Mathematics

OBJECTIVES The purpose of this study was to determine the prognostic accuracy of electron beam computed tomographic (CT) scanning of the coronary arteries and the relationship of coronary calcification to standard coronary disease risk factors and C-reactive protein (CRP) in the prediction of atherosclerotic cardiovascular disease (ASCVD) events in apparently healthy middle-age persons. BACKGROUND As a screening test for coronary artery disease (CAD), electron beam CT scanning remains controversial. METHODS In a prospective, population-based study, 4,903 asymptomatic persons age 50 to 70 years underwent electron beam CT scanning of the coronary arteries. RESULTS At 4.3 years, follow-up was available in 4,613 participants (94%), and 119 had sustained at least one ASCVD event. Subjects with ASCVD events had higher baseline coronary calcium scores (median [interquartile range], Agatston method) than those without events: 384 (127, 800) versus 10 (0, 86) (p 0.0001). For coronary calcium score threshold 100 versus 100, relative risk (95% confidence interval) was 9.6 (6.7 to 13.9) for all ASCVD events, 11.1 (7.3 to 16.7) for all CAD events, and 9.2 (4.9 to 17.3) for non-fatal myocardial infarction and death. The coronary calcium score predicted CAD events independently of standard risk factors and CRP (p 0.004), was superior to the Framingham risk index in the prediction of events (area under the receiver-operating characteristic curve of 0.79 0.03 vs. 0.69 0.03, p 0.0006), and enhanced stratification of those falling into the Framingham categories of low, intermediate, and high risk (p 0.0001). CONCLUSIONS The electron beam CT coronary calcium score predicts CAD events independent of standard risk factors, more accurately than standard risk factors and CRP, and refines Framingham risk stratification. (J Am Coll Cardiol 2005;46:158-65) © 2005 by the American College of Cardiology Foundation Most coronary artery disease (CAD) events occur on a substrate of moderate to severe atherosclerosis (1-4). This fact, together with recognition of the limitations of conventional risk fa ctor assessment and improvements in technol-See page 173 ogy, has generated increasing interest in noninvasive measures of atherosclerosis. These include carotid intima-media thickness (5), ankle-brachial index (6), and fast computed tomographic (CT) scanning of the coronary arteries. Coronary calcification occurs in rough proportion to the severity of underlying atherosclerosis (7,8) and can be measured with a high degree of accuracy and reproducibility with electron beam CT (9,10). However, the use of electron beam CT scanning as a screening test for CAD has been and remains controversial (11,12). The strongest supporting evidence has come from retrospective analyses of commercial scanning databases (13-16), which are subject to referral bias, and the only prospective study has yielded conflicting results (17-19). Therefore, we sought to determine the prognostic accuracy of electron beam CT scanning of the coronary arteries and the relationship of coronary calcifica-tion to standard CAD risk factors and C-reactive protein (CRP) in the prediction of atherosclerotic cardiovascular disease (ASCVD) events in apparently healthy adults. METHODS General study design has been described in detail elsewhere (20) and is diagrammed in Figure 1. The primary purpose of the St. Francis Heart Study was to compare the prognostic accuracy of electron beam CT scanning of the coronary arteries with that of standard and putative CAD risk factors in a setting of primary prevention. Accordingly, men and women age 50 to 70 years were considered eligible provided they had no history, symptoms (Rose questionnaire [21]), or signs of ASCVD. Other exclusion criteria included indications for risk factor modification or conditions that might interfere with the conduct or conclusions of a natural history

This is a brief report on some unusual iron concretions that were found buried in an untouched silicate clay deposit on the north shore of Long Island, New York. (Includes photos of the samples as well as X-ray diffraction crystallographic analyses.) Powder scraped off of the concretions revealed unusual patterns upon magnification. A personal note of the author's connection to the location is included at the end.

The objective of this study was to assess the risk of multiple recurrences after an initial seizure recurrence in childhood. In a prospective study, 407 children were followed for a mean of 9.6 years from the time of their first unprovoked seizure. Data regarding each seizure recurrence were obtained and analyzed using statistical methods for survival analysis. The cumulative risk of a second seizure was 29%, 37%, 43%, and 46% at 1, 2, 5, and 10 years, respectively. Of the 182 children who experienced a second seizure, 131 (72%) experienced a third seizure, 105 (58%) have had 4 or more seizures, and 52 (29%) have experienced 10 or more seizures. The cumulative risk of a third seizure was 57%, 63%, and 71% at 1, 2, and 5 years, respectively, after the second seizure. After a third seizure, the cumulative risk of another seizure was 69%, 72%, and 81% at 1, 2, and 5 years, respectively. After a second seizure, factors associated with an increased risk of additional recurrences included a remote symptomatic etiology (rate ratio ‫؍‬ 1.7) and the occurrence of a second seizure within 6 months of the first seizure (rate ratio ‫؍‬ 1.7). After a second seizure, the risk of subsequent seizures was greater than 50% even in the lowest risk group. With the exception of etiology, factors associated with an increased risk of multiple recurrences after the initial seizure were different than those associated with multiple recurrences after a second seizure. Factors associated with multiple recurrent seizures may be different than those associated with an initial recurrence. As most patients who experience a second seizure experience further seizures, these data suggest that two seizures are a sufficient epidemiological criterion for the definition of epilepsy.

(See editorial comments by Drs. Magaziner, Miller, and Resnick on pp 464-466) OBJECTIVES: To identify resident-and caregiver-related factors that influence hip protector (HP) usage. DESIGN: Prospective observational cohort study over 6 weeks. SETTING: A 409-bed nursing home located in New York City. PARTICIPANTS: Fifty-two residents and 60 certified nursing assistants (CNAs). INTERVENTION: Free HPs were provided to residents enrolled in the study. MEASUREMENTS: HP adherence (number of hours HPs were worn/shift); HP users (subjects who used HPs for more than 1 hour during any 8-hour shift as recorded by CNAs in week 6 or who used HPs at checks performed by research staff in week 6 and intended future use); CNAs' scores on a questionnaire quantifying osteoporosis knowledge, opinions on HPs, job satisfaction, and health locus of control. RESULTS: Sixty-eight percent of residents were HP users. Factors independently associated with this outcome included male sex, age, Parkinson's disease, family involvement , impaired cognition, dependent ambulation, and CNAs' sense that chance affects health outcomes. In mul-tivariate models, anxiety, resistive behaviors, ambulation, and fall history in residents and CNAs' perceptions of HPs and their sense of how chance or other staff determine health outcomes predicted HP adherence. CONCLUSION: Resident-related factors and CNAs' sense of external controls predicted HP users and HP adherence. CNAs' understanding of osteoporosis and HP affected only HP adherence. Most resident-related factors were not re-mediable but might help to target likely HP users. To improve HP adherence, educational programs should be designed to improve CNAs' understanding of osteoporosis and HP. Larger studies are needed to confirm these findings. E ach year, 60% of nursing home (NH) residents experience a fall, the most common precipitant of hip fracture. 1,2 In 1985, 34,000 residents were hospitalized for a hip fracture. 1 One-year mortality after a hip fracture in these individuals is 24% to 35%, 1,2 and fewer than 60% return to premorbid function. 1 Hip protectors (HPs) may reduce the risk of a hip fracture if worn during a fall, but optimal benefit is predicated on high rates of HP adherence. 3-5 In previous studies, adherence in diverse populations ranged from 20% to 92%. 3,6-8 Poor adherence is common even in NH environments, where NH staff provide most resident care. 9 Research on caregiver influences in other domains of care indicates that knowledge, impressions of an intervention's utility, time constraints, caregiver validation , and institutional commitment are fundamental elements to achieving and maintaining nursing staff motivation. 10,11 Early work with HPs focused on descriptive evaluations of adherence and the concerns of residents and care-givers. 12-14 More-recent trials have shown that staff motivation, institutional commitment, and educational programs are critical to enhancing adherence in the NH. 15-19 No studies have been conducted that quantitatively describe the relationship between HP usage and resident and staff-related factors. Identifying factors associated with HP usage could inform the development of successful HP programs. This study was designed to identify resident-specific (e.g., functional impairments and comorbidity) and caregiver-specific (e.g., osteoporosis knowledge and opinions about HPs) factors that are independently associated with HP use in the NH setting. The caregivers were certified nursing assistants (CNAs), who are responsible for 90% of the direct care provided to NH residents. 9,11 Information regarding residents' HP usage was linked with caregivers' knowledge and opinions of osteoporosis, HPs, job satisfaction, and determinants of health outcomes using an instrument specifically created for this purpose. A secondary objective was to establish the comparability between adherence assessments recorded by caregivers and those recorded by the study investigators.

Treatment reduced total cholesterol by 26.5% to 30.4% (p < 0.0001), low-density lipoprotein cholesterol by 39.1% to 43.4% (p < 0.0001), and triglycerides by 11.2% to 17.0% (p ≤ 0.02) but had no effect (p = 0.80) on progression of coronary calcium score (Agatston method). ...

Background: This paper provides a theoretical perspective for hypothesis testing when the null hypothesis is true. An example of a hypothetical simple clinical experiment is provided in order to give a framework for the presentation of the theoretical concepts. Monte Carlo (MC) simulations were conducted based on the mathematical model derived from the experiment. Methods: MC simulations were performed using R. A sample proportion was obtained from the outcomes of all patients of the hypothetical clinical experiment. Utilizing the mathematical model of a binomial random variable (RV) with parameters n and p0, a simulated sample proportion was obtained for n = 100, 1000 and 10000. The parameter p0 was set to .5 for all simulations. The MC simulations replicated the experiment 40, 400 and 4000 times. The proportion of times that the null hypothesis was rejected, as well as the percentage of error in rejecting the null hypothesis compared to the theoretical value of .05 for a two tailed z test was obtained for each set of simulations. Results: Overall, the percentage of error in rejecting the null hypothesis was small. This error was highly dependent on the sample size but not of the number of MC simulations. Conclusions: Monte Carlo simulations can prove useful in clarifying the concepts behind hypothesis testing. Additionally, they can yield information about the validity of this procedure as it relates to the statistical theory behind simple as well as more complex clinical and epidemiological studies and the analysis of the data obtained from them.

The assumption that the sampling distribution of the crude odds ratio (ORcrude) is a log-normal distribution with parameters mu and sigma leads to the incorrect conclusion that the expectation of the log of ORcrude is equal to the parameter mu. In fact, exp(mu) is the median of the lognormal distribution, not the mean. If a different parameter is obtained as the expected value of the lognormal distribution, then this quantity can be used to obtain a new estimate of the true odds ratio (ORtrue). Here, simulations are conducted based on a simple randomized clinical trial study design. The simulations demonstrate that the new estimate of ORtrue (based on the expectation of the lognormal distribution function) yields interval estimates that are more statistically valid than the standard method. These interval estimates are obtained by both a parametric bootstrap method and a calculated percentile method. The statistical conclusion validity of the estimated confidence intervals are based on the intended coverage probability (ie the probability the confidence interval contains ORtrue). Additionally, an interval based hypothesis test based on the improved confidence interval estimate has higher power to reject the null hypothesis that ORtrue is equal to one when the alternative hypothesis is true (ie ORtrue is not equal to one) than the standard hypothesis test when the intervention is protective.

I utilize Monte Carlo simulations to examine the effectiveness of a common training algorithm applied to a very simple learning problem given as an introductory example in a popular text on the subject. (See a video of the full presentation without this code above).

The purpose of this study was to determine the prognostic accuracy of electron beam computed tomographic (CT) scanning of the coronary arteries and the relationship of coronary calcification to standard coronary disease risk factors and C-reactive protein (CRP) in the prediction of atherosclerotic cardiovascular disease (ASCVD) events in apparently healthy middle-age persons. BACKGROUND As a screening test for coronary artery disease (CAD), electron beam CT scanning remains controversial. METHODS In a prospective, population-based study, 4,903 asymptomatic persons age 50 to 70 years underwent electron beam CT scanning of the coronary arteries. RESULTS At 4.3 years, follow-up was available in 4,613 participants (94%), and 119 had sustained at least one ASCVD event. Subjects with ASCVD events had higher baseline coronary calcium scores (median [interquartile range], Agatston method) than those without events: 384 (127, 800) versus 10 (0, 86) (p Ͻ 0.0001). For coronary calcium score threshold Ն100 versus Ͻ100, relative risk (95% confidence interval) was 9.6 (6.7 to 13.9) for all ASCVD events, 11.1 (7.3 to 16.7) for all CAD events, and 9.2 (4.9 to 17.3) for non-fatal myocardial infarction and death. The coronary calcium score predicted CAD events independently of standard risk factors and CRP (p ϭ 0.004), was superior to the Framingham risk index in the prediction of events (area under the receiver-operating characteristic curve of 0.79 Ϯ 0.03 vs. 0.69 Ϯ 0.03, p ϭ 0.0006), and enhanced stratification of those falling into the Framingham categories of low, intermediate, and high risk (p Ͻ 0.0001). CONCLUSIONS The electron beam CT coronary calcium score predicts CAD events independent of standard risk factors, more accurately than standard risk factors and CRP, and refines Framingham risk stratification.

We consider the bordism theory generated by quadruples (M k, f; X; g) where Mk is an oriented smooth manifold f: Mk-f X is a map, and g: Mk + R k is a smooth map exhibiting only the simplest, i.e. fold, singularities. We show this theory represents the unreduced stable homotopy of X, and we give a variant representing the groups n,(l"S"(X) for S"(X) the unreduced suspension of X. We interpret these results as giving a sub-space OFSn(X) of 0"S"(X) with the inclusion flus'+ n"s"(X) a natural weak equivalence. We then give configuration space models F,,(X) and a natural weak equivalence co,,: F,,(X)+ 0~S"(X). Finally we give a category theoretic model for the functor F,,(). This allows us to interpret the previous results as a geometric proof of the Barratt-Priddy-Quillen equivalence OmS"(x) + BS(m)+ x 2, and as an unstable, functorial geometric version of this equivalence.

We consider the bordism theory generated by quadruples (M k, f; X; g) where Mk is an oriented smooth manifold f: Mk-f X is a map, and g: Mk + R k is a smooth map exhibiting only the simplest, i.e. fold, singularities. We show this theory represents the unreduced stable homotopy of X, and we give a variant representing the groups n,(l"S"(X) for S"(X) the unreduced suspension of X. We interpret these results as giving a sub-space OFSn(X) of 0"S"(X) with the inclusion flus'+ n"s"(X) a natural weak equivalence. We then give configuration space models F,,(X) and a natural weak equivalence co,,: F,,(X)+ 0~S"(X). Finally we give a category theoretic model for the functor F,,(). This allows us to interpret the previous results as a geometric proof of the Barratt-Priddy-Quillen equivalence OmS"(x) + BS(m)+ x 2, and as an unstable, functorial geometric version of this equivalence.