Showing papers on "Confidence interval published in 1982"

A Confidence Interval for the Median Survival Time

Abstract: A nonparametric asymptotic confidence interval for the median survival time is developed for the case where data are subject to arbitrary right censoring. This is accomplished by inverting a generalization of the sign test for censored data. A simulation study shows that this nonparametric confidence interval performs well for a variety of underlying survival functions. The procedure is applied to data from a clinical trial that compared f'our dosage regimens of 5-uorouracil.

Batch Size Effects in the Analysis of Simulation Output

Abstract: Batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment. Several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and/or independence, and the resulting incorrect probabilities of the confidence interval covering the mean. This paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions. These effects include (1) correct probability of covering the mean, (2) an increase in expected half length, (3) an increase in the standard deviation and coefficient of variation of the half length, and (4) an increase in the probability of covering points not equal to the mean. For any sample size and independent and normal batch means, the results are (1) the effects of less than 10 batches are large and the effects of more than 30 batches small, and (2) additional batches have lesser effects on ...

Estimating Survivorship when the Subjects are Visited Periodically

Abstract: Statistical methods for estimating and comparing constant survival rates are developed here for sampling designs in which survival of a subject is checked at irregular intervals. The maximum likelihood estimator is derived and shown to be readily calculated using an iterative procedure that starts with the Mayfield (1975) estimate as a trial value. Sampling distributions of this estimator and of the product of two or more estimates are skewed, and normalizing transformations are provided to facilitate valid confidence interval estimation. The sampling distribution of the difference between two independent estimates is found to be sufficiently normal without transformation to allow valid use of conventional normal theory procedures for testing differences and determining sample size for specified power. Statistical validity under the variable intensity sampling design does require that the duration of intervisit periods vary independently of observer perceptions concerning the survival status of the subject and, in order to achieve robustness with respect to the assumption of constant survivorship, sampling intensity must vary independently of any temporal changes in the daily survival rate. Investigators are warned no, to return earlier than planned to subjects thought to have died, as this observer behavior may cause serious bias in the survivorship estimate.

Subjective Confidence in Forecasts.

Abstract: Forecasts have little value to decision makers unless it is known how much confidence to place in them. Those expressions of confidence have, in turn, little value unless forecasters are able to assess the limits of their own knowledge accurately Previous research has shown very robust patterns in the judgements of individuals who have not received special training in confidence assessment: Knowledge generally increases as confidence increases. However, it increases too swiftly, with a doubling of confidence being associated with perhaps a 50 per cent increase in knowledge. With all but the easiest of tasks, people tend to be overconfident regarding how much they know These results have typically been derived from studies of judgements of general knowledge. The present study found that they also pertained to confidence in forecasts. Indeed, the confidence-knowledge curves observed here were strikingly similar to those observed previously. The only deviation was the discovery that a substantial minority of judges never expressed complete confidence in any of their forecasts. These individuals also proved to be better assessors of the extent of their own knowledge Apparently confidence in forecasts is determined by processes similar to those that determine confidence in general knowledge. Decision makers can use forecasters assessments in a relative sense, in order to predict when they are more and less likely to be correct. However, they should be hesitant to take confidence assessments literally. Someone is more likely to be right when he or she is ‘certain’than when he or she is ‘fairly confident’; but there is no guarantee that the certain forecast will come true.

Confidence Interval Procedures for the Weibull Process With Applications to Reliability Growth

Abstract: The Weibull Process (a nonhomogeneous Poisson process with intensity r(t) = λβt β−1) is considered as a stochastic model for the Duane (1964) reliability growth postulate. Under this model the mean time between failure (MTBF) for the system at time t is given by M(t) = [r(t)]−1. Small sample and asymptotic confidence intervals on M(t) are discussed for failure- and time-truncated testing. Tabled values to compute the confidence intervals and numercial examples illustrating these procedures are presented.

Statistical methods for estimating attributable risk from retrospective data

Abstract: This paper extends Levin's measure of attributable risk to adjust for confounding by aetiologic factors other than the exposure of interest. One can estimate this extended measure from case-control data provided either (i) from the control data one can estimate exposure prevalence within each stratum of the confounding factor; or (ii) one has additional information available concerning the confounder distribution and the stratum-specific disease rates. In both cases we give maximum likelihood estimates and their estimated asymptotic variances, and show them to be independent of the sampling design (matched vs. random). Computer simulations investigate the behaviour of these estimates and of three types of confidence intervals when sample size is small relative to the number of confounder strata. The simulations indicate that attributable risk estimates tend to be too low. The bias is not serious except when exposure prevalence is high among controls. In this case the estimates and their standard error estimates are also highly unstable. In general, the asymptotic standard error estimates performed quite well, even in small samples, and even when the true asymptotic standard error was too small. By contrast, the bootstrap estimate tended to be too large. None of the three confidence intervals proved superior in accuracy to the other two. Thus there appears no advantage in using the log-based interval suggested by Walter which is always longer than the simpler symmetric interval.

A General Method for Constructing Simultaneous Confidence Intervals

Abstract: A general method is proposed for constructing simultaneous confidence intervals that gives special emphasis to any preselected finite spanning subset in a linear space of estimable functions. The method has a wide range of application, including regression analysis. The length of a confidence interval is determined as the solution to a linear programming problem. The studentized maximum modulus distribution can be used to choose critical values for conservative control of the overall confidence level. The method is compared to Scheffe's procedure.

Estimation and interpretation of genetic distance in empirical studies.

Abstract: Linear functions of Nei's genetic-distance statistic are calculated frequently in the literature of population genetics. Variance estimates for these linear functions are either not presented or incorrectly calculated. Part of the problem stems from the common assumption that distance statistics are independent random variables. This assumption is not generally correct. We describe methods for estimating the variance of linear combinations of genetic-distance statistics. We also suggest a method for constructing confidence intervals on genetic-distance statistics when these values are small (< 0·10) and their distribution deviates substantially from normal.

The Statistical Analysis of Population Growth Rates Calculated from Schedules of Survivorship and Fecunidity

Abstract: Population growth rates can be estimated from sample cohort schedules of survivorship and fecundity, but the variation inherent in these estimates has received little attention. We define an ideal population such that it is completely described by the probabilities governing age—specific survival and reproduction. We define the lifetime contribution of an individual to population growth in a manner analogous to Fisher's (1931) reproductive values. The mean of these individual contributions is equal to the finite rate of increase for the population. We then investigate the properties of sample cohorts drawn from an ideal population. Estimates of population growth rates that are based on sample cohorts are shown to be biased. The magnitude of the bias decreases as the number of individuals used to construct the sample schedules of survivorship and fecundity is increased. This relationship conflicts with the statistical desirability of maximizing the number of estimates of the population growth rate. Bias can be reduced by pooling individual schedules to calculate a single estimate of the growth rate of the population within which individual contributions are defined. When cohort size is small, we recommend a modified jackknifing procedure for further reducing bias. To demonstrate the application of these methods, we obtain a 95% confidence interval for a rate of increased based on a sample cohort of aphids.

Approximate confidence intervals for probabilities of survival and quantiles in life-table analysis.

Abstract: For survival probabilities with censored data, Rothman (1978, Journal of Chronic Diseases 31, 557-560) has recommended the use of quadratic confidence limits based on the assumption that the product of the 'effective' sample size at time t and the life-table estimate of the survival probability past time t follows a binomial distribution. This paper shows that the proposed confidence limits are asymptotically correct for continuous survival data. These intervals, as well as those based on the arcsine transformation, the logit transformation and the log(--log) transformation, are compared by simulation to those based on Greenwood's formula--the usual method of interval estimation in life-table analysis. With large amounts of data, the alternatives to the Greenwood method all produce acceptable intervals. On the basis of overall performance, the intervals suggested by Rothman are preferred for smaller samples. Any of these methods may be used to generate confidence sets for the median survival time or for any other quantile.

Ectopic pregnancy and prior induced abortion.

Abstract: We compared the prior pregnancy histories of 85 multigravid women with an ectopic pregnancy and 498 multigravid delivery comparison subjects. We found a relationship between the number of prior induced abortions and the risk of ectopic pregnancy: the crude relative risk of ectopic pregnancy was 1.6 for women with one prior induced abortion and 4.0 for women with two or more prior induced abortions; however, use of multivariate techniques to control confounding factors reduced the relative risks to 1.3 (95 per cent confidence interval, 0.6-2.7) and 2.6 (95 per cent confidence interval, 0.9-7.4), respectively. The analysis suggests that induced abortion may be one of several risk factors for ectopic pregnancy, particularly for women who have had abortions plus pelvic inflammatory disease or multiple abortions.

A Confidence Interval for an Exponential Parameter from a Hybrid Life Test

Abstract: In life testing, type I and type II censoring may be combined to form a hybrid life test. Epstein (1954) introduced this testing scheme and Epstein (1960b) proposed a two-sided confidence interval to estimate the mean lifetime, 8, of an exponential lifetime following such a test. His conjecture is modified slightly and a proof is given that establishes the validity of the proposed confidence interval.

Nonparametwic Confidence Intervals for the Median in the Presence of Right CensoriIlg

Abstract: A method is proposed for constructing nonpararnetric confidence intervals for the median of a survival distribution. The method applies when survival data are subject to random right censoring. The confidence interval is constructed by inverting a hypothesis test, the test used being one that generalizes the binomial test to accommodate censoring. A nonparametric estimate of the eventual failure time for each censored observation modifies the usual binomial test statistic. The estimates are computed using the Kaplan-Meier product-limit estimate of the survival function. A large simulation study indicates that the nonparametric method performs well for various survival distributions of different shapes. Two existing techniques that assume exponentiality perform well for exponential data; they give good coverage probabilities with intervals that are shorter than those provided by the nonparametric approach. The nonparametric intervals exhibit superior coverage probabilities when data are generated from nonexponential distributions. This is the case for Weibull data with both increasing and decreasing hazard functions. The nonparametric construction is appropriate for samples of size 10 or greater with up to 50% censoring. A Monte Carlo study supports the use of a binomial distribution to approximate the exact discrete distribution of the test statistic. Median survival time is often used for evaluation of the efficacy of a treatment for a chronic disease. One would like to provide a confidence interval for the median, as well as a point estimate. When little is known about the shape of the survival distribution, an interval is needed for which no particular parametric form for the distribution is assumed. A nonparametric confidence interval for the median is easily formed when all observations are complete. The problem increases in subtlety and complexity when incomplete or censored observations exist. In this paper, a method is proposed for constructing nonparametric confidence intervals for the median when observations may be right-censored. The distribution of survival time may be either discrete or continuous, and it need not have finite moments. The method does assume, however, that the censoring mechanism is noninformative, in that censoring acts independently of survival time; see Lagakos (1979). In the absence of censoring, the usual construction of a nonparametric confidence interval for the median inverts the sign test. This test is based upon the number of failures that occur beyond the hypothesized value of the median. The present paper generalizes the procedure to allow for right censoring, by using the Kaplan-Meier estimate of survival to approximate the number of failures beyond the hypothesized median. Confidence interval estimation when data are censored has received recent attention in

Stein's two-stage procedure and exact consistency

Abstract: Stein (1945 and 1949) achieved the exact probability coverage for a fixed-width confidence interval estimation of a normal mean when the variance is unknown. To achieve this type of exact result of “consistency” (in the Chow—Robbins (1965) sense), we notice that the assumption of normal distributions for the population is not essential. It can be replaced by less restrictive conditions on independence and pivotal nature of some suitable statistics. This is our Theorem 1. Examples are provided from negative exponential, symmetric normal (Rao, 1973, pp. 196–198) and normal populations. A similar type of problem is discussed for inverse Gaussian (see Folks & Chhikara, 1978) parameters. Modified two-stage procedures are proposed along the lines of Mukhopadhyay (1980) and are shown to be asymptotically “first-order efficient” (in the Ghosh—Mukhopadhyay (1981) sense). We also develop and study some properties of two-stage fixed-width confidence intervals constructed along the lines of Birnbaum & Healy ...

Non-parametric Bayesian Models for Samples from Finite Populations

Abstract: SUMMARY Using Ferguson's (1973) non-parametric priors in a Bayesian analysis of finite popula- tions, we show that asymptotically, at least, the usual estimates and confidence intervals for the population mean in simple and stratified random samples can be justified in Bayesian terms. We then apply these models for estimating population percentiles, and a new procedure for interval estimates in stratified sampling is developed. AT present there are a number of general approaches in the statistical literature for making inferences based on data selected from a finite population. Many of these are summarized in Smith (1976). Probably the most widely used methodology, in practice, is the design-based inference from random samples, where criteria such as bias and mean-squared error, derived from the sampling distribution of the data, are used. This methodology does not preclude the possibility that the estimator may be based on an inherent superpopulation model; however, confidence intervals and mean-squared errors are based only on the probability distribution of the design, and ignore the model. One of the reasons for the popularity of this approach may be that it is non-parametric in nature and sample sizes tend to be large for many applications, so that the loss of efficiency compared with parametric superpopulation approaches is considered less important than the robustness of the design-based approach with respect to a wide class of models.

Robust multiple comparisons

Abstract: The use of several robust estimators of location with their associated variance estimates in a modified T-method for pairwise multiple comparisons between treatment means was compared with the sample mean and variance and with the k-sample rank sum test. The methods were compared with respect to the stability of their experimentwise error rates under a variety of non-normal situations (robustness of validity) and their average confidence interval lengths (robustness of efficiency).

Improving the normal approximation when constructing one-sided confidence intervals for binomial or Poisson parameters

Abstract: SUMMARY We show that the usual normal approximation used during the construction of onesided confidence intervals for binomial or Poisson parameters can be significantly in error due to skewness in the underlying distribution. We provide a simple method of correcting for skewness, and demonstrate that it is effective both in theory and in practice.

Cluster Sampling Estimation of the Variance of Abundance Estimates Derived from Quantitative Echo Sounder Surveys

Abstract: Serial correlation in data collected from fisheries acoustic surveys may have an effect on the precision and accuracy of fish abundance estimates. A simple random sample approach to the data analysis yields unreliable confidence intervals for mean population density when the degree of serial correlation in the data is high. The results of a simulation analysis indicate that more reliable confidence intervals can be obtained using cluster sampling estimation techniques.Key words: acoustic surveys, fish abundance estimates, cluster sampling, serial correlation

The performance of three approximate confidence limit methods for the odds ratio

Abstract: The performance of three approximate confidence limit methods for the odds ratio, R, is studied at the 95% level in the unconditional sample space. There are: the method proposed by Cornfield (Proceedings of the 3rd Berkeley Symposium 1956;4:135-48), the logit method with 1/2 corrections first considered by Woolf (Ann Hum Genet 1955;19:251-3), and the test-based method proposed by Miettinen (Am J Epidemiol 1976;103:226-35). Cornfield's method comes closest to attaining the normal confidence coefficient. The logit method typically has actual confidence coefficients somewhat too large with disparate tail areas. The latter is ascribed in part to the enhanced skewness induced by the logit transformation itself. The test-based method has actual coefficients uniformly less than nominal when R not equal to 1. This underestimation is worse in finite samples than Halperin found it to be asymptotically. Although the Cornfield and test-based methods have the same confidence coefficients for R = 1, the test-based method is more likely to cover distant values of R not equal to 1 when in fact R = 1. It is concluded that Cornfield's method without the continuity correction is the preferred approximate method in the unconditional space as, with the continuity correction, it was previously found to be in the conditional space.

Confidence Intervals of a Climatic Signal

Abstract: In order to interpret climate statistics correctly, the definitions of climate change, signal-to-noise ratio and statistical significance are clarified. It is proposed to test the significance of climate statistics by the use of confidence intervals, since they are more informative than merely testing the null hypothesis that the true response is zero. The confidence intervals of the mean difference, variance ratio and signal-to-noise ratio are formulated and applied to a climate sensitivity study. It is also proposed to make a multivariate test of a response pattern by the use of joint confidence intervals, since they are more informative than merely testing the null hypothesis that the true response is everywhere zero. These intervals can also be applied to test the joint significance of the amplitude and phase of the seasonal cycles of a response.

Drug Activity and Therapeutic Synergism in Cancer Treatment

Abstract: In work involving modeling of response surfaces to describe the effects of cancer chemotherapy treatments, it is important to define activity and therapeutic synergism in a statistically defensible manner. This requires the construction of confidence intervals around the estimated optimal treatment which has been achieved by use of an indirect method first proposed by Box and Hunter. Activity for a drug or a combination can be claimed at 100(1 - α)% level of confidence when the 100(1 - α)% confidence interval about the optimal treatment excludes a zero dose. Results of treatment of B16 melanoma and Lewis lung carcinoma with 3,4-dihydroxybenzohydroxamic acid are used to demonstrate this definition. Extensions of this concept lead to a statistically valid definition of therapeutic synergism. If the confidence region about the optimum combination of k drug does not contact any of the k − 1 dimensional subspaces, then a k drug therapeutic synergism can be claimed. In the event that a k drug therapeutic synergism cannot be claimed, there may be subsets of the drugs which do combine with therapeutic synergy. These concepts are demonstrated by two- and three-drug combination experiments in L1210-bearing C57BL/6 × DBA/2 F1 (B6D2F1) mice. Razoxane and dacarbazine show therapeutic synergism at a 95% confidence level. A three-drug combination of 5-fluorouracil, Teniposide, and mitomycin C is considered. In this case, although the estimated optimum treatment includes 48.1 mg of 5-fluorouracil per kg, 15.9 mg of Teniposide per kg, and 3.9 mg of mitomycin C per kg, the confidence region generated failed to confirm at an 80% level of confidence that 5-fluorouracil was a necessary component of the best treatment.

Confidence Intervals for the Coverage of Low Coverage Samples

Abstract: The coverage of a random sample from a multinomial population is defined to be the sum of the probabilities of the observed classes. The problem is to estimate the coverage of a random sample given only the number of classes observed exactly once, twice, etc. This problem is related to the problem of estimating the number of classes in the population. Non-parametric confidence intervals are given when the coverage is low such that a Poisson approximation holds. These intervals are related to a coverage estimator of Good (1953).

Shortest confidence and prediction intervals for the log-normal

Abstract: We provide the shortest prediction interval for X, and the shortest confidence interval for the median of X, when X has the log-normal distribution for both the case a2, the variance of log X, known and unknown. Tables are given to assist the practitioner in constructing these intervals. A real-life example is provided to illustrate the results.