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PubMed1990

Confidence intervals for effect parameters common in cancer epidemiology.

This paper reviews approximate confidence intervals for some effect parameters common in cancer epidemiology. These methods have computational feasibility and give nearly nominal coverage rates. In the analysis of crude data, the simplest type of epidemiologic analysis, parameters of interest are the odds ratio in case-control studies and the rate ratio and difference in cohort studies. These parameters can estimate the instantaneous-incidence-rate ratio and difference that are the most meaningful effect measures in cancer epidemiology. Approximate confidence intervals for these parameters including the classical Cornfield's method are mainly based on efficient scores. When some confounding factors exist, stratified analysis and summary measures for effect parameters are needed. Since the Mantel-Haenszel estimators have been widely used by epidemiologists as summary measures, confidence intervals based on the Mantel-Haenszel estimators are described. The paper also discusses recent developments in these methods.

Case-Control Studies↗
PubMed1993

Confidence intervals and controlled clinical trials: incompatible tools for medical research.

The probabilistic rationale for statistical design and analysis of clinical trials is random assignment. While arithmetic and mathematical formulations may be identical to those used with random samples, we should not indiscriminately borrow tools from survey sample methods. Specifically, the confidence interval should be used sparingly, if at all. Observations have an internal validity, within the clinical trial, with no basis for claims of quantitative external generalizability. Confidence intervals encourage an unnecessary dependence on statistical analysis when the careful design should allow the data to speak for itself. Confidence intervals encourage a statistical focus and statistical conclusions that ignore scientific context and misrepresent relationships among results from related research. The clinician is presented with information about population parameters when facing confidence intervals. These do not address questions about treatment and prognosis of an individual patient. Confidence intervals are particularly distracting when a clinical trial has failed to produce anticipated results. The clinical trial is the model research tool for clinical medical research, founded on randomization. The confidence interval is a statistical tool for parameter estimation based on population sampling concepts. These tools are incompatible.

Clinical Trials as Topic↗
PubMed2001

Statistical and probabilistic approaches to confidence intervals of linear calibration in liquid chromatography.

The aim of this paper is to compare the reliability of two approaches to estimate the 95% confidence intervals of linear calibration in real situations. One is the statistical approach, which is well known in statistics, and the other is the probabilistic approach, which is based on a theory to predict the precision of instrumental analyses mainly from signal and noise, called FUMI (Function of Mutual Information) theory. The high-performance liquid chromatographic determination of quisalofop and maltose is taken as an example. Calibration lines obtained under the same experimental conditions are superimposed on the 95% confidence intervals to investigate whether the resulting confidence intervals can include all the calibration lines reasonably. A pair of 95% confidence intervals (upper and lower limits) can be calculated from each calibration line, but varies from calibration line to calibration line, although obtained under the same experimental conditions. The variability and reliability of the 95% intervals are also examined.

Calibration↗
PubMed1992

[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↗
PubMed2000

A comparison of several procedures to estimate the confidence interval for attributable risk in case-control studies.

The estimation of a confidence interval for attributable risk from the logistic model based on data from case-control studies is a problem for which an accepted solution is lacking. Two methods, one based on the delta method and one bootstrap on the population base, have been described but their accuracy has not been compared. We present two other methods, one based on a jack-knife approach and the other using a bootstrap on two samples (cases and controls). The four methods are compared in a simulation study. The four methods are also applied to a case-control study on risk factors for preterm delivery; the confidence intervals are obtained assuming normality and by logarithmic transformation. When attributable risk is not smooth (for example, when exposure prevalence is low) both the jack-knife and the delta method tend to fail. If attributable risk is close to zero or one, normality cannot be assumed and log-transformed confidence intervals must be used. Finally, the extension to matched studies is analysed using a case-control study on risk factors of cutaneous malignant melanoma. In this situation, the population-based bootstrap is not available.

Abruptio Placentae↗
PubMed2006

A comparison of algorithms for calculating glaucoma change probability confidence intervals.

PURPOSE: To evaluate the ability to detect change in standard automated perimetry data using 4 different methods for calculating the glaucoma change probability (GCP). METHODS: A database of stable visual fields, collected within 1 week from 35 glaucoma patients and within 6 months from 15 normal patients, was used to determine confidence intervals for GCP using 4 different methods. The methods classified visual field locations on the basis of either defect or mean threshold, and used test-retest data or baseline-less-follow-up data to determine values for the confidence intervals. The specificity of the 4 methods was measured using 3700 locations artificially generated to simulate stable visual field data. The sensitivity of the methods was measured using 3330 artificially generated locations that decreased in either a linear, curvilinear, or bi-linear fashion by 2, 3, or 4 dB per year on average. RESULTS: Using GCP with confidence intervals built using the methods described in the literature (on the basis of defect and test-retest differences) resulted in a higher specificity than techniques based on mean threshold. However, the mean-based methods were more sensitive at detecting a decrease in a location. Building confidence intervals using the difference between a baseline and the current measurement (baseline-less-follow-up), rather than test-retest differences, also improved the detection of visual field progression. CONCLUSIONS: Stratifying baseline visual field measurements based on defect and eccentricity as described in the literature results in an unusually high specificity: 98% accuracy in classifying the same stable data that generated the 95% confidence intervals, rather than the expected 95% accuracy. By stratifying measurements based on mean threshold, and using baseline-less-follow-up rather than test-retest differences to build 95% confidence intervals, sensitivity is increased by 14.1%. This increase in sensitivity comes with a corresponding 2.2% decrease in specificity.

Adult↗
PubMedDate not supplied

The use of confidence intervals for individual utilities: limits to formal decision analysis for treatment choice.

This paper discusses the use of confidence intervals for utility measurements. Classic test theory is applied to estimate confidence intervals for utilities. The theory is enhanced to calculate confidence areas for combined utilities and confidence bands for the threshold line. As an example it is shown that, if confidence intervals are taken into account, the implied preferred treatment of T3-larynx carcinoma patients is uncertain for a wide range of utilities, considering the mediocre reliability of most methods of utility assessment. This implies that although utility measurement and formal decision analysis can be a useful way to look at the decision problem, ambiguity, which must be resolved by other means, will often remain.

Aged↗
PubMed1994

The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results.

Although there is a growing understanding of the importance of statistical power considerations when designing studies and of the value of confidence intervals when interpreting data, confusion exists about the reverse arrangement: the role of confidence intervals in study design and of power in interpretation. Confidence intervals should play an important role when setting sample size, and power should play no role once the data have been collected, but exactly the opposite procedure is widely practiced. In this commentary, we present the reasons why the calculation of power after a study is over is inappropriate and how confidence intervals can be used during both study design and study interpretation.

Bayes Theorem↗
PubMed2001

Application of nonparametric models for calculating odds ratios and their confidence intervals for continuous exposures.

Calculating odds ratios and corresponding confidence intervals for exposures that have been measured using a continuous scale presents important limitations in the traditional practice of analytical epidemiology. Approximations based on linear models require making arbitrary assumptions about the shape of the relation curve or about its breakpoints. Categorical analyses generally have low statistical efficiency, and cutpoints for the categories are in most cases arbitrary and/or opportunistic. The use of logistic generalized additive models to calculate odds ratios does not require these assumptions and allows great flexibility and adequate statistical efficiency. Based on the asymptotic normality of the logarithm of the odds ratio, the authors propose the use of an approximate analytical expression for the corresponding covariance matrix, which will allow the construction of confidence intervals for odds ratios that can be interpreted as in the classical parametric context. The authors illustrate this procedure by examining the relation between glycemia and risk of postoperative infection, using data obtained from a cohort study of patients undergoing surgery in Santiago, Spain (January 1996--March 1997). The authors found that glycemia values below 75 mg/dl and above 130 mg/dl were associated with increased risk of postoperative infection.

Blood Glucose↗
PubMed2004

Bootstrap confidence intervals for medical costs with censored observations.

Medical costs data with administratively censored observations often arise in cost-effectiveness studies of treatments for life-threatening diseases. Mean of medical costs incurred from the start of a treatment until death or a certain time point after the implementation of treatment is frequently of interest. In many situations, due to the skewed nature of the cost distribution and non-uniform rate of cost accumulation over time, the currently available normal approximation confidence interval has poor coverage accuracy. In this paper, we propose a bootstrap confidence interval for the mean of medical costs with censored observations. In simulation studies, we show that the proposed bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution. When there is light censoring on medical costs (< or =25 per cent), we found that the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy. For heavily censored cost data (censoring rate > or =30 per cent) with larger sample sizes (n > or =200), the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy. We also illustrate the use of our methods in a real example.

Computer Simulation↗
PubMed2005

Bootstrap confidence intervals for the mode of the hazard function.

In many applications of lifetime data analysis, it is important to perform inferences about the mode of the hazard function in situations of lifetime data modeling with unimodal hazard functions. For lifetime distributions where the mode of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can be obtained. However, these results might not be very accurate for small sample sizes and/or large proportion of censored observations. Considering the log-logistic distribution for the lifetime data with shape parameter beta>1, we present and compare the accuracy of asymptotical confidence intervals with two confidence intervals based on bootstrap simulation. The alternative methodology of confidence intervals for the mode of the log-logistic hazard function are illustrated in three numerical examples.

Confidence Intervals↗
PubMed1991

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↗
PubMed2006

Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements.

Metabolic fluxes, estimated from stable isotope studies, provide a key to quantifying physiology in fields ranging from metabolic engineering to the analysis of human metabolic diseases. A serious drawback of the flux estimation method in current use is that it does not produce confidence limits for the estimated fluxes. Without this information it is difficult to interpret flux results and expand the physiological significance of flux studies. To address this shortcoming we derived analytical expressions of flux sensitivities with respect to isotope measurements and measurement errors. These tools allow the determination of local statistical properties of fluxes and relative importance of measurements. Furthermore, we developed an efficient algorithm to determine accurate flux confidence intervals and demonstrated that confidence intervals obtained with this method closely approximate true flux uncertainty. In contrast, confidence intervals approximated from local estimates of standard deviations are inappropriate due to inherent system nonlinearities. We applied these methods to analyze the statistical significance and confidence of estimated gluconeogenesis fluxes from human studies with [U-13C]glucose as tracer and found true limits for flux estimation in specific human isotopic protocols.

Blood Glucose↗
PubMed2005

On confidence intervals for within-subjects designs.

Confidence intervals (CIs) for means are frequently advocated as alternatives to null hypothesis significance testing (NHST), for which a common theme in the debate is that conclusions from CIs and NHST should be mutually consistent. The authors examined a class of CIs for which the conclusions are said to be inconsistent with NHST in within-subjects designs and a class for which the conclusions are said to be consistent. The difference between them is a difference in models. In particular, the main issue is that the class for which the conclusions are said to be consistent derives from fixed-effects models with subjects fixed, not mixed models with subjects random. Offered is mixed model methodology that has been popularized in the statistical literature and statistical software procedures. Generalizations to different classes of within-subjects designs are explored, and comments on the future direction of the debate on NHST are offered.

Confidence Intervals↗
PubMed2005

Assessing equivalence or non-inferiority in screening tests with paired and independent binomial endpoints through confidence intervals for the odds ratio.

The confidence interval (CI) on the population average (PA) odds ratio (OR) is a useful measure of agreement among different diagnostic methods when no gold standard is available. It can be calculated by the repeated measures logistic regression procedure (GENMOD, SAS). We compare the width of CIs from paired and independent samples with an identical number of measurements and an identical probability of positive response among them. For two and three diagnostic methods with binomial endpoints, the best performing sampling strategy is analytically described. The asymptotic formulae of the ratio of the CI widths for paired and independent samples are provided. We numerically study the dependence of the width of the CIs on the number of positive concordant outcomes. The width of CIs from independent samples is an increasing function of the sample size with a saturation asymptote and rather weak dependence on the argument. The width of CIs from paired samples is a decreasing function of the sample size with a saturation asymptote and significant dependence on the argument when the sample size is small. If curves for paired and independent samples intersect, a critical sample size exists. At this point, a small change in the sample size can reverse the choice of the best performing sampling policy. We numerically validated the robustness of the critical point to variations of the conditional OR.

Analysis of Variance↗
PubMed1988

Unfavourable outcomes of drug therapy--subjective probability versus confidence intervals.

To investigate how individual predictions compare with confidence intervals, we asked 50 medical residents and 28 graduate students with biostatistics training to estimate unfavourable outcomes of drug therapy (therapeutic failures and side-effects) in groups of 10 and 20 patients. The predictions made by physicians and graduate students were similar for both sample sizes and types of outcome. The majority (58%) of estimates were greater than the upper limit of the 95% confidence interval, a bias that may hamper the correct interpretation of therapeutic risks in medical decision-making.

Adult↗
PubMed2003

Accurate confidence intervals for binomial proportion and Poisson rate estimation.

Estimates of proportion and rate-based performance measures may involve discrete distributions, small sample sizes, and extreme outcomes. Common methods for uncertainty characterization have limited accuracy in these circumstances. Accurate confidence interval estimators for proportions, rates, and their differences are described and MATLAB programs are made available. The resulting confidence intervals are validated and compared to common methods. The programs search for confidence intervals using an integration of the Bayesian posterior with diffuse priors to measure the confidence level. The confidence interval estimators can find one or two-sided intervals. For two-sided intervals, either minimal-length, balanced-tail probabilities, or balanced-width can be selected.

Binomial Distribution↗
PubMed1998

Bootstrap confidence intervals for cost-effectiveness ratios: some simulation results.

Recently, a number of papers have brought up the issue of how to make cost-effectiveness (CE) studies stochastic, i.e. how to obtain confidence intervals for CE ratios. In this note we present a bootstrap procedure for estimating bias-corrected confidence intervals for CE ratios. The bootstrap procedure is tested in a simulation study based on the assumptions made in a recent paper by Wakker and Klaassen in this journal. We test two variants of CE ratio bootstrap confidence intervals. The first is a bootstrap analogue of the parametric method proposed by Wakker and Klaassen which gives results similar to those obtained with the parametric method. However, computing bootstrap confidence intervals directly for the CE ratio produce results closer to the predetermined significance level.

Algorithms↗