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PubMed1990

Use of the confidence interval function.

Graphics displaying all confidence intervals around a point estimate have been referred to as P-value functions and consonance intervals. We recommend use of the term confidence interval function (CI function) rather than P-value function. The CI function is useful because it simultaneously depicts point estimation, variability, and the relation of these two factors to the null value. The usefulness of the CI function in demonstrating the concepts of effect modification and confounding, in meta-analysis, and in the comparison of various confidence interval procedures is evaluated. Software packages that produce CI functions are described.

Confidence Intervals↗

PubMed1991

Confidence intervals for post-test probability.

Confidence intervals are a natural way to describe the uncertainty of post-test probability in diagnostic tests. We consider confidence intervals for two different scenarios. At a site, for example, hospital emergency room or student health centre, with measured values of disease prevalence, sensitivity and specificity available, the confidence interval is similar to results in the literature, but at a site where measured values of these indices are unavailable, we develop a method, using the values of disease prevalence, sensitivity and specificity from other sites, to obtain a confidence interval for post-test probability. We use the diagnosis of strep throat to illustrate the results. We also obtain confidence intervals from simulations to compare with the results of both scenarios.

Adult↗

PubMed1991

Confidence intervals for the MMPI-2.

The confidence intervals for the Minnesota Multiphasic Personality Inventory (MMPI-2) clinical scales were investigated. Based on the clinical scale reliabilities published in the MMPI-2 manual, estimated true scores, standard errors of measurement for estimated true scores, and 95% confidence intervals centered around estimated true scores were calculated at 5-point MMPI-2 T-score intervals. The relationships between obtained T-scores, estimated true T-scores, scale reliabilities, and confidence intervals are discussed. The possible role of error measurement in defining scale high point and code types is noted.

Adult↗

PubMed1985

Generalization of distribution--free confidence intervals for bioavailability ratios.

The confidence interval approach to bioavailability assessment depends first on selection of the confidence level, usually 95%, and then determination of the confidence limits for the expected bioavailability ratio AUC(Test)/AUC(Reference). In practice, however, it is sometimes of greater interest to know the probability that the expected bioavailability will fall below a critical value, for example 0.75, or within a clinically set bioequivalence range, for example 0.80 to 1.25. Up to now, posterior probability distributions have been suggested, based on classical analysis of variance (ANOVA) with its rather restrictive assumptions, including that of a (logarithmic) normal distribution. In this report, a distribution-free confidence interval based on the Wilcoxon signed-rank statistic has been generalized so that confidence probabilities can be obtained for any given confidence limits. In the case of unimodal and almost symmetrical sampling distributions, the results obtained are very similar to those of the ANOVA-based posterior probability distribution. However, skewed or multimodal sampling distributions are better reflected by the proposed distribution-free method, and more valid information is obtained in these cases, as demonstrated by examples.

Biological Availability↗

PubMed1989

Statistical significance versus clinical relevance. Part III. Methods for calculating confidence intervals.

Formulae for calculating confidence intervals for different types of studies and conditions are presented. These include means, proportions, difference in means and proportions for paired and unpaired data, more complicated analyses of variance, medians, quantiles, relative risks (odd ratios), standardised ratios and rates, intercepts, slopes and correlation coefficients in regression and correlation analyses, as well as survival proportions calculated in survival analysis. For less frequently used formulae, examples are included.

Clinical Trials as Topic↗

PubMed1992

Two-sample nonparametric estimation and confidence intervals under truncation.

We consider point estimates and confidence intervals for the difference in location or scale between two populations when the observations are subject to truncation. We suggest procedures analogous to those for the complete-sample case. A rigorous justification is presented to support the proposed confidence interval procedure. Finally, some simulations verify the properties of the estimators and confidence intervals. We illustrate the procedure using data on tumor size.

Algorithms↗

PubMed1989

Sample sizes for constructing confidence intervals and testing hypotheses.

Although estimation and confidence intervals have become popular alternatives to hypothesis testing and p-values, statisticians usually determine sample sizes for randomized clinical trials by controlling the power of a statistical test at an appropriate alternative, even those statisticians who recommend the use of confidence intervals for inference. There is merit in achieving consistency in the techniques for data analysis and sample size determination. To that end, this paper compares sample size determination with use of the length of the confidence interval with that obtained by control of power.

Angina Pectoris↗

PubMed1992

Expanded confidence intervals, one-sided tests, and equivalence testing.

An argument, based on expanded confidence intervals, is given for always performing one-sided tests. However, if goals are not one-sided and "follow-up" inferences are required, then the usual two-sided confidence intervals (corresponding to two-sided tests) are generally appropriate. When equivalence testing is required (the goal being to show that treatments are "not too different"), expanded confidence intervals are more efficient than Westlake's symmetrical confidence intervals.

Confidence Intervals↗

PubMed1990

[Confidence intervals instead of p-values].

International scientific journals expect authors of articles to an increasing extent to calculate confidence intervals for their statistical findings. Confidence intervals are more informative than p-values in hypothesis testing as the confidence interval expresses how great the value of an investigated effect may be anticipated to be in the population. Examples of calculation of confidence intervals are presented on the basis of data frequently occurring in medical investigations.

Confidence Intervals↗

PubMed1987

A measurement of the efficacy of nosocomial infection control using the 95 per cent confidence interval for infection rates.

From 1981 through 1985, the authors studied the changes in monthly nosocomial infection rates at the University of Virginia Hospital in Charlottesville, Virginia using the 95% confidence interval for infection rates as a marker of the efficacy of infection control activities. For a 99-month baseline period, monthly infection rates were calculated and the 95% confidence interval was established. In the 60 study months, each monthly rate was compared with the 95% confidence interval for that particular month. At the end of each study year, the monthly infection rates were incorporated into the existing confidence interval. Of 60 monthly rates during the study period, 30 were below the confidence interval (p less than 0.00001), two were above the confidence interval (p = 0.23), and 28 were within the confidence interval. Since there was no reduction in surveillance activity, patient case-mix index, or laboratory sensitivity for organism recovery, these results suggest that monthly nosocomial infection rates at this hospital have decreased when compared with the baseline period. The use of the 95% confidence interval may provide a measure of the efficacy of infection control activities, suggest temporal intervals requiring more intensive infection surveillance, and provide a method for examining the variability in monthly infection rates.

Cross Infection↗

PubMed1992

Confidence intervals in medical research.

The utility of confidence intervals in a wide variety of situations in the medical field is re-emphasized, with examples drawn from controlled clinical trials, disease control programmes, vaccine trials and laboratory studies. It is shown that the confidence interval approach is more informative than a mere test of statistical significance, and should therefore be employed as an useful adjuvant. Since proportions are widely quoted in medical literature and as the determination of the exact confidence limits for a binomial proportion is iterative and time-consuming, an assessment is made of 15 published methods which provide approximate confidence limits; the 'Square root transformation' method is recommended since it is accurate and the computation of limits is relatively easy. In the case of a difference between two proportions, the usual method may be employed if sample sizes exceed 75; for smaller sample sizes (even for sizes of 5), the Jeffreys-Perks method is very satisfactory and is therefore recommended.

Confidence Intervals↗

PubMed1988

Recommendations for the use of Taylor series confidence intervals for estimates of vaccine efficacy.

A simple formula for calculating confidence intervals by means of a Taylor series variance approximation has been recommended for gauging the precision of estimates of vaccine efficacy. To evaluate the performance of Taylor series 95% confidence intervals for vaccine efficacy, we conducted a simulation study for commonly expected values of vaccine efficacy, risk of disease in the unvaccinated population, and sample sizes of the vaccinated and unvaccinated groups. In the first simulation, the sample size in the vaccinated group was 500 or 1000, whereas that in the unvaccinated group ranged from 10 to 1000. The confidence intervals were accurate when the sample size in the unvaccinated group was >/=50 and the risk of disease was 0.3-0.9. In contrast, the intervals were too narrow when all three of the following situations occurred: the number of unvaccinated was small (10 or 20), the true vaccine efficacy was relatively low (60% or 80%), and the risk of disease was 0.5-0.9. Furthermore, when the true vaccine efficacy was high (90% or 95%) and the disease risk in the unvaccinated was low (0.1 and 0.2), the confidence intervals were too broad, especially when the unvaccinated sample size was <50. Additional simulations with a sample size in the vaccinated group of 200 gave broad intervals for 95% vaccine efficacy (for all values of disease risk) and for 90% vaccine efficacy when the disease risk was </=0.3.

Epidemiologic Methods↗

PubMed1990

Genetic counseling in rare syndromes: a resampling method for determining an approximate confidence interval for gene location with linkage data from a single pedigree.

Multipoint linkage analysis is a powerful method for mapping a rare disease gene on the human gene map despite limited genotype and pedigree data. However, there is no standard procedure for determining a confidence interval for gene location by using multipoint linkage analysis. A genetic counselor needs to know the confidence interval for gene location in order to determine the uncertainty of risk estimates provided to a consultant on the basis of DNA studies. We describe a resampling, or "bootstrap," method for deriving an approximate confidence interval for gene location on the basis of data from a single pedigree. This method was used to define an approximate confidence interval for the location of a gene causing nonsyndromal X-linked mental retardation in a single pedigree. The approach seemed robust in that similar confidence intervals were derived by using different resampling protocols. Quantitative bounds for the confidence interval were dependent on the genetic map chosen. Once an approximate confidence interval for gene location was determined for this pedigree, it was possible to use multipoint risk analysis to estimate risk intervals for women of unknown carrier status. Despite the limited genotype data, the combination of the resampling method and multipoint risk analysis had a dramatic impact on the genetic advice available to consultants.

Chromosome Mapping↗

PubMed1987

Effective sample sizes for confidence intervals for survival probabilities.

We examine various methods to estimate the effective sample size for construction of confidence intervals for survival probabilities. We compare the effective sample sizes of Cutler and Ederer and Peto et al., as well as a modified Cutler-Ederer effective sample size. We investigate the use of these effective sample sizes in the common situation of many censored observations that intervene between the time point of interest and the last death before this time. We note that there is no a priori reason to treat upper and lower confidence intervals in a symmetric fashion since censored survival data are by nature asymmetric. We recommend the use of the Cutler-Ederer effective sample size in construction of upper confidence intervals and the Peto effective sample size in construction of lower confidence intervals. Two examples with real data demonstrate the differences between confidence intervals formed with different effective sample sizes. This study also illustrates the need for caution in the application of simulation studies to real problems.

Bacterial Infections↗

PubMed1986

Population forecasts and confidence intervals for Sweden: a comparison of model-based and empirical approaches.

This paper compares several methods of generating confidence intervals for forecasts of population size. Two rest on a demographic model for age-structured populations with stochastic fluctuations in vital rates. Two rest on empirical analyses of past forecasts of population sizes of Sweden at five-year intervals from 1780 to 1980 inclusive. Confidence intervals produced by the different methods vary substantially. The relative sizes differ in the various historical periods. The narrowest intervals offer a lower bound on uncertainty about the future. Procedures for estimating a range of confidence intervals are tentatively recommended. A major lesson is that finitely many observations of the past and incomplete theoretical understanding of the present and future can justify at best a range of confidence intervals for population projections. Uncertainty attaches not only to the point forecasts of future population, but also to the estimates of those forecasts' uncertainty.

Forecasting↗

PubMed1985

Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model.

A procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects. This procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability. The confidence interval can be defined in terms of the output of a least squares analysis. It can be computed by a graphical or iterative technique requiring the diagonalization of an m X m matrix or, alternatively, the inversion of a number of m X m matrices. Confidence intervals that are approximate can be obtained with much less computational burden, using either of two approaches. The various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects. Corresponding to each interval procedure is a significance test and one or more estimators.

Analysis of Variance↗

PubMed1988

On sample-size and power calculations for studies using confidence intervals.

A recent trend in epidemiologic analysis has been away from significance tests and toward confidence intervals. In accord with this trend, several authors have proposed the use of expected confidence intervals in the design of epidemiologic studies. This paper discusses how expected confidence intervals, if not properly centered, can be misleading indicators of the discriminatory power of a study. To rectify such problems, the study must be designed so that the confidence interval has a high probability of not containing at least one plausible but incorrect parameter value. To achieve this end, conventional formulas for power and sample size may be used. Expected intervals, if properly centered, can be used to design uniformly powerful studies but will yield sample-size requirements far in excess of previously proposed methods.

Epidemiologic Methods↗

PubMed1992

Bronchodilator testing "confidence intervals" based on the level of bronchial responsiveness.

"Confidence intervals" based upon inhalation of placebo have been proposed as criteria for defining a significant response to an inhaled bronchodilator. The published intervals were derived from a clinically heterogeneous population. We calculated the difference (delta) between spirometric data before and after placebo in 109 consecutive patients referred for methacholine bronchoprovocation challenge testing. The mean delta, expressed both as a percent change and as actual volume change for both the FVC and FEV1, was not significantly different in patients with bronchial hyperresponsiveness, as compared to subjects with a negative methacholine challenge test; however, the variance of measurements in hyperresponsive subjects was significantly greater than that of the normal population. In addition, as the category of responsiveness increased from mild to moderate to severe hyperresponsiveness, so did the variance within these groups. A negative correlation between the measured PC20FEV1 and the volume and percent change was noted. We conclude that patients with hyperresponsive airways may display increased spirometric variation before and after placebo. This general approach for establishing normal limits for defining a significant response appears to be valid, but the actual values used may vary, depending on the composition of the population tested and the goals of the study. Also, the use of the term, "confidence intervals," in this context is inappropriate; and we propose, instead, the use of percentiles and the simpler terms, upper 90th or 95th percentiles.

Adult↗