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At least 19 recordsLinked to original sources
PubMed2006

Bayesian decision threshold, detection limit and confidence limits in ionising-radiation measurement.

Based on Bayesian statistics and the Bayesian theory of measurement uncertainty, characteristic limits such as the decision threshold, detection limit and limits of a confidence interval can be calculated taking into account all sources of uncertainty. This approach consists of the complete evaluation of a measurement according to the ISO Guide to the Expression of Uncertainty in Measurement (GUM) and the successive determination of the characteristic limits by using the standard uncertainty obtained from the evaluation. This procedure is elaborated here for several particular models of evaluation. It is, however, so general that it allows for a large variety of applications to similar measurements. It is proposed for the revision of those parts of DIN 25482 and ISO 11929 that are still based on conventional statistics and, therefore, do not allow to take completely into account all the components of measurement uncertainty in the calculation of the characteristic limits.

Algorithms↗
PubMed1984

The ubiquitous 2X2 table, its parameters and their confidence limits.

The confidence limits for all parameters derived from a 2X2 contingency table are uniquely determined by the limiting matrices that arise from adding or subtracting certain values to or from the four cell entries. Various methods to determine these addends are discussed and a computer program is presented that produces reliable results. The limiting matrices thus produced bypass the more complicated expressions for the standard errors of the many epidemiological parameters that are used to interpret the 2X2 table.

Epidemiologic Methods↗
PubMed1992

Simple SAS macros for the calculation of exact binomial and Poisson confidence limits.

Statistical analysis using confidence intervals is now a preferred approach in the medical literature, and confidence limits for binomial proportions and Poisson counts are commonly required. Normal approximations of varying accuracy are often used in such situations and it is not generally realised that non-iterative exact solutions are available. This paper shows that the exact binomial and Poisson confidence limits can be expressed very simply in terms of the inverse beta and inverse gamma distributions, and describes two macros in the SAS programming language to perform the computations. The exact solutions are compared with some approximations and further applications of the techniques are described.

Binomial Distribution↗
PubMed1997

On confidence limits associated with Chow and Shao's joint confidence region approach for assessment of bioequivalence.

Confidence limits associated with Chow and Shao's 90% joint confidence region method (C&S CR limits) were derived to assess the bioequivalence (BE) of drug products. The C&S CR method provides three conditions that must be simultaneously satisfied to conclude BE, which is applicable only for raw scale data. The C&S CR limits method extends its applicability to both raw scale and log-transformed data. In addition, it is easy to interpret. The quantitative limits provide information, such as how much the test product deviates from the reference product in bioavailability. The data sets of peak plasma concentration (C(max)) and area under plasma concentration curve (AUC) of 13 BE studies involving 10 drugs were used to compare the performances of classic confidence interval (classic CI), C&S CR, and C&S CR limits methods. The results indicate that the same BE conclusion can be reached for C&S CR and C&S CR limits methods. The C&S CR and its limits method offered a distinctive advantage in terms of percentage passing the BE criteria by taking account of the correlation and variability of sample means. Similar BE conclusion was observed for C&S CR limits method by using raw and log-transformed data in this study.

Biological Availability↗
PubMed1980

Simplified approach to confidence limited in radioimmunassay.

A simple method of calculating confidence limits for radioimmunoassay data is presented. The method involves the use of the within-assay variation in dose estimate of three routine quality-control specimens, measured in repeated assays, to estimate the confidence limits for results on unknown samples. Results for control specimens are combined by calculating the unique quadratic curve fitting a graph of within-assay standard deviation vs mean value for each control. This method requires no special data accumulation or advanced computing equipment. For cortisol, lutropin, and thyroxine radioimmunoassays, confidence limits calculated in this way have been compared with those calculated from the variance of the response variable "B/B0" in repeated standard curves. Both methods agree well with actual limits observed when plasma pools containing a wide range of hormone concentrations are assayed repeatedly.

Evaluation Studies as Topic↗
PubMed1998

Confidence limits made easy: interval estimation using a substitution method.

The use of confidence intervals has become standard in the presentation of statistical results in medical journals. Calculation of confidence limits can be straightforward using the normal approximation with an estimate of the standard error, and in particular cases exact solutions can be obtained from published tables. However, for a number of commonly used measures in epidemiology and clinical research, formulae either are not available or are so complex that calculation is tedious. The author describes how an approach to confidence interval estimation which has been used in certain specific instances can be generalized to obtain a simple and easily understood method that has wide applicability. The technique is applicable as long as the measure for which a confidence interval is required can be expressed as a monotonic function of a single parameter for which the confidence limits are available. These known confidence limits are substituted into the expression for the measure--giving the required interval. This approach makes fewer distributional assumptions than the use of the normal approximation and can be more accurate. The author illustrates his technique by calculating confidence intervals for Levin's attributable risk, some measures in population genetics, and the "number needed to be treated" in a clinical trial. Hitherto the calculation of confidence intervals for these measures was quite problematic. The substitution method can provide a practical alternative to the use of complex formulae when performing interval estimation, and even in simpler situations it has major advantages.

Confidence Intervals↗
PubMed1988

Small-sample confidence limits for parameters under inequality constraints with application to quantal bioassay.

A family of methods is presented for constructing confidence limits for the parameters of a collection of distributions when a simple ordering is assumed among the parameters. The methods are shown to yield confidence limits that are exact or conservative for finite samples. For discrete distributions, one of the methods produces confidence limits that are at least as tight as the limits produced by a commonly used single-sample procedure. Confidence limits are demonstrated for a binomial quantal bioassay problem assuming a nondecreasing dose-response function. Results of a simulation study show that competing asymptotic methods can produce serious discrepancies between nominal and actual coverage probabilities for binomial samples of sizes up to 30, and demonstrate that the new approach can be competitive with the asymptotic methods when the latter maintain their nominal error rates.

Animals↗
PubMed2001

Likelihood contour method for the calculation of asymptotic upper confidence limits on the risk function for quantitative responses.

This article develops a computationally and analytically convenient form of the profile likelihood method for obtaining one-sided confidence limits on scalar-valued functions phi = phi(psi) of the parameters psi in a multiparameter statistical model. We refer to this formulation as the likelihood contour method (LCM). In general, the LCM procedure requires iterative solution of a system of nonlinear equations, and good starting values are critical because the equations have at least two solutions corresponding to the upper and lower confidence limits. We replace the LCM equations by the lowest order terms in their asymptotic expansions. The resulting equations can be solved explicitly and have exactly two solutions that are used as starting values for obtaining the respective confidence limits from the LCM equations. This article also addresses the problem of obtaining upper confidence limits for the risk function in a dose-response model in which responses are normally distributed. Because of normality, considerable analytic simplification is possible and solution of the LCM equations reduces to an easy one-dimensional root-finding problem. Simulation is used to study the small-sample coverage of the resulting confidence limits.

Dose-Response Relationship, Drug↗
PubMed1993

Confidence limits based on the first occurrence of an event.

Confidence limits for population prevalence based on the first occurrence of an item in a medical database, or for incidence based on time to first occurrence, should be based on the geometric or exponential distributions, respectively. These intervals are presented and compared with the corresponding intervals based on the binomial and Poisson distributions. The lower confidence limits are shown to be the same, but the upper limits are smaller, hence leading to shorter intervals. Applications of these intervals are also presented.

Confidence Intervals↗
PubMed2005

Observer-based rather than population-based confidence limits for determining probability of change in visual fields.

Determining confidence intervals on psychophysical thresholds is straight forward if the psychometric function is known. In clinical settings, however, there is only partial information about the psychometric function, hence confidence limits are usually derived from test-retest data collected from many subjects. In this paper, we introduce a computational technique for deriving confidence limits for an individual's endpoint threshold using data typically obtained in a clinical setting, rather than a database of test-retest performance. The technique uses probabilistic analysis of all possible response sequences in a test procedure. We then extend this procedure to allow for levels of typical uncertainty in data measurement.

Algorithms↗
PubMed1994

Estimating confidence limits on a standardised mortality ratio when the expected number is not error free.

OBJECTIVE: The aim was to demonstrate how the beta distribution may be used to find confidence limits on a standardised mortality ratio (SMR) when the expected number of events is subject to random variation and to compare these limits with those obtained with the standard exact approach used for SMRs and with a Fieller-based confidence interval. DESIGN: The relationship of the binomial and the beta distributions is explained. For cohort studies in which deaths are counted in exposed and unexposed groups exact confidence limits on the relative risk are found conditional on the total number of observed deaths. A similar method for the SMR is justified by analogy between the SMR and the relative risk found from such cohort studies, and the fact that the relevant (beta) distribution does not require integer parameters. SOURCE OF DATA: Illustrative examples of hypothetical data were used, together with a MINITAB macro (see appendix) to perform the calculations. MAIN RESULTS: Exact confidence intervals that include error in the expected number are much wider than those found with the standard exact method. Fieller intervals are comparable with the new exact method provided the observed and expected numbers (taken to be means of Poisson variates) are large enough to approximate normality. As the expected number is increased, the standard method gives results closer to the new method, but may still lead to different conclusions even with as many as 100 expected. CONCLUSIONS: If there is reason to suppose the expected number of deaths in an SMR is subject to sampling error (because of imprecisely estimated rates in the standard population) then exact confidence limits should be found by the methods described here, or approximate Fieller-based limits provided enough events are observed and expected to approximate normality.

Adolescent↗
PubMed1996

Statistics for studying quanta at synapses: resampling and confidence limits on histograms.

This paper describes some statistical methods for working with data on quantal sizes. Since quantal sizes often do not fit to normal probability distribution functions, statistics based on the normal distribution are inappropriate. Resampling methods can be used to determine confidence limits and to test whether two sets of data differ by chance. Some hypotheses about the nature of quanta are based on apparent peaks and valleys in histograms. Confidence limits can be placed on the bins in the histogram by using the Kolomorogov-Smirnov statistic or by resampling. The confidence limits should assist in the evaluation of the significance of the valleys.

Animals↗
PubMed1994

Statistical analysis of synaptic transmission: model discrimination and confidence limits.

Procedures for discriminating between competing statistical models of synaptic transmission, and for providing confidence limits on the parameters of these models, have been developed. These procedures were tested against simulated data and were used to analyze the fluctuations in synaptic currents evoked in hippocampal neurones. All models were fitted to data using the Expectation-Maximization algorithm and a maximum likelihood criterion. Competing models were evaluated using the log-likelihood ratio (Wilks statistic). When the competing models were not nested, Monte Carlo sampling of the model used as the null hypothesis (H0) provided density functions against which H0 and the alternate model (H1) were tested. The statistic for the log-likelihood ratio was determined from the fit of H0 and H1 to these probability densities. This statistic was used to determine the significance level at which H0 could be rejected for the original data. When the competing models were nested, log-likelihood ratios and the chi 2 statistic were used to determine the confidence level for rejection. Once the model that provided the best statistical fit to the data was identified, many estimates for the model parameters were calculated by resampling the original data. Bootstrap techniques were then used to obtain the confidence limits of these parameters.

Algorithms↗
PubMed1998

Sample size determination for controlling the upper confidence limit of incidence rate of a binomial endpoint.

Assume that in a comparative clinical study the primary endpoint is a binary event, such as life or death. A new treatment or therapy is tested for a significant reduction of the incidence of the binary event compared with a control group. Another objective is to ensure that the incidence in the new treatment group is below some clinically acceptable value. This is done by calculating the exact upper 95% confidence limit for the probability of the event. The study is considered successful if the upper confidence limit is lower than a historical threshold, as well as if there is a significant reduction in the incidence of the event by the new treatment. In this article, we provide an exact method for calculating the sample size so that there will be adequate power to ensure that the exact upper confidence limit is below the threshold. Based on this we can design a study to achieve both objectives.

Binomial Distribution↗
PubMed2002

Investigation of the single case in neuropsychology: confidence limits on the abnormality of test scores and test score differences.

Neuropsychologists often need to estimate the abnormality of an individual patient's test score, or test score discrepancies, when the normative or control sample against which the patient is compared is modest in size. Crawford and Howell [The Clinical Neuropsychologist 12 (1998) 482] and Crawford et al. [Journal of Clinical and Experimental Neuropsychology 20 (1998) 898] presented methods for obtaining point estimates of the abnormality of test scores and test score discrepancies in this situation. In the present study, we extend this work by developing methods of setting confidence limits on the estimates of abnormality. Although these limits can be used with data from normative or control samples of any size, they will be most useful when the sample sizes are modest. We also develop a method for obtaining point estimates and confidence limits on the abnormality of a discrepancy between a patient's mean score on k-tests and a test entering into that mean. Computer programs that implement the formulae for the confidence limits (and point estimates) are described and made available.

Brain Damage, Chronic↗
PubMed1990

Confidence limits for low induced frequencies of oncogenic transformation in the presence of a background.

The problem is addressed of assessing realistic confidence limits for oncogenic transformation rates when the incidence of transformation is small, and there is a background present. It is shown that the commonly used approximations for assessing the confidence interval on the radiation-induced transformation rate (t1) and the control rate (t2) are inadequate when only a small number of transformants are observed. Accurate techniques are described for these cases for the estimation of confidence limits of t1, t2 and also t1-t2.

Cell Transformation, Neoplastic↗
PubMed2005

An easy to use method to approximate Poisson confidence limits.

Despite the ever larger choice of softwares and statistical packages allowing fast and accurate computation of binomial and Poisson confidence limits, there is always a need for a simple and reliable formula allowing non-computerized computations. The method proposed in this paper is derived from the Freeman and Tukey's variance stabilizing transformation for a random Poisson variable and adjusted for giving the best fit with the exact Poisson values. Despite its simplicity, allowing its use in any circumstances, this method provides very satisfactory results and a much better fit than classical formula based on the normal approximation, even if a continuity correction is used. It allows computation of Poisson confidence limits both for count or rates and proportions.

Biometry↗