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PubMed1996

Quickbasic program for exact and mid-P confidence intervals for a binomial proportion.

Computation of the exact confidence interval for a binomial proportion is tedious and requires iterative computer techniques. A Quickbasic program for the IBM PC computer is described that accomplishes the confidence interval calculation accurately, quickly, and with no limits placed on the confidence level, or the size of the numerator or denominator. If desired, the mid-P confidence interval can be computed. The compiled program takes one second on the IBM PC 386/33 without a math co-processor.

Algorithms↗
PubMed1998

A note on confidence intervals in cost-effectiveness analysis.

How to obtain confidence intervals for cost-effectiveness ratios is complicated by the statistical problems of obtaining a confidence interval for a ratio of random variables. Different approaches have been suggested in the literature, but no consensus has been reached. We propose an alternative simple solution to this problem. By multiplying the effectiveness units by the price per effectiveness unit, both costs and benefits can be expressed in monetary terms and standard statistical techniques can be used to estimate a confidence interval for net benefits. This approach avoids the ratio estimation problem and explicitly recognizes that the price per effectiveness unit has to be known to provide cost-effectiveness analysis with a useful decision rule.

Confidence Intervals↗
PubMed1997

A non-iterative accurate asymptotic confidence interval for the difference between two proportions.

I propose a new confidence interval for the difference between two binomial probabilities that requires only the solution of a quadratic equation. The procedure is based one estimating the variance of the observed difference at the boundaries of the confidence interval, and uses least squares estimation rather than maximum likelihood as previously suggested. The proposed procedure is non-iterative, agrees with the conventional test of equality of two binomial probabilities, and, even for fairly small sample sizes, appears to yields actual 95 per cent confidence intervals with mean or median probabilities of coverage very close to 0.95. The Yates continuity correction appears to generate confidence intervals with the conditional probability of coverage at least equal to nominal levels.

Binomial Distribution↗
PubMed1997

The use of likelihood-based confidence intervals in genetic models.

This article describes the computation and relative merits of likelihood-based confidence intervals, compared to other measures of error in parameter estimates. Likelihood-based confidence intervals have the advantage of being asymmetric, which is often the case with structural equation models for genetically informative studies. We show how the package Mx provides confidence intervals for parameters and functions of parameters in the context of a simple additive genetic, common, and specific environment threshold model for binary data. Previously published contingency tables for major depression in adult female twins are used for illustration. The support for the model shows a marked skew as the additive genetic parameter is systematically varied from zero to one. The impact of allowing different prevalence rates in MZ vs. DZ twins is explored by fitting a model with separate threshold parameters and comparing the confidence intervals. Despite the improvement in fit of the different prevalence model, the confidence intervals on all parameters broaden, owing to their covariance.

Adult↗
PubMed2006

Comparing median lethal concentration values using confidence interval overlap or ratio tests.

Experimenters in toxicology often compare the concentration-response relationship between two distinct populations using the median lethal concentration (LC50). This comparison is sometimes done by calculating the 95% confidence interval for the LC50 for each population, concluding that no significant difference exists if the two confidence intervals overlap. A more appropriate test compares the ratio of the LC50s to 1 or the log(LC50 ratio) to 0. In this ratio test, we conclude that no difference exists in LC50s if the confidence interval for the ratio of the LC50s contains 1 or the confidence interval for the log(LC50 ratio) contains 0. A Monte Carlo simulation study was conducted to compare the confidence interval overlap test to the ratio test. The confidence interval overlap test performs substantially below the nominal alpha = 0.05 level, closer to p = 0.005; therefore, it has considerably less power for detecting true differences compared to the ratio test. The ratio-based method exhibited better type I error rates and superior power properties in comparison to the confidence interval overlap test. Thus, a ratio-based statistical procedure is preferred to using simple overlap of two independently derived confidence intervals.

Animals↗
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↗
PubMed2006

Repeated confidence intervals in self-designing clinical trials and switching between noninferiority and superiority.

In self-designing clinical trials, repeated confidence intervals are derived for the parameter of interest where the results of the independent study stages are combined using the generalized inverse chi-square-method. The confidence intervals can be calculated at each interim analysis and always hold the predefined overall nominal confidence level. Moreover, the confidence intervals calculated during the course of the trial are nested in the sense that a calculated interval is completely contained in all the previously calculated intervals. During the course of the self-designing trial the sample sizes as well as the number of study stages can be determined simultaneously in a completely adaptive way. The adaptive procedure allows an early stop for significance. The clinical trial may be originally designed either to show noninferiority or superiority. However, in each interim analysis, it is possible to change the planning from showing superiority to showing noninferiority or vice versa. Since the repeated confidence intervals are nested, there is no risk to loose the noninferiority once showed when, after an interim analysis, the trial is continued in an attempt to reach superiority. A simulation study investigates the behavior of the considered confidence intervals. The performance of the derived nested repeated confidence intervals is also demonstrated in examples showing both kinds of switching during an ongoing trial.

Biometry↗
PubMed2006

Calculating confidence intervals for impact numbers.

BACKGROUND: Standard effect measures such as risk difference and attributable risk are frequently used in epidemiological studies and public health research to describe the effect of exposures. Recently, so-called impact numbers have been proposed, which express the population impact of exposures in form of specific person or case numbers. To describe estimation uncertainty, it is necessary to calculate confidence intervals for these new effect measures. In this paper, we present methods to calculate confidence intervals for the new impact numbers in the situation of cohort studies. METHODS: Beside the exposure impact number (EIN), which is equivalent to the well-known number needed to treat (NNT), two other impact numbers are considered: the case impact number (CIN) and the exposed cases impact number (ECIN), which describe the number of cases (CIN) and the number of exposed cases (ECIN) with an outcome among whom one case is attributable to the exposure. The CIN and ECIN represent reciprocals of the population attributable risk (PAR) and the attributable fraction among the exposed (AFe), respectively. Thus, confidence intervals for these impact numbers can be calculated by inverting and exchanging the confidence limits of the PAR and AFe. EXAMPLES: We considered a British and a Japanese cohort study that investigated the association between smoking and death from coronary heart disease (CHD) and between smoking and stroke, respectively. We used the reported death and disease rates and calculated impact numbers with corresponding 95% confidence intervals. In the British study, the CIN was 6.46, i.e. on average, of any 6 to 7 persons who died of CHD, one case was attributable to smoking with corresponding 95% confidence interval of [3.84, 20.36]. For the exposed cases, the results of ECIN = 2.64 with 95% confidence interval [1.76, 5.29] were obtained. In the Japanese study, the CIN was 6.67, i.e. on average, of the 6 to 7 persons who had a stroke, one case was attributable to smoking with corresponding 95% confidence interval of [3.80, 27.27]. For the exposed cases, the results of ECIN = 4.89 with 95% confidence interval of [2.86, 16.67] were obtained. CONCLUSION: The consideration of impact numbers in epidemiological analyses provides additional information and helps the interpretation of study results, e.g. in public health research. In practical applications, it is necessary to describe estimation uncertainty. We have shown that the calculation of confidence intervals for the new impact numbers is possible by means of known methods for attributable risk measures. Therefore, estimated impact numbers should always be complemented by appropriate confidence intervals.

Cohort Studies↗
PubMed2006

Comparison of confidence intervals for adjusted attributable risk estimates under multinomial sampling.

The epidemiologic concept of the adjusted attributable risk is a useful approach to quantitatively describe the importance of risk factors on the population level. It measures the proportional reduction in disease probability when a risk factor is eliminated from the population, accounting for effects of confounding and effect-modification by nuisance variables. The computation of asymptotic variance estimates for estimates of the adjusted attributable risk is often done by applying the delta method. Investigations on the delta method have shown, however, that the delta method generally tends to underestimate the standard error, leading to biased confidence intervals. We compare confidence intervals for the adjusted attributable risk derived by applying computer intensive methods like the bootstrap or jackknife to confidence intervals based on asymptotic variance estimates using an extensive Monte Carlo simulation and within a real data example from a cohort study in cardiovascular disease epidemiology. Our results show that confidence intervals based on bootstrap and jackknife methods outperform intervals based on asymptotic theory. Best variants of computer intensive confidence intervals are indicated for different situations.

Adult↗
PubMed2000

Confidence intervals for the mean of diagnostic test charge data containing zeros.

In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log-normal distribution. Under such a model, we propose three different interval estimation procedures: a percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are only first-order accurate and that the bootstrap-based one-sided confidence interval is second-order accurate. For two-sided confidence intervals, all three proposed methods are second-order accurate. A simulation study in finite-sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)-based interval except for the case of one-sided lower end-point intervals when the skewness is very small. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias-corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.

Biometry↗
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↗
PubMed1993

Confidence intervals for hearing loss allocation estimates.

A method for estimating confidence intervals for hearing loss allocation estimates is developed and demonstrated. Based on the ISO-1999 model for the combination of noise-induced permanent threshold shift (NIPTS) and age-related permanent threshold shift (ARPTS), the probabilities of different pairs of NIPTS and ARPTS values can be represented by a three-dimensional joint probability density function (JPDF). When the JPDF is intersected by equal-probability planes, the resulting ellipses define the confidence intervals. This method makes conservative assumptions that will usually overestimate the width of the confidence interval.

Aging↗
PubMed1997

Confidence intervals of evolutionary distances between sequences and comparison with usual approaches including the bootstrap method.

Two methods are commonly employed for evaluating the extent of the uncertainty of evolutionary distances between sequences: either some estimator of the variance of the distance estimator, or the bootstrap method. However, both approaches can be misleading, particularly when the evolutionary distance is small. We propose using another statistical method which does not have the same defect: interval estimation. We show how confidence intervals may be constructed for the Jukes and Cantor (1969) and Kimura two-parameter (1980) estimators. We compare the exact confidence intervals thus obtained with the approximate intervals derived by the two previous methods, using artificial and biological data. The results show that the usual methods clearly underestimate the variability when the substitution rate is low and when sequences are short. Moreover, our analysis suggests that similar results may be expected for other evolutionary distance estimators.

Algorithms↗
PubMed2006

Weighted confidence interval construction for binomial parameters.

Confidence intervals, in general, have become an important aspect of reporting statistical results. In particular, interval estimators for binomial proportions have been studied extensively in recent literature. The large-sample Wald intervals are known to perform poorly, but the Wilson intervals have been shown to perform well in a variety of situations. One criticism is the relative difficulty of computing the Wilson or quadratic intervals in comparison to the Wald intervals. We offer a computational formula for the Wilson intervals that is a weighted estimator of the observed proportion, p, and that based on an uninformative prior, 1/2. This contribution enhances our understanding of the coverage behavior of the Wilson intervals. In addition, we contrast the Wilson intervals with other well-known intervals for the case of zero successes.

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↗
PubMed1996

Confidence intervals for calibration with neural networks.

Based on neural network calibration the confidence intervals of aromaticity determination from infrared reflectance spectra of raw brown coals were estimated by means of the bootstrap method, a simplified Monte Carlo Simulation. The standard deviations and the confidence intervals were estimated to characterise the analysis error.It is shown that confidence intervals of non-linear analysis methods like Back Propagation Neural Networks (BPNN) can be estimated by the bootstrap method. The estimated confidence intervals of the calibration confirm the analysis by BPNN.

Journal Article↗