John Concato

A simulation study of the number of events per variable in logistic regression analysis

We performed a Monte Carlo study to evaluate the effect of the number of events per variable (EPV) analyzed in logistic regression analysis. The simulations were based on data from a cardiac trial of 673 patients in which 252 deaths occurred and seven variables were cogent predictors of mortality; the number of events per predictive variable was (252/7 =) 36 for the full sample. For the simulations, at values of EPV = 2, 5, 10, 15, 20, and 25, we randomly generated 500 samples of the 673 patients, chosen with replacement, according to a logistic model derived from the full sample. Simulation results for the regression coefficients for each variable in each group of 500 samples were compared for bias, precision, and significance testing against the results of the model fitted to the original sample. For EPV values of 10 or greater, no major problems occurred. For EPV values less than 10, however, the regression coefficients were biased in both positive and negative directions; the large sample variance estimates from the logistic model both overestimated and underestimated the sample variance of the regression coefficients; the 90% confidence limits about the estimated values did not have proper coverage; the Wald statistic was conservative under the null hypothesis; and paradoxical associations (significance in the wrong direction) were increased. Although other factors (such as the total number of events, or sample size) may influence the validity of the logistic model, our findings indicate that low EPV can lead to major problems.

RANDOMIZED, CONTROLLED TRIALS, OBSERVATIONAL STUDIES, AND THE HIERARCHY OF RESEARCH DESIGNS

BACKGROUND In the hierarchy of research designs, the results of randomized, controlled trials are considered to be evidence of the highest grade, whereas observational studies are viewed as having less validity because they reportedly overestimate treatment effects. We used published meta-analyses to identify randomized clinical trials and observational studies that examined the same clinical topics. We then compared the results of the original reports according to the type of research design. METHODS A search of the Medline data base for articles published in five major medical journals from 1991 to 1995 identified meta-analyses of randomized, controlled trials and meta-analyses of either cohort or case-control studies that assessed the same intervention. For each of five topics, summary estimates and 95 percent confidence intervals were calculated on the basis of data from the individual randomized, controlled trials and the individual observational studies. RESULTS For the five clinical topics and 99 reports evaluated, the average results of the observational studies were remarkably similar to those of the randomized, controlled trials. For example, analysis of 13 randomized, controlled trials of the effectiveness of bacille Calmette-Guérin vaccine in preventing active tuberculosis yielded a relative risk of 0.49 (95 percent confidence interval, 0.34 to 0.70) among vaccinated patients, as compared with an odds ratio of 0.50 (95 percent confidence interval, 0.39 to 0.65) from 10 case-control studies. In addition, the range of the point estimates for the effect of vaccination was wider for the randomized, controlled trials (0.20 to 1.56) than for the observational studies (0.17 to 0.84). CONCLUSIONS The results of well-designed observational studies (with either a cohort or a case-control design) do not systematically overestimate the magnitude of the effects of treatment as compared with those in randomized, controlled trials on the same topic.

Importance of events per independent variable in proportional hazards regression analysis II. Accuracy and precision of regression estimates

The analytical effect of the number of events per variable (EPV) in a proportional hazards regression analysis was evaluated using Monte Carlo simulation techniques for data from a randomized trial containing 673 patients and 252 deaths, in which seven predictor variables had an original significance level of p < 0.10. The 252 deaths and 7 variables correspond to 36 events per variable analyzed in the full data set. Five hundred simulated analyses were conducted for these seven variables at EPVs of 2, 5, 10, 15, 20, and 25. For each simulation, a random exponential survival time was generated for each of the 673 patients, and the simulated results were compared with their original counterparts. As EPV decreased, the regression coefficients became more biased relative to the true value; the 90% confidence limits about the simulated values did not have a coverage of 90% for the original value; large sample properties did not hold for variance estimates from the proportional hazards model, and the Z statistics used to test the significance of the regression coefficients lost validity under the null hypothesis. Although a single boundary level for avoiding problems is not easy to choose, the value of EPV = 10 seems most prudent. Below this value for EPV, the results of proportional hazards regression analyses should be interpreted with caution because the statistical model may not be valid.

Obstructive sleep apnea as a risk factor for type 2 diabetes.

PURPOSE Cross-sectional studies have documented the co-occurrence of obstructive sleep apnea (hereafter, sleep apnea) with glucose intolerance, insulin resistance, and type 2 diabetes mellitus (hereafter, diabetes). It has not been determined, however, whether sleep apnea is independently associated with the subsequent development of diabetes, accounting for established risk factors. METHODS This observational cohort study examined 1233 consecutive patients in the Veteran Affairs Connecticut Healthcare System referred for evaluation of sleep-disordered breathing; 544 study participants were free of preexisting diabetes and completed a full, attended, diagnostic polysomnogram. The study population was divided into quartiles based on severity of sleep apnea as measured by the apnea-hypopnea index. The main outcome was incident diabetes defined as fasting glucose level >126 mg/dL and a corresponding physician diagnosis. Compliance with positive airway pressure therapy, and its impact on the main outcome, also was examined. RESULTS In unadjusted analysis, increasing severity of sleep apnea was associated with an increased risk of diabetes (P for linear trend <.001). After adjusting for age, sex, race, baseline fasting blood glucose, body mass index, and weight change, an independent association was found between sleep apnea and incident diabetes (hazard ratio per quartile 1.43; confidence interval 1.10-1.86). Among patients with more severe sleep apnea (upper 2 quartiles of severity), 60% had evidence of regular positive airway pressure use, and this treatment was associated with an attenuation of the risk of diabetes (log-rank test P=.04). CONCLUSION Sleep apnea increases the risk of developing diabetes, independent of other risk factors. Among patients with more severe sleep apnea, regular positive airway pressure use may attenuate this risk.

Resilience of community-dwelling older persons.

Objectives:  To assess resilience of community‐dwelling older persons using a new scale based on response to a stressful life event and to identify the demographic, clinical, functional, and psychosocial factors associated with high resilience.

Treatment decisions for localized prostate cancer: asking men what's important.

AbstractOBJECTIVE: To identify what factors men consider important when choosing treatment for prostate cancer, and to assess why men reject watchful waiting as a treatment option. PARTICIPANTS: One hundred two consecutive men with newly diagnosed localized prostate cancer identified from hospital and community-based urology practice groups. MEASUREMENTS: Patients were asked open-ended questions about likes and dislikes of all treatments considered, how they chose their treatment, and reasons for rejecting watchful waiting. The interviews were conducted in person, after the men had made a treatment decision but before they received the treatment. MAIN RESULTS: The most common reasons for liking a treatment were removal of tumor for radical prostatectomy (RP) (n=15), evidence for external beam radiation (EBRT) (n=6), and short duration of therapy for brachytherapy (seeds) (n=25). The most frequently cited dislikes were high risk of incontinence for RP (n=46), long duration of therapy for EBRT (n=29), and lack of evidence for seeds (n=16). Only 12 men chose watchful waiting. Fear of future consequences, cited by 64% (n=90) of men, was the most common reason to reject watchful waiting. CONCLUSION: In discussing treatment options for localized prostate cancer, clinicians, including primary care providers, should recognize that patients’ decisions are often based on specific beliefs regarding each therapy’s intrinsic characteristics, supporting evidence, or pattern of complications. Even if patients do not recall a physician recommendation against watchful waiting, this option may not be chosen because of fear of future consequences.

Observational Versus Experimental Studies: What’s the Evidence for a Hierarchy?

SummaryThe tenets of evidence-based medicine include an emphasis on hierarchies of research design (i.e., study architecture). Often, a single randomized, controlled trial is considered to provide “truth,” whereas results from any observational study are viewed with suspicion. This paper describes information that contradicts and discourages such a rigid approach to evaluating the quality of research design. Unless a more balanced strategy evolves, new claims of methodological authority may be just as problematic as the traditional claims of medical authority that have been criticized by proponents of evidence-based medicine.

Readmission and Death After Hospitalization for Acute Ischemic Stroke 5-Year Follow-Up in the Medicare Population

Background and Purpose— Stroke is a leading cause of hospital admission among the elderly. Although studies have examined subsequent vascular outcomes, limited data are available regarding the full burden of hospital readmission after stroke. We sought to determine the rates of hospital readmissions and mortality and the reasons for readmission over a 5-year period after stroke. Methods— This retrospective observational cohort study included Medicare beneficiaries aged >65 years who survived hospitalization for an acute ischemic stroke (International Classification of Diseases, Ninth Revision, Clinical Modification codes 434 and 436) and who were discharged from Connecticut acute care hospitals in 1995. This population was followed from discharge in 1995 through 2000 using part A Medicare claims and Social Security Administration mortality data. The primary outcome was hospital readmission and mortality and readmission diagnosis. Results— Among 2603 patients discharged alive, more than half had died or been readmitted at least once during the first year after discharge (1388/2603, 53.3%), and <15% survived admission-free for 5 years (372/2603, 14.3%). The reasons for hospital readmission varied over time, with stroke remaining a leading cause for readmission (3.9 to 6.1% of patients annually). Acute myocardial infarction accounted for a comparable number of readmissions (4.2 to 6.0% of patients annually). The most common diagnostic category associated with readmission, however, was pneumonia or respiratory illnesses, with an annual readmission rate between 8.2% and 9.0% throughout the first 5 years after stroke. Conclusions— Few stroke patients survive for 5 years without a hospital readmission. Between the acute care setting and readmission to the hospital, a window of opportunity may exist for interventions, beyond prevention of recurrent vascular events alone, to reduce the huge public health burden of poststroke morbidity.

Racial Disparities in Stroke Risk Factors The Impact of Socioeconomic Status

Background and Purpose— In the US, blacks have a higher incidence of stroke and more severe strokes than whites. Our objective was to determine if differences in income, education, and insurance, as well as differences in the prevalence of stroke risk factors, accounted for the association between ethnicity and stroke. Methods— We used data from the Third National Health and Nutrition Survey (NHANES III), a cross-sectional sample of the noninstitutionalized US population (1988–1994), and included blacks and whites aged 40 years or older with a self-reported stroke history. Income was assessed using a ratio of income to US Census Bureau annual poverty threshold. Results— Among 11 163 participants, 2752 (25%) were black and 619 (6%) had a stroke history (blacks: 160/2752 [6%]; whites: 459/8411 [6%]; P=0.48). Blacks had a higher prevalence of 5 risk factors independently associated with stroke: hypertension, treated diabetes, claudication, higher C-reactive protein, and inactivity; whites had a higher prevalence of 3 risk factors: older age, myocardial infarction, and lower high-density lipoprotein cholesterol. Ethnicity was independently associated with stroke after adjusting for the 8 risk factors (adjusted odds ratio, 1.32; 95% CI, 1.04 to 1.67). Ethnicity was not independently associated with stroke after adjustment for income and income was independently associated with stroke (adjusted odds ratios for: ethnicity, 1.15; 95% CI, 0.88 to 1.49; income, 0.89; 95% CI, 0.82 to 0.95). Adjustment for neither education nor insurance altered the ethnicity–stroke association. Conclusions— In this study of community-dwelling stroke survivors, ethnic differences exist in the prevalence of stroke risk factors and income may explain the association between ethnicity and stroke.

The Ratio of FEV1 to FVC as a Basis for Establishing Chronic Obstructive Pulmonary Disease

RATIONALE The lambda-mu-sigma (LMS) method is a novel approach that defines the lower limit of normal (LLN) for the ratio of FEV1/FVC as the fifth percentile of the distribution of Z scores. The clinical validity of this threshold as a basis for establishing chronic obstructive pulmonary disease is unknown. OBJECTIVE To evaluate the association between the LMS method of determining the LLN for the FEV1/FVC, set at successively higher thresholds, and clinically meaningful outcomes. METHODS Using data from a nationally representative sample of 3,502 white Americans aged 40-80 years, we stratified the FEV1/FVC according to the LMS-LLN, with thresholds set at the 5th, 10th, 15th, 20th, and 25th percentiles (i.e., LMS-LLN5, LMS-LLN10, etc.). We then evaluated whether these thresholds were associated with an increased risk of death or prevalence of respiratory symptoms. Spirometry was not specifically completed after a bronchodilator. MEASUREMENTS AND MAIN RESULTS Relative to an FEV1/FVC greater than or equal to LMS-LLN25 (reference group), the risk of death and the odds of having respiratory symptoms were elevated only in participants who had an FEV1/FVC less than LMS-LLN(5), with an adjusted hazard ratio of 1.68 (95% confidence interval, 1.34-2.12) and an adjusted odds ratio of 2.46 (95% confidence interval, 2.01-3.02), respectively, representing 13.8% of the cohort. Results were similar for persons aged 40-64 years and those aged 65-80 years. CONCLUSIONS In white persons aged 40-80 years, an FEV1/FVC less than LMS-LLN5 identifies persons with an increased risk of death and prevalence of respiratory symptoms. These results support the use of the LMS-LLN5 threshold for establishing chronic obstructive pulmonary disease.