Estimating confidence intervals for cost-effectiveness ratios: an example from a randomized trial

Cost-effectiveness ratios usually appear as point estimates without confidence intervals, since the numerator and denominator are both stochastic and one cannot estimate the variance of the estimator exactly. The recent literature, however, stresses the importance of presenting confidence intervals for cost-effectiveness ratios in the analysis of health care programmes. This paper compares the use of several methods to obtain confidence intervals for the cost-effectiveness of a randomized intervention to increase the use of Medicaid's Early and Periodic Screening, Diagnosis and Treatment (EPSDT) programme. Comparisons of the intervals show that methods that account for skewness in the distribution of the ratio estimator may be substantially preferable in practice to methods that assume the cost-effectiveness ratio estimator is normally distributed. We show that non-parametric bootstrap methods that are mathematically less complex but computationally more rigorous result in confidence intervals that are similar to the intervals from a parametric method that adjusts for skewness in the distribution of the ratio. The analyses also show that the modest sample sizes needed to detect statistically significant effects in a randomized trial may result in confidence intervals for estimates of cost-effectiveness that are much wider than the boundaries obtained from deterministic sensitivity analyses.     

Bootstrapping correlation coefficients using univariate and bivariate sampling.

A new univariate sampling approach for bootstrapping correlation coefficients is proposed and evaluated. Bootstrapping correlations to define confidence intervals or to test hypotheses has previously relied on repeated bivariate sampling of observed (x,y) values to create an empirical sampling distribution. Bivariate sampling matches the logic of confidence interval construction, but hypothesis testing logic suggests that x and y should be sampled independently. This study uses Monte Carlo methods to compare the univariate bootstrap with 3 bivariate bootstrap procedures and with the traditional parametric procedure, using various sample sizes, population correlations, and population distributions. Results suggest that the univariate bootstrap is superior to other bootstrap procedures in many hypothesis testing settings, and even improves on parametric hypothesis testing in certain cases. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Influence of infection on patent ductus arteriosus and chronic lung disease in premature infants weighing 1000 grams or less

OBJECTIVES: To test the hypotheses that (1) infection increases ductal dilatory prostaglandins and inflammatory mediators that may influence the closure of a patent ductus arteriosus (PDA), increasing the incidence of late episodes of PDA (after 7 days) and the rate of closure failures, and (2) the concurrence of PDA and infection increases the risk of chronic lung disease (CLD). METHODS: One hundred fourteen premature infants (birth weight, 500 to 1000 gm) were prospectively assessed for PDA and infection. Serum levels of 6-ketoprostaglandin F1 alpha and tumor necrosis factor alpha were measured routinely in all infants and when PDA or infection was present. Multivariate assessment of risk factors for PDA closure failure and for CLD was done by logistic regression, and expressed as an odds ratio and as 95% confidence intervals. RESULTS: Late PDA episodes were more frequent in infants with infection than in those without infection. A temporally related infection (<5 days between both diagnoses) was associated with an increased risk of PDA closure failure (odds ratio, 19.1 (confidence interval, 4 to 90)). In addition to birth weight and the severity of initial respiratory failure, PDA and infection increased the risk of CLD (odds ratio, 11.7 (confidence interval, 1.7 to 81) for PDA; odds ration, 3.1 (confidence interval, 1 to 11) for infection). Furthermore, when both factors were temporally related, they further increased the risk of CLD (odds ratio, 29.6 (confidence interval, 4.5 to >100)). Infants with infection and those with PDA had higher levels of 6-ketoprostaglandin F1 alpha than did control subjects. Levels of tumor necrosis factor alpha were also elevated in infants with infection and in those with late PDA. CONCLUSIONS: Infection adversely influences PDA outcome by increasing the risk of late ductal reopening and PDA closure failures. Increased levels of prostaglandins and tumor necrosis factor alpha in infants with infection may explain the poor PDA outcome. The concurrence of PDA and infection potentiates their negative effects on the risk of CLD.     

Confidence intervals for the cross-validated multiple correlation in predictive regression models.

Presents improved procedures to approximate confidence intervals for ρ–2 and ρc–2 in both fixed and random predictor models. These approximations require neither point estimates nor variance estimates and are analytically shown to be precise enough for most practical prediction purposes. An application of confidence intervals in regression model development is also given. (16 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Correlations redux.

Correlational analysis is a cornerstone method of statistical analysis, yet most presentations of correlational techniques deal primarily with tests of significance. The focus of this article is obtaining explicit expressions for confidence intervals for functions of simple, partial, and multiple correlations. Not only do these permit tests of hypotheses about differences but they also allow a clear statement about the degree to which correlations differ. Several important differences of correlations for which tests and confidence intervals are not widely known are included among the procedures discussed. Among these is the comparison of 2 multiple correlations based on independent samples. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Regression models: calculating the confidence interval of effects in the presence of interactions

The main goal of regression analysis (multiple, logistic, Cox) is to assess the relationship of one or more exposure variables to a response variable, in the presence of confounding and interaction. The confidence interval for the regression coefficient of the exposure variable, obtained through the use of a computer statistical package, quantify these relationships for models without interaction. Relationships between variables that present interactions are represented by two or more terms, and the corresponding confidence intervals can be calculated 'manually' from the covariance matrix. This paper suggests an easy procedure for obtaining confidence intervals from any statistical package. This procedure is applicable for modifying variables which are continuous as well as categorical.     

In search of power and significance: issues in the design and analysis of stochastic cost-effectiveness studies in health care

Application of techniques such as cost-effectiveness analysis (CEA) is growing rapidly in health care. There are two general approaches to analysis: deterministic models based upon assumptions and secondary analysis of retrospective data, and prospective stochastic analyses in which the design of a clinical experiment such as randomised controlled trial is adapted to collect patient-specific data on costs and effects. An important methodological difference between these two approaches is in the quantification and analysis of uncertainty. Whereas the traditional CEA model utilizes sensitivity analysis, the mean-variance data on costs and effects from a prospective trial presents the opportunity to analyze cost-effectiveness using conventional inferential statistical methods. In this study we explored some of the implications of moving economic appraisal away from deterministic models and toward the experimental paradigm. Our specific focus was on the feasibility and desirability of constructing statistical tests of economic hypotheses and estimation of cost-effectiveness ratios with associated 95% confidence intervals. We show how relevant variances can be estimated for this task and discuss the implications for the design and analysis of prospective economic studies.     

An inferential confidence interval method of establishing statistical equivalence that corrects Tryon's (2001) reduction factor.

Evidence of group matching frequently takes the form of a nonsignificant test of statistical difference. Theoretical hypotheses of no difference are also tested in this way. These practices are flawed in that null hypothesis statistical testing provides evidence against the null hypothesis and failing to reject H? is not evidence supportive of it. Tests of statistical equivalence are needed. This article corrects the inferential confidence interval (ICI) reduction factor introduced by W. W. Tryon (2001) and uses it to extend his discussion of statistical equivalence. This method is shown to be algebraically equivalent with D. J. Schuirmann's (1987) use of 2 one-sided t tests, a highly regarded and accepted method of testing for statistical equivalence. The ICI method provides an intuitive graphic method for inferring statistical difference as well as equivalence. Trivial difference occurs when a test of difference and a test of equivalence are both passed. Statistical indeterminacy results when both tests are failed. Hybrid confidence intervals are introduced that impose ICI limits on standard confidence intervals. These intervals are recommended as replacements for error bars because they facilitate inferences. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Hair-color products and risk for non-Hodgkin's lymphoma: a population-based study in the San Francisco bay area

OBJECTIVES: As part of a large, epidemiologic study of non-Hodgkin's lymphoma, this study investigated a possible association between use of hair-color products and non-Hodgkin's lymphoma. METHODS: A population-based case-control study was conducted in the San Francisco Bay area. Of 4108 participants, 2544 were questioned about use of hair-color products. Control subjects were identified by use of random-digit dialing. RESULTS: Ever use of hair-color products was reported by 56% of case and 56% of control women and 10% of case and 9% of control men. Risks were not elevated for women for use of any hair-color products. Men who ever used semipermanent hair color had slightly elevated risks for non-Hodgkin's lymphoma, with trends associated with greater lifetime frequency of use and frequency of use per year, although individual confidence intervals overlapped unity. These elevated risks were diminished with exclusive use of semipermanent products, and confidence intervals overlapped unity. CONCLUSIONS: Integration of our results with those from experimental animal studies and other epidemiologic studies provides little convincing evidence linking non-Hodgkin's lymphoma with normal use of hair-color products in humans.     

Comparative evaluation of modified trichrome and Uvitex 2B stains for detection of low numbers of microsporidial spores in stool specimens

At present, the laboratory diagnosis of intestinal infections caused by microsporidia depends on the detection of the typical spores either with a modified trichrome stain (MTS) or by staining with fluorochromes. The purpose of the present study was (i) to compare staining with MTS (MTS method) and the staining with the fluorochrome Uvitex 2B (U2B method) with respect to their sensitivities and specificities, particularly in the presence of low numbers of spores, and (ii) to evaluate their reliabilities under routine laboratory conditions. First, 30 negative human stool specimens as well as 30 specimens enriched with a low concentration of microsporidial spores were examined. The U2B and MTS methods detected 27 and 30, of the positive samples, respectively (95% confidence intervals for sensitivity, 0.73 to 0.98 for the U2B method and 0.88 to 1.00 for the MTS method) without yielding false-positive results (95% confidence intervals for specificity, 0.88 to 1.00 for the MTS and U2B methods). In addition, analysis of serial dilutions of 17 stool specimens from AIDS patients containing microsporidia revealed comparable detection thresholds (P = 0.52) for both methods. Finally, 40 slides prepared from one stool specimen containing very few microsporidia and 40 negative slides were included in the routine diagnostic program during 1 month in order to monitor laboratory handling and run-to-run variations. Again, both methods exhibited comparable sensitivities (95% confidence intervals, 0.83 to 0.99 for the MTS method and 0.91 to 1.00 for the U2B method) and specificities (95% confidence intervals, 0.91 to 1.00 for the MTS and U2B methods). In conclusion, MTS and U2B methods are equally useful in the diagnosis of microsporidiosis. However, since detection thresholds for both methods differed considerably in all diluted stool specimens, performance of a combination of both methods may be more sensitive than the performance of only one procedure in the event of very low numbers of microsporidial spores.     

Power analysis and determination of sample size for covariance structure modeling.

A framework for hypothesis testing and power analysis in the assessment of fit of covariance structure models is presented. We emphasize the value of confidence intervals for fit indices, and we stress the relationship of confidence intervals to a framework for hypothesis testing. The approach allows for testing null hypotheses of not-good fit, reversing the role of the null hypothesis in conventional tests of model fit, so that a significant result provides strong support for good fit. The approach also allows for direct estimation of power, where effect size is defined in terms of a null and alternative value of the root-mean-square error of approximation fit index proposed by J. H. Steiger and J. M. Lind (1980). It is also feasible to determine minimum sample size required to achieve a given level of power for any test of fit in this framework. Computer programs and examples are provided for power analyses and calculation of minimum sample sizes. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Appearance of 1-2 Mbp giant DNA fragments as an early common response leading to cell death induced by various substances that cause oxidative stress

OBJECTIVE: To present an application of logistic regression modelling to estimate ratios of proportions, such as prevalence ratio or relative risk, and the Delta Method to estimate confidence intervals. METHOD: The Delta Method was used because it is appropriate for the estimation of variance of non-linear functions of random variables. The method is based on Taylor's series expansion and provides a good approximation of variance estimates. A computer program, utilizing the matrix module of SAS, was developed to compute the variance estimates. A practical demonstration is presented with data from a cross-sectional study carried out on a sample of 611 women, to test the hypothesis that the lack of housework sharing is associated with high scores of psychological symptoms as measured by a validated questionnaire. RESULTS: Crude and adjusted prevalence ratio estimated by logistic regression were similar to those estimated by tabular analysis. Also, ranges of the confidence intervals of the prevalence ratio according to the Delta Method were nearly equal to those obtained by the Mantel-Haenszel approach. CONCLUSIONS: The results give support to the use of the Delta Method for the estimation of confidence intervals for ratios of proportions. The method should be seen as an alternative for situations in which the need to control a large number of potential confounders limits the use of stratified analysis.     

Appraisals of emotion-eliciting events: Testing a theory of discrete emotions.

A recent theory by I. J. Roseman (1979, 1984) attempts to specify the particular appraisals of events that elicit 16 discrete emotions. This study tested hypotheses from the latest version of the theory and compared them with hypotheses derived from appraisal theories proposed by M. B. Arnold (1960) and by K. R. Scherer (1988), using procedures designed to address some prior methodological problems. Results provided empirical support for numerous hypotheses linking particular appraisals of situational state (motive-inconsistent/motive-consistent), motivational state (punishment/reward), probability (uncertain/certain), power (weak/strong), legitimacy (negative outcome deserved/positive outcome deserved), and agency (circumstances/other person/self) to particular emotions. Where hypotheses were not supported, new appraisal–emotion relationships that revise the theory were proposed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bootstrap Type I error rates for the correlation coefficient: An examination of alternate procedures.

This study examines three bootstrap procedures for estimating confidence intervals for the correlation coefficient. Results indicate that all three procedures produce slight inflation of the Type I error rate but that the inflation varies by method. Accordingly, choice of bootstrap procedure is an important consideration when testing hypotheses about correlations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Accuracy in parameter estimation for targeted effects in structural equation modeling: Sample size planning for narrow confidence intervals.

In addition to evaluating a structural equation model (SEM) as a whole, often the model parameters are of interest and confidence intervals for those parameters are formed. Given a model with a good overall fit, it is entirely possible for the targeted effects of interest to have very wide confidence intervals, thus giving little information about the magnitude of the population targeted effects. With the goal of obtaining sufficiently narrow confidence intervals for the model parameters of interest, sample size planning methods for SEM are developed from the accuracy in parameter estimation approach. One method plans for the sample size so that the expected confidence interval width is sufficiently narrow. An extended procedure ensures that the obtained confidence interval will be no wider than desired, with some specified degree of assurance. A Monte Carlo simulation study was conducted that verified the effectiveness of the procedures in realistic situations. The methods developed have been implemented in the MBESS package in R so that they can be easily applied by researchers. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Sample Size for Multiple Regression: Obtaining Regression Coefficients That Are Accurate, Not Simply Significant.

An approach to sample size planning for multiple regression is presented that emphasizes accuracy in parameter estimation (AIPE). The AIPE approach yields precise estimates of population parameters by providing necessary sample sizes in order for the likely widths of confidence intervals to be sufficiently narrow. One AIPE method yields a sample size such that the expected width of the confidence interval around the standardized population regression coefficient is equal to the width specified. An enhanced formulation ensures, with some stipulated probability, that the width of the confidence interval will be no larger than the width specified. Issues involving standardized regression coefficients and random predictors are discussed, as are the philosophical differences between AIPE and the power analytic approaches to sample size planning. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Confidence intervals or surfaces? Uncertainty on the cost-effectiveness plane

Although cost-effectiveness analysis is not new, it is only recently that economic analysis has been conducted alongside clinical trials. Whereas in the past economic analysts most often used sensitivity analysis to examine the implications of uncertainty for their results, the existence of patient-level data on costs and effects opens up the possibility of statistical analysis of uncertainty. Unfortunately, ratio statistics can cause problems for standard statistical methods of confidence interval estimation. The recent health economics literature contains a number of suggestions for estimating confidence limits for ratios. In this paper, we begin by reviewing the different methods of confidence interval estimation with a view to providing guidance concerning the most appropriate method. We go on to argue that the focus on confidence interval estimation for cost-effectiveness ratios in the recent literature has been concerned more with problems of estimation than with problems of decision-making. We argue that decision-makers are most likely to be interested in one-sided tests of hypothesis and that confidence surfaces are better suited to such tests than confidence intervals. This approach is consistent with decision-making on the cost-effectiveness plane and with the cost-effectiveness acceptability curve approach to presenting uncertainty due to sampling variation in stochastic cost-effectiveness analyses.     

Comments on a commentary: statistical evaluation of split mouth caries trials

When results of split mouth caries trials are reported, the most frequently used outcome measures are "effectiveness" and "net gain". In a recent review by Riordan & FitzGerald (Community Dent Oral Epidemiol 1994;22:192-7) of the statistical analysis of data from such trials, the close connection between effectiveness and the traditional epidemiological outcome measure, relative risk, was pointed out and the latter measure was recommended. The confidence intervals for these parameters were, however, incorrect. This note provides valid confidence intervals for net gain, effectiveness and relative risk based on data from split mouth trials and presents examples of the calculations.     

Strategies to manipulate reliability: impact on statistical associations

OBJECTIVE: To examine the effects of improving measurement reliability on associations between risk factors and childhood psychiatric disorder. METHOD: Data were from a general population sample of parents (N = 211) with children aged 6 to 16 years. Reliability of measurement was improved in three ways: by increasing the number of items in a scale (internal-consistency reliability), by averaging assessments of the same variables collected on two different occasions, and by constructing latent variable measures. To assess the effects of improving reliability, selected risk factors were regressed on parental assessments of childhood oppositional defiant disorder (ODD) and overanxious disorder (OAD). RESULTS: Improving reliability led to systematic increases in the magnitude of standardized regression coefficients between family dysfunction and ODD (beta = .30-.51) and between family dysfunction and OAD (beta = .24-.48). In multiple regression, improving reliability served to strengthen the specificity of associations between ODD, OAD, and family dysfunction and maternal depressed mood. Although latent variable methods produced the largest associations, the standard errors of these estimates were also larger, resulting in wider confidence intervals and slightly larger significance values. CONCLUSIONS: Improving reliability of measurement results in larger associations between risk factors and childhood disorder and may increase the opportunity of revealing differential associations between variables.     

Inhibition of bicarbonate transport protects embryonic heart against reoxygenation-induced dysfunction

Calculation of reference limits by regression analysis makes it unnecessary to partition the reference data into subgroups, and age-dependent limits can be estimated within as narrow age intervals as necessary. However, the reliability of the regression-based reference limits has not been considered before. To get valid regression-based confidence intervals (CIs) for reference limits, one must evaluate the convolution of two distributions. In this study, age-dependent reference limits with corresponding CIs were produced for blood hemoglobin concentrations over the age interval from newborns to 12 months. We describe how the variance associated with the reference limits can be estimated, and present a Table from which appropriate values can be chosen for the calculation of regression-based reference limits and exact CIs. Also, an equation for the calculation of approximate CIs is given. The data were modeled by linear regression in several cumulative age groups to find the transition zone where the slope changed. After defining this cutoff point, piecewise linear regression was applied. Reference limits and their CIs calculated by conventional and piecewise linear regression methods were almost the same in older age groups but differed significantly during the period of most rapid age-dependent changes, i.e., during the 2 months after birth.