Showing papers on "Confidence interval published in 1990"

Prognostic Implications of Echocardiographically Determined Left Ventricular Mass in the Framingham Heart Study

Abstract: A pattern of left ventricular hypertrophy evident on the electrocardiogram is a harbinger of morbidity and mortality from cardiovascular disease. Echocardiography permits the noninvasive determination of left ventricular mass and the examination of its role as a precursor of morbidity and mortality. We examined the relation of left ventricular mass to the incidence of cardiovascular disease, mortality from cardiovascular disease, and mortality from all causes in 3220 subjects enrolled in the Framingham Heart Study who were 40 years of age or older and free of clinically apparent cardiovascular disease, in whom left ventricular mass was determined echocardiographically. During a four-year follow-up period, there were 208 incident cardiovascular events, 37 deaths from cardiovascular disease, and 124 deaths from all causes. Left ventricular mass, determined echocardiographically, was associated with all outcome events. This relation persisted after we adjusted for age, diastolic blood pressure, pulse pressure, treatment for hypertension, cigarette smoking, diabetes, obesity, the ratio of total cholesterol to high-density lipoprotein cholesterol, and electrocardiographic evidence of left ventricular hypertrophy. In men, the risk factor-adjusted relative risk of cardiovascular disease was 1.49 for each increment of 50 g per meter in left ventricular mass corrected for the subject's height (95 percent confidence interval, 1.20 to 1.85); in women, it was 1.57 (95 percent confidence interval, 1.20 to 2.04). Left ventricular mass (corrected for height) was also associated with the incidence of death from cardiovascular disease (relative risk, 1.73 [95 percent confidence interval, 1.19 to 2.52] in men and 2.12 [95 percent confidence interval, 1.28 to 3.49] in women). Left ventricular mass (corrected for height) was associated with death from all causes (relative risk, 1.49 [95 percent confidence interval, 1.14 to 1.94] in men and 2.01 [95 percent confidence interval, 1.44 to 2.81] in women). We conclude that the estimation of left ventricular mass by echocardiography offers prognostic information beyond that provided by the evaluation of traditional cardiovascular risk factors. An increase in left ventricular mass predicts a higher incidence of clinical events, including death, attributable to cardiovascular disease.

Ulcerative colitis and colorectal cancer. A population-based study.

Abstract: Background The risk of colorectal cancer is increased among patients with ulcerative colitis. The magnitude of this increase in risk and the effects of the length of follow-up, the extent of disease at diagnosis, and age at diagnosis vary substantially in different studies. Methods To provide accurate estimates of the risk of colorectal cancer among patients with ulcerative colitis, we studied a population-based cohort of 3117 patients given a diagnosis of ulcerative colitis from 1922 through 1983 who were followed up through 1984. Results Ninety-two cases of colorectal cancer occurred in 91 patients. As compared with the expected incidence, the incidence of colorectal cancer in the cohort was increased (standardized incidence ratio [ratio of observed to expected cases] = 5.7; 95 percent confidence interval, 4.6 to 7.0). Less extensive disease at diagnosis was associated with a lower risk; for patients with ulcerative proctitis, the standardized incidence ratio was 1.7 (95 percent confidence interval, 0.8 to 3.2); for those with left-sided colitis, 2.8 (95 percent confidence interval, 1.6 to 4.4); and for those with pancolitis (extensive colitis, or inflammation of the entire colon), 14.8 (95 percent confidence interval, 11.4 to 18.9). Age at diagnosis and the extent of disease at diagnosis were strong and independent risk factors for colorectal cancer. For each increase in age group at diagnosis (less than 15 years, 15 to 29 years, 30 to 39 years, 40 to 49 years, 50 to 59 years, and greater than or equal to 60 years), the relative risk of colorectal cancer, adjusted for the extent of disease at diagnosis, decreased by about half (adjusted standardized incidence ratio = 0.51; 95 percent confidence interval, 0.46 to 0.56). The absolute risk of colorectal cancer 35 years after diagnosis was 30 percent for patients with pancolitis at diagnosis and 40 percent for those given this diagnosis at less than 15 years of age. Conclusions Close surveillance and perhaps even prophylactic proctocolectomy should be recommended for patients given a diagnosis of pancolitis, especially those who are less than 15 years of age at diagnosis.

Appendicular bone density and age predict hip fracture in women. The Study of Osteoporotic Fractures Research Group.

Abstract: To determine whether measurement of bone density predicts hip fracture in women, we prospectively studied 9703 nonblack women aged 65 years and older who had measurements of bone mineral density using single-photon absorptiometry in the calcaneus, distal radius, and proximal radius. During an average of 1.6 years of follow-up, 53 hip fractures occurred. The risk of hip fracture was inversely related to bone density at all three measurement sites. After adjusting for age, the relative risk of hip fracture was 1.66 for a decrease of 1 SD in the bone density at the calcaneus (95% confidence interval, 1.22 to 2.26), 1.55 (95% confidence interval, 1.13 to 2.11) at the distal radius, and 1.41 (95% confidence interval, 1.06 to 1.88) at the proximal radius. None of the three measurements was a significantly better predictor of hip fracture than the others. After adjusting for bone mineral density, the risk of hip fracture doubled for each 10-year increase in age (relative risk, 2.09; 95% confidence interval, 1.31 to 3.33). We conclude that decreased bone density in the appendicular skeleton is associated with an increased risk of hip fracture, but this accounts for only part of the age-related increase in risk of hip fracture among older women. ( JAMA . 1990;263:665-668)

Calculation and uncertainty analysis of 210Pb dates for PIRLA project lake sediment cores

Abstract: Lead-210 assay and dating are subject to several sources of error, including natural variation, the statistical nature of measuring radioactivity, and estimation of the supported fraction. These measurable errors are considered in calculating confidence intervals for 210Pb dates. Several sources of error, including the effect of blunders or misapplication of the mathematical model, are not included in the quantitative analysis. First-order error analysis and Monte Carlo simulation (of cores from Florida PIRLA lakes) are used as independent estimates of dating uncertainty. CRS-model dates average less than 1% older than Monte Carlo median dates, but the difference increases non-linearly with age to a maximum of 11% at 160 years. First-order errors increase exponentially with calculated CRS-model dates, with the largest 95% confidence interval in the bottommost datable section being 155±90 years, and the smallest being 128±8 years. Monte Carlo intervals also increase exponentially with age, but the largest 95% occurrence interval is 152±44 years. Confidence intervals calculated by first-order methods and ranges of Monte Carlo dates agree fairly well until the 210Pb date is about 130 years old. Older dates are unreliable because of this divergence. Ninety-five per cent confidence intervals range from about 1–2 years at 10 years of age, 10–20 at 100 years, and 8–90 at 150 years old.

The effect of warfarin on mortality and reinfarction after myocardial infarction.

Abstract: Background and Methods. The use of oral anticoagulation in the long-term treatment of survivors of acute myocardial infarction has been highly controversial. We therefore randomly assigned 1214 patients who had recovered from acute myocardial infarction (mean interval from the onset of symptoms to randomization, 27 days) to treatment with warfarin (607 patients) or placebo (607 patients) for an average of 37 months (range, 24 to 63). Results. At the end of the treatment period, there had been 123 deaths in the placebo group and 94 in the warfarin group — a reduction in risk of 24 percent (95 percent confidence interval, 4 to 44 percent; P = 0.027). A total of 124 patients in the placebo group had reinfarctions, as compared with 82 in the warfarin group — a reduction of 34 percent (95 percent confidence interval, 19 to 54 percent; P = 0.0007). Furthermore, we observed a reduction of 55 percent (95 percent confidence interval, 30 to 77 percent) in the number of total cerebrovascular accidents in th...

Platelet hyperreactivity and prognosis in survivors of myocardial infarction.

Abstract: We tested the hypothesis that an increase in spontaneous aggregability of platelets in vitro predicts mortality and coronary events in patients who have survived a recent myocardial infarction. A cohort of 149 survivors of infarction entered our study three months after the index infarction and was followed for five years. At entry and at intervals of six months, spontaneous platelet aggregation (SPA) was tested and graded as positive (aggregation within 10 minutes), intermediate (aggregation after 10 to 20 minutes), or negative (no aggregation within 20 minutes). During follow-up, 6.4 percent (6 of 94) of the patients in the SPA-negative group died, as compared with 10.3 percent (3 of 29) in the SPA-intermediate group and 34.6 percent (9 of 26) in the SPA-positive group. As compared with the SPA-negative group, the SPA-intermediate group had a relative risk of death of 1.6 (95 percent confidence interval, 0.5 to 5.5) and the SPA-positive group had a risk of 5.4 (95 percent confidence interval, 2...

Confusion of confidence intervals and credibility intervals in meta-analysis.

Abstract: A review of 30 meta-analyses that have been conducted in organizational behavior and human resource management using procedures described by Hunter, Schmidt, and Jackson (1982) suggests that there is confusion regarding the use and interpretation of confidence intervals and credibility intervals. This confusion can lead to conflicting conclusions about the relationships between variables

A simple method to calculate the confidence interval of a standardized mortality ratio (SMR)

Abstract: In analyzing standardized mortality ratios (SMRs), it is of interest to calculate a confidence interval for the true SMR. The exact limits of a specific interval can be obtained by means of the Poisson distribution either within an iterative procedure or by one of the tables. The limits can be approximated in using one of various shortcut methods. In this paper, a method is described for calculating the exact limits in a simple and easy way. The method is based on the link between the chi 2 distribution and the Poisson distribution. Only a table of the chi 2 distribution is necessary.

Correction of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error

Abstract: If several risk factors for disease are considered in the same multiple logistic regression model, and some of these risk factors are measured with error, the point and interval estimates of relative risk corresponding to any of these factors may be biased either toward or away from the null value. A method is provided for correcting point and interval estimates of relative risk obtained from logistic regression for measurement error in one or more continuous variables. The method requires a separate validation study to estimate the coefficients from the multivariate linear regression model relating the surrogate variables to the vector of true risk factors. Similar methods have been suggested by other authors, but none provides a means of correcting the confidence intervals which include a component of variability due to estimation of the measurement error parameters from a validation study. An example is provided from a prospective study of dietary fat, calories, and alcohol in relation to breast cancer, and from a validation study of the questionnaire used to assess these nutrients. Before correcting for measurement error, the age-adjusted relative risk for a 25 g increment in alcohol intake was 1.33 (95% confidence interval (CI) 1.14-1.55); after correcting for measurement error, the relative risk increased to 1.62 (95% CI 1.23-2.12). Similarly, for a 10 g increment in saturated fat intake, the age-adjusted relative risk was 0.94 (95% CI 0.83-1.06); after correcting for measurement error, the relative risk was 0.84 (95% CI 0.59-1.20). These results indicate that the failure to find a substantial positive association between breast cancer risk and saturated fat intake cannot be explained by measurement error in fat, calories, or alcohol.

Self-evaluated health and mortality among the elderly in New Haven, Connecticut, and Iowa and Washington counties, Iowa, 1982-1986

Abstract: The ability of global self-evaluations of health to predict survival in follow-up studies is tested in two samples of elderly, noninstitutionalized adults. Data from the Yale Health and Aging Project, New Haven, Connecticut (n = 2,812), and the 65+ Rural Health Study, Iowa and Washington counties, Iowa (n = 3,673), were used to investigate the association between 1982 self-evaluated global health status (excellent, good, fair, poor) and survivorship from 1982 to 1986. Despite extensive controls for physical health status in the form of measures of disabilities and chronic conditions, sociodemographic characteristics, and health risk behaviors at the beginning of the follow-up period, and the use of analytic techniques which take into account the stratified sample design of the New Haven data, poor self-perceptions of health significantly increase the risk of mortality. Adjusted odds ratios for the extreme categories ("poor" as compared with "excellent") for New Haven men and women were 5.33 (95% confidence interval (CI) 1.93-14.75) and 2.99 (95% CI 1.30-6.91), respectively; for Iowa men and women they were 4.84 (95% CI 2.22-10.57) and 3.16 (95% CI 1.49-6.71). Respondents reporting "fair" and "good" health also show elevated risks of mortality in dose-response fashion. Self-perceptions of health status appear to be a factor of unique prospective significance in mortality studies.

Confidence intervals on stratigraphic ranges

Abstract: Observed stratigraphic ranges almost always underestimate true longevities. Strauss and Sadler (1987, 1989) provide a method for calculating confidence intervals on the endpoints of local stratigraphic ranges. Their method can also be applied to composite sections; confidence intervals may be placed on times of origin and extinction for entire species or lineages. Confidence interval sizes depend only on the length of the stratigraphic range and the number of fossil horizons. The technique's most important assumptions are that fossil horizons are distributed randomly and that collecting intensity has been uniform over the stratigraphic range. These assumptions are more difficult to test and less likely to be fulfilled for composite sections than for local sections.Confidence intervals give useful baseline estimates of the incompleteness of the fossil record, even if the underlying assumptions cannot be tested. Confidence intervals, which can be very large, should be calculated when the fossil record is used to assess absolute rates of molecular or morphological evolution, especially for poorly preserved groups. Confidence intervals have other functions: to determine how rich the fossil record has to be before radiometric dating errors become the dominant source of error in estimated times of origin or extinction; to predict future fossil finds; to predict which species with fossil records should be extant; and to assess phylogenetic hypotheses and taxonomic assignments.

Decline in the risk of myocardial infarction among women who stop smoking.

Abstract: To assess the relation of smoking cessation to the risk of a first myocardial infarction in women, we compared the smoking habits of 910 patients who had had their first myocardial infarction with those of 2375 controls in a hospital-based case-control study of women from 25 to 64 years of age. The estimate of relative risk among current smokers as compared with women who had never smoked was 3.6 (95 percent confidence interval, 3.0 to 4.4). Among exsmokers overall, the corresponding estimate of relative risk was 1.2 (95 percent confidence interval, 1.0 to 1.7). Among exsmokers, the estimate of relative risk was significantly elevated among women who had stopped smoking less than two years previously (relative risk, 2.6; 95 percent confidence interval, 1.8 to 3.8). Most of the increase in the risk had dissipated among the women who had stopped smoking two to three years previously, and the estimate of relative risk among the women who had not smoked for three or more years was virtually indistinguishable from that among the women who had never smoked. The same pattern of decline was apparent regardless of the amount smoked, the duration of smoking, the age of the women, or the presence of other predisposing factors. These data suggest that in women, as in men, the increase in the risk of a first myocardial infarction among cigarette smokers declines soon after the cessation of smoking and is largely dissipated after two or three years.

A case-control study of Alzheimer's disease

Abstract: A case-control study of Alzheimer's disease (AD) was conducted to evaluate the roles of family history of dementing disease and AD, and medical conditions, particularly those related to the viral and immune hypotheses in AD. One hundred and eighty-three clinically diagnosed patients were identified between 1980 and 1985 through the Geriatric and Family Services clinic at the University of Washington hospital, and 18 patients were identified during the same time period through the Veteran's Administration Medical Center in Seattle, Washington. Telephone interviews were conducted with spouses (87.7%) and children (12.3%) of the patients. Each patient was matched to a friend or nonblood relative of the patient by age, sex, and the relationship between the patient and his or her respondent, for a total of 130 matched pairs. The odds ratio for AD was elevated if a first-degree relative was reported to have a history of dementia (odds ratio, 2.21; 95% confidence interval, 1.17 to 4.18). This risk was especially elevated if a sibling was affected (odds ratio, 4.04; 95% confidence interval, 1.37 to 11.90); the highest risk to the proband was observed if a sibling had presumed AD (odds ratio, 5.92; 95% confidence interval, 1.59 to 21.96). The risk increased with increasing numbers of first-degree family members affected for both a history of dementia and presumed AD. We found little difference between patients and control subjects with respect to the age of the mother or father at the time of the subject's birth. No statistically significant differences were observed between the two groups with regard to conditions that might support the immune and viral hypothesis in AD, smoking, or alcohol problems.

Successful Allogeneic Transplantation of T-Cell–Depleted Bone Marrow from Closely HLA-Matched Unrelated Donors

Abstract: We describe a four-year experience with bone marrow transplantation involving closely HLA-matched unrelated donors and 55 consecutive patients with hematologic disease who were seven months to 48.6 years old (median, 18 years). An intensive pretransplantation conditioning regimen and graft-versus-host disease (GVHD) prophylaxis with CD3-directed T-cell depletion and cyclosporine were employed. Durable engraftment was achieved in 50 of 53 patients who could be evaluated (94 percent; 95 percent confidence interval, 83 to 98 percent). Acute GVHD of Grade II to IV developed in 46 percent of the patients (confidence interval, 27 to 66 percent). The incidence and severity of acute GVHD were increased in recipients of HLA-mismatched marrow as compared with recipients of phenotypically matched marrow (incidence of 53 percent [confidence interval, 37 to 68 percent] vs. 17 percent [confidence interval, 5 to 45 percent]; P less than 0.05). Extensive chronic GVHD and deaths not due to relapse also tended to be more frequent when HLA-mismatched marrow was used, but not significantly so. With a median follow-up of more than 19 months (range, greater than 9 to greater than 39), the actuarial disease-free survival of transplant recipients with leukemia and a relatively good prognosis (acute leukemia in first remission and chronic myelogenous leukemia in chronic phase) was 48 percent (confidence interval, 24 to 73 percent), and that of recipients with more aggressive leukemia was 32 percent (confidence interval, 18 to 51 percent); the actuarial survival of recipients with non-neoplastic disease was 63 percent (confidence interval, 31 to 86 percent). We conclude that marrow transplantation with closely HLA-matched unrelated donors can be effective treatment for neoplastic and non-neoplastic diseases. Although transplants from phenotypically HLA-matched unrelated donors appear to be most effective, transplants with limited HLA disparity can also be successful in some patients.

Prospective study of estrogen replacement therapy and risk of breast cancer in postmenopausal women.

Abstract: We prospectively examined the use of estrogen replacement therapy in relation to breast cancer incidence in a cohort of women 30 to 55 years of age in 1976. During 367 187 person-years of follow-up among postmenopausal women, 722 incident cases of breast cancer were documented. Overall, past users of replacement estrogen were not at increased risk (relative risk, 0.98; 95% confidence interval, 0.81 to 1.18), including even those with more than 10 years since last [corrected] use (relative risk after adjustment for established risk factors, 0.70; 95% confidence interval, 0.45 to 1.10). However, the risk of breast cancer was significantly elevated among current users (relative risk, 1.36; 95% confidence interval, 1.11 to 1.67). Among current users, a stronger relationship was observed with increasing age but not with increasing duration of use. These data suggest that long-term past use of estrogen replacement therapy is not related to risk of breast cancer but that current use may modestly increase risk.

Incidence of hypertension and stroke in relation to body fat distribution and other risk factors in older women.

Abstract: The relation between body fat distribution, as measured by the waist-to-hip circumference ratio, and the 2-year incidences of hypertension and stroke were examined in a cohort of 41,837 women aged 55-69 years. Women who developed hypertension were 2.1 (95% confidence interval 1.7-2.6) times more likely to be in the upper tertile of waist-to-hip ratio than those who did not. Adjustment for age, body mass index (kilograms per meter squared), cigarette smoking, physical activity, alcohol intake, and education level reduced this odds ratio to 1.6 (95% confidence interval 1.3-2.1). Women who developed a stroke were also 2.1 (95% confidence interval 1.5-2.9) times more likely to be in the upper tertile of waist-to-hip ratio than those who did not. Adjustment for the same covariates also lowered this odds ratio to 1.6 (95% confidence interval 1.1-2.4). Further adjustment for hypertension and diabetes mellitus reduced the estimated risk of stroke due to elevated waist-to-hip ratio to 1.3 (95% confidence interval 0.8-2.1). Hypertension, diabetes mellitus, and cigarette smoking remained significantly associated with stroke incidence in the multivariate model. These results indicate that abdominal adiposity, as measured by an increased waist-to-hip ratio, increases the risks of hypertension and stroke, even after accounting for overall body mass. The association of abdominal adiposity with risk of stroke is related, in part, to the association of abdominal adiposity with hypertension and diabetes.

Simulation Output Analysis Using Standardized Time Series

Abstract: The method of standardized time series STS was proposed by Schruben as an approach for constructing asymptotic confidence intervals for the steady-state mean from a single simulation run. The STS method "cancels out" the variance constant while other methods attempt to consistently estimate the variance constant. Our goal in this paper is to generalize the STS method and to study some of its basic properties. Starting from a functional central limit theorem FCLT for the sample mean of the simulated process, a class of mappings of C[0,1] to ℝ is identified, each of which leads to a STS confidence interval. One of these mappings leads to the batch means method. A lower bound is obtained for the expected length of the asymptotic as the run size becomes large STS confidence intervals. This lower bound is not attained, but can be approached arbitrarily closely, by STS confidence intervals. Methods that consistently estimate the variance constant do realize this lower bound. The variance of the length of a STS confidence interval is of larger order in the run length than is that for the regenerative method.

Snoring in a Hispanic-American Population: Risk Factors and Association With Hypertension and Other Morbidity

Abstract: • Snoring was investigated in a survey of respiratory disease in Hispanic-Americans of a New Mexico community. A population-based sample of 1222 adults was studied with questionnaires and measurements of height, weight, and blood pressure. The age-adjusted prevalence of regular loud snoring was 27.8% in men and 15.3% in women. Snoring prevalence increased with age and obesity in both men and women. Cigarette smoking was also associated with snoring, but chronic obstructive lung disease and alcohol consumption were not. Snorers more frequently had hypertension, ischemic heart disease, and excessive daytime sleepiness. In contrast to other studies, after adjustment for confounding factors, there was no effect of snoring on hypertension (odds ratio, 1.0; 95% confidence interval, 0.7 to 1.5), but an effect on myocardial infarction was still demonstrable (odds ratio, 1.8; 95% confidence interval, 0.9 to 3.6). The association of snoring with sleepiness suggests that respiratory disturbance of sleep related to upper airway obstruction, such as sleep apnea, occurs more frequently in snorers in this population. ( Arch Intern Med . 1990;150:597-601)

Estimates of absolute cause-specific risk in cohort studies.

Abstract: In this paper we study methods for estimating the absolute risk of an event c1 in a time interval [t1, t2], given that the individual is at risk at t1 and given the presence of competing risks. We discuss some advantages of absolute risk for measuring the prognosis of an individual patient and some difficulties of interpretation for comparing two treatment groups. We also discuss the importance of the concept of absolute risk in evaluating public health measures to prevent disease. Variance calculations permit one to gauge the relative importance of random and systematic errors in estimating absolute risk. Efficiency calculations were also performed to determine how much precision is lost in estimating absolute risk with a nonparametric approach or with a flexible piecewise exponential model rather than a simple exponential model, and other calculations indicate the extent of bias that arises with the simple exponential model when that model is invalid. Such calculations suggest that the more flexible models will be useful in practice. Simulations confirm that asymptotic methods yield reliable variance estimates and confidence interval coverages in samples of practical size.

The effects of measurement errors on relatwe risk regressions

Abstract: This paper concerns the effects of random error in numerical measurements of risk factors (covariates) in relative risk regressions. When not dependent on outcome (nondifferential), such error usually attenuates relative risk estimates (shifts them toward one) and leads to spuriously narrow confidence intervals. The presence of measurement error also reduces precision of estimates and power of significance tests. However, significance levels obtained by using the approximate measurements are usually valid and as powerful as possible given the measurement error. The attenuation in risk estimate depends not only on the size (variance) of the measurement error, but also on its distributional form, on whether it is dependent on the true level of the risk factor (whether it is of "Berkson" type), on the variance and distributional form of true levels of the risk factor, on the functional form of the regression (exponential or linear), and on the confounding variables included in the model. Error in measuring confounding variables leads to loss of control of confounding, leaving residual bias. Uncomplicated techniques of correcting the effects of measurement error in simple models in which distributions are assumed normal are available in the statistical literature. For these corrections, information on measurement error variance is required. Some approaches appropriate for more general models have been proposed, but these appear to be insufficiently developed for routine application.

Vasectomy and the risk of prostate cancer

Abstract: An unexpected association between history of vasectomy and increased risk of prostate cancer emerged when multiple comparisons were carried out in data collected from 1976-1988 in a US hospital-based case-control study of many diseases and exposures. The association was assessed in detail in these data, in a comparison of 220 men with first episodes of prostate cancer with 571 noncancer controls and 960 cancer controls. The age-adjusted relative risk of prostate cancer was 5.3 (95% confidence interval 2.7-10) when noncancer controls were used and 3.5 (95 percent confidence interval 2.1-6.0) when cancer controls were used. The magnitude of the relative risk estimate appeared to be unrelated to the length of the interval after vasectomy. Allowance for several factors did not alter the estimates, but we did not have information on testosterone level or sexual activity, which may have been confounding factors. The association was stronger among men most likely to have been under more intensive medical surveillance; selective detection of asymptomatic cancer in such men would have led to an excess of cases. Further studies are needed to rule out chance, bias from medical surveillance, and uncontrolled confounding as explanations for the finding.

Parameter estimation following group sequential hypothesis testing

Abstract: SUMMARY Parameter estimation techniques which fail to adjust for the interim analyses of group sequential test designs will introduce bias in much the same way that the repeated use of single sample hypothesis testing causes inflation of the type one statistical error rate. Methods based on the duality of hypothesis testing and interval estimation require definition of an ordering for the outcome space for the test statistic. In this paper, estimation following a group sequential hypothesis test for the mean of a normal distribution with known variance is investigated. A proposed ordering of the sample space based on the maximum likelihood estimate of the mean is found to result in estimates which compare favourably with estimates computed from orderings investigated by Tsiatis, Rosner & Mehta (1984) and Chang & O'Brien (1986) for a variety of group sequential designs. The proposed ordering is then adapted for use when the sizes of groups accrued between analyses is random.

The Association Between Chlamydia trachomatis and Ectopic Pregnancy: A Matched-Pair, Case-Control Study

Abstract: We performed a case-control study of the association of past exposure to Chlamydia trachomatis and ectopic pregnancy with 306 case patients with an ectopic pregnancy and 266 pregnant patients who served as controls. The geometric mean antichlamydial antibody titer among cases was 75 ±10.2 vs 13±11.0 among controls. The matched-pair odds ratio for ectopic pregnancy and IgG titer of 1:64 or greater to C trachomatis was 3.0 (95% confidence interval, 2.1 to 4.4). Adjusting for age at first intercourse, total lifetime partners, douching, history of infertility, and parity yielded a relative risk of 2.4 (95% confidence interval, 1.5 to 3.3). Current douching remained an independent risk factor after controlling for chlamydial exposure, with an adjusted relative risk of 2.1 (95% confidence interval, 1.3 to 3.5). The population attributable fraction for chlamydial infection was 0.47 and that for douching was 0.45. The results stress the need for control of C trachomatis infections and for further study of specific douching behaviors as risk factors for ectopic pregnancy. ( JAMA . 1990;263:3164-3167)

Variance calculations and confidence intervals for estimates of the attributable risk based on logistic models.

Abstract: The attributable risk (AR), defined as AR = [Pr(disease) - Pr(disease/no exposure)]/Pr(disease), measures the proportion of disease risk that is attributable to an exposure. Recently Bruzzi et al. (1985, American Journal of Epidemiology 122, 904-914) presented point estimates of AR based on logistic models for case-control data to allow for confounding factors and secondary exposures. To produce confidence intervals, we derived variance estimates for AR under the logistic model and for various designs for sampling controls. Calculations for discrete exposure and confounding factors require covariances between estimates of the risk parameters of the logistic model and the proportions of cases with given levels of exposure and confounding factors. These covariances are estimated from Taylor series expansions applied to implicit functions. Similar calculations for continuous exposures are derived using influence functions. Simulations indicate that those asymptotic procedures yield reliable variance estimates and confidence intervals with near nominal coverage. An example illustrates the usefulness of variance calculations in selecting a logistic model that is neither so simplified as to exhibit systematic lack of fit nor so complicated as to inflate the variance of the estimate of AR.

A meta-analysis of alcoholic beverage consumption in relation to risk of colorectal cancer.

Abstract: Quantitative methods were used to review epidemiologic data relating consumption of alcoholic beverages to risk of colorectal cancer. The data (27 studies) supported the presence of a weak association. For consumption of two alcoholic beverages daily, on average the relative risk of colorectal cancer was 1.10 (95% confidence interval 1.05-1.14). Other findings were: (1) the association did not vary according to gender or site within the large bowel; (2) results from follow-up studies (relative risk 1.32, 95% confidence interval 1.16-1.51) suggested a stronger relationship than those from case-control studies (relative risk 1.07, 95% confidence interval 1.02-1.12); and (3) the evidence supporting beverage specificity was not conclusive, although the results were consistent with a stronger association with consumption of beer (relative risk 1.26, 95% confidence interval 1.13-1.41) than with consumption of wine (relative risk 1.11, 95% confidence interval 0.91-1.36) or liquor (relative risk 1.13, 95% confidence interval 0.99-1.29). Because the magnitude of the association between alcohol consumption and risk of colorectal cancer was small, the findings regarding a causal role of alcohol were inconclusive.

Standard errors and confidence intervals in nonlinear regression: comparison of Monte Carlo and parametric statistics

Abstract: A Monte Carlo method is employed to characterize distributions of parameter values calculated in nonlinear regression problems. Accurate estimates of confidence intervals are easily obtained. Two illustrative numerical examples are provided to compare the Monte Carlo uncertainty estimates with those derived by use of standard methods of parametric statistics. The customary assumptions that (1) the effects of covariances between pairs of the parameters can bc ignored and (2) that the distributions of the parameters are normal are shown to lead to significant errors, up to 2and 3-fold in the calculated uncertainties. The Monte Carlo method is free from these assumptions and their associated errors.