoff, D., and Kolassa, J.E. (1997), The Common Cold in Frail Older Persons: Impact of Rhinovirus and Coronavirus in a Senior Daycare Center, Journal of the American Geriatrics Society
Kolassa, J.E. (1998), Uniformity of Double Saddlepoint Conditional Probability Approximations, Journal of Multivariate Analysis
This paper presents results showing that the error involved in using the double saddlepoint distribution function approximations of Skovgaard (1987, J. Appl. Probab. 24 875-887) are uniformly bounded. Particular attention is paid to distributions of sufficient statistics arising from generalized linear models. This work is intended in part to validate the use of the Markov Chain Monte Carlo by Kolassa and Tanner (1994, J. Amer. Statist. Assoc. 89 697-702) using these conditional distribution function approximations.
Wood, J.P., Kolassa, J.E., and McBride, J.T. (1998), Changes in Alveolar Septal Border Lengths with Postnatal Lung Growth, American Journal of Physiology
Kolassa, J.E. (1999), Confidence Intervals for Parameters Lying in a Random Polygon, Canadian Journal of Statistics
This paper presents algorithms for computing confidence intervals and regions for elements of a parameter vector when the signs of linear combinations of unknown parameters are observed, but the coefficients contain experimental error. These methods were proposed in the geochemical literature by Kolassa (1992) as a method specific to petrology. Experimental data are used to give linear constraints, involving quantities measured with error, on unknown free energies and entropies of a chemical reaction. Confidence intervals are given for these parameters, and these are compared with more naive approaches.
Kolassa, J.E. (1999), Convergence and Accuracy of Gibbs Sampling for Conditional Distributions in Generalized Linear Models, Annals of Statistics
This paper presents convergence conditions for a Markov chain constructed using Gibbs sampling, when the equilibrium distribution is the conditional sampling distribution of sufficient statistics from a generalized linear model. For cases when this unidimensional sampling is done approximately rather than exactly, the difference between the target equilibrium distribution and the resulting equilibrium distribution is expressed in terms of the difference between the true and approximating univariate conditional distributions. These methods are applied to an algorithm facilitating approximate conditional inference in canonical exponential families.
Falsey, A.R., Walsh, E.E., Looney, R.J., Kolassa, J.E., Formica, M.A., Criddle, M.C., Hall, W.J. (1999), Comparison of respiratory syncytial virus humoral immunity and response to infection in young and elderly adults, J. Med. Virol.
Falsey, A., Criddle, M.M., Kolassa, J.E., McCann, R.M., Brower, C., and Hall, W. (1999), Evaluation of a Handwashing Intervention to Reduce Respiratory Illness Rates in Senior Day-Care Centers, Infection Control and Hospital Epidemiology
Looney, R.J., Falsey, A., Campbell, D., Torres, A., Kolassa, J., Brower, C., McCann, R., Menegus, M., McCormick, K., Frampton, P., Hall, W., and Abraham, G.N. (1999), Role of Cytomegalovirus in the T cell changes seen in elderly individuals, Clinical Immunology
Lanphear, B.P., Howard, C., Eberly, S., Auinger, P., Kolassa, J., Weitzman, M., Schaffer, S.J., and Alexander, K. (1999), Primary Prevention of Childhood Lead Exposure: A Randomized Trial of Dust Control, Pediatrics
Kolassa, J.E., and Tanner, M.A. (1999), Small Sample Confidence Regions in Exponential Families, Biometrics
This article presents an algorithm for small-sample conditional confidence regions for two or more parameters for any discrete regression model in the generalized linear interactive model family. Regions are constructed by careful inversion of conditional hypothesis tests. This method presupposes the use of approximate or exact techniques for enumerating the sample space for some components of the vector of sufficient statistics conditional on other components. Such enumeration may be performed exactly or by exact or approximate Monte Carlo, including the algorithms of Kolassa and Tanner (1994, Journal of the American Statistical Association 89, 697-702; 1999, Biometrics 55, 246-251). This method also assumes that one can compute certain conditional probabilities for a fixed value of the parameter vector. Because of a property of exponential families, one can use this set of conditional probabilities to directly compute the conditional probabilities associated with any other value of the vector of the parameters of interest. This observation dramatically reduces the computational effort required to invert the hypothesis test to obtain the confidence region. To construct a region with confidence level 1 - alpha, the algorithm begins with a grid of values for the parameters of interest. For each parameter vector on the grid (corresponding to the current null hypothesis), one transforms the initial set of conditional probabilities using exponential tilting and then calculates the p value for this current null hypothesis. The confidence region is the set of parameter values for which the p value is at least alpha.
Kolassa, J.E. and Tanner, M.A. (1999), Approximate Monte Carlo Conditional Inference in Exponential Families, Biometrics
This article presents an algorithm for approximate frequentist conditional inference on two or more parameters for any regression model in the Generalized Linear Model (GLIM) family. We thereby extend highly accurate inference beyond the cases of logistic regression and contingency tables implemented in commercially available software. The method makes use of the double saddlepoint approximations of Skovgaard (1987, Journal of Applied Probability 24, 875-887) and Jensen (1992, Biometrika 79, 693-703) to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics. This approximation is then used in conjunction with noniterative Monte Carlo methods to generate a sample from a distribution that approximates the joint distribution of the sufficient statistics associated with the parameters of interest conditional on the observed values of the sufficient statistics associated with the nuisance parameters. This algorithm is an alternate approach to that presented by Kolassa and Tanner (1994, Journal of the American Statistical Association 89, 697-702), in which a Markov chain is generated whose equilibrium distribution under certain regularity conditions approximates the joint distribution of interest. In Kolassa and Tanner (1994), the Gibbs sampler was used in conjunction with these univariate conditional distribution function approximations. The method of this paper does not require the construction and simulation of a Markov chain, thus avoiding the need to develop regularity conditions under which the algorithm converges and the need for the data analyst to check convergence of the particular chain. Examples involving logistic and truncated Poisson regression are presented.
Kolassa, J.E. (2000), Explicit Bounds for Geometric Convergence of Markov Chains, Journal of Applied Probability
Kolassa, J.E. (2001), Saddlepoint Approximation at the Edges of a Conditional Sample Space, Statistics and Probability Letters
Saddlepoint methods present a convenient way to approximate probabilities associated with canonical sufficient statistic vectors in generalized linear models. Implementing saddlepoint approximations requires calculating maximum likelihood estimators for the associated parameters. When the sufficient statistic vector lies at the edge of the sample space, maximum likelihood estimators may not exist. This paper describes how to modify saddlepoint approximation to work in these cases.
Kolassa, J.E. (2001), Bounding Convergence Rates for Markov Chains: An Example of the Use of Computer Algebra, Statistics and Computing
Falsey, A.R., Walsh, E.E., Francis, C.W., Looney, R.J., Kolassa, J.E., Hall, W.J., and Abraham, G.N. (2001), Response of C-Reactive Protein (CRP) and Serum Amyloid A (SAA) to Influenza A Infection in Older Adults, Journal of Infectious Diseases
Horan, J.T., Francis, C.W., Falsey, A.R., Kolassa, J., Smith, B.H., and Hall, W.J. (2001), Prothrombotic changes in hemostatic parameters and C-reactive protein in the elderly with winter acute respiratory tract infections, Thrombosis and Haemostasis
Kissel, J.T., McDermott, M.P., Mendell, J.R., King, W.M., Pandya, S., Griggs, R.C., Tawil, R., and the FSY-DY Gruop (2001), Randomized, double-blind, placebo-controlled trial of albuterol in facioscapulohumeral dystrophy, Neurology
Background/Objectives: Animal and human studies suggest that β2-adrenergic agonists exert anabolic effects on muscles, inducing and preventing atrophy after a variety of insults. Based on data from an open-label trial of albuterol in 15 patients with facioscapulohumeral dystrophy (FSHD), the authors conducted a randomized, double-blind, placebo-controlled trial of sustained-release albuterol in this disease.
Methods: Ninety patients were randomized to three groups: placebo; 8.0 mg albuterol twice daily; or 16.0 mg albuterol twice daily. Patients were treated for 1 year with assessments at baseline and weeks 13, 26, and 52. The primary outcome was the 52-week change in global strength by maximum voluntary isometric contraction testing (MVICT). Secondary outcomes included changes at 52 weeks in strength by manual muscle testing (MMT), grip strength, functional testing, and muscle mass assessed by dual energy x-ray absorptiometry (DEXA).
Results: Eighty-four patients completed the study. The mean changes in composite MVICT scores were not significantly different between the groups (mean ± SD: placebo 0.20 ± 0.91; low dose −0.04 ± 0.84; high dose 0.08 ± 0.98). Similarly, there were no differences in the mean MMT change (placebo 0.04 ± 0.16; low dose −0.03 ± 0.13; high dose 0.00 ± 0.15). Grip improved in both treatment groups compared to placebo (placebo −0.53 ± 4.13, low dose +1.90 ± 3.34 [p = 0.02], high dose +1.70 ± 4.13 [p = 0.03]). The high-dose group had a significant increase in lean mass by DEXA (+1.57 ± 1.71 kg) compared to placebo (0.25 ± 2.24; p = 0.007). Albuterol was well tolerated; side effects included cramps, tremors, insomnia, and nervousness.
Conclusions: Although albuterol did not improve global strength or function in patients with FSHD, it did increase muscle mass and improve some measures of strength.
Looney, J.L., Hasan, M.S., Coffin, D., Campbell, D., Falsey, A.R., Kolassa, J.E., Agosti, J.M., Abraham, G.N., and Evans, T.G. (2001), Hepatitis B Immunization of Healthy Elderly Adults: Relationship between Naive CD4+ T Cells and Primary Immune Response, and Evaluation of GM-CSF as an Adjuvant, Journal of Clinical Immunology
Tawil, R., Griggs, R., Jackson, C., Amato, A., Barohn, R., Nations, S., Kissel, J., Mendell, J., Genge, A., Karpati, G., Rose, M., McDermott, M., Pandya, S., Myers, D., Herberlin, L., King, W., Holt, S., Finch, L., Cowman, J., Cos, L., Wrench, M., Sherman, C., Harding, K., Downing, K., Triguero, M., Morrison, C., Holloway, R., Higgins, D., Kolassa, J., Janciuras, J., Martens, W., Gregory, S., and Blood, C. (2001), Randomized pilot trial of beta INF1a (Avonex) in patients with inclusion body myositis, Neurology
Jing, B-Y., Kolassa, J.E., and Robinson, J. (2002), Partial saddlepoint approximations for transformed means, Scandinavian Journal of Statistics
The full saddlepoint approximation for real valued smooth functions of means requires the existence of the joint cumulant generating function for the entire vector of random variables which are being transformed. We propose a mixed saddlepoint-Edgeworth approximation requiring the existence of a cumulant generating function for only part of the random vector considered, while retaining partially the relative nature of the errors. Tail probability approximations are obtained under conditions which enable the approximations to be used in resampling situations and hence to obtain a result on the relative error of coverage in the case of the bootstrap approximation to the confidence interval for the Studentized mean.
Yang, B., and Kolassa, J.E. (2002), Saddlepoint Approximation for the Distribution Function Near the Mean, Annals of the Institute of Statistical Mathematics
We repair numerical difficulties in applying saddlepoint tail probability approximations when the ordinate at which the approximation is evaluated is near the mean of the distribution approximated. These modifications apply to double saddlepoint approximations to conditional distributions as well.
Kolassa, J.E. (2003), Saddlepoint Distribution Function Approximations in Biostatistical Inference, Statistical Methods in Medical Research
Applications of saddlepoint approximations to distribution functions are reviewed. Calculations are provided for marginal distributions and conditional distributions. These approximations are applied to problems of testing and generating confidence intervals, particularly in canonical exponential families.
Kolassa, J.E. (2003), Multivariate Saddlepoint Tail Probability Approximations, Annals of Statistics
This paper presents a saddlepoint approximation to the cumulative distribution function of a random vector. The proposed approximation has accuracy comparable to that of existing expansions valid in two dimensions, and may be applied to random vectors of arbitrary length, subject only to the requirement that the distribution approximated either have a density or be confined to a lattice, and have a cumulant generating function. The result is derived by directly inverting the multivariate moment generating function. The result is applied to sufficient statistics from a regression model with exponential errors, and compared to an existing method in two dimensions. The result is also applied to multivariate inference from a data set arising from a case control study of endometrial cancer.
Kolassa, J.E. (2003), Algorithms for Approximate Conditional Inference, Statistics and Computing
This paper presents a method for listing the sample space for a conditional distribution in a discrete generalized linear model. This tabulation is used in conjunction with saddlepoint methods to approximate the associated conditional probabilities. These probabilities are used to calculate conditional p-values.
Kolassa, J.E. (2003), Continuity Correction for the Score Statistic in Discrete Regression Models, Crossing Boundaries: Statistical Essays in Honor of Jack Hall (ed. Kolassa, J.E., and Oakes, D.)
This paper corrects the usual chi-squared approximation to the distribution function of the conditional score statistic in a generalized linear model, when the underlying distribution is discrete. The proposed method corrects by a multiple of the difference between the number of sufficient statistics lying in the acceptance region for the test and the volume of this region. The multiplier is calculated from the multivariate Edgeworth approximation to the distribution of a lattice random vector.
Cohen, A., Kolassa, J.E., and Sackrowitz, H.B. (2004), A test for homogeneity of odds ratios in ordered 2x2 tables, Biometrical Journal
Consider K ordered 2x2 contingency tables. A new test of the null hypothesis that the odds ratios of these tables are equal vs the alternative hypothesis that the odds ratios are nondecreasing, is recommended. The test is exact (non-asymptotic), is easily carried out (software is available), and has other favorable properties.
Kolassa, J.E. (2004), Approximate Multivariate Conditional Inference Using the Adjusted Profile Likelihood, Canadian Journal of Statistics
The author proposes saddlepoint approximation methods that are adapted to multivariate conditional inference in canonical exponential families. Several approaches to approximating conditional discrete distributions involve dividing an approximation to the full joint mass function, summed over tail regions of interest, by an approximate marginal density. The author first approximates this conditional likelihood by the adjusted profile likelihood, and then applies a multivariate saddlepoint approximation. He also presents formulas to aid in performing simultaneously the profiling and maximizing steps.
Kolassa, J.E., and Yang, B. (2004), Smooth and Accurate Multivariate Confidence Regions, Journal of the American Statistical Association
This article describes multivariate approximate conditional confidence regions for canonical exponential families. These confidence regions have actual coverage probabilities that are closer to their nominal levels than are the actual coverage probabilities of traditional normal theory regions and have boundaries that are smoother than those obtained by inverting traditional exact tests. Our method is based on constructing one-dimensional conditional tests, combining p values, and inverting. More specifically, consider a statistical model with three parameters, of which two are of interest and one is not of interest. We generate a confidence region for the two parameters of interest by first generating a confidence interval for one of the parameters, conditional on sufficient statistics associated with the other interest parameter and the nuisance parameter. For values of this bounded parameter inside the confidence interval, we determine a confidence interval for the remaining interest parameter conditional on the sufficient statistic associated with the nuisance parameter. This procedure determines the boundaries of a confidence region. This method is illustrated through applications to logistic and positive Poisson regression examples, in which parameters of interest are alternative representations of a single underlying physical quantity; in our examples, they represent the effectiveness of a study drug relative to a standard drug in a crossover trial, measured under two different orderings, and the intensity of infection among a certain demographic group, measured in two different day care centers.
Tseng, C.L., Brimacombe, M., Xie, M., Rajan, M., Wang, H., Kolassa, J., Crystal, S., Chen, T.C., Pogach, L., and Safford, M. (2005), Seasonal Patterns in Monthly A1c Values, American Journal of Epidemiology
Thompson, W., Wang, H., Xie, M., Kolassa, J., Rajan, M., Tseng, C.-L., Crystal, S., Zhang, Q., Vardi, Y., Pogach, L., and Safford, M.M. (2005), Assessing Quality of Diabetes Care by Measuring Longitudinal Changes in Hemoglobin A1c in the Veterans Health Administration, Health Services Research
Context
A1c levels are widely used to assess quality of diabetes care provided by health care systems. Currently, cross-sectional measures are commonly used for such assessments.
Objective
To study within-patient longitudinal changes in A1c levels at Veterans Health Administration (VHA) facilities as an alternative to cross-sectional measures of quality of diabetes care.
Design
Longitudinal study using institutional data on individual patient A1c level over time (October 1, 1998–September 30, 2000) with time variant and invariant covariates.
Setting
One hundred and twenty-five VHA facilities nationwide, October 1, 1998–September 30, 2000.
Patients
Diabetic veteran users with A1c measurement performed using National Glycosylated Hemoglobin Standardization Project certified A1c lab assay methods.
Exposures
Characteristics unlikely to reflect quality of care, but known to influence A1c levels, demographics, and baseline illness severity.
Main Outcome Measure
Monthly change in A1c for average patient cared for at each facility.
Results
The preponderance of facilities showed monthly declines in within-patient A1c over the study period (mean change of 0.0148 A1c units per month, range 0.074 to 0.042). Individual facilities varied in their monthly change, with 105 facilities showing monthly declines (70 significant at .05 level) and 20 showing monthly increases (5 significant at .05 level). Case-mix adjustment resulted in modest changes (mean change of 0.0131 case-mix adjusted A1c units per month, range 0.079 to 0.043). Facilities were ranked from worst to best, with attached 90 percent confidence intervals. Among the bottom 10 ranked facilities, four remained within the bottom decile with 90 percent confidence.
Conclusions
There is substantial variation in facility-level longitudinal changes in A1c levels. We propose that evaluation of change in A1c levels over time can be used as a new measure to reflect quality of care provided to populations of individuals with chronic disease.
Cohen, A., Kolassa, J.E., and Sackrowitz, H.B. (2005), A Four Action Problem with Ordered Categorical Data: Are Two Distributions the Same, Ordered, or Otherwise?, Statistics and Probability Letters
Consider a 2xJ contingency table under the product multinomial model when the J categories are ordered. We compare the two distributions by deciding among the following four choices: (i) distributions are the same; (ii) distribution 1 is stochastically larger than distribution 2; (iii) distribution 2 is stochastically larger than distribution 1; (iv) neither (i), (ii), or (iii). A four action problem is posed and two procedures are considered. One ad hoc and the second procedure is a conditional Bayes procedure, where the conditioning is on the marginal row and column totals. The problem was motivated by a data set comparing survey methods dealing with economic damage to farms by deer.
Yang, B., and Kolassa, J.E. (2005), A Refinement to Approximate Conditional Inference, Statistics and Probability Letters
This manuscript considers inference on a single parameter in a multivariate canonical exponential family, where the effect of nuisance parameters on the p-value is mitigated by conditioning on the event that the sufficient statistics associated with the nuisance parameters lie in a neighborhood about the observed value. This manuscript has three aims. First, we provide a method for approximating p-values using approximate conditioning that is more accurate than that presented by Pierce and Peters (Biometrika 86 (1999) 265--277), at the price of greater computational difficulty. Second, we examine the sensitivity of approximate conditioning methods to the values of the nuisance parameters. Third, we describe a method for presenting a valid approximate-conditioning observed significance level accounting for this dependence on the nuisance parameters.
Pogach, L., Xie, M., Shentue, Y., Tseng, CL., Maney, M., Rajan, M., Tiwari, A., Kolassa, J., Helmer, D., Crystal, S., and Safford, M. (2005), Diabetes healthcare quality report cards: how accurate are the grades?, American Journal of Managed Care
Lev, E., Eller, L., Kolassa, J., Gejerman, G., Colella, J., Lane,P. , Scrofine, S., Esposito, M., Lanteri, V., Scheuch, J., Munver, R., Galli, B., Watson, R., and Sawczuk, I. (2006), Exploratory factor analysis: strategies used by patients to promote health, World Journal of Urology
Cohen, A., Kolassa, J.E., and Sackrowitz, H.B. (2006), A test for the equality of multinomial distributions vs increasing convex order,Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe (ed. Sun, J., DasGupta, A., Melfi, V., and Page, C.)
Recently Liu and Wang derived the likelihood ratio test (LRT) statistic and its asymptotic distribution for testing equality of two multinomial distributions vs. the alternative that the second distribution is larger in terms of increasing convex order (ICX). ICX is less restrictive than stochastic order and is a notion that has found applications in insurance and actuarial science. In this paper we propose a new test for ICX. The new test has several advantages over the LRT and over any test procedure that depends on asymptotic theory for implementation. The advantages include the following:
(i) The test is exact (non-asymptotic).
(ii) The test is performed by conditioning on marginal column totals (and row totals in a full multinomial model for a
(iii) The test has desirable monotonicity properties. That is, the test is monotone in all practical directions (to be formally defined).
(iv) The test can be carried out computationally with the aid of a computer program.
(v) The test has good power properties among a wide variety of possible alternatives.
(vi) The test is admissible.
The basis of the new test is the directed chi-square methodology developed by Cohen, Madigan, and Sackrowitz.
Scheetz, L.J., Zhang, J., and Kolassa, J.E. (2007), Using Crash Scene Variables to Predict the Need for Trauma Center Care in Older Persons, Research in Nursing and Health
Cohen, A., Kolassa, J., and Sackrowitz, H.B. (2007), "A smooth version of the step-up procedure for multiple tests hypotheses", Journal of Statistical Planning and Inference 3352-3360
Kolassa, J.E. (2007), A Proof of the Asymptotic Equivalence of Two Tail Probability Approximations, Communications in Statistics -- Theory and Methods
This article considers asymptotic approximations to tail probabilities of a random variable whose distribution depends on a parameter n heuristically representing sample size. Random variables considered have cumulant generating functions with properties similar to that of sums of independent and identically distributed random variables. Probability approximations of Robinson (1982) and Lugannani and Rice (1980) are shown to be equivalent to a relative size O(1/n), under regularity conditions no stronger than the weaker of those necessary to prove either of the two approximations. Applications to permutation testing are discussed.
Kolassa, J.E., and Robinson, J. (2007), Conditional Saddlepoint Approximations for Noncontinuous and Nonlattice Distributions," Journal of Statistical Planning and Inference
Scheetz, L.J., Zhang, J., and Kolassa, J.E. (2008), Evaluating Injury Databases as a Preliminary Step in the Development of a Triage Decision Rule, Journal of Nursing Scholarship
Sheetz, L.J., Zhang, J., Kolassa, J.E., Allen, P., and Allen, M. (2008), Evaluation of Injury Databases as a Preliminary Step to Developing a Triage Decision Rule, Journal of Nursing Research
Xu, L., and Kolassa, J.E. (2008), "Testing the Difference of Two Binomial Proportions: Comparison of Continuity Corrections for Saddlepoint Approximation, Communications in Statistics -- Theory and Methods
Zhang, J., and Kolassa, J.E. (2008), "Saddlepoint approximation for the distribution of the modified signed root of likelihood ratio statistics near the mean, Communications in Statistics -- Theory and Methods
Safford, M.M., Brimacombe, M., Zhang, Q., Rajan, M., Xie, M., Thompson, W., Kolassa, J., Maney, M., and Pogach, L. (2009), Patient complexity in quality comparisons for glycemic control: an observational study, Implementation Science
Scheetz, L.J., Zhang, J. and John Kolassa, J. (2009), Classification tree modeling to identify severe and moderate vehicular injuries in young and middle-aged adults, Artificial Intelligence in Medicine
Golmohammadi, D., Creese, R.C., Valian, H., and Kolassa J. (2009), Supplier selection based on a neural network model using genetic algorithm, IEEE Trans Neural Netw.
In this paper, a decision-making model was developed to select suppliers using neural networks (NNs). This model used historical supplier performance data for selection of vendor suppliers. Input and output were designed in a unique manner for training purposes. The managers' judgments about suppliers were simulated by using a pairwise comparisons matrix for output estimation in the NN. To obtain the benefit of a search technique for model structure and training, genetic algorithm (GA) was applied for the initial weights and architecture of the network. The suppliers' database information (input) can be updated over time to change the suppliers' score estimation based on their performance. The case study illustrated shows how the model can be applied for suppliers' selection.
Lev, E. L., Eller, L.S., Gejerman, G., Kolassa, J., Colella, J., Pezzino, J., Lane, P., Munver, R., Esposito, M., Sheuch, J., Lanteri, V., Sawczuk, I (2009), Quality of Life of Men Treated for Localized Prostate Cancer: Outcomes at 6 and 12 Months", Supportive Cancer Care
Li, J., and Kolassa, J.E. (2010), Multivariate Marginal and Conditional Saddlepoint Tail Probability Approximations, Bernoulli
We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant generating function. The method is applied to some examples, including a real data set from a case-control study of endometrial cancer. The method contains less terms and is easier to implement than existing methods, while showing an accuracy comparable to those methods.
Lev, E.L., Kolassa, J., and Bakken, L.L. (2010), Faculty mentors' and students' perceptions of students' research self-efficacy, Nursing Education Today
Kolassa, J.E., and Robinson, J. (2011), Saddlepoint approximations for likelihood ratio like statistics with applications to permutation tests, Annals of Statistics
We obtain two theorems extending the use of a saddlepoint approximation to multi parameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative error of order 1/n. In the second, we give multivariate generalizations of the Lugannani–Rice and Barndorff-Nielsen or r* formulas for the approximations. These theorems are applied to obtain permutation tests based on the likelihood ratio-like statistics for the k sample and the multivariate two-sample cases. Numerical examples are given to illustrate the high degree of accuracy, and these statistics are compared to the classical statistics in both cases.
Kolassa, J.E., and Bhagavatula, H.G. (2012), "Accurate Approximations to the Distribution of a Statistic Testing Symmetry in Contingency Tables", Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman (ed. D. Fourdrinier, E. Marchand, and A.L. Ruhkin)
This manuscript examines this task of approximating significance levels for a test of symmetry in square contingency tables. The null sampling distribution of this test statistic is the same as that of the sum of squared independent centered binomial random variables, weighted by their separate sample size; each of these variables may be taken to have success probability half. This manuscript applies an existing asymptotic correction to the standard chi-squared approximation to the distribution of the quadratic form of a random vector confined to a multivariate lattice, when the quadratic form is formed from the inverse variance matrix of the random vector. This manuscript also investigates non-asymptotic corrections to approximations to this distribution, when the separate binomial sample sizes are small.
Zhang, J., and Kolassa, J.E. (2013), "A practical procedure to find matching priors for frequentist inference", Communications in Statistics -- Theory and Methods
In the manuscript, we present a practical way to find the matching priors proposed by Welch & Peers (1963) and Peers (1965). We investigate the use of saddlepoint approximations combined with matching priors and obtain p-values of the test of an interest parameter in the presence of nuisance parameter. The advantage of our procedure is the flexibility of choosing different initial conditions so that one can adjust the performance of the test. Two examples have been studied, with coverage verified via Monte Carlo simulation. One relates to the ratio of two exponential means, and the other relates the logistic regression model. Particularly, we are interested in small sample settings.
Kolassa, J.E., and Seifu, Y. (2013), "Nonparametric Multivariate Inference on Shift Parameters", Academic Radiology
Rationale and objectives: Consider a study evaluating the prognostic value of prostate-specific antigen (PSA), in the presence of Gleason score, in differentiating between early and advanced prostate cancer. This data set features subjects divided into two groups (early versus advanced cancer), with one manifest variable (PSA), one covariate (Gleason score), and one stratification variable (hospital, taking three values). We present a nonparametric method for estimating a shift in median PSA score between the two groups, after adjusting for differences in Gleason score and stratifying on hospital. This method can also be extended to cases involving multivariate manifest variable. Materials and methods: Our method uses estimating equations derived from an existing rank-based estimator of the area under the receiver operating characteristic curve (AUC). This existing AUC estimator is adjusted for stratification and for covariates. We use the adjusted AUC estimator to construct a family of tests by shifting manifest variables in one of the treatment groups by an arbitrary constant. The null hypothesis for these tests is that the AUC is half. We report the set of shift values for which the null hypothesis is not rejected as the resulting confidence region. Results: Simulated data show performance consistent with the distributional approximations used by the proposed methodology. This methodology is applied to two examples. In the first example, the mean difference in PSA levels between advanced and nonadvanced prostate cancer patients is estimated, controlling for Gleason score. In the second example, to assess the degree to which age and baseline tumor size are prognostic factors for breast cancer recurrence, differences in age and tumor size between subjects with recurrent and nonrecurrent breast cancer, stratified on Tamoxifen treatment and adjusting for tumor grade, are estimated. Conclusions: The proposed methodology provides a nonparametric method for a statistic measuring adjusted AUC to be used to estimate shift between two manifest variables.
Kolassa, J.E. (2016), "Inference in the Presence of Likelihood Monotonicity for Polytomous and Logistic Regression", Advances in Pure Mathematics
This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logistic regression problem, using existing techniques to reduce this conditional logistic regression problem to one with fewer observations and fewer covariates, such that probabilities for the canonical sufficient statistic of interest, conditional on remaining sufficient statistics, are identical, and translating this conditional logistic regression problem back to the multinomial regression setting. This reduced multinomial regression problem does not exhibit monotonicity of its likelihood, and so conventional asymptotic techniques can be used.
Hao, Y., and Kolassa, J.E. (2016), "Multiple Comparisons in the Analysis of a Crossover Trial: PTSD of U.S. Soldiers", Statistics in Biosciences
Crossover trials are used in a variety of fields, such as medicine, biology, psychology, and some commercial goods investigations. The aim of this paper is to extend a methodology for multiple comparisons to the problem of testing in crossover trials with two treatments. These two treatments are given in two orderings, treatment A first or treatment B first. We perform inference on the effect of one treatment relative to the effect of the other, without assuming that these effects are independent of treatment ordering, using techniques from order-restricted inference and multiple comparisons, and compare to some existing multiple comparison tests.
Krause-Parello, C.A., and Kolassa, J. (2016), "Pet Therapy: Enhancing Social and Cardiovascular Wellness in Community Dwelling Older Adults", Journal of Community Health Nursing
Pet therapy can be therapeutic for older adults living in the community. A crossover design was used to examine changes in blood pressure and heart rate before and after a pet therapy visit versus a volunteer-only visit in 28 community dwelling older adults. Relationships among stress, pet attitude, social support, and health status were also examined. Study findings supported that pet therapy significantly decreased blood pressure and heart rate. Ultimately, the findings supported the notion that community health nurses should consider developing and implementing pet therapy programs in the communities they serve. Further implications for community health nurses are discussed.
Zhu, Y., and Kolassa, J.E. (2017), "Assessing and Comparing the Accuracy of Various Bootstrap Methods", Communications in Statistics - Theory and Methods
We evaluate the performance of various bootstrap methods for constructing confidence intervals for mean and median of several common distributions. Using Monte Carlo simulation, we assessed performance by looking at coverage percentages and average confidence interval lengths. Poor performance is characterized by coverage deviating from 0.95 and large confidence interval lengths. Undercoverage is of greater concern than overcoverage. We also assess the performance of bootstrap methods in estimating the parameters of the Cox Proportional Hazard model and Accelerated Failure Time model.
Kolassa, J.E., and Robinson, J. (2017), "Nonparametric Tests for Multi-parameter M-Estimators", Journal of Multivariate Analysis
We consider likelihood ratio like test statistics based on M-estimators for multi-parameter hypotheses for some commonly used parametric models where the assumptions on which the standard test statistics are based are not justified. The nonparametric test statistics are based on empirical exponential families and permit us to give bootstrap methods for the tests. We further consider saddlepoint approximations to the tail probabilities used in these tests. This generalizes earlier work of Robinson et al. (2003) in two ways. First, we generalize from bootstraps based on resampling vectors of both response and explanatory variables to include bootstrapping residuals for fixed explanatory variables, resulting in a surprising result for the weighted resampling. Second, we obtain a theorem for tail probabilities under weak conditions providing essential justification for the approximation to bootstrap results for both cases. We use as examples linear regression, non-linear regression and generalized linear models under models with independent and identically distributed residuals or vectors of observations, giving numerical illustrations of the results.
Krause-Parello, C., Levy, C., Holman, E., and Kolassa, J.E. (2018), "Effects of VA Facility Dog on Hospitalized Veterans Seen by a Palliative Care Psychologist: An Innovative Approach to Impacting Stress Indicators", American Journal of Hospice and Palliative Medicine
The United States is home to 23 million veterans. In many instances, veterans with serious illness who seek healthcare at the VA receive care from a palliative care service. Animal-assisted intervention (AAI) is gaining attention as a therapeutic stress reducing modality; however, its effects have not been well studied in veterans receiving palliative care in an acute care setting. A crossover repeated-measures study was conducted to examine the effects of an animal-assisted intervention (AAI) in the form of a therapy dog on stress indicators in 25 veterans on the palliative care service at the VA Eastern Colorado Healthcare System in Denver, CO. Veterans had a visit from a therapy dog and the dog's handler, a clinical psychologist (experimental condition) and an unstructured visit with the clinical psychologist alone (control condition). Blood pressure, heart rate, and the salivary biomarkers cortisol, alpha-amylase, and immunoglobulin A were collected before, after, and 30-minutes after both the experimental and control conditions. Significant decreases in cortisol were found when the before time period was compared to the 30-minutes after time period for both the experimental ( p = 0.007) and control condition ( p = 0.036). A significant decrease in HR was also found when the before time period was compared to the 30-minutes after time period for both the experimental ( p = 0.0046) and control ( p = 0.0119) condition. Results of this study supported that a VA facility dog paired with a palliative care psychologist had a measurable impact on salivary cortisol levels and HR in veterans.
Chen, X., and Kolassa, J. (2018), "Various Improved Approximations to Distributions of Quadratic Test Statistics for Dependent Rank Sums", Biomedical Journal of Scientific and Technical Research
This paper presents a modified chi-square approximation to the distribution of test statistics arising from multivariate ranked data. The modification arises from an improvement to the estimated variance matrix of the responses and from corrections for continuity and skewness and kurtosis of the rank sum statistics.
Xie, M., Kolassa, J., Liu, D., Liu, R., and Liu, S. (2018), "Does an observed zero-total-event study contain information for inference of odds ratio in meta-analysis?", Statistics and Its Interface
This note is concerned with the contribution of an observed zero-total-event study, defined to be a study which observes zero events in both treatment and control arms, in meta-analysis. It provides a comparison of two approaches, namely the regular likelihood approach and the classical conditional likelihood approach, from several perspectives. This topic has long been debated, and it has received much renewed interest recently, in part due to the divergent views on the handling of zero-total-event studies in the high profile publication Nissen and Wolski (2007). Following a careful study of both approaches and an illustration of a numerical example, we find that, when we assume the underlying population event rates are not zero, an observed zero-total-event study actually contains information for inference on the parameters such as the common odds ratio in meta-analysis and cannot be left out in our analysis. This is contrary to the belief held by many statisticians that an observed zero-total-event study does not contribute to meta-analysis because it does not contain any information concerning the common odds ratio. The latter belief is mainly formed based on conditional likelihood arguments and/or that an observed zero-total-event study alone cannot provide a meaningful confidence interval for the odds ratio. Our finding should help clarify a difficult question concerning how to deal with zero-total-event studies in meta-analysis of rare event studies.
Krause-Parello, C.A., Thames, M., Ray, C.M., and Kolassa, J. (2018), "Examining the Effects of a Service-Trained Facility Dog on Stress in Children Undergoing Forensic Interview for Allegations of Child Sexual Abuse", Journal of Child Sexual Abuse
Disclosure of child sexual abuse can be a stressful experience for the child. Gaining a better understanding of how best to serve the child, while preserving the quality of their disclosure, is an ever-evolving process. The data to answer this question come from 51 children aged 4-16 (M = 9.1, SD = 3.5), who were referred to a child advocacy center in Virginia for a forensic interview (FI) following allegations of sexual abuse. A repeated measures design was conducted to examine how the presence of a service-trained facility dog (e.g. animal-assisted intervention (AAI) may serve as a mode of lowering stress levels in children during their FIs. Children were randomized to one of the two FI conditions: experimental condition (service-trained facility dog present-AAI) or control condition (service-trained facility dog not present- standard forensic interview). Stress biomarkers salivary cortisol, alpha-amylase, immunoglobulin A (IgA), heart rate, and blood pressure, and Immunoglobulin A were collected before and after the FI. Self-report data were also collected. Results supported a significant decrease in heart rate for those in the experimental condition (p = .0086) vs the control condition (p = .4986). Regression models revealed a significant decrease in systolic and diastolic blood pressure in the experimental condition (p = .03285) and (p = .04381), respectively. Statistically significant changes in alpha-amylase and IgA were also found in relation to disclosure and type of offense. The results of this study support the stress reducing effects of a service-trained facility dog for children undergoing FI for allegations of child sexual abuse.
Cohen, A., Kolassa, J., and Sackrowitz, H. (2019), "Penalized likelihood and multiple testing", Biometrical Journal
The classical multiple testing model remains an important practical area of statistics with new approaches still being developed. In this paper we develop a new multiple testing procedure inspired by a method sometimes used in a problem with a different focus. Namely, the inference after model selection problem. We note that solutions to that problem are often accomplished by making use of a penalized likelihood function. A classic example is the Bayesian information criterion (BIC) method. In this paper we construct a generalized BIC method and evaluate its properties as a multiple testing procedure. The procedure is applicable to a wide variety of statistical models including regression, contrasts, treatment versus control, change point, and others. Numerical work indicates that, in particular, for sparse models the new generalized BIC would be preferred over existing multiple testing procedures.
Morales, K., Krause-Parello, C.A, Hatzfeld, J.J., Simpson, M., Friedmann, E., Kolassa, J., and Wilson, C. (2019), "Strategic Aeromedical Evacuation (AE): Examining Biological and Psychosocial Stress in AE Patients", Military Behavioral Health
Aeromedical evacuation (AE) transports a military patients with a variety of medical conditions from foreign theaters back to the United States for medical treatment. Biological (e.g., alpha-amylase, immunoglobulin A, cortisol, blood pressure, and heart rate) and psychosocial stress measures were collected in (N=36) AE patients upon U.S. arrival and before transport to their final military destinations. Biological stress measures were not significantly related to psychosocial measures. Findings provide an important understanding of stress in the AE population and a foundation from which to evaluate future stress mitigation strategies and gage the need for supportive care in the AE system.
Zawada, J., Kolassa, J.E., and Seifu, Y. (2019), "Statistical Significance: Reliability of P-Values Compared to Other Statistical Summaries", Current Trends in Biostatistics and Biometrics
Statistical inference has strongly relied on the use of p-values to draw conclusions. For over a decade this reliance on the p-value has been questioned by researches and academics. The question of whether p-values are truly the best standard, and what other possible statistics could replace p-values l has been discussed deeply. We set out to understand the amount of variation within p-values, and to find if they really are as reliable as the frequency of their use would suggest. To answer this question, we studied a set of clinical trials over the past two years. We also aim to describe the variety of information included in drag labels, and determine whether this information conforms to FDA guidelines. We found a large variation in the presentation of clinical trial data, much of which was not in line with the guidelines of the FDA. Our findings also show that among the clinical trials we studied there is more variation among the p-values than among the estimates. From this, we can conclude that the estimates from clinical trials should hold a heavy weight in the decision of whether or not to approve the drug. This finding suggests that there is validity to the skepticism of the reliance on p-values, and that further studies need to be done to find a new, more reliable, standard in statistical inference.
Kolassa, J.E., and Kuffner, T.A. (2020), "On the validity of the formal Edgeworth expansion for posterior densities", Annals of Statistics
We consider a fundamental open problem in parametric Bayesian theory, namely the validity of the formal Edgeworth expansion of the posterior density. While the study of valid asymptotic expansions for posterior distributions constitutes a rich literature, the validity of the formal Edgeworth expansion has not been rigorously established. Several authors have claimed connections of various posterior expansions with the classical Edgeworth expansion, or have simply assumed its validity. Our main result settles this open problem. We also prove a lemma concerning the order of posterior cumulants which is of independent interest in Bayesian parametric theory. The most relevant literature is synthesized and compared to the newly-derived Edgeworth expansions. Numerical investigations illustrate that our expansion has the behavior expected of an Edgeworth expansion, and that it has better performance than the other existing expansion which was previously claimed to be of Edgeworth type.
Yang, J. and Kolassa, J.E. (2021), "The Impact of Application of Jackknife to the Sample Median", American Statistician
The jackknife is a reliable tool for reducing the bias of a wide range of estimators. This note demonstrates that even such versatile tools have regularity conditions that can be violated even in relatively simple cases, and that caution needs to be exercised in their use. In particular, we show that the jackknife does not provide the expected reliability for bias-reduction for the sample median, because of subtle changes in behavior of the sample median as one moves between even and odd sample sizes. These considerations arose out of class discussions in a MS-level nonparametrics course.