Open access medical statistics

php and incorporate the Creative Commons Attribution – Non Commercial (unported, v3.0) License (http://creativecommons.org/licenses/by-nc/3.0/). By accessing the work you hereby accept the Terms. Non-commercial uses of the work are permitted without any further permission from Dove Medical Press Limited, provided the work is properly attributed. For permission for commercial use of this work, please see paragraphs 4.2 and 5 of our Terms (https://www.dovepress.com/terms.php). Open Access Medical Statistics 2018:8 25–33 Open Access Medical Statistics Dovepress

Observational studies, common in clinical trials, often suffer from a lack of random assignment of the treatment. This can lead to large differences in covariates between the treated and untreated groups, which should be accounted for prior to inference, hypothesis tests, etc. Propensity score methods are frequently used to control for potentially confounding covariates when assessing causal effects of treatment on outcome. In this review, we introduce four adjustment methods based on propensity scores including matching, stratification, inverse probability of treatment weighting and covariate adjustment. Also, we give a general description of these four methods and provide some visual tools to assess covariate balance between the treated and untreated groups. We confirm the feasibility of propensity score methods by analyzing the Health Evaluation and Linkage to Primary care clinic clinical data. Keywords: propensity score, covariate balance, observational studies, association analysis, HELP Clinic, proc glm, proc logistic, cat.psa, box.psa

Background: S-adenosylmethionine (AdoMet) is available for the treatment of intrahepatic cholestasis in different doses and in different administration forms. The aim of this study was to develop a categorization model, also called a nomogram, to discern if there was a relationship between prescribers’ treatment preferences and patient baseline characteristics for the treatment options, and to assess whether effectiveness was positively correlated with prescriber preference. Materials and methods: Baseline characteristics of patients in a post-marketing observational study (PMOS) were analyzed by multinomial logistic regression to produce preference probabilities for the prescription of different AdoMet starting regimens: 400 mg injection, 800 mg injection, and 800 mg oral tablets. Grid-optimization based on the preference probabilities was used to subdivide the patients into seven relative treatment preference categories. Subsequently, for each category, the effectiveness of the three treatments was assessed by determining the response rate after 2 weeks of treatment for each treatment group. Results: Elevated total bilirubin values, high Child–Pugh scores, and symptomatic cholestasis were associated with prescriber preference for the 800 mg injection, whereas low total bilirubin and low Child–Pugh scores were related to prescriber preference for the 400 mg injection. In the absence of cholestatic symptoms, the 800 mg tablet starting regimen was preferred. In the category where the baseline characteristics did not come to a more- or less-preferred treatment, the response rates were highest for the 800 mg tablets group (67%) and lowest in the 400 mg injection group (50%); however, the total sample size in this category was small (N = 22). Conclusion: Categorization of patients into treatment preference groups based on baseline data might be an interesting approach to assess the validity of the treatment preference versus the respective treatment effectiveness as shown in a PMOS with three AdoMet treatment regimens. Keywords: S-adenosylmethionine, intrahepatic cholestasis, multinomial logistic regression, propensity scores, grid optimization, prescriber preference

Purpose: The main purpose of this study was to explore possible modeling approaches of time-to-good control of hypertension using Cox proportional hazard (Cox-PH) and frailty models, using data from Bahir-Dar Felege Hiwot Referral Hospital. Patients and methods: An institution-based retrospective cohort study was conducted in June 2014. The study population consisted of all hypertensive patients who had visited the hospital at least three times between January 1, 2009, to December 31, 2013. Five hundred patients were selected using simple random sampling. The data were collected by trained data collectors using a checklist. Statistical Package for the Social Sciences version 20 and R software were used for data entry and to process the data, respectively. First, a single covariate analysis was done using Cox-PH and univariate frailty models. Then, all variables that were significant were included in the multivariable analysis. Results: The median survival time of hypertensive patients to attain good control was 48 months, and the mean survival time was 43.6 months. Age and systolic blood pressure (SBP) of patients had a negative relationship with the outcome. However, fasting blood sugar (FBS) had a positive relationship with the outcome. Moreover, the results showed that the progression of outcome depended on the patient’s age. Conclusion: Cox-PH-based analysis revealed that the factors that affected good control of hypertensive patients were age, SBP, FBS, and creatinine. The result of the univariate frailty analysis showed that there was unobserved heterogeneity between individuals in the study setup, which indicated that there were unmeasured covariates. Keywords: hypertension, time-to-event, Cox proportional hazard, frailty model, Schoenfeld residuals, good control of hypertension

Optimal look back period and summary method for Elixhauser comorbidity measures in a US population-based electronic health record database Yannick Fortin,1,2 James AG Crispo,1–4 Deborah Cohen,2,5,6 Douglas S McNair,7 Donald R Mattison,1,8 Daniel Krewski1,2,8 1McLaughlin Centre for Population Health Risk Assessment, 2School of Epidemiology, Public Health and Preventive Medicine, University of Ottawa, Ottawa, ON, Canada; 3Fulbright Canada, 4Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA; 5Canadian Population Health Initiative, Canadian Institute for Health Information, Ottawa, 6Institute for Health Policy, Management and Evaluation, University of Toronto, Toronto, ON, Canada; 7Cerner Corporation, Kansas City, MO, USA; 8Risk Sciences International, Ottawa, ON, Canada Background: Comorbidity risk-adjustment tools are widely used in health database research to control for clinical differences between individuals, but they need to be validated a priori. This study aimed to identify the optimal parameters for predicting all-cause inhospital mortality using Quan's enhanced Elixhauser comorbidity measures (ECMs) in the US-based Cerner Health Facts® (HF) electronic health record database.Methods: Health care recipients aged 18–89 years between 2002 and 2011 were included. Prevalent comorbidities recorded, 1) during the index encounter; 2) in the prior year; and 3) in the prior 2 years were identified using the ECMs. Multiple logistic regression models, with inhospital mortality at index and at 1 year as the predicted outcomes, were fitted with comorbidities summarized as binary indicators, total counts, or weighted scores for the three look back periods. Baseline variables included sex and age. The receiver operating characteristic (ROC) curves of the competing models were compared with a non-parametric Mann–Whitney U test to identify the optimal parameters.Results: A sample of 3,273,298 unique health care recipients were included, of whom 31,298 (1.0%) and 50,215 (1.5%) died during the index encounter and within the 1-year follow-up, respectively. Models of comorbidity based on binary and weighted indicators had near-identical performance and were statistically better than the models based on total counts (p < 0.0001). Discrimination of inhospital mortality was highest with a look back period limited to the index encounter, while inhospital mortality at 1 year was best predicted with 1 year of look back (p < 0.0001).Conclusion: In Cerner HF, the binary and weighted methods for summarizing the Quan ECM were the best predictors of all-cause inhospital mortality at index and at 1 year. Observed differences in predictive performance between models with diagnostic ascertainment periods of up to 2 years of look back were statistically significant but not practically important. Keywords: comorbidity, ICD-9, electronic health records, risk adjustment, mortality, statistical modeling

A multistate model is more complicated than competing risk models and composed of finite number of states and transitions between states. Unlike competing risk models, this model has the ability to assess the effect of occurrence order of time-to-event data. Pleural effusion (PE) is a severe complication that often occurs after allogeneic hematopoietic stem cell transplantation (HSCT). Many patients develop pleural effusion during the first 100 days after allogeneic HSCT and graft-versus-host disease (GVHD) occurs either before or after the development of PE, implying that the occurrence order of PE and GVHD (i.e., PE after GVHD vs. GVHD after PE) would influence on the incidence, risk factors and mortality of pleural effusion. One can use either Cox proportional models or competing risk models to evaluate these values, but neither method is able to incorporate the occurrence order of incidence into the model. To resolve this difficulty, we developed a multistate model describing several possible events and event-related dependences and applied to a retrospective study of 606 patients, including eight covariates.

com/terms.php and incorporate the Creative Commons Attribution – Non Commercial (unported, v3.0) License (http://creativecommons.org/licenses/by-nc/3.0/). By accessing the work you hereby accept the Terms. Non-commercial uses of the work are permitted without any further permission from Dove Medical Press Limited, provided the work is properly attributed. For permission for commercial use of this work, please see paragraphs 4.2 and 5 of our Terms (https://www.dovepress.com/terms.php). Open Access Medical Statistics 2016:6 9–20 Open Access Medical Statistics Dovepress

The development of biosensors that produce time series data will facilitate improvements in biomedical diagnostics and in personalized medicine. The time series produced by these devices often contains characteristic features arising from biochemical interactions between the sample and the sensor. To use such characteristic features for determining sample class, similarity-based classifiers can be utilized. However, the construction of such classifiers is complicated by the variability in the time domains of such series that renders the traditional distance metrics such as Euclidean distance ineffective in distinguishing between biological variance and time domain variance. The dynamic time warping (DTW) algorithm is a sequence alignment algorithm that can be used to align two or more series to facilitate quantifying similarity. In this article, we evaluated the performance of DTW distance-based similarity classifiers for classifying time series that mimics electrical signals produced by nanotube biosensors. Simulation studies demonstrated the positive performance of such classifiers in discriminating between time series containing characteristic features that are obscured by noise in the intensity and time domains. We then applied a DTW distance-based k-nearest neighbors classifier to distinguish the presence/absence of mesenchymal biomarker in cancer cells in buffy coats in a blinded test. Using a train-test approach, we find that the classifier had high sensitivity (90.9%) and specificity (81.8%) in differentiating between EpCAM-positive MCF7 cells spiked in buffy coats and those in plain buffy coats.

Background: Cluster randomized trials (CRTs) are a popular trial design. In most CRTs, researchers assume equal cluster sizes when calculating sample sizes. When clusters vary, assuming equal sized clusters may result in low study power. There are two common approaches to sample size calculations for varying cluster sizes. One approach uses a harmonic mean ( m̄H ) of cluster sizes, while the other incorporates the squared coefficient of variation ( cv2 ) of cluster sizes. We performed simulations to compare empirical power between the two methods as well as the arithmetic mean method for a continuous endpoint. Study design: We considered cluster sizes that follow uniform distributions and performed 20,000 simulations under each scenario. Endpoints were analyzed using: 1) an individual-level linear regression model with Gaussian random intercepts for clusters; 2) an individual-level t-statistic with cluster-robust standard errors; 3) a generalized estimating equations (GEE) model with exchangeable correlation structure; and 4) a GEE model with independent correlation structure and robust standard errors. Results: When the Gaussian random effects or the GEE model with exchangeable correlation structure was considered, the m̄H method had 80% power. The cv2 method had power of 85%–88%. However, when the data were analyzed using a t-statistic or the GEE model with independent correlation structure, the power of cv2 method was 80%. The m̄H method produced power of 71%–76%. Conclusion: The performance of the sample size methods depends on the data analysis approaches. The degree of disparity in power depends also on the intracluster correlation coefficient. These findings emphasize the maxim that researchers should consider methods of analysis when designing CRTs to allow for appropriate sample size calculations. Keywords: cluster randomized trial, varying cluster sizes, empirical power, harmonic mean, coefficient of variation, continuous endpoint

When there are three or more nominal categories of a response variable, the binomial logistic regression approach is widely used to model the relationships of exposure variables with different binomial responses one at a time. However, some of the separate binomial comparisons would be redundant. This approach is also suboptimal because of the loss of information that will result when only a subset of the data is analyzed at a time and the multiple testing problems arising from analysis of several pairs of categories. These drawbacks of fitting separate binomial regression models to a multicategory nominal outcome variable can be overcome using a single multinomial regression modeling framework. In this study, we compared the results using a multinomial regression with the separate two binomial regressions to determine factors associated with excess and inadequate weight gain during pregnancy in a data set from a gestational weight gain study involving a cross-sectional survey of 312 women with singleton pregnancies. We found that both approaches identified the same set of predictors, ie, higher neuroticism, planning to gain more weight than the recommended level, and bedtime television watching, with P -values ≤0.05 of the excessive (versus appropriate) weight gain, for which the subgroup size was moderate. The final list of significant predictors of inadequate (versus appropriate) weight gain identified by multinomial regression were planned weight gain below the recommended range, overweight or obese women, and bedtime television watching, while those by a separate binomial approach were self-efficacy towards achieving healthy weight, lack of weight satisfaction, and bedtime television watching, which differed between the two approaches where the final set of predictors were identified by a variable selection process and the comparisons were made in a small subgroup. A multinomial approach is a useful analytical framework that researchers may consider when they have multinomial response categories because this approach allows nonredundant comparisons to be made, avoiding the need to analyze a subset of the data one at a time and also allows for risk prediction of multinomial categories from a well validated multinomial model, and will not lead to multiple testing problems. Keywords: gestational weight gain, pregnancy, multinomial logistic regression, binomial logistic regression, risk factors

Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two non-interacting cell lines were grown in the same culture, and counts of each species were recorded at periodic times. The relative growth of population ratios was found to depend on the initial proportion, in contradiction with the traditional exponential growth model. The proposed explanation is the variability of growth rates for clones inside the same cell line. This leads to a log-quadratic growth model that provides both a theoretical explanation to the phenomenon that was observed, and a better fit to our growth data.

An 8-week clinical trial was designed to evaluate the efficacy of the single pill combination (SPC) of telmisartan and amlodipine in treating patients with severe hypertension. The primary endpoint was change from baseline in mean (seated trough cuff) systolic blood pressure (SBP) following 8 weeks of treatment. Secondary endpoints included changes in SBP from baseline to weeks 6, 4, 2, and 1. In order to demonstrate superiority of the SPC, statistical significance has to be achieved in comparisons with both components (telmisartan and amlodipine). In this paper, various approaches are applied to analyze this set of longitudinal data. Superiority of SPC over each component drug can be established for all time points, starting from week 1. The clinical conclusion is robust regardless of the longitudinal analysis methodologies being applied. Keywords: amlodipine, telmisartan, longitudinal data analysis, last observation carried forward, mixed model repeated measures, grouping method

Genomic studies have become commonplace, with thousands of gene expressions typically collected on single or multiple platforms and analyzed. Unaccounted time-ordered or epigenetic aspects of genetic expression may lead to a version of Simpson's paradox, ie, time-aggregated overall effects that do not reflect within strata patterns. Without clear functional models to motivate clustering and fitting algorithms, these confounding related issues require consideration. Several basic examples motivate discussion and more appropriate models for analysis of expression data are reviewed. Keywords: Simpson's paradox, aggregation effects, mediation, genomics

The need to understand large database structures is an important issue in biological and medical science. This review paper is aimed at quantitative medical researchers looking for guidance in modeling large numbers of variables in medical research, how this relates to standard linear models and the geometry that underlies their analysis. Issues reviewed include LASSO-related approaches, principal-component based analysis, and issues of model stability and interpretation. Model misspecification issues related to potential nonlinearities are also examined, as is the Bayesian perspective on these issues.

Correspondence: John S Fry PN Lee Statistics and Computing, Sutton, Surrey SM2 5DA, UK Tel +44 208 642 8265 Fax +44 208 642 2135 Email johnfry@pnlee.co.uk Abstract: In long-term carcinogenicity studies, the Peto test is the standard method for analyzing lesions that are not observable in life, taking into account differential between-group mortality. This method requires knowledge for each animal in each group of when the animal died, whether a lesion was seen postmortem, and the context of observation (ie, whether the lesion was fatal [considered to have contributed to its death] or whether it was incidental [seen in an animal dying for an unrelated reason]). The Peto test was not designed to take severity of the lesion into account. Age-adjusted analysis taking severity into account can be carried out using a stratified version of the Kruskal–Wallis one-way analysis of variance by ranks, but this does not take context of observation into account. Here, we describe an extended version of the stratified Kruskal–Wallis test that both allows analysis of lesions graded on severity and takes fatality of the lesion into account. This includes both a test for between-group heterogeneity and a test for dose-related trend, and provides a powerful method for analyzing such data. The Peto and Kruskal–Wallis tests may be considered special cases of this more general test. The test may be applied not only to nonneoplastic lesions (such as chronic progressive nephropathy), where pathologists often grade severity on a 5-point scale, but also to preneoplastic and neoplastic lesions, carrying out a single analysis of focal hyperplasia, benign tumor, and malignant tumor of a specific histological type, regarding these as successive stages of a progressive condition.

Due to the ever-increasing complexity of scientific technologies and resulting data, consulting statisticians are becoming more involved in the design, conduct, and analysis of biomedical research. This requires extensive collaboration between the consulting statistician and nonstatisticians, such as researchers, clinicians, and corporate executives. Consequently, a successful consulting career is becoming ever more dependent on the statistician's ability to effectively communicate with nonstatisticians. This is especially true when more complex, nontraditional analytical methods are required. In this paper, we examine the collaboration between statisticians and nonstatisticians from three different professional perspectives. Integrating these perspectives, we discuss ways to help the consulting statistician generate productive dialogue with clients. Finally, we examine how universities can better prepare students for careers in statistical consulting by incorporating more communication-based elements into their curriculum and by offering students ample opportunities to collaborate with nonstatisticians. Overall, we designed this exercise to help the consulting statistician generate dialogue with clients that results in more productive collaborations and a more satisfying work experience. Keywords: statistical consulting, nontraditional analysis, communication

Bayesian methods enable the "prior" (or informative) beliefs of an audience to be combined with the results of a clinical trial to arrive at a final "posterior" belief. This example concerns previously published data from a double-blind placebo-controlled trial of propranolol to reduce the number of episodes of migraine, where subjects were crossed-over after 3 months of treatment. The informative prior range was supplied by an educated audience (members of our Faculty of Neurology) who were given review papers on propranolol in migraine prophylaxis and placebo responses in migraine trials. We used logistic regression models to try to predict those whose symptoms improved (based on treatment or on the time period under consideration; ie, the first or second 3-month period, or based on both factors considered together). The posterior was generated using the Markov–Chain Monte–Carlo methods. For the original dataset, the Bayesian posteriors tended to be more tightly defined than those with no prior or minimally informative prior beliefs, thus yielding firmer conclusions in light of the trial. When compared with a larger dataset (which was generated from the original, but was arrived at by multiplying the number of observations by 10), the influence of prior beliefs was much less marked, but the posteriors did tend to be marginally more narrowly defined. This finding is in keeping with existing work on Bayesian methods, highlighting their value in aiding interpretation of trials with a small number of observations. Keywords: Bayesian, migraine, randomized trial, placebo, propranolol

Group classification based on high-dimensional data: application to differential scanning calorimetry plasma thermogram analysis of cervical cancer and control samples Shesh N Rai,1,2 Jianmin Pan,1 Alex Cambon,2 Jonathan B Chaires,3–5 Nichola C Garbett3,4 1Biostatistics Shared Facility, James Graham Brown Cancer Center, University of Louisville, 2Department of Bioinformatics and Biostatistics, University of Louisville, 3Biophysical Core Facility, James Graham Brown Cancer Center, University of Louisville, 4Department of Medicine, University of Louisville, 5Department of Biochemistry and Molecular Biology, University of Louisville, Louisville, KY, USA Abstract: Differential scanning calorimetry has been applied to identify protein denaturation patterns, or thermograms, in blood plasma samples that are indicative of health status. Data sets generated by differential scanning calorimetry are high dimensional, and it is complex to analyze and classify thermogram patterns. The I-RELIEF method is commonly used for group classification from high-dimensional data sets, such as gene expression data. We report the development and validation of a new method of data reduction and modeling of high-dimensional data sets. The performance of our method was demonstrated through its application to the analysis of differential scanning calorimetry plasma thermogram data. Our method was found to provide superior classification performance compared with the I-RELIEF method. Keywords: plasma thermogram, differential scanning calorimetry, group classification

Background: The purpose of this work was to estimate the average effect of the covariate of interest when the outcome variable is dichotomized from a continuous variable and data are incomplete, with the missing data not missing at random (NMAR). The motivating example is to estimating the effect of vitamin D levels on secondary hyperparathyroidism among patients with chronic kidney disease. Methods: The average effect of the covariate of interest is computed by a two-step procedure. In the first step, we identify the conditional distribution of the original variable given the covariates by obtaining the parameter estimates. In the second step, we draw the predictive values from the identified distribution, and create binary values from the predictive values by dichotomizing them at the threshold. Results: According to the simulation results, the biases of the effects between logistic regression with the complete data and the estimated logistic regression with the converted binary variable are negligible. For the application example, the effect of vitamin D on the occurrence of secondary hyperparathyroidism is highly significant in the complete case analysis, but only a modest effect of vitamin D on secondary hyperparathyroidism is observed under the NMAR assumption. Conclusion: It is impossible to find consistent estimates without knowing the exact nature of the missing data when the missing data mechanism is NMAR. Also, the outcome variable is binary, so we may be faced with an unidentifiability problem when the missing data mechanism is NMAR. To avoid this problem, we estimated the average effect of the covariate of interest in the framework of a generalized linear model from the relationship between a dichotomized outcome and a continuous original outcome, and the estimated effect showed negligible bias according to this simulation. Keywords: average effect, NMAR, not missing at random, dichotomized events, secondary hyperparathyroidism

Correspondence: Daniel Lee McGee Department of Mathematical Sciences, University of Puerto Rico, Mayaguez, Puerto Rico 00681-5000 Tel +1 787 263 3828 Fax + 1 787 265 5454 Email daniel.mcgee@upr.edu Background: This article presents cohort studies that use data from the National Health Information Survey from 1986 to 1994 and compares the effectiveness of Cox proportional hazards models that assume a linear relationship between body mass index (BMI) and the risk of prostate cancer with models that assume a J-shaped relationship. Methods and results: Our study found that for black males over 40 years of age, neither a linear nor a J-shaped relationship yielded a statistically significant model. With white males over 40 years, assuming a linear relationship did not yield a statistically significant model (P = 0.582). When we assume a J-shaped relationship, the optimal change point where the risk of prostate cancer death is minimized occurs when the BMI is 25.5. Among white males over 40 years with BMI , 25.5, an inverse relationship was found (P = 0.009). Among white males over 40 years with BMI . 25.5, a direct relationship was found (P = 0.017). Conclusion: With this data set, we found that for white males over 40 years, Cox proportional hazards models that assume a J-shaped relationship between BMI and prostate cancer death provide a much better fit than models assuming a linear relationship.