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At least 19 recordsLinked to original sources
PubMed2004

Communicating the uncertainty in research findings: confidence intervals.

Confidence intervals (CIs) are an effective means of quantifying the uncertainty inherent in study results. Alongside considerations of possible sources of bias in the study design, CIs describe the extent to which study results are applicable in general, beyond the participants involved in the study. We discuss CI use and interpretation for some commonly encountered study designs. We highlight a close relation between CIs and p-values, such that presentation of 95% CIs can make it redundant to state whether a corresponding p-value is less than 0.05. We encourage researchers to use CIs to present their research findings, rather than relying on p-values alone.

Biomedical Research↗
PubMed1999

Bias-corrected confidence intervals for the concentration parameter in a dilution assay.

Interval estimates of the concentration of target entities from a serial dilution assay are usually based on the maximum likelihood estimator. The distribution of the maximum likelihood estimator is skewed to the right and is positively biased. This bias results in interval estimates that either provide inadequate coverage relative to the nominal level or yield excessively long intervals. Confidence intervals based on both log transformation and bias reduction are proposed and are shown through simulations to provide appropriate coverage with shorter widths than the commonly used intervals in a variety of designs. An application to feline AIDS research, which motivated this work, is also presented.

Acquired Immunodeficiency Syndrome↗
PubMedDate not supplied

Can't miss: conquer any number task by making important statistics simple. Part 4. Confidence intervals with t distributions, standard error, and confidence intervals for proportions.

Healthcare quality professionals need to understand and use inferential statistics to interpret sample data from their organizations. Since in quality improvement and healthcare research studies, all the data from a population often are not available, investigators take samples and make inferences about that population using inferential statistics. This series of six articles will give readers an understanding of the concepts of inferential statistics, as well as the specific tools for calculating confidence intervals and tests of statistical significance for samples of data. The statistical principles are equally applicable to quality improvement and healthcare research studies. This article, Part 4, starts with a review of the information contained in Parts 1, 2, and 3, which appeared in the July/August 2003 issue of the Journal for Healthcare Quality. This article describes t distributions and how these are used to calculate confidence intervals for estimating a population mean based on a sample mean of a continuous variable. Part 4 concludes with a discussion of standard error, margin of error, and confidence intervals for estimating a population proportion based on a sample proportion from a binomial variable.

Confidence Intervals↗
PubMed2004

Redefining the confidence interval.

The confidence interval, its close cousin the p-value, and other statistical summaries of data are widely used in science, including the occupational and environmental health sciences, but they are almost as widely misused. My purpose here is to review some basic matters that should be covered in every introductory statistics course, but are generally omitted. More specifically, some of the many assumptions that are needed in the usual forms of analysis are reviewed.

Confidence Intervals↗
PubMed2004

Interval-censored survival time data: confidence intervals for the non-parametric survivor function.

Survival data are described as interval censored when the failure time is not measured exactly but is known only to have occurred within a defined interval. In this paper, we describe and assess three methods for calculating pointwise confidence intervals for the non-parametric survivor function estimated from interval-censored data: the first based on the full information matrix, the second a modification of this approach involving deletion of rows and columns of the information matrix corresponding to zero estimates prior to inversion and the third based on likelihood ratio inference. In a simulation study the likelihood ratio method gave the most accurate confidence intervals with coverage consistently close to the nominal level of 95 per cent.

Antiviral Agents↗
PubMedDate not supplied

Understanding and using confidence intervals in clinical research.

Confidence intervals contain a wealth of clinically relevant information that is not available in the P value and usual significance testing. Numerous articles discuss the hazards of interpreting study results based solely on the P value, raising both practical and philosophical concerns. The general recommendation is that clinical research should not just test hypotheses, but also describe magnitudes of clinical effect. To this end, the confidence interval is a crucial tool in interpreting clinical studies. In this report, we show how one may use confidence intervals to gain further insight into clinical research. For example, by using confidence intervals, one can identify statistically significant results that are clinically imprecise, or conversely, statistically nonsignificant results that are quite precise. In addition, confidence intervals, like the P value, are influenced by sample size. We show how sample sizes that are sufficiently large to test hypotheses may be too small to generate precise estimates of the magnitude of effect. The application and interpretation of confidence intervals are demonstrated through the use of several examples.

Chorioamnionitis↗
PubMed2001

Calculating confidence intervals for the number needed to treat.

The number needed to treat (NNT) has gained much attention in the past years as a useful way of reporting the results of randomized controlled trials with a binary outcome. Defined as the reciprocal of the absolute risk reduction (ARR), NNT is the estimated average number of patients needed to be treated to prevent an adverse outcome in one additional patient. As with other estimated effect measures, it is important to document the uncertainty of the estimation by means of an appropriate confidence interval. Confidence intervals for NNT can be obtained by inverting and exchanging the confidence limits for the ARR provided that the NNT scale ranging from 1 through infinity to -1 is taken into account. Unfortunately, the only method used in practice to calculate confidence intervals for ARR seems to be the simple Wald method, which yields too short confidence intervals in many cases. In this paper it is shown that the application of the Wilson score method improves the calculation and presentation of confidence intervals for the number needed to treat. Control Clin Trials 2001;22:102-110

Confidence Intervals↗
PubMed2000

Improving the calculation of confidence intervals for the number needed to treat.

The number needed to treat has gained much attention in the past years as a useful way of reporting the results of randomised controlled trials with a binary outcome. Defined as reciprocal of the absolute risk reduction the number needed to treat is the estimated number of patients who need to be treated to prevent an adverse outcome in one additional patient. As with other estimated effect measures, it is important to document the uncertainty of the estimation by means of an appropriate confidence interval. Confidence intervals for the number needed to treat can be obtained by inverting and exchanging the confidence limits for the absolute risk reduction. Unfortunately, the only method used in practice for calculating a confidence interval for the absolute risk reduction seems to be the usual asymptotic method, which yields confidence intervals which are too short in many cases. In this paper it is shown that the application of the Wilson score method improves the calculation and presentation of confidence intervals for the number needed to treat.

Bias↗
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↗
PubMed1996

Confidence intervals in QTL mapping by bootstrapping.

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) was investigated using simulation. Empirical confidence intervals were calculated using a bootstrap resampling method for a backcross population derived from inbred lines. Sample sizes were either 200 or 500 individuals, and the QTL explained 1, 5, or 10% of the phenotypic variance. The method worked well in that the proportion of empirical confidence intervals that contained the simulated QTL was close to expectation. In general, the confidence intervals were slightly conservatively biased. Correlations between the test statistic and the width of the confidence interval were strongly negative, so that the stronger the evidence for a QTL segregating, the smaller the empirical confidence interval for its location. The size of the average confidence interval depended heavily on the population size and the effect of the QTL. Marker spacing had only a small effect on the average empirical confidence interval. The LOD drop-off method to calculate empirical support intervals gave confidence intervals that generally were too small, in particular if confidence intervals were calculated only for samples above a certain significance threshold. The bootstrap method is easy to implement and is useful in the analysis of experimental data.

Animals↗
PubMed1981

Comparisons of confidence intervals for attributable risk.

Confidence intervals for the attributable risk in various epidemiologic study designs are obtained, via a transformation, from the confidence interval for the natural logarithm of the product of the probability of being exposed to the risk factor, and the risk ratio minus one. When the estimated attributable risk is between .21 and .79, the width of the logarithmic transformation (LT)-based interval is less than that for a maximum likelihood (ML)-based interval. This simple sufficient condition applies to all three well-known epidemiologic study designs. Computer simulation results further demonstrate the superiority of the LT-based interval to the ML-based one when the sufficient condition is satisfied.

Epidemiologic Methods↗
PubMed1999

Test-based exact confidence intervals for the difference of two binomial proportions.

Confidence intervals are often provided to estimate a treatment difference. When the sample size is small, as is typical in early phases of clinical trials, confidence intervals based on large sample approximations may not be reliable. In this report, we propose test-based methods of constructing exact confidence intervals for the difference in two binomial proportions. These exact confidence intervals are obtained from the unconditional distribution of two binomial responses, and they guarantee the level of coverage. We compare the performance of these confidence intervals to ones based on the observed difference alone. We show that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance.

Biometry↗
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↗
PubMedDate not supplied

[VI: Confidence intervals--an alternative for p values].

Confidence intervals combine the ideas of clinical relevance and statistical significance by using one instructive expression, which enables remarkable reduction of table structures and result sections in scientific publications. Confidence interval based conclusions can be transferred from a clinical trial to its underlying study population with respect to a residual statistical error probability, i.e. the significance concept is retained. However, their presentation using the original unit of the clinical endpoint under consideration allows for immediate interpretation of the results' clinical impact. For example, the comparison of two therapy groups based on a binary endpoint becomes feasible using the relative risk's confidence interval. If "1" is not contained in the interval, the therapy groups significantly differ concerning this endpoint. The larger the interval turns out, the less precise the characterisation of the "real" risk value based on the study risk estimate. The larger the risk estimate turns out, the more clinical relevance.

Antibiotic Prophylaxis↗
PubMed2004

Interval estimation by simulation as an alternative to and extension of confidence intervals.

There are numerous techniques for constructing confidence intervals, most of which are unavailable in standard software. Modern computing power allows one to replace these techniques with relatively simple, general simulation methods. These methods extend easily to incorporate sources of uncertainty beyond random error. The simulation concepts are explained in an example of estimating a population attributable fraction, a problem for which analytical formulas can be quite unwieldy. First, simulation of conventional intervals is illustrated and compared to bootstrapping. The simulation is then extended to include sampling of bias parameters from prior distributions. It is argued that the use of almost any neutral or survey-based prior that allows non-zero values for bias parameters will produce an interval estimate less misleading than a conventional confidence interval. Along with simplicity and generality, the ease with which simulation can incorporate these priors is a key advantage over conventional methods.

Computer Simulation↗