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An issue of statistical analysis in controlled multi-centre studies: how shall we weight the centres?

When analysing data from a controlled multi-centre study, an important issue is how to weight each centre to assess the overall treatment effect. The unweighted analysis, which weights all centres equally, was recommended by many statisticians and the U.S. Food and Drug Administration, and has been routinely utilized as the primary statistical method for many phase III clinical studies in the pharmaceutical industry. The weighted analysis, which weights centres relative to the number of patients in them, was considered not meaningful in the presence of treatment-by-centre interaction. This paper demonstrates why we should hesitate to use the unweighted analysis as the primary statistical method of a study from a statistical power perspective. It also shows that the weighted analysis is meaningful, even in the presence of treatment-by-centre interaction, and that it is generally the preferred approach.

Controlled Clinical Trials as Topic↗

Multivariate data analysis for outcome studies.

The use of multivariate statistical techniques for analyzing the complex data often gathered in outcome studies is discussed. The multivariate analysis of variance (MANOVA) is suggested for multiple group studies common to outcome studies. This technique can be utilized for a large number of specific research designs whenever multiple outcome measures are collected. MANOVA offers two specific advantages over more familiar univariate approaches: it presents better control over Type 1 error rates while preserving statistical power, and it allows more thorough analysis of complex data.

Humans↗

Meta-analysis: budesonide treatment for collagenous colitis.

BACKGROUND: Collagenous colitis is typified by chronic watery diarrhoea and characteristic histological alterations of the colonic mucosa without endoscopic abnormalities. Budesonide, a corticosteroid with high first-pass metabolism has been examined in collagenous colitis, but studies to date have had small numbers, and relatively low statistical power. AIM: A meta-analysis of existing published trials was undertaken to evaluate the treatment effect of budesonide in collagenous colitis. METHODS: All pertinent literature sources were searched for published reports in English of budesonide use in collagenous colitis. MEDLINE and EMBASE databases were reviewed, as well as bibliographies from published articles and available abstracts from relevant meetings. Literature that met prespecified criteria was selected for the meta-analysis. RESULTS: Three trials were included in the meta-analysis. Budesonide significantly decreased stool frequency (budesonide vs. placebo OR: 20.1, 95% CI: 7.0-57.5, P < 0.0001). In general, budesonide treatment was well-tolerated. CONCLUSIONS: Budesonide is clinically effective short-term in collagenous colitis, and seems to be relatively well-tolerated. Clinicians can consider this drug as a reasonable option for patients with this disorder.

Anti-Inflammatory Agents↗

Risk factors for Alzheimer's disease: the EURODEM collaborative re-analysis of case-control studies.

Case-control studies of risk factors for Alzheimer's disease have been hampered by low statistical power. Here, we present a collaborative analysis of 11 case-control studies of Alzheimer's disease. The original data of these studies were pooled and re-analyzed. The risk factors considered in this analysis were family history of dementia and related disorders, maternal age at index birth, head trauma, medical and psychiatric history and environmental exposures. This paper gives a brief overview of the findings of the re-analysis.

Age Factors↗

Meta-analysis of the association between tryptophan hydroxylase and suicidal behavior.

Tryptophan hydroxylase (TPH) has been the candidate gene of focus in many of the association studies of suicidal behavior in recent years. Initial positive findings with respect to an association between the TPH gene and suicidal behavior have been replicated, but not consistently. Typically, individual studies have investigated small samples, and thus they repeatedly had insufficient statistical power to detect a positive association. Meta-analysis is one approach that can be used to achieve greater statistical power and may be helpful in providing a more conclusive understanding. We used meta-analytic techniques to investigate the association between an intron 7 polymorphism in the TPH gene and suicidal behavior. A total of 39 publications were identified and reviewed, 17 of which were selected for inclusion in this study. We performed two meta-analyses. One compared suicide attempters or completers (N = 1,290) with healthy controls (N = 2,295); the other compared suicide attempters (N = 625) with nonattempters (N = 1,475). None of these studies provided evidence for association (odds ratio (OR) = 1.14, 95% confidence interval (CI) = 0.97-1.34 for the former and OR = 0.96, 95% CI = 0.77-1.20 for the latter). The combined results from comparisons within both groups showed no overall association between suicidal behavior and an intron 7 polymorphism of the TPH gene.

Humans↗

[The possibility of modern segregation analysis to discriminate monogenic and multifactorial types of the inheritance of traits. The reliability of models and the power of the analysis].

Using computer simulation of family data sets within segregation analysis limits the comparative research of the autosomal major locus model (MLM) and the multifactorial model (MFM) which described the basic types of inheritance of the alternative traits (affected--nonaffected) has been conducted. Robustness of models (statistical aspect) and the power of the analysis (its possibility to discriminate MLM and MFM) are tested. It is shown that permissible level of relative errors for estimated population's frequency is increased, when the values of parameters of models are increased (with decrease of sporadic cases' portion). The power of the analysis is the greatest in the field of greatest robustness of models: the higher the parameters of models, the portion of sporadic cases being low, the stronger the power of the analysis. MFM satisfactorily describes family distribution given by additive MLM. On the contrary, if the MLM corresponds to the multifactorial traits, this model is additive. It is shown that the possibility of the analysis to reject alternative model is decreased when determination of model grows down.

Genes↗

Prednisone withdrawal in kidney transplant recipients on cyclosporine and mycophenolate mofetil--a prospective randomized study. Steroid Withdrawal Study Group.

BACKGROUND: Prospective randomized trials have shown a reduced rate of acute rejection (AR) in mycophenolate mofetil-treated kidney transplant recipients. We hypothesized that this increased protection from AR could allow successful prednisone (P) withdrawal in cyclosporine/mycophenolate mofetil/P-treated recipients. METHODS: A multicenter, prospective, randomized, double-blind trial of P withdrawal at 3 months post-transplant was initiated. Entry criteria were: primary transplant, adult, no AR by 90 days, mycophenolate mofetil dose > or =2 g/day, cyclosporine dose = 5-15 mg/kg/ day, P dose = 10-15 mg/day. Study participants were randomized to have P tapered over 8 weeks (beginning at 3 months posttransplant) to 0 vs. 10 mg/day. Prestudy power analysis determined 500 recipients should be randomized for 80% statistical power to test equivalence of the primary endpoint, AR, or treatment failure at 1 year posttransplant. By design, the study was to be stopped if interim data precluded reaching equivalence. An established data safety monitoring board monitored the study. RESULTS: After 266 patients were enrolled, the patient enrollment was stopped (after safety monitoring board review) because of excess rejection in the P withdrawal group. The Kaplan-Meier estimate of the cumulative incidence of rejection or treatment failure within 1 year posttransplant (+/-95% confidence interval) for the maintenance group was 9.8% (4.4%; treatment failure, 14.9%); for the withdrawal group, 30.8% (21.0%; 39.3%). Treatment differences in the distribution of time to event were highly significant (P = 0.0007). Of note, risk was higher in blacks (39.6%) versus nonblacks (16.0%) (P<0.001). At 1 year post-transplant, there was no difference between groups in patient or graft survival. For the patients with functioning grafts at 6 months posttransplant, withdrawal patients had lower cholesterol (P = 0.0005), had higher creatinine (P = 0.03), and were less likely to use antihypertensives (P = 0.001). These differences persist to 1 yr posttransplant. CONCLUSIONS: We conclude that for recipients on cyclosporine/mycophenolate mofetil/P with no AR at 90 days, the chance of developing subsequent AR is small; if P is tapered and withdrawn, the risk increases (but the majority remain free of acute and chronic rejection). After withdrawal, the risk of AR is different for blacks versus nonblacks. Withdrawal patients had a lower cholesterol level and less need for antihypertensives.

Adolescent↗

Statistical power and analytical quantification.

It is suggested that power analysis should be formally incorporated into quantification experiment reports in order to substantiate the conclusions derived from experimental data more effectively. The article addressed the issues of power analysis calculation, sample size estimation and appropriate data reporting in quantitative analytical comparisons. Illustrative examples from the literature are used to show how the described power analysis theory could be applied in practice.

Chemistry Techniques, Analytical↗

Time-series analysis of seasonal changes of the O inversion polymorphism of Drosophila subobscura.

We have studied seasonal variation (spring, early summer, last summer and autumn) of inversion polymorphisms of the O chromosome of Drosophila subobscura in a natural population over 15 years. The length of the study allowed us to investigate the temporal behavior (short-term seasonal changes and long-term directional trends) of the O arrangements by the powerful statistical method of time series analysis. It is shown that the O inversion polymorphisms varied on two different time scales: short-term seasonal changes repeated over the years superimposed on long-term directional trends. All the common arrangements (O3+4+7, Osr, O3+4+8) showed significant cyclic seasonal changes, and all but one of these arrangements (O3+4+7) showed significant long-term trends. Moreover, the degree of seasonality was different for different arrangements. Thus, O3+4+7 and OST showed the highest seasonality, which accounted for approximately 61 and 47% of their total variances, respectively. The seasonal changes in the frequencies of chromosome arrangements were significantly associated with the seasonal variation of the climate (temperature, rainfall, humidity and insolation). In particular, O3+4+7 and OST, the arrangements with the greatest seasonal component, showed the strongest association with all climatic factors investigated, especially to the seasonal changes of extreme temperature and humidity.

Animals↗

The comparative efficacy of trazodone and imipramine in the treatment of depression.

OBJECTIVE: To review published clinical trials comparing the efficacy of trazodone with that of tricyclic antidepressant medication. DATA SOURCES: MEDLINE was searched for relevant articles published from 1983 to 1991. The bibliography of a review article was searched for further references. STUDY SELECTION: In all, 25 clinical trials were found. Six of these met the methodologic assessment criteria (adapted from the McMaster guidelines for the evaluation of clinical trials), which included the stipulation of a score of 18 or more on the Hamilton depression rating scale and a 50% reduction in that score as an outcome measure. DATA EXTRACTION: All six studies compared trazodone with imipramine. Data describing response to the treatments were extracted, and post-hoc power estimates were calculated. The analysis also involved statistical tests of a modified null hypothesis, the generation of confidence intervals (CIs) and a meta-analysis. DATA SYNTHESIS: All the studies found no significant difference in the efficacy of trazodone and imipramine. However, the statistical power of most of them was less than 50% and often less than 10%; thus there was a low probability that differences would be detected. The results of statistical tests of the modified null hypothesis, inspection of the CIs and the results of the meta-analysis all suggested that trazodone, and imipramine are equally efficacious. CONCLUSION: The application of various techniques for the analysis of equivalence data suggests that trazodone and imipramine are of approximately equivalent efficacy. The data are compatible with small differences in efficacy, but the differences are of a magnitude such that they are unlikely to be of clinical significance.

Clinical Trials as Topic↗

Mortality in offspring of parents with psychotic disorders: a critical review and meta-analysis.

OBJECTIVE: Mortality risk in offspring of parents with psychotic disorders is a sensitive and important topic, but evidence on which to base plans for preventive services is limited. The authors synthesized evidence for mortality risk among offspring of parents with psychotic disorders and examined potential modifiers of risk such as offspring age and parental diagnosis. METHOD: Electronic reference and citation databases were searched. Secondary analyses were carried out to generate relative risk estimates and perform post hoc statistical power calculations. A meta-analysis of the association between maternal psychotic disorder and fetal death/stillbirth was conducted. RESULTS: Most of the relevant studies investigated the relationship between exposure to maternal schizophrenia and perinatal or infant mortality outcomes but were not truly population-based and lacked adequate power. Studies published since 1960 generally indicated higher than expected mortality risk in exposed offspring. Meta-analysis indicated an almost twofold higher risk of fetal death/stillbirth among offspring of women with psychoses. Notable gaps in the existing evidence include outcome beyond the first year of life, cause-specific mortality, and effects of exposure to specific parental conditions other than schizophrenia and of exposure to paternal versus maternal disorder. Etiological mechanisms are not fully understood. CONCLUSIONS: Large-scale population-based studies are needed to understand mortality risk in offspring of parents with psychoses. In the absence of etiological evidence, only general preventive measures can be taken. Prevention of offspring mortality at an early age is most likely to be achieved by identification and treatment of maternal disorder and greater provision of support to these vulnerable families.

Adolescent↗

The use of statistical methodology for the analysis of QA data.

Modern statistical methods offer the quality assurance professional a powerful set of tools for the analysis of health care data. By using well-established procedures the quality assurance professional can isolate and quantify the relative degree of problems, determine statistical significance, and allocate resources towards problem resolution. This article briefly covers the concepts of hypothesis testing and statistical significance and their role in assisting the health care professional to assign priorities for use in problem resolution. Several statistical tests are described in the context of health care data analysis. The distinction between parametric, and non-parametric tests is made and a set of guidelines included on when and where the respective tests should be applied. An outline for the application of these statistical tests to several example situations is presented. Some details of population identification, sampling, and data organization are covered. Interpretation of results in the context of different problem situations is also covered.

Data Collection↗

Myopia progression in adolescent wearers of soft contact lenses and spectacles.

The purpose of this 3-year, randomized clinical trial was to determine the difference in myopia progression in adolescents wearing soft contact lenses over a control group wearing spectacles. A total of 175 adolescents between the ages of 11 and 14 years were randomized into 2 groups, spectacle wearers and soft contact lens wearers. The main result was that the spherical equivalent change between the groups showed no clinical or statistically significant difference. However, when a power vector analysis was used, which uses all the refractive error data, a small but statistically significant (F test = 4.24, T2 = 17.35, p < 0.01) difference between the groups was found (i.e., the refractive error of the spectacle wearers had a slight increase in astigmatism). It can be concluded that soft contact lens wear does not lead to additional myopia progression in adolescents.

Adolescent↗

Effect of stents in reducing restenosis in small coronary arteries: a meta-analysis.

The ability of stents to reduce restenosis was established in larger coronary arteries. Clinical trials of stenting in smaller vessels have yielded conflicting results due in part to their sample sizes. The aim of this meta-analysis was to increase the statistical power by pooling data from these clinical trials. Trials were identified from Medline search, review of recent cardiology meetings' abstracts, and manual review of bibliographies. Studies were included if they were prospective randomized controlled trials. Endpoints examined included a dichotomized definition of angiographic restenosis, target lesion revascularization (TLR), target vessel revascularization (TVR), or any repeat revascularization. Pooling of data was performed by calculating a Mantel-Haenszel odds ratio (OR). The analysis included 2,598 patients enrolled in eight clinical trials. Stenting significantly reduced restenosis (OR = 0.62; 95% CI = 0.61-0.63). Concordantly, stenting reduced TLR (OR = 0.49), TVR (OR = 0.90), and any revascularization (OR = 0.48). This meta-analysis supports the hypothesis that stenting reduces restenosis in small coronary arteries as well as in larger coronary arteries. The apparent discordant result of individual clinical trials was due in part to underpowering related to small sample sizes.

Angioplasty, Balloon, Coronary↗

Evaluation of 13 short tandem repeat loci for use in personal identification applications.

Personal identification by using DNA typing methodologies has been an issue in the popular and scientific press for several years. We present a PCR-based DNA-typing method using 13 unlinked short tandem repeat (STR) loci. Validation of the loci and methodology has been performed to meet standards set by the forensic community and the accrediting organization for parentage testing. Extensive statistical analysis has addressed the issues surrounding the presentation of "match" statistics. We have found STR loci to provide a rapid, sensitive, and reliable method of DNA typing for parentage testing, forensic identification, and medical diagnostics. Valid statistical analysis is generally simpler than similar analysis of RFLP-VNTR results and provides powerful statistical evidence of the low frequency of random multilocus genotype matching.

Alleles↗

Macrolide therapy for Chlamydia pneumoniae in the secondary prevention of coronary artery disease: a meta-analysis of randomized controlled trials.

STUDY OBJECTIVE: As recent studies have shown that antibiotic therapy to eradicate Chlamydia pneumoniae may be beneficial in the secondary prevention of coronary artery disease, and studies to date may have lacked statistical power, we conducted a meta-analysis of randomized controlled trials to determine the role of antibiotic therapy in this patient population. DESIGN: Systematic review and meta-analysis of randomized controlled trials. PATIENTS: A total of 12,032 patients from nine studies. MEASUREMENTS AND MAIN RESULTS: We searched MEDLINE, EMBASE, the Cochrane Controlled Trials Register, and abstracts of conference proceedings to identify pertinent studies. The random effects model was used to estimate a pooled relative risk. Heterogeneity was assessed using the bootstrap version of the Q statistic with 1000 replications. In total, we reviewed nine randomized controlled trials enrolling 12,032 patients; six enrolled patients with acute coronary syndrome, two enrolled patients with stable coronary artery disease, and one enrolled a mixed population. Compared with placebo, macrolide therapy was not associated with a significant reduction in any coronary event (relative risk [RR] 0.98, 95% confidence interval [CI] 0.88-1.08), myocardial infarction or angina (RR 0.89, 95% CI 0.68-1.16), or overall mortality (RR 0.95, 95% CI 0.81-1.12). CONCLUSION: Our results do not support routine use of antichlamydial therapy for secondary prevention of coronary events.

Antibiotic Prophylaxis↗

Postprandial response of gastric slow waves: correlation of serosal recordings with the electrogastrogram.

Controversial interpretations have been given to the postprandial increase in the dominant power (amplitude) of the electrogastrogram (EGG). The aim of this study was to find an appropriate interpretation of the postprandial EGG power changes. Simultaneous serosal and cutaneous recordings of gastric myoelectrical activity were made in 11 patients with gastroparesis in the fasting state and after the ingestion of 8 oz of water. The dominant frequency and corresponding power of the recording before and after water were computed using the power spectral analysis method. It was found that the dominant frequency of the EGG was the same as that of the serosal recording in 10 patients. One patient showed a substantial amount of dysrhythmia and no obvious dominant frequency was noted. A decrease in the dominant frequency was found in these 10 patients after the ingestion of water. Tachygastria of higher than 4 cycles/min was observed in one of 11 patients both in the prewater and postwater states. Consistent changes in amplitude after a drink of water were noted in both serosal recording and EGG. Statistical analysis demonstrated that the dominant power change after water computed from the EGG was correlated with that observed in the serosal recording (r = 0.757, P = 0.007). In conclusion, exogenous stimulation, such as ingestion of water, may change the amplitude of the gastric slow wave and this change is reflected in the EGG, suggesting that the change of the slow-wave amplitude is an important contributing factor to the postprandial change in the EGG dominant power.

Adult↗