Test-based Confidence Intervals Research Articles

Analysis of two binomial proportions in noninferiority confirmatory trials.

In this article, we propose considering an approximate exact score (AES) test for noninferiority comparisons and we derive its test-based confidence interval for the difference between two independent binomial proportions. This test was published in the literature, but not its associated confidence interval. The p-value for this test is obtained by using exact binomial probabilities with the nuisance parameter being replaced by its restricted maximum likelihood estimate. Calculated type I errors revealed that the AES method has important advantages for noninferiority comparisons over popular asymptotic methods for adequately powered confirmatory clinical trials, at 80% or 90% statistical power. For unbalanced sample sizes of the compared groups, type I errors for the asymptotic score method were shown to be higher than the nominal level in a systematic pattern over a range of true proportions, but the AES method did not suffer from such a problem. On average, the true type I error of the AES method was closer to the nominal level than all considered methods in the empirical comparisons. In rare cases, type I errors of the AES test exceeded the nominal level, but only by a small amount. Presented examples showed that the AES method can be more attractive in practice than practical exact methods. In addition, p-value and confidence interval of the AES method can be obtained in <30 s of computer time for most confirmatory trials. Theoretical arguments, combined with empirical evidence and fast computation time should make the AES method attractive in statistical practice.

Peripartum events and molar-incisor hypomineralisation (MIH) amongst young patients in southwest France.

This was to investigate the association of peripartum events with the occurrence of MIH. This study, carried out between 2010 and 2011, was based on objective information noted in child health booklets on putative risk factors for MIH during the Peripartum period, aged between 6 to 28years. The target population consisted of patients with MIH and a control group. Among the 849 patients examined by two calibrated paediatric dentists, 75 patients with MIH were recorded. These patients attended for consultation either at the teaching dental hospital of Bordeaux (France) or at a private dental practice (Bordeaux, France). Pearson's Chi-squared test was used and Odds ratios (OR) with 95% test-based confidence intervals (CI) were calculated. Correlations were observed between hypoxia during delivery and occurrence of MIH (OR=6.1; CI=1.7-21.85), and also between birth by caesarean section and MIH (OR=2.9; CI=1.2-6.9). There was no association between prematurity and MIH. Peripartum events such as hypoxia during birth or delivery by caesarean section are suggested to be risk factors for the occurrence of MIH in this population.

Misunderstandings about Q and 'Cochran's Q test' in meta-analysis.

Many meta-analyses report using 'Cochran's Q test' to assess heterogeneity of effect-size estimates from the individual studies. Some authors cite work by W. G. Cochran, without realizing that Cochran deliberately did not use Q itself to test for heterogeneity. Further, when heterogeneity is absent, the actual null distribution of Q is not the chi-squared distribution assumed for 'Cochran's Q test'. This paper reviews work by Cochran related to Q. It then discusses derivations of the asymptotic approximation for the null distribution of Q, as well as work that has derived finite-sample moments and corresponding approximations for the cases of specific measures of effect size. Those results complicate implementation and interpretation of the popular heterogeneity index I(2) . Also, it turns out that the test-based confidence intervals used with I(2) are based on a fallacious approach. Software that outputs Q and I(2) should use the appropriate reference value of Q for the particular measure of effect size and the current meta-analysis. Q is a key element of the popular DerSimonian-Laird procedure for random-effects meta-analysis, but the assumptions of that procedure and related procedures do not reflect the actual behavior of Q and may introduce bias. The DerSimonian-Laird procedure should be regarded as unreliable.

Metaprop: a Stata command to perform meta-analysis of binomial data.

BackgroundMeta-analyses have become an essential tool in synthesizing evidence on clinical and epidemiological questions derived from a multitude of similar studies assessing the particular issue. Appropriate and accessible statistical software is needed to produce the summary statistic of interest.MethodsMetaprop is a statistical program implemented to perform meta-analyses of proportions in Stata. It builds further on the existing Stata procedure metan which is typically used to pool effects (risk ratios, odds ratios, differences of risks or means) but which is also used to pool proportions. Metaprop implements procedures which are specific to binomial data and allows computation of exact binomial and score test-based confidence intervals. It provides appropriate methods for dealing with proportions close to or at the margins where the normal approximation procedures often break down, by use of the binomial distribution to model the within-study variability or by allowing Freeman-Tukey double arcsine transformation to stabilize the variances. Metaprop was applied on two published meta-analyses: 1) prevalence of HPV-infection in women with a Pap smear showing ASC-US; 2) cure rate after treatment for cervical precancer using cold coagulation.ResultsThe first meta-analysis showed a pooled HPV-prevalence of 43% (95% CI: 38%-48%). In the second meta-analysis, the pooled percentage of cured women was 94% (95% CI: 86%-97%).ConclusionBy using metaprop, no studies with 0% or 100% proportions were excluded from the meta-analysis. Furthermore, study specific and pooled confidence intervals always were within admissible values, contrary to the original publication, where metan was used.Electronic supplementary materialThe online version of this article (doi:10.1186/2049-3258-72-39) contains supplementary material, which is available to authorized users.

Aetiology of molar-incisor hypomineralisation (MIH) in Brazilian children.

To determine the potential aetiological factors related to molar-incisor hypomineralisation (MIH) in Brazilian children. A total of 1,151 children aged 7-12years (mean 8.86±1.28), born and living in the urban area of Araraquara, Brazil, were examined by two examiners evaluating the presence of MIH according to criteria suggested by the European Academy of Paediatric Dentistry (2003). Their mothers completed a structured questionnaire about medical history, from pregnancy to the first 3years of the children's life. Descriptive analyses of data and odds ratios (OR) with 95% test-based confidence intervals (CI) were estimated. Chi-square test was used to evaluate the differences between groups. The prevalence of MIH in the children was 12.3%. The interviewing response rate was 90.4%. The prevalence of miscarriage history (25 vs. 15.4%; OR=1.21; 95% CI 0.30-4.92) and occurrence of anaemia (23 vs. 12.4%; OR=2.07; 95% CI 0.50-8.63) were higher in mothers from MIH group than those from non-MIH group. However, these associations were not statically significant. In the children's medical history, rhinitis, bronchitis (56.5 vs. 52.5%; OR=1.17; 95% CI 0.82-1.68), and high fever (20.4 vs. 18.2%; OR=1.14; 0.73-1.76) were more prevalent in MIH group, but there were no significant differences between the groups (p>0.05). No possible aetiological factor investigated was associated with MIH. Prospective studies are needed to define the aetiological factors involved with MIH.

Molar Incisor Hypomineralisation: Possible aetiological factors in children from urban and rural areas

To analyse factors potentially associated with molar incisor hypomineralisation (MIH) development. METH¬ODS: A population-based study was carried out with 903 children aged from 6-12 years old, born and residing in rural and urban areas of the town of Botelhos, State of Minas Gerais, Brazil. Their mothers completed a structured medical history questionnaire, from pregnancy to the child's 3rd year of life. Two examiners evaluated children for MIH according to criteria suggested by the European Academy of Paediatric Dentistry. Descriptive analyses of the data and odds ratios (OR) with 95% test-based confidence intervals (CI) were estimated. Chi-square test was used to evaluate the differences between groups. The prevalence of MIH in children from rural area (RA) was significantly higher than those from the urban area (UA) (24.9% versus 17.8%, p= 0.01). In urban children, neither significant associations with MIH nor medical problems were found. In rural children, however, MIH was significantly more common among those whose mothers had experienced medical problems during pregnancy (OR=2.11; 1.01-4.37 CI 95%; p=0.04), who had throat infections (OR=2.93; 1.47-5.87 CI 95%; p=0.01), who had high fever (OR=1.91; 1.07-3.39 CI 95%; p=0.02), and who had used amoxicillin associated with other antibiotics (OR=1.92; 1.02-3.62 CI 95%; p=0.04) during the first 3 years of life. This study suggests a link between MIH and health problems during pregnancy, as well as environmental factors.

Statistical Methods for Integrating Randomized Clinical Studies for Evaluation of Combination Treatment Therapy

In regulatory applications, evaluation of a combination drug at a fixed dose is based on pairwise comparisons of the combination with its component drugs. These comparisons generate the least expected gain of the combination relative to its components as the key effect parameter for evaluation. Two test methods are developed for the evaluation to combine multiple clinical studies that are deemed combinable. One test method is based on a linear combination of the Min tests from individual studies. In the other test method, weighted estimators are first derived for the pairwise comparisons between the combination and the respective components by combining the studies. A Min test is then applied to these estimators. The latter test method tends to be more powerful than the former test method. A test-based confidence interval is constructed for the least expected gain of the combination relative to its components. A test for heterogeneity across studies is also developed.

Statistical Inference For Risk Difference in an Incomplete Correlated 2 × 2 Table

AbstractIn some infectious disease studies and 2‐step treatment studies, 2 × 2 table with structural zero could arise in situations where it is theoretically impossible for a particular cell to contain observations or structural void is introduced by design. In this article, we propose a score test of hypotheses pertaining to the marginal and conditional probabilities in a 2 × 2 table with structural zero via the risk/rate difference measure. Score test‐based confidence interval will also be outlined. We evaluate the performance of the score test and the existing likelihood ratio test. Our empirical results evince the similar and satisfactory performance of the two tests (with appropriate adjustments) in terms of coverage probability and expected interval width. Both tests consistently perform well from small‐ to moderate‐sample designs. The score test however has the advantage that it is only undefined in one scenario while the likelihood ratio test can be undefined in many scenarios. We illustrate our method by a real example from a two‐step tuberculosis skin test study.

ON TESTING EQUIVALENCE OF THREE POPULATIONS

We consider analysis of clinical trials in which the objective is to show that three populations are equivalent. Equivalence is defined in terms of δ, the maximum difference in population means; a one-sided hypothesis test of δ is considered. We provide the distribution of the maximum pairwise difference in sample means, and we use this distribution to find critical values for tests of size 0.100, 0.050, 0.025, and 0.010. When standard errors are not equal among the three treatments, a simple adjustment is proposed to control the type I error rate. These tests are applied to studying the equivalence of three binomial proportions. Test-based confidence intervals are discussed. Two examples illustrate the proposed methods.

Maternal exposure to prescription and non-prescription pharmaceuticals or drugs of abuse and risk of craniosynostosis.

The pre- and peri-natal drug exposures reported by women participating in a case-control study of children in Colorado were examined for association with infant craniosynostosis. Mothers of case and control children underwent a standardized telephone interview and obstetric and newborn medical record review. The interview included questions on the use of prescription and non-prescription drugs, nutritional supplements, recreational and drugs of abuse. The mother's obstetric record was abstracted for information about pharmacologic agents taken before and during the antepartum period. There were no statistically significant risk ratios associating craniosynostosis with prenatal exposure to hydantoin, valproic acid, or cocaine. Mothers of four case children and one control child reported specific exposure to retinoic acid. There were no statistically significant increases in the odds ratio (OR) for any suture type among children exposed to hypoxigenic agents, sympathomimetic or parasympatholytic agents, or metal-containing agents. The OR was 1.87 (lower bound of the two-sided 95% test-based confidence interval (CI): 1.08) among children with sagittal/lambdoid suture synostosis who were exposed to nitrosatable drugs chlorpheniramine, chlordiazepoxide, and nitrofurantoin compared to controls. Certain nitrosatable drugs may be associated with increased risk of infant sagittal/lambdoid craniosynostosis. A possible mechanism related to ischaemia/reperfusion injury is suggested.

The advantages of community-randomized trials for evaluating lifestyle modification

Observational studies may provide suggestive evidence for the results of behavior change and lifestyle modification, but they do not replace randomized trials for comparing interventions. To obtain a valid comparison of competing intervention strategies, randomized trials of adequate size are the recommended approach. Randomization avoids bias, achieves balance (on average) of both known and unknown predictive factors between intervention and comparison groups, and provides the basis of statistical tests. The value of randomization is as relevant when investigating community interventions as it is for studies that are directed at individuals. Randomization by group is less efficient statistically than randomization by individual, but there are reasons why randomization by group (such as community) may be chosen, including feasibility of delivery of the intervention, political and administrative considerations, avoiding contamination between individuals allocated to competing interventions, and the very nature of the intervention. One example is the Community Intervention Trial for Smoking Cessation (COMMIT), which involved 11 matched pairs of communities and randomized within these pairs to active community-level intervention versus comparison. For analysis of results, community-level permutation tests (and corresponding test-based confidence intervals) can be designed based on the randomization distribution. The advantages of this approach are that it is robust, and the unit of randomization is the unit of analysis, yet it can incorporate individual-level covariates. Such covariates can play a role in imputation for missing values, adjustment for imbalances, and separate analyses in demographic subsets (with appropriate tests for interaction). A communityrandomized trial can investigate a multichannel community-based approach to lifestyle modification, thus providing generalizability coupled with a rigorous evaluation of the intervention.

Interplay between Design and Analysis for Behavioral Intervention Trials with Community as the Unit of Randomization

This paper outlines an approach for the design and analysis of randomized controlled trials investigating community-based interventions for behavioral change aimed at health promotion. The approach is illustrated using the Community Intervention Trial for Smoking Cessation (COMMIT), conducted from 1988 to 1993, involving 11 pairs of communities in North America, matched on geographic location, size, and sociodemographic factors. The situation discussed is when assignment to intervention is done at the community level; for COMMIT, the very nature of the intervention required this. The number of communities as a key determinant of the statistical power of the trial. The use of matched pairs of communities can achieve a gain in statistical efficiency. Randomization is used to obtain an unbiased assessment of the intervention effect; randomization also provides the basis for statistical analysis. Permutation tests (and corresponding test-based confidence intervals), using community as the unit of analysis, follow directly from the randomization distribution. Within this framework, individual-level covariates can be used for imputation of missing values and for adjusting analyses of intervention effect.

Increased risk of craniosynostosis with higher antenatal maternal altitude.

During the 1980s, the Colorado Department of Health received reports from several high-altitude communities of clusters of the malformation craniosynostosis. In a population-based, case-control study, we examined the association between overall and trimester-specific maternal antenatal altitude exposure and the occurrence of infant craniosynostosis. We identified case children through a statewide registry and randomly sampled control children from birth records. By telephone interview, each mother provided data on the locations of all antenatal residences and places of employment as well as other factors. Staff mapped all locations and abstracted the corresponding altitudes. The odds ratio (OR) of any synostosis for a time-weighted mean antenatal altitude of > or = 2000 metres (high altitude) versus < 2000 metres (low altitude) was 1.4 (lower bound of the one-sided 95% test-based confidence interval (CI): 0.9). The OR was elevated in smokers but not in non-smokers. As compared to non-smokers, the OR of any synostosis for high-altitude smokers was 4.6 (lower bound of the 95% one-sided exact CI: 1.7). Particularly elevated were the corresponding OR of coronal (18.1, 4.4) and metopic synostosis (16.3, 2.8), and OR for high-altitude exposure during the second trimester (any synostosis: 6.4, 1.99; coronal: 28.6, 6.1; metopic: 26.7, 4.1). Antenatal maternal high-altitude exposure and smoking are associated with increased risk of infant craniosynostosis, perhaps through generation of intermittent hypoxaemia.

Risk Analysis in Cohort Studies with Heterogeneous Strata. A Global χ2-Test for Dose-Response Relationship, Generalizing the Mantel-Haenszel Procedure

In cohort studies the Mantel-Haenszel estimator ORMH is computed from sample data and is used as a point estimator of relative risk. Test-based confidence intervals are estimated with the help of the asymptotic chi-squared distributed MH-statistic chi 2MHS. The Mantel-extension-chi-squared is used as a test statistic for a dose-response relationship. Both test statistics--the Mantel-Haenszel-chi as well as the Mantel-extension-chi--assume homogeneity of risk across strata, which is rarely present. Also an extended nonparametric statistic, proposed by Terpstra, which is based on the Mann-Whitney-statistics assumes homogeneity of risk across strata. We have earlier defined four risk measures RRkj (k = 1,2,...,4) in the population and considered their estimates and the corresponding asymptotic distributions. In order to overcome the homogeneity assumption we use the delta-method to get "test-based" confidence intervals. Because the four risk measures RRkj are presented as functions of four weights gik we give, consequently, the asymptotic variances of these risk estimators also as functions of the weights gik in a closed form. Approximations to these variances are given. For testing a dose-response relationship we propose a new class of chi 2(1)-distributed global measures Gk and the corresponding global chi 2-test. In contrast to the Mantel-extension-chi homogeneity of risk across strata must not be assumed. These global test statistics are of the Wald type for composite hypotheses.(ABSTRACT TRUNCATED AT 250 WORDS)

A method for combining matched and unmatched binary data. Application to randomized, controlled trials of photocoagulation in the treatment of diabetic retinopathy.

A method for combining matched and unmatched data is described and was applied to the results of randomized, controlled trials of photocoagulation in the treatment of diabetic retinopathy. A pooled estimate from the matched and unmatched studies was obtained by adaptation of the Mantel-Haenszel method, where the strata were unmatched studies and matched pairs within studies. A test of significance was based on the Mantel-Haenszel chi-square statistic, the latter also being used to calculate test-based confidence intervals. A test of homogeneity was performed by combining Mantel-Haenszel chi-square statistics from the matched and unmatched studies. By these methods, the combined estimate of the risk of deterioration of visual acuity for those receiving photocoagulation (relative to a risk of unity for those not receiving photocoagulation) was 0.37 (95 per cent confidence interval 0.29-0.46). The chi-square statistic (1 df) for an effect of treatment was 87.75 (p less than 0.0001). The chi-square statistic for homogeneity of relative risk among studies was 11.20 (4 df, p less than 0.05). However, this result was influenced disproportionately by one small matched study.

Farming occupations and mortality from non-Hodgkin's lymphoma in Utah. A case-control study.

The association between farming occupations and the incidence of non-Hodgkin's lymphoma (NHL) was examined in a case-control study using a cancer registry to identify cases and controls and death certificates to determine the occupation and industry of employment of cancer patients. Case subjects were white males with a diagnosis of NHL who died between 1967 and 1982; control subjects were white males who died of colon cancer during the same period. Control and case subjects were frequency-matched for age and year of diagnosis; county of residence was not a matching variable. Death certificates with codable occupational information were located for 90% of the 249 case and 293 control subjects. A stratified analysis using test-based confidence intervals revealed an increased risk of NHL among farmers. The overall odds ratio, controlling for age and for year of diagnosis, was 1.3 (90% confidence limits 0.9-2.3). For diagnoses during 1952 through 1965, the odds ratio was 6.6, and for diagnoses during 1966 through 1971, the odds ratio was 3.1. The increased odds ratio was most pronounced among those aged 45 to 64 years at the time of diagnosis and those living in rural counties.

A Comparison of Reflected Versus Test-Based Confidence Intervals for the Median Survival Time, Based on Censored Data

The small-sample performance of some recently proposed nonparametric methods of constructing confidence intervals for the median survival time, based on randomly right-censored data, is compared with that of two new methods. Most of these methods are equivalent for large samples. All proposed intervals are either 'test-based' or 'reflected' intervals, in the sense defined in the paper. Coverage probabilities for the interval estimates were obtained by exact calculation for uncensored data, and by stimulation for three life distributions and four censoring patterns. In the range of situations studied, 'test-based' methods often have less than nominal coverage, while the coverage of the new 'reflected' confidence intervals is closer to nominal (although somewhat conservative), and these intervals are easy to compute.