Theodore R. Holford

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.

A randomized, controlled trial of methylprednisolone or naloxone in the treatment of acute spinal-cord injury: Results of the second national acute spinal cord injury study

In 1990, the Second National Acute Spinal Cord Injury Study reported that high-dosage methylprednisolone improves neurologic recovery in spinal-injured humans. The study showed that patients who received the drug within 8 hr after injury improved, whereas those who received the drug later did not. The drug significantly increased recovery even in severely injured patients who were admitted with no motor or sensory function below the lesion, contradicting a long-held dogma that such patients would not recover. Some researchers, however, have questioned the stratification of the patient population, the use of summed neurologic change scores, and the absence of functional assessments. The stratification by injury severity and treatment time was planned a priori and based on objective criteria. Detailed analyses revealed no differences between groups attributable to stratification or randomization. While multivariate analyses of the summed neurologic scores were used, the conclusions were corroborated by other analytical approaches that did not rely on summed scores. For example, treatment with methylprednisolone more than doubled the probability that patients would convert from quadriplegia or paraplegia to quadriparesis or paraparesis, analgesia to hypalgesia, and anesthesia to hypesthesia. The treatment also significantly improved neurologic scores in lumbosacral segments, indicating that beneficial effects were not limited to segments close to the lesion site. The treatment did not significantly affect mortality or morbidity. The study strongly suggests that methylprednisolone has significant beneficial effects in human spinal cord injury, that these effects occur only when the drug is given within 8 hr, and that it helps even in patients with severe spinal cord injuries. These conclusions have important implications for spinal cord injury care and research.

A Multicomponent Intervention to Prevent Delirium in Hospitalized Older Patients

BACKGROUND Since in hospitalized older patients delirium is associated with poor outcomes, we evaluated the effectiveness of a multicomponent strategy for the prevention of delirium. METHODS We studied 852 patients 70 years of age or older who had been admitted to the general-medicine service at a teaching hospital. Patients from one intervention unit and two usual-care units were enrolled by means of a prospective matching strategy. The intervention consisted of standardized protocols for the management of six risk factors for delirium: cognitive impairment, sleep deprivation, immobility, visual impairment, hearing impairment, and dehydration. Delirium, the primary outcome, was assessed daily until discharge. RESULTS Delirium developed in 9.9 percent of the intervention group as compared with 15.0 percent of the usual-care group, (matched odds ratio, 0.60; 95 percent confidence interval, 0.39 to 0.92). The total number of days with delirium (105 vs. 161, P=0.02) and the total number of episodes (62 vs. 90, P=0.03) were significantly lower in the intervention group. However, the severity of delirium and recurrence rates were not significantly different. The overall rate of adherence to the intervention was 87 percent, and the total number of targeted risk factors per patient was significantly reduced. Intervention was associated with significant improvement in the degree of cognitive impairment among patients with cognitive impairment at admission and a reduction in the rate of use of sleep medications among all patients. Among the other risk factors per patient there were trends toward improvement in immobility, visual impairment, and hearing impairment. CONCLUSIONS The risk-factor intervention strategy that we studied resulted in significant reductions in the number and duration of episodes of delirium in hospitalized older patients. The intervention had no significant effect on the severity of delirium or on recurrence rates; this finding suggests that primary prevention of delirium is probably the most effective treatment strategy.

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.

A Randomized, Controlled Trial of Methylprednisolone or Naloxone in the Treatment of Acute Spinal-Cord Injury

Abstract Studies in animals indicate that methylprednisolone and naloxone are both potentially beneficial in acute spinal-cord injury, but whether any treatment is clinically effective remains uncertain. We evaluated the efficacy and safety of methylprednisolone and naloxone in a multicenter randomized, double-blind, placebo-controlled trial in patients with acute spinal-cord injury, 95 percent of whom were treated within 14 hours of injury. Methylprednisolone was given to 162 patients as a bolus of 30 mg per kilogram of body weight, followed by infusion at 5.4 mg per kilogram per hour for 23 hours. Naloxone was given to 154 patients as a bolus of 5.4 mg per kilogram, followed by infusion at 4.0 mg per kilogram per hour for 23 hours. Placebos were given to 171 patients by bolus and infusion. Motor and sensory functions were assessed by systematic neurologic examination on admission and six weeks and six months after injury. After six months the patients who were treated with methylprednisolone within eigh...

International patterns and trends in thyroid cancer incidence, 1973–2002

During the past several decades, an increasing incidence of thyroid cancer has been reported in many parts of the world. To date, no study has compared the trends in thyroid cancer incidence across continents. We examined incidence data from cancer incidence in five continents (CI5) over the 30-year period 1973–2002 from 19 populations in the Americas, Asia, Europe, and Oceania. Thyroid cancer rates have increased from 1973–1977 to 1998–2002 for most of the populations except Sweden, in which the incidence rates decreased about 18% for both males and females. The average increase was 48.0% among males and 66.7% among females. More recently, the age-adjusted international thyroid cancer incidence rates from 1998 to 2002 varied 5-fold for males and nearly 10-fold for females by geographic region. Considerable variation in thyroid cancer incidence was present for every continent but Africa, in which the incidence rates were generally low. Our analysis of published CI5 data suggests that thyroid cancer rates increased between 1973 and 2002 in most populations worldwide, and that the increase does not appear to be restricted to a particular region of the world or by the underlying rates of thyroid cancer.

The estimation of age, period and cohort effects for vital rates

In models for vital rates which include effects due to age, period and cohort, there is aliasing due to a linear dependence among these three factors. This dependence arises both when age and period intervals are equal and when they are not. One solution to the dependence is to set an arbitrary constraint on the parameters. Estimable functions of the parameters are invariant to the particular constraint applied. For evenly spaced intervals, deviations from linearity are estimable but only a linear function of the three slopes is estimable. When age and period intervals have different widths, further aliasing occurs. It is assumed that the number of deaths in the numerator of the rate equation has a Poisson distribution. The calculations are illustrated with data on mortality from prostate cancer among nonwhites in the U.S.

Genetic variation in TNF and IL10 and risk of non-Hodgkin lymphoma: a report from the InterLymph Consortium

BACKGROUND Common genetic variants in immune and inflammatory response genes can affect the risk of developing non-Hodgkin lymphoma. We aimed to test this hypothesis using previously unpublished data from eight European, Canadian, and US case-control studies of the International Lymphoma Epidemiology Consortium (InterLymph). METHODS We selected 12 single-nucleotide polymorphisms for analysis, on the basis of previous functional or association data, in nine genes that have important roles in lymphoid development, Th1/Th2 balance, and proinflammatory or anti-inflammatory pathways (IL1A, IL1RN, IL1B, IL2, IL6, IL10, TNF, LTA, and CARD15). Genotype data for one or more single-nucleotide polymorphisms were available for 3586 cases of non-Hodgkin lymphoma and for 4018 controls, and were assessed in a pooled analysis by use of a random-effects logistic regression model. FINDINGS The tumour necrosis factor (TNF) -308G-->A polymorphism was associated with increased risk of non-Hodgkin lymphoma (p for trend=0.005), particularly for diffuse large B-cell lymphoma, the main histological subtype (odds ratio 1.29 [95% CI 1.10-1.51] for GA and 1.65 [1.16-2.34] for AA, p for trend <0.0001), but not for follicular lymphoma. The interleukin 10 (IL10) -3575T-->A polymorphism was also associated with increased risk of non-Hodgkin lymphoma (p for trend=0.02), again particularly for diffuse large B-cell lymphoma (p for trend=0.006). For individuals homozygous for the TNF -308A allele and carrying at least one IL10 -3575A allele, risk of diffuse large B-cell lymphoma doubled (2.13 [1.37-3.32], p=0.00083). INTERPRETATION Common polymorphisms in TNF and IL10, key cytokines for the inflammatory response and Th1/Th2 balance, could be susceptibility loci for non-Hodgkin lymphoma. Moreover, our results underscore the importance of consortia for investigating the genetic basis of chronic diseases like cancer.

Restricted activity among community-living older persons: incidence, precipitants, and health care utilization.

Restricted activity, defined as staying in bed for at least half a day or cutting down on ones usual activities because of an illness or injury (1), has high face validity as a measure of health and functional status, especially for older persons, who often value quality of life over longevity (2). The importance of restricted activity was recognized more than 20 years ago in the U.S. Surgeon Generals original Healthy People Report (3), which identified reduction of restricted activity as one of its two major goals for older persons. Subsequently, several clinical trials of preventive interventions have included restricted activity as a key outcome measure (4-7). Despite this attention, relatively little is known about the epidemiology of restricted activity among older persons. Previous studies, based largely on one-time assessments, have suggested that only a minority of community-living older persons experience restricted activity in the course of 1 year (8, 9). The factors precipitating restricted activity, moreover, have not been well defined. Finally, whether older persons seek medical attention in the setting of restricted activity has not been studied. Those who do not seek attention may consider restricted activity to be a normal part of aging and may miss a chance for successful evaluation and intervention. In this prospective cohort study, we sought to better elucidate the epidemiology of restricted activity in community-living older persons. Our goals were to more accurately estimate the rate of restricted activity, identify the health-related and non-health-related problems leading to restricted activity, and determine whether restricted activity is associated with increased health care utilization. Methods Study Sample The study sample comprised the 754 participants of the Precipitating Events Project, a longitudinal study of nondisabled, community-living persons 70 years of age or older. Participants in the Precipitating Events Project were identified from a computerized list of 3157 age-eligible members of a large health plan in New Haven, Connecticut. Members were eligible if they were communityliving, English-speaking, and nondisabled (that is, required no personal assistance) in four key activities of daily livingbathing, walking, dressing, and transferring from a chair. Plan members were excluded on the basis of three criteria: diagnosis of a terminal illness with a life expectancy less than 12 months, plans to move out of the New Haven area during the next 12 months, and significant cognitive impairment with no available proxy. Enrollment To minimize potential selection effects, a computerized randomization program was used to assign each age-eligible health plan member a unique number. Screening for eligibility and enrollment proceeded sequentially from March 1998 to October 1999. Potential participants were sent a letter that briefly described the study and explained that they would be contacted by phone. During the phone interview, eligibility was assessed, and a home visit was scheduled among consenting eligible persons. During the home visit, eligibility was verified, informed consent was obtained, and a comprehensive baseline assessment was completed. On the basis of gait speed, cognitive status, and age, participants were categorized into one of three risk groups for disability by using a model developed and validated in an earlier study (Table 1) (10). To ensure that enough participants were included in each risk group, participants were enrolled in a 4:2:1 ratio for low, intermediate, and high risk for disability, respectively. Table 1. Risk Model for Disability and Number of Participants Enrolled, according to Phase Assembly of the Precipitating Events Project cohort is shown in the Figure. We applied our stratified sampling strategy in three phases. In phase 1, all eligible and consenting persons were enrolled. In phase 2, persons were excluded from the study if they indicated during the screening telephone interview that they had walked 0.5 mile or for 30 minutes continuously without stopping within the past month. In phase 3, persons who were eligible based on the screening telephone interview were excluded from the study if they were found to have low risk for disability during the home visit. The enrollment procedures in phases 2 and 3 were otherwise identical to those in phase 1. Figure. Assembly of Precipitating Events Project cohort. The number of participants enrolled in each of the three phases is shown in Table 1. During phase 1, 77% of the participants had low risk for disability. Phase 2 was designed to decrease this percentage by excluding persons who were likely to have low risk for disability. The sensitivity and specificity of the screening question used during phase 2 were 66% and 76%, respectively, for low disability risk (based on gold standard data from the first 282 participants enrolled during phase 1). Other candidate screening questions, alone or in combination, had a lower sensitivity or specificity (or both). As shown in the Figure, only 4.6% (126 of 2735) of the health plan members who could be contacted declined to complete the screening telephone interview, and 75.2% (754 of 1002) of the eligible members agreed to participate in the study. Persons who declined to participate did not differ significantly from those who were enrolled in terms of age or sex. Baseline Data Collection Trained research nurses used standard instruments to perform baseline interviews and assessments. Clinical data included 13 self-reported, physician-diagnosed chronic conditions: hypertension; myocardial infarction; congestive heart failure; stroke; diabetes; arthritis; hip fracture; fracture of wrist, arm, or spine since 50 years of age; amputation of leg; chronic lung disease; cirrhosis or liver disease; cancer (other than minor skin cancers); and Parkinson disease. Cognitive status was assessed by using the Folstein Mini-Mental State Examination (11). Timed rapid gait was assessed by having the participants walk back and forth over a 10-foot course as quickly and safely as possible (10). Follow-up Data Collection The occurrence of restricted activity and health-related and non-health-related problems leading to restricted activity were ascertained during monthly telephone interviews by using a standardized, four-step protocol. First, participants were asked two questions related to restricted activity: Since we last talked on [date of last interview], have you stayed in bed for at least half a day due to an illness, injury, or other problem? and Since we last talked on [date of last interview], have you cut down on your usual activities due to an illness, injury, or other problem? Second, if participants had restricted activity (that is, answered yes to either question), they were asked sequentially whether they had had any of 24 prespecified problems since we last talked on [date of last interview]. To develop our list of potential problems, we identified common physical and mental health symptoms that community-living older persons had reported in previous studies (12-14), and we supplemented these symptoms with other events that we deemed important on the basis of our own clinical and research experience (15). Third, immediately after each yes response to a specific problem, participants were asked, Did this problem cause you to stay in bed for at least half a day or to cut down on your usual activities? (that is, did it lead to restricted activity). Finally, participants with restricted activity were asked to specify any other reasons why they stayed in bed for at least half a day or cut down on their usual activities. Participants without restricted activity were not asked about the specific problems. During pilot testing, we found that the test-retest reliability of this four-step protocol was high, with a value of 0.90 for the presence or absence of restricted activity and a value of 0.75 or greater for the presence or absence of 20 of the 24 problems leading to restricted activity (mean time between assessments, 4.1 days among 20 persons). The value was less than 0.6 for only 3 of the problems (swelling in feet or ankles, fear of falling, and frequent or painful urination). During the monthly telephone interviews, participants were also asked whether they had stayed at least overnight in a hospital and whether they had seen a physician in the office or emergency department since their last interview. The research protocol was approved by the Yale University School of Medicine Institutional Review Board. Statistical Analysis We calculated the rate of restricted activity for the overall cohort and for subgroups defined by sex and risk for disability by dividing the number of months in which participants reported staying in bed for at least half a day or cutting down on their usual activities by the total person-months of follow-up. These analyses were repeated for staying in bed for at least half a day and for cutting down on ones usual activities alone (that is, without staying in bed for at least half a day). We then calculated the overall and stratified rates for each of the prespecified problems leading to restricted activity by using person-months with restricted activity as the denominator. The mean number of problems per episode of restricted activity was also calculated. Finally, the rates of health care utilization, including physician office visits, emergency department visits, and hospital admissions, were calculated for months with and months without restricted activity. The events of interest in this study were potentially recurrent in nature; that is, participants may have experienced restricted activity or used health care services in more than one month. Because standard statistical approaches based on the binomial or Poisson distributions assume independence among events, we used alternative methods, designed specifically for recurrent events, t

Pulse pressure and risk for myocardial infarction and heart failure in the elderly

OBJECTIVES We sought to determine whether pulse pressure (PP), a measure of arterial stiffness, is an independent predictor of the incidence of coronary heart disease (CHD), congestive heart failure (CHF) and overall mortality among community-dwelling elderly. BACKGROUND Current hypertension guidelines classify cardiovascular risk on the basis of elevated systolic blood pressure (SBP) or diastolic blood pressure (DBP) without considering their combined effects. Recent studies suggest that PP is a strong predictor of cardiovascular end points, but few data are available among community elderly. METHODS The study sample included 2,152 individuals age > or =65 years, who were participants in the Established Populations for Epidemiologic Study of the Elderly program, free of CHD and CHF at baseline and still alive at one year after enrollment. Blood pressure was measured at baseline. Incidence of CHD, incidence of CHF and total mortality were monitored in the following 10 years. RESULTS There were 328 incident CHD events, 224 incident CHF events and 1,046 persons who died of any cause. Pulse pressure showed a strong and linear relationship with each end point. After adjusting for demographics, comorbidity and CHD risk factors, a 10-mm Hg increment in PP was associated with a 12% increase in CHD risk (95% confidence interval [CI], 2% to 22%), a 14% increase in CHF risk (95% CI, 5% to 24%), and a 6% increase in overall mortality (95% CI, 0% to 12%). While SBP and mean arterial pressure (MAP) also showed positive associations with the end points, PP yielded the highest likelihood ratio chi-square. When PP was entered in the model in conjunction with other blood pressure parameters (SBP, DBP, MAP or hypertension stage, respectively), the association remained positive for PP but became negative for the other blood pressure variables. The effect of PP persisted after adjusting for current medication use and was present in normotensive individuals and individuals with isolated systolic hypertension but not in individuals with diastolic hypertension. CONCLUSIONS Elevated PP is a powerful independent predictor of cardiovascular end points in the elderly.