Showing papers on "Confidence interval published in 1988"

Essentials of medical statistics.

Abstract: Basics Frequencies, frequency distributions and histograms Means, standard deviations and standard errors The normal distribution Confidence interval for a mean Significance tests for a single mean Comparison of two means Comparison of several means - analysis of variance Correlation and linear regression Multiple regression Probability Proportions The chi-squared test for contingency tables Further methods for contingency tables Measures of mortality and morbidity Survival analysis The Poisson distribution Goodness of fit of frequency distributions Transformations Non-parametric methods Planning and conducting an investigation Sources of error Sampling methods Cohort and case-control studies Clinical trials and intervention studies Calculation of required sample size Use of computers Appendix: Statistical tables

A case-control study of chorioamnionic infection and histologic chorioamnionitis in prematurity.

Abstract: To study the role of infection in prematurity, we studied the demographic and obstetrical characteristics, chorioamnionic cultures, and placental histologic features of women who delivered prematurely and compared these findings with those in women who delivered at term. Microorganisms were isolated from the area between the chorion and the amnion (chorioamnion) in 23 of 38 placentas (61 percent) from women with preterm labor who delivered before 37 weeks' gestation and in 12 (21 percent) of 56 placentas from women without preterm labor who delivered at term (odds ratio, 5.6; 95 percent confidence interval, 2.1 to 15.6). The most frequent isolates from the placentas of those whose infants were delivered prematurely were Ureaplasma urealyticum (47 percent) and Gardnerella vaginalis (26 percent). The recovery of any organism from the chorioamnion was strongly associated with histologic chorioamnionitis (odds ratio, 7.2; 95 percent confidence interval, 2.7 to 19.5) and with bacterial vaginosis (odds ratio, 3.2; 95 percent confidence interval, 1.1 to 6.6). When multiple logistic regression was used to control for demographic and obstetrical variables, premature delivery was still related to the recovery of organisms from the chorioamnion (odds ratio, 3.8; 95 percent confidence interval, 1.5 to 9.9) and with chorioamnionitis (odds ratio, 5.0; 95 percent confidence interval, 1.6 to 15.3). The proportion of placentas with evidence of infection was highest among those who delivered at the lowest gestational age. We conclude that infection of the chorioamnion is strongly related to histologic chorioamnionitis and may be a cause of premature birth.

Statistics in Medicine: Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates

Abstract: Gardner and Alunan explained the rationale for using estimation and confidence intervals in making inferences from analytical studies and described their calculation for means or proportions and their differences.1 In this paper we present methods for calculating confidence intervals for other common statistics obtained from medical investigations. The techniques for obtaining confidence intervals for estimates of relative risk are described. These can come either from an incidence study, where, for example, the frequency of a congenital malformation at birth is compared in two defined groups of mothers, or from a case-control study, where a group of patients with the disease of interest (the cases) is compared with another group of people without the disease (the controls). The methods of obtaining confidence intervals for standardised disease ratios and rates in studies of incidence, prevalence, and mortality are described. Such rates and ratios are commonly calculated to enable appropriate comparisons to be made between study groups after adjustment for confounding factors like age and sex. The most frequently used standardised indices are the standardised incidence ratio (SIR) and the standardised mortality ratio (SMR). A worked example is included for each method. The calculations have been carried out to full arithmetical precision, as is recom? mended practice,2 although intermediate steps are shown as rounded results. Some of the methods given in this paper are large sample approximations and are not reliable for studies with fewer than about 20 cases. Appropriate design principles for these types of study have to be adhered to since confidence intervals convey only the effects of sampling variation on the precision of the estimated statistics and cannot control for other errors such as biases due to the selection of inappropriate controls or in the methods of collecting the data.

Diminished lung function as a predisposing factor for wheezing respiratory illness in infants.

Abstract: In a prospective study of 124 infants enrolled as newborns, we assessed the relation between initial lung function and the subsequent incidence of lower respiratory tract illness during the first year of life. The risk of having a wheezing illness was 3.7 times higher (95 percent confidence interval, 0.9 to 15.5; P = 0.06) among infants whose values for total respiratory conductance (the reciprocal of the resistance to air flow of the entire respiratory system) were in the lowest third, as compared with infants with values in the upper two thirds of the range of values for the group. Boys with initial values in the lowest third for an indirect index of airway conductance had a 10-fold increase (95 percent confidence interval, 2.2 to 44.2; P = 0.001) in the risk of having a wheezing illness. A 16-fold increase (95 percent confidence interval, 1.7 to 147.1; P = 0.002) in the risk of having a wheezing illness was found among girls whose initial values for lung volume at the end of tidal expiration were in the lowest third. We conclude that diminished lung function is a predisposing factor for the development of a first wheezing illness in infants.

A note on graphical presentation of estimated odds ratios from several clinical trials

Abstract: To display a number of estimates of a parameter obtained from different studies it is common practice to plot a sequence of confidence intervals. This can be useful but is often unsatisfactory. An alternative display is suggested which represents intervals as points on a bivariate graph, and which has advantages. When the data are estimates of odds ratios from studies with a binary response, it is argued that for either type of plot, a log scale should be used rather than a linear scale.

A Method for Computing Profile-Likelihood- Based Confidence Intervals

Abstract: SUMMARY The method of constructing confidence regions based on the generalised likelihood ratio statistic is well known for parameter vectors. A similar construction of a confidence interval for a single entry of a vector can be implemented by repeatedly maximising over the other parameters. We present an algorithm for finding these confidence interval endpoints that requires less computation. It employs a modified Newton-Raphson iteration to solve a system of equations that defines the endpoints.

Use of the Automatic External Defibrillator in the Management of Out-of-Hospital Cardiac Arrest

Abstract: The automatic external defibrillator is a simple device that can be used by nonprofessional rescuers to treat cardiac arrest. In 1287 consecutive patients with out-of-hospital cardiac arrest, we assessed the results of initial treatment with this device by firefighters who arrived first at the scene, as compared with the results of standard defibrillation administered by paramedics who arrived slightly after the firefighters. Of 276 patients who were initially treated by firefighters using the automatic defibrillator, 84 (30 percent) survived to hospital discharge (expected rate according to a logistic model, 17 percent; P less than 0.001), as compared with 44 (19 percent) of 228 patients when fire-fighters delivered only basic cardiopulmonary resuscitation and the first defibrillation was performed after the arrival of the paramedic team. Few patients with conditions other than ventricular fibrillation survived. In a multivariate analysis of characteristics that influenced survival after ventricular fibrillation, a better survival rate was related to a witnessed collapse (odds ratio, 3.9; 95 percent confidence interval, 2.0 to 7.6), younger age (odds ratio, 1.2; 95 percent confidence interval, 1.0 to 1.4), the presence of "coarse" (higher-amplitude) fibrillation (odds ratio, 4.2; 95 percent confidence interval, 1.6 to 11.0), a shorter response time for paramedics (odds ratio, 1.4; 95 percent confidence interval, 1.0 to 2.1), and initial treatment by firefighters using an automatic external defibrillator (odds ratio, 1.8; 95 percent confidence interval, 1.1 to 2.9). These findings support the widespread use of the automatic external defibrillator as an important part of the treatment of out-of-hospital cardiac arrest, although the overall impact of the use of this device on community survival rates is still uncertain.

A Meta-analysis of Alcohol Consumption in Relation to Risk of Breast Cancer

Abstract: Epidemiologic findings regarding the relation between alcohol consumption and risk of breast cancer have been inconsistent. We performed a meta-analysis (a quantitative review) of the available data. To evaluate whether there was a dose-response relation between alcohol consumption and risk of breast cancer, we fitted mathematical models to the pooled data. There was strong evidence to support a dose-response relation in both the case-control and follow-up epidemiologic data. Using the dose-response curves that we calculated, the risk of breast cancer at an alcohol intake of 24 g (1 oz) of absolute alcohol daily (about two drinks daily) relative to nondrinkers was 1.4 (95% confidence interval, 1.0 to 1.8) in the case-control data and was 1.7 (95% confidence interval, 1.4 to 2.2) in the follow-up data. We interpret these findings not as proof of causality, but as strongly supportive of an association between alcohol consumption and risk of breast cancer. ( JAMA 1988;260:652-656)

Calculating confidence intervals for some non-parametric analyses.

Abstract: Gardner and Altman1 described the rationale behind the use of confidence intervals and gave methods for their calculation for a population mean and for differences between two population means for paired and unpaired samples. These methods are based on sample means, standard errors, and the t distribution and should strictly be used only for continuous data from Normal distributions (although small deviations from Normality are not important2). For non-Normal continuous data the median of the population or the sample is preferable to the mean as a measure of location. Medians are also appropriate in other situations?for example, when measurements are on an ordinal scale. This paper describes methods of calculating confidence intervals for a population median or for other population quantiles from a sample of observations. Calculations of confidence intervals for the difference between two population medians or means (a non-parametric approach rather than the parametric approach mentioned above) for both unpaired and paired samples are described. Worked examples are given for each situation. Because of the discrete nature of some of the sampling distribu? tions involved in non-parametric analyses it is not usually possible to calculate confidence intervals with exactly the desired level of confidence. Hence, if a 95% confidence interval is wanted the choice is between the lowest possible level of confidence over 95% (a "conservative" interval) and the highest possible under 95%. There is no firm policy on which of these is preferred, but we will mainly describe conservative intervals in this paper. The exact level of confidence associated with any particular approximate level can be calculated from the distribution of the statistic being used. The methods outlined for obtaining confidence intervals are described in more detail in textbooks on non-parametric statistics.3 The calculations can be carried out using the statistical computer package MINITAB.4 A method for calculating confidence intervals for Spearman's rank correlation coefficient is given in an accom? panying paper.5 A confidence interval indicates the precision of the sample statistic as an estimate of the overall population value. Confidence intervals convey the effects of sampling variation but cannot control for non-sampling errors in study design or conduct. They should not be used for basic description of the sample data but only for indicating the uncertainty in sample estimates for population values of medians or other statistics.

Cigarette smoking and risk of stroke in middle-aged women.

Abstract: It is known that cigarette smoking is associated with increased risk of both thrombotic and hemorrhagic stroke among men. To test for such an association among women, we examined the incidence of stroke in relation to cigarette smoking in a prospective cohort study of 118,539 women 30 to 55 years of age and free from coronary heart disease, stroke, and cancer in 1976. During eight years of follow-up (908,447 person-years), we identified 274 strokes, comprising 71 subarachnoid hemorrhages, 26 intracerebral hemorrhages, 122 thromboembolic strokes, and 55 strokes about which information was insufficient to permit classification. The number of cigarettes smoked per day was associated positively with the risk of stroke. Compared with the women who had never smoked, those who smoked 1 to 14 cigarettes per day had an age-adjusted relative risk of 2.2 (95 percent confidence interval, 1.5 to 3.3), whereas those who smoked 25 or more cigarettes per day had a relative risk of 3.7 (95 percent confidence interval, 2.7 to 5.1). For women in this latter group, the relative risk of subarachnoid hemorrhage was 9.8 (95 percent confidence interval, 5.3 to 17.9), as compared with those who had never smoked. Adjustment for the effects of relative weight, hypertension, diabetes, history of high cholesterol, previous use of oral contraceptives, postmenopausal estrogen therapy, and alcohol intake did not appreciably alter the association between cigarette use and incidence of stroke. These prospective data support a strong causal relation between cigarette smoking and stroke among young and middle-aged women.

Interval estimates for correlation coefficients corrected for within-person variation: implications for study design and hypothesis testing

Abstract: It is well known that random measurement error can attenuate the correlation coefficient between two variables. One possible solution to this problem is to estimate the correlation coefficient based on an average of a large number of replicates for each individual. As an alternative, several authors have proposed an unattenuated (or corrected) correlation coefficient which is an estimate of the true correlation between two variables after removing the effect of random measurement error. In this paper, the authors obtain an estimate of the standard error for the corrected correlation coefficient and an associated 100% x (1-alpha) confidence interval. The standard error takes into account the variability of the observed correlation coefficient as well as the estimated intraclass correlation coefficient between replicates for one or both variables. The standard error is useful in hypothesis testing for comparisons of correlation coefficients based on data with different degrees of random error. In addition, the standard error can be used to evaluate the relative efficiency of different study designs. Specifically, an investigator often has the option of obtaining either a few replicates on a large number of individuals, or many replicates on a small number of individuals. If one establishes the criterion of minimizing the standard error of the corrected coefficient while fixing the total number of measurements obtained, in almost all instances it is optimal to obtain no more than five replicates per individual. If the intraclass correlation is greater than or equal to 0.5, it is usually optimal to obtain no more than two replicates per individual.

Medial arterial calcification and its association with mortality and complications of diabetes.

Abstract: Medical arterial calcification was studied among 4,553 subjects in a 20-year, longitudinal study of Pima Indians. The prevalence and incidence of medial arterial calcification were highest among men, the elderly, and patients with Type 2 (non-insulin-dependent) diabetes mellitus. Medial arterial calcification was most commonly observed in the feet and appeared to progress proximally. Proportional hazards analysis was used to evaluate risk factors for medial arterial calcification in the feet and to evaluate medial arterial calcification as a risk factor for death and for complications of diabetes. Among diabetic patients, risk factors for medial arterial calcification were impaired vibration perception, long duration of diabetes, and high plasma glucose concentration (p less than 0.01 for each). Among nondiabetic subjects, age, male gender (p less than 0.01 for each), and high serum cholesterol concentration (p = 0.02) were risk factors for medial arterial calcification. Nondiabetic subjects with medial arterial calcification did not have higher mortality rates than subjects without medial arterial calcification (rate ratio = 0.95, 95% confidence interval = 0.7-1.3). Diabetic patients with medial arterial calcification, compared with diabetic patients without medial arterial calcification, had 1.5-fold the mortality rate (95% confidence interval = 1.0-2.1), 5.5-fold the rate of amputations (95% confidence interval = 2.1-14.1), 2.4-fold the rate of proteinuria (95% confidence interval = 1.3-4.5), 1.7-fold the rate of retinopathy (95% confidence interval = 0.98-2.8), and 1.6-fold the rate of coronary artery disease (95% confidence interval = 0.48-5.4).

Bayesian Confidence Intervals for Smoothing Splines

Abstract: The frequency properties of Wahba's Bayesian confidence intervals for smoothing splines are investigated by a large-sample approximation and by a simulation study. When the coverage probabilities for these pointwise confidence intervals are averaged across the observation points, the average coverage probability (ACP) should be close to the nominal level. From a frequency point of view, this agreement occurs because the average posterior variance for the spline is similar to a consistent estimate of the average squared error and because the average squared bias is a modest fraction of the total average squared error. These properties are independent of the Bayesian assumptions used to derive this confidence procedure, and they explain why the ACP is accurate for functions that are much smoother than the sample paths prescribed by the prior. This analysis accounts for the choice of the smoothing parameter (bandwidth) using cross-validation. In the case of natural splines an adaptive method for avo...

Stroke following coronary-artery bypass surgery. A case-control estimate of the risk from carotid bruits.

Abstract: The causes of stroke following coronary-artery bypass surgery are largely unknown. To determine whether carotid bruits increase the risk of these events, we compared 54 patients with postoperative stroke or transient ischemic attacks with 54 randomly selected control patients. Both groups were drawn from 5915 consecutive patients who had coronary bypass surgery at our hospital from 1970 to 1984. Carotid bruits were noted preoperatively in 13 patients with postoperative stroke and in 4 control patients. Case-control analysis showed that the presence of carotid bruits increased the risk of stroke or transient ischemic attacks by 3.9-fold (95 percent confidence interval, 1.2 to 12.8; P less than 0.05). This increased risk remained essentially unchanged after adjustment for potentially confounding variables in a multiple logistic regression analysis. Other factors associated with a significantly increased risk (P less than 0.05) of these neurologic deficits were a history of stroke or transient ischemic attack (odds ratio, 6.0; 95 percent confidence interval, 1.6 to 22.1), a history of congestive heart failure (odds ratio, 5.3; confidence interval, 1.6 to 17.0), mitral regurgitation (odds ratio, 4.3; confidence interval, 1.4 to 12.9), postoperative atrial fibrillation (odds ratio, 3.0; confidence interval, 1.4 to 6.7), a cardiopulmonary-bypass pump time of more than two hours (odds ratio, 2.7; confidence interval, 1.1 to 6.7), and a previous myocardial infarction (odds ratio, 2.3; confidence interval, 1.1 to 5.1). We conclude that the presence of carotid bruits increases the risk of stroke after coronary-artery bypass surgery. However, the absolute magnitude of this risk, 2.9 percent, is small and comparable to the reported risk of stroke from carotid endarterectomy.

A model-based estimate of the mean incubation period for AIDS in homosexual men.

Abstract: Because of the difficulty in identifying the date of exposure to type 1 of the human immunodeficiency virus (HIV-1) infection in persons other than transfusion recipients, studies of the incubation periods for acquired immunodeficiency syndrome (AIDS) have been limited When data from a cohort of 84 homosexual and bisexual men that provided the information to determine the years of conversion of sera infected with HIV-1 were analyzed, a model for the proportion likely to develop AIDS and the incubation period for AIDS in homosexual men could be derived The maximum likelihood estimate for the proportion of infected homosexual men developing AIDS is 099 (90% confidence interval ranging from 038 to 1) Furthermore, the maximum likelihood estimate for the mean incubation period for AIDS in homosexual men is 78 years (90% confidence interval ranging from 42 years to 150 years), which is close to the estimate of 82 years for adults developing transfusion-associated AIDS

Validation of screening tools for identifying hearing-impaired elderly in primary care.

Abstract: Two instruments for the detection of hearing impairment, the Welch-Allyn audioscope (Welch-Allyn Inc, Skaneateles Falls, NY) and the Hearing Handicap Inventory for the Elderly--Screening Version (HHIE-S), were validated against pure tone audiometry in 178 patients over 65 years old screened in primary care practice. The prevalence of hearing impairment in this sample was 30%. The audioscope yielded reproducible results in the physicians' offices and a hearing center. The sensitivity of the audioscope was 94% in both locations, while its specificity was 90% in the hearing center and 72% in the physicians' offices. The HHIE-S yielded reproducible results between the two test locations. An HHIE-S score from 0 to 8 resulted in a likelihood ratio of 0.36 (95% confidence interval, 0.19 to 0.68), and a score of 26 or more yielded a likelihood ratio of 12.00 (95% confidence interval, 2.62 to 55.00) for predicting the presence of hearing impairment. Used together, the two instruments had a test accuracy of 83%. The audioscope and HHIE-S are valid, reliable, inexpensive tools for detecting hearing impairment in the elderly.

A Review of Bootstrap Confidence Intervals

Abstract: On passe en revue plusieurs methodes distinctes basees sur le bootstrap pour construire des intervalles de confiance

On bootstrap resampling and iteration

Abstract: SUMMARY We propose a single unifying approach to bootstrap resampling, applicable to a very wide range of statistical problems. It enables attention to be focused sharply on one or more characteristics which are of major importance in any particular problem, such as coverage error or length for confidence intervals, or bias for point estimation. Our approach leads easily and directly to a very general form of bootstrap iteration, unifying and generalizing present disparate accounts of this subject. It also provides simple solutions to relatively complex problems, such as a suggestion by Lehmann (1986) for 'conditionally' short confidence intervals. We set out a single unifying principle guiding the operation of bootstrap resampling, applicable to a very wide range of statistical problems including bias reduction, shrinkage, hypothesis testing and confidence interval construction. Our principle differs from other approaches in that it focuses attention directly on a measure of quality or accuracy, expressed in the form of an equation whose solution is sought. A very general form of bootstrap iteration is an immediate consequence of iterating the empirical solution to this equation so as to improve accuracy. When employed for bias reduction, iteration of the resampling principle yields a competitor to the generalized jackknife, enabling bias to be reduced to arbitrarily low levels. When applied to confidence intervals it produces the techniques of Hall (1986) and Beran (1987). The resampling principle leads easily to solutions of new, complex problems, such as empirical versions of confidence intervals proposed by Lehmann (1986). Lehmann argued that an 'ideal' confidence interval is one which is short when it covers the true parameter value but not necessarily otherwise. The resampling principle suggests a simple empirical means of constructing such intervals. Section 2 describes the general principle, and ? 3 shows how it leads naturally to bootstrap iteration. There we show that in many problems of practical interest, such as bias reduction and coverage-error reduction in two-sided confidence intervals, each iteration reduces error by the factor n-1, where n is sample size. In the case of confidence intervals our result sharpens one of Beran (1987), who showed that coverage error is reduced by the factor n-2 in two-sided intervals. The main exception to our n-1 rule is coverage error of one-sided intervals, where error is reduced by the factor n-A at each iteration. Our approach to bootstrap iteration serves to unify not just the philosophy of iteration for different statistical problems, but also different techniques of iteration for the same

Stomach cancer after partial gastrectomy for benign ulcer disease.

Abstract: We followed for 25 to 33 years 6459 patients who had undergone partial gastrectomy for benign ulcer disease to determine the incidence of stomach cancer. The overall risk was no different from that among sex- and age-matched controls from the Swedish Cancer Registry (standardized incidence ratio = 0.96; 95 percent confidence limits, 0.78 and 1.16). However, when the patients were classified according to the duration of follow-up after operation, sex, surgical procedure, diagnosis at the time of operation, and age at operation, differences in risk were observed between the subgroups. After adjustment for potential confounding variables, the average adjusted risk increased 28 percent (adjusted standardized incidence ratio = 1.28; 95 percent confidence limits, 1.11 and 1.49) for each successive five-year interval after operation. The adjusted risk was greater among women than men (adjusted standardized incidence ratio = 1.96; 95 percent confidence limits, 1.18 and 3.24). Patients who had undergone a...

One-sided inference about functionals of a density

Abstract: This paper discusses the possibility of truly nonparametric inference about functionals of an unknown density. Examples considered include: discrete functionals, such as the number of modes of a density and the number of terms in the true model; and continuous functionals, such as the optimal bandwidth for kernel density estimates or the widths of confidence intervals for adaptive location estimators. For such functionals it is not generally possible to make two-sided nonparametric confidence statements. However, one-sided nonparametric confidence statements are possible: e.g., "I say with 95% confidence that the underlying distribution has at least three modes." Roughly, this is because the functionals of interest are semicontinuous with respect to the topology induced by a distribution-free metric. Then a neighborhood procedure can be used. The procedure is to find the minimum value of the functional over a neighborhood of the empirical distribution in function space. If this neighborhood is a nonparametric $1 - \alpha$ confidence region for the true distribution, the resulting minimum value lowerbounds the true value with a probability of at least $1 - \alpha$. This lower bound has good asymptotic properties in the high-confidence setting $\alpha$ close to 0.

Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness.

Abstract: Various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically. It is found that the method based on likelihood scores (Koopman, 1984, Biometrics 40, 513-517; Miettinen and Nurminen, 1985, Statistics in Medicine 4, 213-226) performs best in achieving the nominal confidence coefficient, but it may distribute the tail probabilities quite disparately. Using general theory of Bartlett (1953, Biometrika 40, 306-317; 1955, Biometrika 42, 201-203), we correct this method for asymptotic skewness. Following Gart (1985, Biometrika 72, 673-677), we extend this correction to the case of estimating the common ratio in a series of two-by-two tables. Computing algorithms are given and applied to numerical examples. Parallel methods for the odds ratio and the ratio of Poisson parameters are noted.

Assessment of two tests for the diagnosis of canine hyperadrenocorticism

Abstract: The low-dose dexamethasone suppression test and the urinary corticoid/creatinine ratio were assessed in 166 and 150 dogs, respectively, for their value in the diagnosis of hyperadrenocorticism. The diagnostic accuracy of the low-dose dexamethasone suppression test was 0.83, with a 95 per cent confidence interval from 0.76 to 0.88. The urinary corticoid/creatinine ratio had a diagnostic accuracy of 0.91 with a 95 per cent confidence interval from 0.85 to 0.95. The high predictive value of a negative corticoid/creatinine ratio (0.98; confidence interval 0.80 to 1.00) and the low cost of this test makes it preferable for screening purposes to the low-dose dexamethasone suppression test for which the predictive value of a negative test was calculated as 0.5g (confidence interval 0.43 to 0.73).

Statistics in Medicine: Calculating confidence intervals for regression and correlation

Abstract: The most common statistical analyses are those that examine one or two groups of individuals with respect to a single variable, and methods of calculating confidence intervals for means or proportions and their differences have been described previously.' Also common are those analyses that consider the relation between two variables in one group of subjects. We use regression analysis to predict one variable from another, and correlation analysis to see if the values oftwo variables are associated. The purposes of these two analyses are distinct, and usually one only should be used. This paper outlines the calculation of the linear regression equation for predicting one variable from another and shows how to calculate confidence intervals for the population value of the slope and intercept of the line, for the line itself, and for predictions made using the regression equation. It explains how to obtain a confidence interval for the population value ofthe difference between the slopes of regression lines in two groups of subjects and how to calculate a confidence interval for the vertical distance between two parallel regression lines. The calculations of confidence intervals for Pearson's correlation coefficient and Spearman's rank correlation coefficient are described. Worked examples are included to illustrate each method. The calculations have been carried out to full arithmetical precision, as is recommended practice,2 but intermediate steps are shown as rounded results. Methods of calculating confidence intervals for different aspects of regression and correlation are demonstrated, but the appropriate ones to use depend on the particular problem being studied. The interpretation of confidence intervals has been discussed earlier.' Confidence intervals convey only the effects of sampling variation on the estimated statistics and cannot control for other errors such as biases in design, conduct, or analysis.

Analytical goals for the acceptance of common reference intervals for laboratories throughout a geographical area

Abstract: Analytical goals required for the successful transfer of reference intervals between laboratories within a specified limited geographical area, with a population homogeneous for the quantities, are presented. Diagrams are shown which allow the investigation of the influence of analytical imprecision and bias, both separately and in combination, on the percentage of the population outside each reference limit. Figures to evaluate the effect of population sample size on the size of confidence interval around each reference limit are combined with the diagrams for analytical imprecision and bias. The maximum acceptable percentage of the population outside the limit for the 0.90 confidence interval of each of the means +/- 1.96 s reference limits is 4.6% for a population sample size of 120. Based on this, the maximum acceptable imprecision, with no bias, is 0.6 of the total biological standard deviation (sB) and the maximum acceptable bias, with no imprecision, is 0.25 sB.

Statistics and Data Analysis: An Introduction

Abstract: Displaying a Single Group of Numbers Recognizing Shapes of Distributions Finding the Centre of a Distribution Measuring Variability Grouped Data Cumulative Distributions and Percentiles Simple Plots for a Group of Numbers Transforming Data Probability Random Variables and the Normal Distribution Toward Statistical Inference Confidence Intervals Testing a Hypothesis About the Mean Comparing Two Groups of Numbers Several Groups of Numbers Pairs of Numbers: Bivariate Data Analyzing a Linear Relationship Categorical Data and Chi-Squared Analysis.

Risk factors for ectopic pregnancy. A population-based study.

Abstract: To evaluate the association between ectopic pregnancy and 22 potential risk factors, we conducted a population-based case-control study. The investigation included 274 cases diagnosed from 1935 through 1982 in residents of Rochester, Minn, and 548 matched controls selected from live-birth deliveries. Risk factor information documented prior to the last index menstrual period was obtained via medical record abstract. Univariate matched analyses revealed nine variables associated with a significantly elevated relative risk of ectopic pregnancy. Following conditional logistic regression, four variables remained as strong and independent risk factors for ectopic pregnancy: current intrauterine device use (relative risk, 13.7; 95% confidence interval, 1.6 to 120.6), a history of infertility (relative risk, 2.6; 95% confidence interval, 1.6 to 4.2), a history of pelvic inflammatory disease (relative risk, 3.3; 95% confidence interval, 1.6 to 6.6), and prior tubal surgery (relative risk, 4.5; 95% confidence interval, 1.5 to 13.9). Theoretically, any condition that prevents or retards migration of the fertilized ovum to the uterus could predispose a woman to ectopic gestation. Further research is needed to clarify the impact of other potential risk factors in the etiology of ectopic pregnancy.

Sample size determinations for the two rater kappa statistic.

Abstract: This paper gives a method for determining a sample size that will achieve a prespecified bound on confidence interval width for the interrater agreement measure,κ. The same results can be used when a prespecified power is desired for testing hypotheses about the value of kappa. An example from the literature is used to illustrate the methods proposed here.

Coronary heart disease mortality in the western collaborative group study follow-up experience of 22 years

Abstract: In 1960-1961, 3,154 healthy, middle-aged men were entered into the Western Collaborative Group Study, a long-term study of coronary heart disease. A 22-year mortality follow-up of this cohort in 1982-1983 accounted for almost 99% of the cohort, and determined that 214 of the men had died of coronary heart disease. The risk of coronary heart disease mortality was studied for several variables measured at baseline, i.e., Type A/B behavior, systolic blood pressure, serum cholesterol level, cigarette smoking status, and age. Using a proportional hazards regression model, systolic blood pressure, serum cholesterol level, cigarette smoking status, and age were highly significant predictors (p less than 0.001) of 22-year coronary heart disease mortality. Type A/B behavior showed no association with 22-year coronary heart disease mortality (standardized relative hazard (SRH) = 0.98, 95% confidence interval (CI) = 0.85-1.12). Systolic blood pressure, serum cholesterol, and age showed relatively consistent positive associations with coronary heart disease mortality over four successive time intervals after the baseline examination. Cigarette smoking showed a significant positive association in the first and second intervals and a nonsignificant positive association in the third and fourth intervals. Type A/B behavior was positively but not significantly associated with coronary heart disease in the first and third intervals, significantly negatively associated (SRH = 0.70, 95% CI = 0.53-0.93) in the second interval and not associated in the fourth interval. The results confirm the importance of the traditional coronary heart disease risk factors, and raise a substantial question about the importance of Type A/B behavior as a risk factor for coronary heart disease mortality.

Alcohol and fatal injuries among US adults. Findings from the NHANES I Epidemiologic Follow-up Study.

Abstract: Use of alcohol is an important risk factor for fatal injuries. However, little information on the relationship between self-reported alcohol use and subsequent risk of fatal injury is available. Therefore, we examined the relationship between the usual number of drinks consumed per occasion and the incidence of fatal injuries in a cohort of US adults. Using data on self-reported alcohol use obtained from 13 251 adults who were included in the National Health and Nutrition Examination Survey Epidemiologic Follow-up Study (mean length of follow-up, 9.3 years), we calculated the incidence of fatal injury according to the usual number of drinks consumed per occasion. After we adjusted for the effects of age, sex, race, and education, persons who consumed five or more drinks per occasion were nearly twice as likely to die from injuries (relative risk, 1.9; 95% confidence interval, 1.0 to 3.5) than persons who drank fewer than five drinks per occasion. A dose-response relationship was observed between the usual number of drinks consumed per occasion and risk of fatal injury, with persons who reported drinking nine or more drinks per occasion being 3.3 times more likely to die from injuries (95% confidence interval, 1.3 to 8.3). These data demonstrate the impact of alcohol use on mortality from injuries in the United States and suggest that self-reported alcohol consumption is an important indicator of risk for fatal injury. ( JAMA 1988;260:2529-2532)