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Estimating departure from normality.

Departure of a sample from a normal distribution should be assessed by a quantity that is meaningful in terms of the data, rather than merely by the P-value from a test statistic. Indices of departure based on the Shapiro-Francia W' and the Shapiro-Wilk W statistics are derived, and shown to have a natural interpretation in relation to the normal probability plot. A new diagnostic plot is proposed. An example is given which shows the relationship between one of the new indices and errors in calculated reference ranges due to non-normality of the data.

Adult↗

The statistical interpretation of blue-on-yellow visual field loss.

PURPOSE: To evaluate short-wavelength-sensitive perimetry in the detection of glaucomatous field loss. METHODS: The sample consisted of 27 normal subjects, 24 patients with primary open angle glaucoma (POAG), and 27 patients with ocular hypertension (OHT). Blue-on-yellow (B-Y) and standard (W-W) perimetry was undertaken with a modified Humphrey Field Analyzer 640 on one eye of each subject and patient. The B-Y data were corrected for individual ocular media absorption. Results were compared to an age-matched normal database of 50 subjects (age range, 60 to 82 years; mean age, 70.0 years; SD, 6.4 years). Visual field indices and total and pattern deviation probability maps were calculated for both W-W and B-Y fields. RESULTS: The B-Y normal database exhibited increased between-subject variability compared to the W-W normal database (P < 0.001). The greater variability increased with the increase in eccentricity (P < 0.001) and with the increase in age (P = 0.032). All patients with POAG exhibited B-Y field loss; 11 demonstrated greater B-Y loss than the corresponding W-W field. In advanced POAG, the B-Y and the W-W fields were similar. Twenty-five of the 27 normal subjects exhibited normal B-Y fields. Five of the 27 patients with OHT manifested B-Y focal abnormality and a normal W-W field: in two, W-W focal loss subsequently developed. CONCLUSIONS: Short-wavelength-sensitive perimetry can identify visual field loss before that detected by W-W perimetry. However, the increased between-subject variability necessitates stringent statistical analysis in the definition of abnormality.

Aged↗

Optimal gene expression analysis by microarrays.

DNA microarrays make possible the rapid and comprehensive assessment of the transcriptional activity of a cell, and as such have proven valuable in assessing the molecular contributors to biological processes and in the classification of human cancers. The major challenge in using this technology is the analysis of its massive data output, which requires computational means for interpretation and a heightened need for quality data. The optimal analysis requires an accounting and control of the many sources of variance within the system, an understanding of the limitations of the statistical approaches, and the ability to make sense of the results through intelligent database interrogation.

Algorithms↗

Research in primary dental care Part 6: Data analysis.

The analysis of data from a research project seeks to answer the research question which the investigators set at the outset of the study. This article provides information on data analysis for both quantitative and qualitative data, always referring the reader back to their initial research question. Advice is also given on software which can be used for the analysis of data. A guide is provided to the choice of appropriate statistics for studies involving quantitative data.

Data Interpretation, Statistical↗

Maintaining data integrity in randomized clinical trials.

BACKGROUND: The process of attaining and maintaining data integrity is critical to ensure a successful randomized clinical trial. Methodologic strategies to achieve data integrity when repeated measures are used has not been discussed in detail in the literature. The National Institutes of Health requires that data integrity and safety monitoring boards or plans be established for randomized clinical trials. OBJECTIVES: The objectives of this paper are to (a) examine important data collection issues nurse scientists often encounter in randomized clinical trials and (b) present a process that researchers can apply to achieve data integrity. METHODS: The process to achieve data integrity is based on strategies that were developed by an interdisciplinary hospice research team involved in an ongoing National Institutes of Health-funded clinical trial. The process and key issues are illustrated with methodologic examples from the randomized clinical trial and supporting literature. RESULTS: The process of achieving data integrity involves developing protocols in three key areas: data collection, training of data collectors, and data monitoring. The use of these protocols will increase the rigor of the clinical trial and assist in maintaining study validity. CONCLUSIONS: Investigators conducting clinical trials need to consider all issues involved in achieving data integrity and have tested protocols in place throughout the study. These approaches will not only help maintain study validity but also help ensure data of sufficient quantity and quality to achieve the desired statistical power.

Bias↗

Comments on "Cancer Mortality near Oak Ridge, Tennessee".

A recent article by Joseph Mangano concluded that changes in cancer mortality near Oak Ridge (Anderson County) in Tennessee over a 40-year period (1950-1989) suggest an increase in cancer deaths linked to radiation contamination. These conclusions are not supported by available, representative data. In his analysis, Mangano selected for comparison two three-year periods (1950-1952 and 1987-1989) that are not representative of the entire 40 years. An analysis by decade of the 42-year period from 1950 to 1991, using U.S. mortality rates from the National Center for Health Statistics and Tennessee mortality rates from the NCHS and the Tennessee Health Department, shows that the relation between expected and actual cancer deaths for the white population of Anderson County does not differ from that for the State of Tennessee. In addition, changes in methods of reporting death statistics during the 40-year period invalidate any attempt to compare current cause-specific mortality data (such as cancer deaths) with data from the 1950s. Relevant comparisons that can be made for the period 1970-1991 again show that cancer deaths for whites in Anderson County have been statistically equivalent to the expected rates.

Adult↗

[A review of statistical analysis methods in measurement data].

Measurement data, which is obtained by measuring the size of numeric value, is consisted of numerical variables. In clinic research, the collected data covers quite of numerical variables. Composed of those numerical variables, the measurement data has to be correspondingly analyzed in the special statistical methods in the light of their design methods. The statistical methods of measurement data include descriptive statistics and inferential statistics. Descriptive statistics is mainly used to describe the distribution laws and the characters/features of the data. For instance, when measuring the central tendency and dispersion tendency of the data, methods such as calculating the mean and the standard deviation can be considered. Inferential statistics is mainly employed to estimate the confidence limit such as estimating the 95% confidence interval and to have the hypothesis testing in the example of having t test and analysis of variance. By highlighting the specific statistical methods of measurement data, this review intends to help the clinicians and researchers select correct statistical methods in accordance with measurement data.

Data Interpretation, Statistical↗

Standard versus adaptive monitoring procedures: A commentary.

In the standard approach to designing definitive clinical trials, the primary endpoint and test statistic to be used for the primary analysis are specified before trial initiation. The false positive error rate for the null hypothesis and statistical power to detect the targeted size of treatment effect are also specified. Standard monitoring procedures, such as the group sequential guidelines, enable interim monitoring while maintaining the integrity of this approach. In contrast, adaptive monitoring procedures seek to provide flexibility to modify these pre-specified design features during the course of the trial. However, these procedures have several undesirable properties, including lesser statistical efficiency, reduced interpretability of primary outcome results, basing design changes on unreliable interim estimates of efficacy, risks to the integrity and credibility of the trial, loss of flexibility to use emerging results from external sources to alter key design features, and overemphasis of the importance of statistical significance relative to clinical significance.

Clinical Trials Data Monitoring Committees↗

Assessment of inter-rater agreement on the grading of intravascular bubble signals.

Transcutaneous Doppler ultrasonic bubble detectors are widely used in decompression research. However, interpretation of the complex acoustic signals from the bubble detectors involves a degree of subjectivity, and the comparability of grades assigned by different raters must be assessed. Hypothetical data were used to determine an appropriate method for evaluating the comparability of Doppler raters and to illustrate the limitations of many nonparametric statistics. Two sets of real data were then used to evaluate this procedure, the first from a training exercise carried out by Kisman and Masurel (1978, unpublished) and the second from a test tape that was independently scored by five Defence and Civil Institute of Environmental Medicine Doppler technicians. The results were analyzed by a two-stage approach. First, they were entered into contingency tables and checked for large disagreements, a tendency for one rater to grade higher than the other, and the degree of variability. Second, the results were analyzed with the nonparametric weighted kappa statistic. These studies have led to a practical, efficient method for the evaluation of Doppler raters.

Data Interpretation, Statistical↗

A technique for summarizing longitudinal data.

Many studies collect longitudinal data but do not use them efficiently. We propose a technique for reducing a set of longitudinal data into four common summary statistics together with time. These statistics can be used in place of the raw data in further analyses, for example in a regression analysis. Instead of arbitrarily choosing the summary statistics, we derive them mathematically, thus justifying their use. This simplifies the subsequent analyses, and also improves the interpretation of the results. An example from the Framingham Heart Study illustrates the procedure.

Bias↗

Between-subject and within-subject statistical information in dental research.

The evaluation of risk factors in dental research frequently uses observations at multiple sites in the same patient. For this reason, statistical methods that accommodate correlated data are generally used to assess the significance of the risk factors (e.g., generalized estimating equations, generalized linear mixed models). In applications of these methods, it is typically assumed (implicitly, if not explicitly) that between-subject and within-subject comparisons will produce the same estimated effect of the risk factor. When between- and within-subject comparisons conflict, the statistical methods can give biased estimates or results that are difficult to interpret. For illustration, we present two examples from periodontal disease studies in which different statistical methods give different estimates and significance levels for a risk factor. Statistical analyses in dental research should assess whether different sources of information give similar conclusions about risk factors or treatments.

Confounding Factors, Epidemiologic↗

Age-conditional probabilities of developing cancer.

We propose an estimator of the probability of developing a disease in a given age range, conditional on never having developed the disease prior to the beginning of the age range. Our estimator improves the one described by Wun, Merrill and Feuer ( Lifetime Data Analysis 1998; 4, 169-186) that is currently used by the U.S. National Cancer Institute for the SEER Cancer Statistics Review. Both estimators use cross-sectional disease rates and provide an interpretation of these rates in terms of the age-conditional probability of developing disease in a hypothetical cohort. The difficulty of this problem is that rates are not available per person-years alive and disease free, but only per person-years alive. Wun et al. used ad hoc methods to handle this problem which did not properly account for competing risks, did not provide a measure of variability, and only allowed age ranges using prespecified 5-year age intervals. Here we solve the problem under a unified competing risks framework, which allows the calculation of the age-conditional probabilities for any age range. We generalize gamma confidence intervals to apply to our new statistic. Although our new method provides estimates which are numerically similar to that of Wun et al., this paper provides a comprehensive theoretical basis for estimation and inference about the age-conditional probability of developing a disease.

Age of Onset↗

Integrated analysis of transcript profiling and protein sequence data.

Transcript profiling can be used to elucidate the molecular and cellular mechanisms involved in ageing and cancer. A recent study of human gastrointestinal stromal tumours (GISTs) with mutations in the KIT gene, Cancer Res. 61 (2001) 8624 exemplifies a common type of investigation. cDNA microarrays were used to generate measurements for 1987 clones in two types of tissues: 13 KIT mutation-positive GISTs and 6 spindle cell tumours from locations outside the gastrointestinal tract. Statistical problems associated with such two-class, high-dimensional profiling data include simultaneous classification and relevant feature identification, probabilistic clustering and protein sequence family modelling. Here, the GIST data were reexamined using specific solutions to these problems, namely sparse hyperplanes, nai;ve Bayes models and profile hidden Markov models respectively. The integrated analysis of molecular profiling and sequence data highlighted 6 clones that may be of clinical and experimental interest. The protein encoded by one of these putative biomarkers defined a novel protein family present in diverse eucarya. The family may be involved in chromosome segregation and/or stability. One family member is a potential biomarker identified recently from a retrospective analysis of transcript profiles for sporadic breast cancer samples from patients with poor and good prognosis, Signal Process. (in press).

Amino Acid Sequence↗

On combining dose-response data from epidemiological studies by meta-analysis.

Using data from a meta-analysis of the effects of oestrogen replacement therapy on the development of breast cancer, we compared alternative methods for combining dose-response slopes from epidemiological studies. We evaluated issues related both to summarizing data from single studies and to combining results from multiple studies. Findings related to the analysis of individual dose-response studies include: (1) a method of weighing studies that gives greater influence to dose-response slopes that conform to the linear relation of relative risk to duration can lead to large differences in calculated weights as a function of non-linearity; (2) a regression model using a variable-intercept resulted in a mean dose-response slope that increased as much as threefold when compared with the values obtained with a zero-intercept model. When combining results from multiple studies, we found: (1) calculating standard errors of mean dose-response slopes by methods that allow for both among-study and within-study variability (a random-effects type model) gave values different from a method that assumes homogeneity and equal within-study precision (a fixed-effects model); (2) the random-effects model gives mean and standard error results most similar to a bootstrap resampling method as increasing heterogeneity is observed (however, this model could give biased mean estimates compared with the bootstrap method); (3) a components-of-variance model compares favourably with the bootstrap and is easier to apply than the random-effects model. Based on these findings, we recommend the use of methods which incorporate heterogeneity to guard against underestimating the standard error. However, caution is urged because bias in point estimates can occur if extreme heterogeneity is present. Two other observations affect the interpretation of data combined from multiple studies. First, inclusion into a model of quality scores assigned by blinded reviewers had little effect on the mean dose-response slope and its standard error. Second, the number of studies required to achieve desired statistical power, varies with effect size.

Analysis of Variance↗

Statistics in medical journals: developments in the 1980s.

This paper reviews changes in the use of statistics in medical journals during the 1980s. Aspects considered are research design, statistical analysis, the presentation of results, medical journal policy (including statistical refereeing), and the misuse of statistics. Despite some notable successes, the misuse of statistics in medical papers remains common.

Clinical Trials as Topic↗

On the use of the generalized t and generalized rank-sum statistics in medical research.

We have used Monte Carlo methods to compare the type I error properties of the conditional and unconditional versions of the generalized t and the generalized rank-sum tests to those of the independent samples t and Wilcoxon rank-sum tests. Results showed inflated type I errors for the conditional generalized tests but not for the unconditional tests. We also compared the power of the unconditional generalized tests to that of the t and Wilcoxon tests under a variety of conditions. Results showed the generalized tests to be much more efficient than their traditional counterparts in some circumstances, but substantially less powerful in others. Based on these and other considerations, we conclude that the application of these newer statistics in medical research needs further consideration.

Data Interpretation, Statistical↗