Statistical Methods in Medical Research

Various confidence interval estimators have been developed for differences in proportions resulted from correlated binary data. However, the width of the mostly recommended Tango’s score confidence interval tends to be wide, and the computing burden of exact methods recommended for small-sample data is intensive. The recently proposed rank-based nonparametric method by treating proportion as special areas under receiver operating characteristic provided a new way to construct the confidence interval for proportion difference on paired data, while the complex computation limits its application in practice. In this article, we develop a new nonparametric method utilizing the U-statistics approach for comparing two or more correlated areas under receiver operating characteristics. The new confidence interval has a simple analytic form with a new estimate of the degrees of freedom of n − 1. It demonstrates good coverage properties and has shorter confidence interval widths than that of Tango. This new confidence interval with the new estimate of degrees of freedom also leads to coverage probabilities that are an improvement on the rank-based nonparametric confidence interval. Comparing with the approximate exact unconditional method, the nonparametric confidence interval demonstrates good coverage properties even in small samples, and yet they are very easy to implement computationally. This nonparametric procedure is evaluated using simulation studies and illustrated with three real examples. The simplified nonparametric confidence interval is an appealing choice in practice for its ease of use and good performance.

The time-dependent receiver operating characteristic curve is often used to study the diagnostic accuracy of a single continuous biomarker, measured at baseline, on the onset of a disease condition when the disease onset may occur at different times during the follow-up and hence may be right censored. Due to right censoring, the true disease onset status prior to the pre-specified time horizon may be unknown for some patients, which causes difficulty in calculating the time-dependent sensitivity and specificity. We propose to estimate the time-dependent sensitivity and specificity by weighting the censored data by the conditional probability of disease onset prior to the time horizon given the biomarker, the observed time to event, and the censoring indicator, with the weights calculated nonparametrically through a kernel regression on time to event. With this nonparametric weighting adjustment, we derive a novel, closed-form formula to calculate the area under the time-dependent receiver operating characteristic curve. We demonstrate through numerical study and theoretical arguments that the proposed method is insensitive to misspecification of the kernel bandwidth, produces unbiased and efficient estimators of time-dependent sensitivity and specificity, the area under the curve, and other estimands from the receiver operating characteristic curve, and outperforms several other published methods currently implemented in R packages.

In the modern era, cardiovascular biomarkers are often measured in the presence of medication use, such that the observed biomarker value for the treated participants is different than their underlying natural history value. However, for certain predictors (e.g. age, gender, and genetic exposures) the observed biomarker value is not of primary interest. Rather, we are interested in estimating the association between these predictors and the natural history of the biomarker that would have occurred in the absence of treatment. Nonrandom medication use obscures our ability to estimate this association in cross-sectional observational data. Structural equation methodology (e.g. the treatment effects model), while historically used to estimate treatment effects, has been previously shown to be a reasonable way to correct endogeneity bias when estimating natural biomarker associations. However, the assumption that the effects of medication use on the biomarker are uniform across participants on medication is generally not thought to be reasonable. We derive an extension of the treatment effects model to accommodate effect modification. Based on several simulation studies and an application to data from the Multi-Ethnic Study of Atherosclerosis, we show that our extension substantially improves bias in estimating associations of interest, particularly when effect modifiers are associated with the biomarker or with medication use, without a meaningful cost of efficiency.

The aim of this paper is to analyze the impact of response-adaptive randomization rules for normal response trials intended to test the superiority of one of two available treatments. Taking into account the classical Wald test, we show how response-adaptive methodology could induce a consistent loss of inferential precision. Then, we suggest a modified version of the Wald test which, by using the current allocation proportion to the treatments as a consistent estimator of the target, avoids some degenerate scenarios and so it should be preferable to the classical test. Furthermore, we show both analytically and via simulations how some target allocations may induce a locally decreasing power function. Thus, we derive the conditions on the target guaranteeing its monotonicity and we show how a correct choice of the initial sample size allows one to overcome this drawback regardless of the adopted target.

Early identification of individuals at risk for chronic diseases is of significant clinical value. Early detection provides the opportunity to slow the pace of a condition, and thus help individuals to improve or maintain their quality of life. Additionally, it can lessen the financial burden on health insurers and self-insured employers. As a solution to mitigate the rise in chronic conditions and related costs, an increasing number of employers have recently begun using wellness programs, which typically involve an annual health risk assessment. Unfortunately, these risk assessments have low detection capability, as they should be low-cost and hence rely on collecting relatively few basic biomarkers. Thus one may ask, how can we select a low-cost set of biomarkers that would be the most predictive of multiple chronic diseases? In this paper, we propose a statistical data-driven method to address this challenge by minimizing the number of biomarkers in the screening procedure while maximizing the predictive power over a broad spectrum of diseases. Our solution uses multi-task learning and group dimensionality reduction from machine learning and statistics. We provide empirical validation of the proposed solution using data from two different electronic medical records systems, with comparisons over a statistical benchmark.

Methods for detecting imprinting effects have been developed primarily for autosomal markers. However, no method is available in the literature to test for imprinting effects on X chromosome. Therefore, it is necessary to suggest methods for detecting such imprinting effects. In this article, the parental-asymmetry test on X chromosome (XPAT) is first developed to test for imprinting for qualitative traits in the presence of association, based on family trios each with both parents and their affected daughter. Then, we propose 1-XPAT to deal with parent–daughter pairs, each with one parent and his/her affected daughter. By simultaneously considering family trios and parent–daughter pairs, C-XPAT (the combined test statistic of XPAT and 1-XPAT) is constructed to test for imprinting. Further, we extend the proposed methods to accommodate complete (with both parents) and incomplete (with one parent) nuclear families having multiple daughters of which at least one is affected. Simulation results demonstrate that the proposed methods control the size well, irrespective of the inbreeding coefficient in females being zero or non-zero. By incorporating incomplete nuclear families, C-XPAT is more powerful than XPAT using only complete nuclear families. For practical use, these proposed methods are applied to analyse the rheumatoid arthritis data and Turner’s syndrome data.

The usefulness of two-class statistical classifiers is limited when one or both of the conditional misclassification rates is unacceptably high. Incorporating a neutral zone region into the classifier provides a mechanism to refer ambiguous cases to follow-up where additional information might be obtained to clarify the classification decision. Through the use of the neutral zone region, the conditional misclassification rates can be controlled and the classifier becomes useful. Three real-life examples, including applications to prostate cancer and kidney dysfunction following heart surgery, are used to illustrate how neutral zone regions can extract utility from disappointing classifiers that might otherwise be abandoned.

The concordance index is often used to measure how well a biomarker predicts the time to an event. Estimators of the concordance index for predictors of right-censored data are reviewed, including those based on censored pairs, inverse probability weighting and a proportional-hazards model. Predictive and prognostic biomarkers often lose strength with time, and in this case the aforementioned statistics depend on the length of follow up. A semi-parametric estimator of the concordance index is developed that accommodates converging hazards through a single parameter in a Pareto model. Concordance index estimators are assessed through simulations, which demonstrate substantial bias of classical censored-pairs and proportional-hazards model estimators. Prognostic biomarkers in a cohort of women diagnosed with breast cancer are evaluated using new and classical estimators of the concordance index.

We consider a two-group randomized clinical trial, where mortality affects the assessment of a follow-up continuous outcome. Using the worst-rank composite endpoint, we develop a weighted Wilcoxon–Mann–Whitney test statistic to analyze the data. We determine the optimal weights for the Wilcoxon–Mann–Whitney test statistic that maximize its power. We derive a formula for its power and demonstrate its accuracy in simulations. Finally, we apply the method to data from an acute ischemic stroke clinical trial of normobaric oxygen therapy.

It may not always be possible to blind participants of a randomized controlled trial for treatment allocation. As a result, estimators of the actual treatment effect may be biased. In this paper, we will extend a novel method, originally introduced in genetic research, for instrumental variable meta-analysis, adjusting for bias due to unblinding of trial participants. Using simulation studies, this novel method, “Egger Correction for non-Adherence”, is introduced and compared to the performance of the “intention-to-treat,” “as-treated,” and conventional “instrumental variable” estimators. Scenarios considered (time-varying) non-adherence, confounding, and between-study heterogeneity. The effect of treatment on a binary endpoint was quantified by means of a risk difference. In all scenarios with unblinded treatment allocation, the Egger Correction for non-Adherence method was the least biased estimator. However, unless the variation in adherence was relatively large, precision was lacking, and power did not surpass 0.50. As a comparison, in a meta-analysis of blinded randomized controlled trials, power of the conventional IV estimator was 1.00 versus at most 0.14 for the Egger Correction for non-Adherence estimator. Due to this lack of precision and power, we suggest to use this method mainly as a sensitivity analysis.

Estimating causal effects requires important prior subject-matter knowledge and, sometimes, sophisticated statistical tools. The latter is especially true when targeting the causal effect of a time-varying exposure in a longitudinal study. Marginal structural models are a relatively new class of causal models that effectively deal with the estimation of the effects of time-varying exposures. Marginal structural models have traditionally been embedded in the counterfactual framework to causal inference. In this paper, we use the causal graph framework to enhance the implementation of marginal structural models. We illustrate our approach using data from a prospective cohort study, the Honolulu Heart Program. These data consist of 8006 men at baseline. To illustrate our approach, we focused on the estimation of the causal effect of physical activity on blood pressure, which were measured at three time points. First, a causal graph is built to encompass prior knowledge. This graph is then validated and improved utilizing structural equation models. We estimated the aforementioned causal effect using marginal structural models for repeated measures and guided the implementation of the models with the causal graph. By employing the causal graph framework, we also show the validity of fitting conditional marginal structural models for repeated measures in the context implied by our data.

Hida and Tango established a statistical testing framework for the three-arm non-inferiority trial including a placebo with a pre-specified non-inferiority margin to overcome the shortcomings of traditional two-arm non-inferiority trials (such as having to choose the non-inferiority margin). In this paper, we propose a new method that improves their approach with respect to two aspects. We construct our testing statistics based on the best unbiased pooled estimators of the homogeneous variance; and we use the principle of intersection-union tests to determine the rejection rule. We theoretically prove that our test is better than that of Hida and Tango for large sample sizes. Furthermore, when that sample size was small or moderate, our simulation studies showed that our approach performed better than Hida and Tango’s. Although both controlled the type I error rate, their test was more conservative and the statistical power of our test was higher.

In this paper, we consider variable selection in rank regression models for longitudinal data. To obtain both robustness and effective selection of important covariates, we propose incorporating shrinkage by adaptive lasso or SCAD in the Wilcoxon dispersion function and establishing the oracle properties of the new method. The new method can be conveniently implemented with the statistical software R. The performance of the proposed method is demonstrated via simulation studies. Finally, two datasets are analyzed for illustration. Some interesting findings are reported and discussed.

To analyze univariate truncated normal data, in this paper, we stochastically represent the normal random variable as a mixture of a truncated normal random variable and its complementary random variable. This stochastic representation is a new idea and it is the first time to appear in literature. According to this stochastic representation, we derive important distributional properties for the truncated normal distribution and develop two new expectation–maximization algorithms to calculate the maximum likelihood estimates of parameters of interest for Type I data (without and with covariates) and Type II/III data. Bootstrap confidence intervals of parameters for small sample sizes are provided. To evaluate the performance of the proposed methods for the truncated normal distribution, in simulation studies, we first focus on the comparison of estimation results between including the unobserved data counts and excluding the unobserved data counts, and we next investigate the impact of the number of unobserved data on the estimation results. The plasma ferritin concentration data collected by Australian Institute of Sport and the blood fat content data are used to illustrate the proposed methods and to compare the truncated normal distribution with the half normal, the folded normal, and the folded normal slash distributions based on Akaike information criterion and Bayesian information criterion.

Double-sampling schemes using one classifier assessing the whole sample and another classifier assessing a subset of the sample have been introduced for reducing classification errors when an infallible or gold standard classifier is unavailable or impractical. Inference procedures have previously been proposed for situations where an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Here, we consider the case where both classifiers are fallible, proposing and evaluating several confidence interval procedures for a proportion under two models, distinguished by the assumption regarding ascertainment of two classifiers. Simulation results suggest that the modified Wald-based confidence interval, Score-based confidence interval, two Bayesian credible intervals, and the percentile Bootstrap confidence interval performed reasonably well even for small binomial proportions and small validated sample under the model with the conditional independent assumption, and the confidence interval derived from the Wald test with nuisance parameters appropriately evaluated, likelihood ratio-based confidence interval, Score-based confidence interval, and the percentile Bootstrap confidence interval performed satisfactory in terms of coverage under the model without the conditional independent assumption. Moreover, confidence intervals based on log- and logit-transformations also performed well when the binomial proportion and the ratio of the validated sample are not very small under two models. Two examples were used to illustrate the procedures.

Consistency of the propensity score estimators rely on correct specification of the propensity score model. The propensity score is frequently estimated using a main effect logistic regression. It has recently been shown that the use of ensemble machine learning algorithms, such as the Super Learner, could improve covariate balance and reduce bias in a meaningful manner in the case of serious model misspecification for treatment assignment. However, the loss functions normally used by the Super Learner may not be appropriate for propensity score estimation since the goal in this problem is not to optimize propensity score prediction but rather to achieve the best possible balance in the covariate distribution between treatment groups. In a simulation study, we evaluated the benefit of a modification of the Super Learner by propensity score estimation geared toward achieving covariate balance between the treated and untreated after matching on the propensity score. Our simulation study included six different scenarios characterized by various degrees of deviation from the usual main term logistic model for the true propensity score and outcome as well as the presence (or not) of instrumental variables. Our results suggest that the use of this adapted Super Learner to estimate the propensity score can further improve the robustness of propensity score matching estimators.

Population-based cancer screening is often asked but hardly addressed by a question: “How many rounds of screening are required before identifying a cancer of interest staying in the pre-clinical detectable phase (PCDP)?” and also a similar one related to the number of screens required for stopping screening for the low risk group. It can be answered by using longitudinal follow-up data on repeated rounds of screen, namely periodic screen, but such kind of data are rather complicated and fraught with intractable statistical properties including correlated multistate outcomes, unobserved and incomplete (censoring or truncation) information, and imperfect measurements. We therefore developed a negative-binomial-family-based discrete-time stochastic process, taking sensitivity and specificity into account, to accommodate these thorny issues. The estimation of parameters was implemented with Bayesian Markov Chain Monte Carlo method. We demonstrated how to apply this proposed negative-binomial-family-based model to the empirical data similar to the Finnish breast cancer screening program.

Copula mixed models for trivariate (or bivariate) meta-analysis of diagnostic test accuracy studies accounting (or not) for disease prevalence have been proposed in the biostatistics literature to synthesize information. However, many systematic reviews often include case-control and cohort studies, so one can either focus on the bivariate meta-analysis of the case-control studies or the trivariate meta-analysis of the cohort studies, as only the latter contains information on disease prevalence. In order to remedy this situation of wasting data we propose a hybrid copula mixed model via a combination of the bivariate and trivariate copula mixed model for the data from the case-control studies and cohort studies, respectively. Hence, this hybrid model can account for study design and also due to its generality can deal with dependence in the joint tails. We apply the proposed hybrid copula mixed model to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma.

There are several generalized linear mixed models to combine direct and indirect evidence on several diagnostic tests from related but independent diagnostic studies simultaneously also known as network meta-analysis. The popularity of these models is due to the attractive features of the normal distribution and the availability of statistical software to obtain parameter estimates. However, modeling the latent sensitivity and specificity using the normal distribution after transformation is neither natural nor computationally convenient.

In this article, we develop a meta-analytic model based on the bivariate beta distribution, allowing to obtain improved and direct estimates for the global sensitivities and specificities of all tests involved, and taking into account simultaneously the intrinsic correlation between sensitivity and specificity and the overdispersion due to repeated measures.

Using the beta distribution in regression has the following advantages, that the probabilities are modeled in their proper scale rather than a monotonic transform of the probabilities. Secondly, the model is flexible as it allows for asymmetry often present in the distribution of bounded variables such as proportions, which is the case with sparse data common in meta-analysis. Thirdly, the model provides parameters with direct meaningful interpretation since further integration is not necessary to obtain the meta-analytic estimates.