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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

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

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

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

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

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

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

[The confidence interval of micronuclei and chromosome aberration induced by radiation].

This paper proposes a revised method of determining confidence interval of population rate based on statistical theory. The confidence interval of population rate can be obtained accurately by using this method. In addition, it includes a discussion of confidence interval about some basic indexes of micronuclei and chromosome aberration induced by radiation.

Chromosome Aberrations

A confidence interval approach to investigating non-response bias and monitoring response to postal questionnaires.

STUDY OBJECTIVE: The aim was to develop an alternative method of investigating non-response bias in postal surveys, including a method of calculating a final full (100%) coverage confidence interval which avoids the wide intervals of existing approaches. DESIGN AND SETTING: As part of a two stage survey of disablement in the community, a first phase postal questionnaire was sent to 25,168 households in Calderdale, West Yorkshire, England. Confidence intervals were calculated to investigate the precision of estimates using a "no bias" model, where the prevalence in non-responders is assumed to be the same as in responders. RESPONDENTS: A total of 21,889 postal questionnaires were returned (87%), representing households containing 42,826 people aged 16 years and over. This was achieved by the original post (1st wave, 57% response); two further postal follow ups (2nd and 3rd waves, taking the response to 73% and 81% respectively), the latter including a small personal call back; and a final postal follow up (the 4th wave). RESULTS: The cumulative estimated prevalence of those with dependence was plotted as the survey progressed. The final wave full coverage estimated prevalence for those aged 16-64 years was 12.8 per 1000 with 95% confidence intervals of 11.3-14.4 per 1000. The integrity of this estimate holds as long as the true prevalence in non-responders is within the calculated non-response confidence interval under the no bias assumption, 9.7-16.0 per 1000 people. This latter interval represents the tolerance of prevalence in non-responders implied by the no bias assumption. CONCLUSIONS: The findings have general implications for monitoring non-response bias in postal screening questionnaires. The confidence interval approach developed in this paper offers an alternative to existing regression based estimates, giving an indication of the range of prevalence amongst non-responders that could be tolerated before the no bias assumption used by the model is breached. It is suggested that this approach can be used to determine both the extent of bias, and to aid decision making about the appropriate juncture to terminate follow up. It highlights the potential, particularly in the context of a computerised survey operation, of methodological investigation occurring simultaneously with survey operation.

Adolescent

Symmetrical confidence intervals for bioequivalence trials.

The conventional method of setting confidence intervals for the difference of the means of two normal populations gives an interval which is not, in general, symmetrical about zero. A modification of the conventional method which leads to symmetry about zero is discussed and is recommended as particularly appropriate for use in bioequivalence trials. This modification has the effect of decreasing the "effective" length of the confidence interval, on which the decision concerning bioequivalence is based, while increasing the confidence coefficient.

Methods

[Effect measures and confidence intervals].

In order to exemplify the use of effect measures and confidence intervals in epidemiology, it is assumed that a group of patients treated with antiflogistic drugs were compared by repeated gastroscopy with a control group. The effect measures "incidence rate difference" and "incidence rate ratio" are used to compare ulcer incidence in the two groups of patients, and the corresponding confidence intervals are stated. On the other hand, if the registered parameter is prevalence rather than incidence rate, for instance the occurrence of prepyloric erosions at a certain time, the effect measures employed are "risk difference" and "risk ratio". An alternative to the latter is "odds ratio".

Confidence Intervals

A nonstatistical approach to estimating confidence intervals about model parameters: application to respiratory mechanics.

Estimates of parameters obtained by fitting models to physiologic data are of little use unless accompanied by confidence intervals. The standard methods for estimating confidence intervals are statistical, and make the assumption that the fitted model accounts for all the deterministic variation in the data while the residuals between the fitted model and the data reflect only stochastic noise. In practice, this is frequently not the case, as one often finds the residuals to be systematically distributed about zero. In this paper, we develop an approach for assessing confidence in a parameter estimate when the order of the model is clearly less than that of the system being modeled. Our approach does not require a parameter to have a single value located within a region of confidence. Instead, we let the parameter value vary over the data set in such a way as to provide a good fit to the entire data set. We apply our approach to the estimation of the resistance of the respiratory system in which a simple model is fitted to measurements of tracheal pressure and flow by recursive multiple linear regression. The values of resistance required to achieve a good fit are represented as a modified histogram in which the contribution of a particular resistance value to the histogram is weighted by the amount of information used in its determination. Our approach provides parameter frequency distribution functions that convey the degree of confidence one may have in the parameter, while not being based on erroneous statistical assumptions.

Airway Resistance

Confidence intervals for seroprevalence determined from pooled sera.

In population surveys of seroprevalence, it may not be most efficient to test all individual samples. The laboratory and statistical issues encountered when one first pools individual samples into groups of samples before laboratory analyses were discussed recently in relation to the seroprevalence of human immunodeficiency virus. In particular, point and confidence interval estimates for seroprevalence from pooled sera were derived. A potential problem with these confidence intervals is that they may contain negative values. This problem is most likely to occur in low-prevalence populations where pooling is most efficient. An alternative method of obtaining confidence intervals that cannot contain negative values is proposed and an example provided.

Confidence Intervals

The effects of model selection on confidence intervals for the size of a closed population.

One encounters in the literature estimates of some rates of genetic and congenital disorders based on log-linear methods to model possible interactions among sources. Often the analyst chooses the simplest model consistent with the data for estimation of the size of a closed population and calculates confidence intervals on the assumption that this simple model is correct. However, despite an apparent excellent fit of the data to such a model, we note here that the resulting confidence intervals may well be misleading in that they can fail to provide an adequate coverage probability. We illustrate this with a simulation for a hypothetical population based on data reported in the literature from three sources. The simulated nominal 95 per cent confidence intervals contained the modelled population size only 30 per cent of the time. Only if external considerations justify the assumption of plausible interactions of sources would use of the simpler model's interval be justified.

Confidence Intervals

Confidence intervals for the conditional probability of misallocation in discriminant analysis.

In this study we are concerned with the construction of confidence intervals for the conditional probability of misallocation associated with Anderson's classification statistics, W. The available methods of computing confidence intervals for the conditional probability are not satisfactory in practice, mainly because the intervals obtained are fairly inaccurate. A new method is presented which enables intervals with almost the desired level of confidence to be easily computed from the initial samples on which W is based.

Monte Carlo Method

A confidence interval for the ratio of treatment variances in a two-by-two crossover study.

The distance between two variances is usually measured using the ratio, and a confidence interval for this ratio can be used to measure its magnitude. For a two-by-two crossover study, special considerations must be made because the observations for any subject are correlated. Here a confidence interval for the ratio of the treatment variances in a two-by-two crossover study is presented.

Analysis of Variance

[Statistics for dentists. Confidence intervals].

The mean score of a sample deviates most probably from the mean score of the population, in which one is most interested. It is possible to calculate a kind of minimum and maximum value, the so called confidence interval, which indicates the position of the mean score of the population. Some worked examples elucidate the procedure of constructing such confidence intervals for the population mean, using the standard error of the (sample) mean (SEM).

Confidence Intervals