Matched-pair Data Research Articles

Using a correlated probit model approximation to estimate the variance for binary matched pairs

A correlated probit model approximation for conditional probabilities (Mendell and Elston 1974) is used to estimate the variance for binary matched pairs data by maximum likelihood. Using asymptotic data, the bias of the estimates is shown to be small for a wide range of intra-class correlations and incidences. This approximation is also compared with other recently published, or implemented, improved approximations. For the small sample examples presented, it shows a substantial advantage over other approximations. The method is extended to allow covariates for each observation, and fitting by iteratively reweighted least squares.

Analysis of clustered matched-pair data.

Evaluation of the performance of a new diagnostic procedure with respect to a standard procedure arises frequently in practice. The response of interest, often in a dichotomous form, is measured twice, once with each procedure. The two procedures are administered to either two matched individuals, or when practical, to the same individual. A large sample test for matched-pair data is the McNemar test. The main assumption of this test is independent paired responses; however, when more than one outcome from an individual is measured by each procedure, the data are clustered. Examples of such cases can be seen in dental and ophthalmology studies. Variance adjustment methods for the analysis of clustered matched-pair data have been proposed; however, because of unequal cluster sizes, variability of correlation structures within a cluster (within paired responses in a cluster as well as between paired responses in a cluster), and unequal success probabilities among the clusters, the performances of some available methods are not consistent. This research proposes a simple adjustment to the McNemar test for the analysis of clustered matched-pair data. Method of moments is used to calculate a consistent variance estimator. Using Monte Carlo simulation, the size and power of the proposed test are compared to those of two currently available methods. To illustrate practical application, clustered matched-pair data from two clinical studies are analysed.

Analysis of clustered matched-pair data for a non-inferiority study design.

Hypothesis testing of matched-pair data has been adapted for equivalence (one- and two-sided) study designs; however, a statistical problem arises when more than one measurement is recorded for each study subject. Ignoring the correlation between the repeated measurements per subject may underestimate the standard error of the parameter estimate. A method of testing for non-inferiority or equivalence of clustered matched-pair data is not yet available. This paper proposes a Wald-type test statistic for a non-inferiority hypothesis and applies it to the comparison of two diagnostic procedures.

The effect of age on vestibular rehabilitation outcomes.

The purpose of the retrospective chart review was to compare vestibular rehabilitation outcomes in young versus older adults. Retrospective matched design. Twenty-three persons with vestibular disorders aged 20 to 40 years were matched by gender, vestibular diagnosis, and vestibular function test results to 23 older adults aged 60 to 80 years. The patients were treated with a custom-designed physical therapy exercise program. Patients completed the Dizziness Handicap Inventory, the Activities-Specific Balance Confidence (ABC) scale, and the Dynamic Gait Index; number of falls; and rated the severity of their dizziness. The two-sample test, the Mann-Whitney test, and McNemar's test for correlated proportions were used to determine whether there was a difference in scores between the two age groups at the beginning and end of physical therapy. During the initial evaluation, older adults reported having statistically greater space and motion discomfort and more severe symptoms on a scale of 0 to 100. Younger adults had more impaired DGI scores and a higher proportion of caloric testing abnormalities. After rehabilitation, overall improvement was seen in both the younger and older populations. There were no statistical differences between the two groups on the DHI, the DGI, reported symptoms at discharge, or number of falls. When only the complete matched-pair data were analyzed, there were no statistically significant differences between the age groups in the proportion of patients demonstrating clinical improvement. Age does not significantly influence the beneficial effects of vestibular rehabilitation for persons with vestibular disorders.

Diagnostics for conformity of paired quantitative measurements.

Matched pairs data arise in many contexts - in case-control clinical trials, for example, and from cross-over designs. They also arise in experiments to verify the equivalence of quantitative assays. This latter use (which is the main focus of this paper) raises difficulties not always seen in other matched pairs applications. Since the designs deliberately vary the analyte levels over a wide range, issues of variance dependent on mean, calibrations of differing slopes, and curvature all need to be added to the usual model assumptions such as normality. Violations in any of these assumptions invalidate the conventional matched pairs analysis. A graphical method, due to Bland and Altman, of looking at the relationship between the average and the difference of the members of the pairs is shown to correspond to a formal testable regression model. Using standard regression diagnostics, one may detect and diagnose departures from the model assumptions and remedy them - for example using variable transformations. Examples of different common scenarios and possible approaches to handling them are shown.

Matched-pair cohort methods in traffic crash research

Standard analysis of matched-pair cohort data requires information only from pairs in which at least one had the study outcome. This can be useful in traffic fatality studies of characteristics that can vary among vehicle occupants, such as seat belt use, as crash databases often lack information about vehicles in which all survived. However, matching crash victims who were in the same vehicle does not necessarily eliminate confounding by vehicle or crash related factors, because the matched occupants must be in different seat positions. This paper reviews three methods for estimating relative risks in matched-pair crash data. The first, Mantel–Haenszel stratified methods, may produce biased estimates if seat position is associated with the outcome. The second, the double-pair comparison method, was designed to deal with confounding by seat position. If the effects of seat position vary according to some vehicle or crash characteristic which is associated with the study exposure, adjustment for this characteristic may be needed to produce unbiased estimates. Third, conditional Poisson regression and Cox proportional hazards regression can produce unbiased estimates, but may require model interaction terms between seat position and vehicle or crash characteristics. This paper reviews some of the strengths and limitations of each of these methods, and illustrates their use in simulated and real crash data.

Bayesian analysis of matched pairs

In this paper we address three main questions connected with the statistical analysis of matched pairs, mainly from a Bayesian viewpoint. These sort of data appear when measurements are made on the same individuals before and after a treatment is applied. The first question refers to the issue of how to construct statistical models for matched pairs data that reflect the dependendency of the posttreatment observation on the pretreatment one. The second one, addresses the problem of seeking for those statistical models for which inferences on the effect of the treatment only depends on some simple summaries of the data, for instance the differences or quotiens among the corresponding paired data. The third issue is concerned with testing the effectiveness or not of the treatment, that is, with testing whether or not the parameter which measures the effect has a definite value representing the no effect scenario. This problem is addressed here from a default model choice perspective. As an application of the preceding, the important additive normal model is fully analyzed. Finally, a nonparametric Bayesian test on the effectiveness of the treatment is developed. This is particularly appropriate when we are confident on the direction of the effectiveness or not of the treatment expressed by the data but not on its magnitude.

A Permutation Test for Nonindependent Matched Pair Data

The paired t-test and the Wilcoxon signed-rank test are often conducted to compare two continuous outcomes from paired observations. An assumption underlying these tests is that the responses from pair to pair are mutually independent. However, the assumption is violated in certain applications such as site-specific data in periodontal research. An adjustment to the paired t-test to account for the clustering effect has been well developed. But the adjustment relies on either large sample theory or the assumption that the observations being analyzed follow a normal distribution. In this paper, we propose a permutation test for matched pair clustered data which are valid in small samples. We developed and reviewed software to carry out the proposed test. The proposed test is applied to real-life data.

A Comparison of Models for Clustered Binary Outcomes: Analysis of a Designed Immunology Experiment

SUMMARY The lymphocyte proliferative assay (LPA) of immune competence was conducted on 52 subjects, with up to 36 processing conditions per subject, to evaluate whether samples could be shipped or stored overnight, rather than being processed on fresh blood as currently required. The LPA study resulted in clustered binary data, with both cluster level and cluster-varying covariates. Two modelling strategies for the analysis of such clustered binary data are through the cluster-specific and population-averaged approaches. Whereas most research in this area has focused on the analysis of matched pairs data, in many situations, such as the LPA study, cluster sizes are naturally larger. Through considerations of interpretation and efficiency of these models when applied to large clusters, the mixed effect cluster-specific model was selected as most appropriate for the analysis of the LPA data. The model confirmed that the LPA response is significantly impaired in individuals infected with the human immunodeficiency virus (HIV). The LPA response was found to be significantly lower for shipped and overnight samples than for fresh samples, and this effect was significantly stronger among HIV-infected individuals. Surprisingly, an anticoagulant effect was not detected.

Combined Quality Improvement Ratio: A Method for a More Robust Evaluation of Changes in Screening Rates

It has been proposed that a ratio of the discordant cells from a McNemar's Chi-square table be used as a measure of quality improvement, and that this measure be called the Quality Improvement Ratio (QuIR). As proposed, patients enrolled in only one year of a two-year study are excluded from the McNemar's table of the QuIR. Since the original proposal of the McNemar's Chi-square in 1947 included application to matched pair data, a more comprehensive analysis would be possible if the single-year enrollees were matched into pairs. Patients enrolled in only the first study year are matched and paired with patients enrolled in only the second study year. The pairs are matched on variables important to the disease or process being evaluated. The matched pairs are combined with the repeatedly measured subjects to increase the statistical power of the analysis. The Combined Quality Improvement Ratio (CQuIR) is demonstrated with parameters from the original articles, in a--Markov chain Monte-Carlo simulation, so a direct comparison can be made. CQuIR improved statistical power, especially in simulations of small populations. In some simulations the statistical power was double that of the QuIR alone. Although the QuIR provides important information, the CQuIR allows more of the data to be used to evaluate the effect of interventions in policy, delivery, and practice. The increase in statistical power of the CQuIR over the QuIR can facilitate successful evaluation of health care services.

Logrank test for bivariate survival data

The logrank test procedure for testing bivariate symmetry against asymmetry in matched-pair data is proposed. The presented test statistic is based on Mantel-Haenszel type statistics evaluated at diagonal grid points on the plane obtained from distinct uncensored failure times. The asymptotic results of the proposed test are derived and an example is shown to illustrate the methodology.

Methods for the Analysis of Pair-Matched Binary Data from School-based Intervention Studies

In the evaluation of school-based intervention programs, students' knowledge, behavior, and attitudes about a particular issue are typically assessed before and after the intervention. The effectiveness of the intervention can then be gauged by comparing these "pre-treatment" and "post-treatment" responses. In the most rigorous evaluations, students are randomized to the intervention or control group. However, instead of randomizing individual students to treatment, most school-based studies rely on clustered randomization schemes. This is generally operationalized as the assignment of schools to treatment condition, although students within schools serve as the units of observation. Because there tends to be positive correlation between responses from students at the same school, the assumption of statistical independence is violated; hence, application of statistical tests that ignore this correlation can result in biased significance levels. This paper explores two statistical methods that account for this correlation in analyzing binary data. A proposal for adapting these methods for application to matched pairs data is presented. The performance of the methods is evaluated via simulation study.

A Method for Comparing Positive Rates of Two Blood Culture Systems

McNemar's test is used to compare two marginal positive rates from an independent sample of paired binary data. When the pairs are not mutually independent, the McNemar's test may not be valid. In this paper, we propose a random-effects regression model for comparing two marginal probabilities from nonindependent matched pairs data with covariates. An example of comparing positive rates of two blood culture systems illustrates this method. In this example, there is no external gold standard, the paired data are clustered, the data with negative results from both systems are not available, and one culture-specific covariate is involved. The computing method for the maximum likelihood estimation is efficient.

A Prospective Study of Insulin Sensitivity and Glucose Metabolism in Women Using a Continuous Subdermal Levonorgestrel Implant System

Decreased insulin sensitivity and deterioration in oral glucose tolerance curves have been reported with oral contraceptive use, particularly with those containing levonorgestrel. However, the subdermal levonorgestrel systems release a lower dosage of steroid and avoid the first pass through the liver that occurs with oral administration. We hypothesized, therefore, that continuous subdermal levonorgestrel has no significant effect on insulin sensitivity and other indices of glucose metabolism. Nine women desiring a subdermal hormonal contraceptive system were recruited for this longitudinal prospective study. Each subject underwent a 3-hour frequently sampled intravenous glucose tolerance test immediately before insertion and after 6 months of continuous use. Insulin sensitivity and glucose effectiveness were determined using a mathematical minimal modeling approach. Glucose clearance and fasting and peak levels of glucose and insulin were examined as well. The matched-pair data were analyzed using paired t tests. There was no significant change in insulin sensitivity, glucose effectiveness, glucose clearance, or fasting or peak insulin levels. Fasting glucose levels remained within a normal range. Subdermal levonorgestrel appears to have no significant effect on tissue insulin sensitivity or glucose metabolism after 6 months of continuous use.

Statistical applications for in vitro diagnostic tests and other medical device clinical trials *

Some statistical methods applied to in vitro diagnostic tests for the three primary indications (screening, diagnosis, and monitoring) are discussed. Various examples with practical statistical applications are presented including test for k by k ordered categorical matched-pair data for screening of cervical cancer, receiver operating characteristic (ROC) curve for diagnosis or screening, and the Cox time-to-event model to estimate relative risk of first cancer progression by monitoring carcinoembryonic (CEA) levels for stage IV breast cancer patients.

Conditions for consistent estimation in mixed‐effects models for binary matched‐pairs data

AbstractParametric mixed‐effects logistic models can provide effective analysis of binary matched‐pairs data. Responses are assumed to follow a logistic model within pairs, with an intercept which varies across pairs according to a specified family of probability distributions G. In this paper we give necessary and sufficient conditions for consistent covariate effect estimation and present a geometric view of estimation which shows that when the assumed family of mixture distributions is rich enough, estimates of the effect of the binary covariate are typically consistent. The geometric view also shows that under the conditions for consistent estimation, the mixed‐model estimator is identical to the familar conditional‐likelihood estimator for matched pairs. We illustrate the findings with some examples.

State Public Lending Practice and Industrial Real Estate Mortgage Default: The New York Experience

This study assesses the relationship between selected public lender practices, real estate net equity, and industrial mortgage loan default. Seven lending practices and three advance indicators of default are tested on a matched-pair data set drawn from the second-mortgage portfolio of the New York State Job Development Authority (NYJDA). Results show that bankruptcy and negative net equity are strongly associated with default among the study population. No relationship is found between the strength of original loan guarantees or the lending subsidy and default. Also, negative net equity, liens, and late junior mortgages are useful predictors of default 1 year prior to the event. The NYJDA and similar public lenders should consider systematic monitoring of net equity, liens, late junior mortgages, and current financial statements of loan guarantors.

Micronucleus formation in peripheral-blood lymphocytes from smokers and the influence of alcohol- and tea-drinking habits.

In recent years, studies on the genotoxic effects of smoking and its modifying factors have been widely followed with interest. In this report, frequencies of micronuclei (MNF) in peripheral-blood lymphocytes in 220 healthy smokers have been detected by the micronucleus test by finger-skin puncture, which needs only 1 to 2 drops of peripheral blood. On the basis of analysis of matched-pair data, the modifying effects of alcohol and tea are discussed. Our results show that (I) smoking significantly increases MNF in lymphocytes as compared with healthy non-smokers (p less than 0.01); (2) alcohol significantly increases MNF in smokers (p less than 0.01); (3) tea decreases MNF induced by smoking (p less than 0.01). Therefore, the anti-carcinogenic role of tea merits further study.

Application of the McNemar test to non‐independent matched pair data

McNemar's one degree of freedom chi-square test for the equality of proportions appears frequently in the analysis of pairs of matched, binary outcome data (Y1i, Y2i). An assumption underlying this test is that the responses from pair to pair are mutually independent. In certain applications, however, the pairs may represent repeated measurements on the same experimental unit, and hence this assumption is violated. In this paper we suggest an adjustment to the McNemar test to account for the repeated measures clustering effect and we report on a Monte Carlo simulation that evaluates the effectiveness of this approach.

Some comments on analysis techniques for censored water quality data

When investigating trace substances in ambient water, a proportion of water sample concentrations is usually below limits of detection. In medical and industrial reliability studies, comparisons are often made of time to event data which includes right censored observations indicating only that an observation is greater than a specified value. In this paper consideration is given to the application of non-parametric procedures, widely used in the analysis of time to event data, to water quality data which is left censored.A non-parametric estimate of the cumulative distribution function for left censored water quality data can be generated quite easily. For the comparison of levels of trace substances it is necessary to combine an unconditional likelihood for the proportion of observations below a detection limit with a partial likelihood for the portion of the distribution above the detection limit in order to make use of regression methodology. The details of this are outlined and an example is given which compares levels of toxic substances at the head and mouth of the Niagara river.When comparisons are based on matched pair data, further modifications are necessary. A development paralleling that for time to event data is given. Consideration is also given to model extensions which allow for a dependence between observations at the same location over a period of time.The presentation is introductory and designed to illustrate the potential of some available methodology for use in the analysis of water quality data.