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In diagnostic radiology, the multireader multicase (MRMC) design and the free-response receiver operating characteristics (FROC) method are often used in combination. The cross-correlated data generated by the MRMC-FROC study leads to difficulties in the corresponding analysis, and the need to include covariates in the model further complicates the subsequent analysis. In this paper, we propose a regression approach based on three new measures with good interpretability. The correlation structure of the original test results is taken directly into account in the estimation procedure. The proposed method also allows the inclusion of continuous or discrete covariates. Consistent and asymptotically normal estimators are derived for the new measures. Simulation studies are conducted to evaluate the performance of the proposed approach. The simulation results show that the regression approach performs well under a wide range of scenarios. We also apply the proposed regression approach to a diagnostic study of computer-aided diagnosis in lung cancer.

Diagnostic accuracy, a measure of diagnostic tests for correctly identifying patients with or without a target disease, plays an important role in evidence-based medicine. Diagnostic accuracy of a new test ideally should be evaluated by comparing to a gold standard; however, in many medical applications it may be invasive, costly, or even unethical to obtain a gold standard for particular diseases. When the accuracy of a new candidate test under evaluation is assessed by comparison to an imperfect reference test, bias is expected to occur and result in either overestimates or underestimates of its true accuracy. In addition, diagnostic test studies often involve repeated measurements of the same patient, such as the paired eyes or multiple teeth, and generally lead to correlated and clustered data. Using the conventional statistical methods to estimate diagnostic accuracy can be biased by ignoring the within-cluster correlations. Despite numerous statistical approaches have been proposed to tackle this problem, the methodology to deal with correlated and clustered data in the absence of a gold standard is limited. In this article, we propose a method based on the composite likelihood function to derive simple and intuitive closed-form solutions for estimates of diagnostic accuracy, in terms of sensitivity and specificity. Through simulation studies, we illustrate the relative advantages of the proposed method over the existing methods that simply treat an imperfect reference test as a gold standard in correlated and clustered data. Compared with the existing methods, the proposed method can reduce not only substantial bias, but also the computational burden. Moreover, to demonstrate the utility of this approach, we apply the proposed method to the study of National-Eye-Institute-funded Telemedicine Approaches to Evaluating of Acute-Phase Retinopathy of Prematurity (e-ROP), for estimating accuracies of both the ophthalmologist examination and the image evaluation.

In prognosis studies to evaluate association between a continuous biomarker and a survival outcome, investigators often classify subjects into two subclasses of the high- and low-expression groups and apply simple survival analysis techniques of the Kaplan-Meier method and the logrank test. The high- and low-expressions are defined according to whether or not the observation of the biomarker is higher than the cut-off value, which is heterogeneous across studies. The heterogeneous definitions of the cut-off value make it difficult to apply the standard meta-analysis techniques. We propose a method to estimate the concordance index for a survival outcome synthesizing published prognosis studies, in which the Kaplan-Meier estimates for the high- and low-expression groups are reported. We illustrate our proposed method with a real dataset for meta-analysis of prognosis studies evaluating Ki-67 in early breast cancer and evaluate its performance with a simulation study.

Parallel-group thorough QT/QTc studies focus on the change of QT/QTc values at several time-matched points from a pretreatment day (baseline) to a posttreatment day for different groups of treatment. The International Council for Harmonisation E14 stresses that QTc prolongation beyond a threshold represents high cardiac risk and calls for a test on the largest time-matched treatment effect (QTc prolongation). QT/QTc analysis usually assumes a jointly multivariate normal (MVN) distribution of pretreatment and posttreatment QT/QTc values, with a blocked compound symmetry covariance matrix. Existing methods use an analysis of covariance (ANCOVA) model including day-averaged baseline as a covariate to deal with the MVN model. However, the ANCOVA model tends to underestimate the variation of the estimator for treatment effects, resulting in the inflation of empirical type I error rate when testing whether the largest QTc prolongation is beyond a threshold. In this article, we propose two new methods to estimate the time-matched treatment effects under the MVN model, including maximum likelihood estimation and ordinary-least-square-based two-stage estimation. These two methods take advantage of the covariance structure and are asymptotically efficient. Based on these estimators, powerful tests for QT/QTc prolongation are constructed. Simulation shows that the proposed estimators have smaller mean square error, and the tests can control the type I error rate with high power. The proposed methods are applied on testing the carryover effect of diltiazem to inhibit dofetilide in a randomized phase 1 trial.

Covariates associated with treatment-effect heterogeneity can potentially be used to make personalized treatment recommendations towards best clinical outcomes. Methods for treatment-selection rule development that directly maximize treatment-selection benefits have attracted much interest in recent years, due to the robustness of these methods to outcome modeling. In practice, the task of treatment-selection rule development can be further complicated by missingness in data. Here we consider the identification of optimal treatment-selection rules for a binary disease outcome when measurements of an important covariate from study participants are partly missing. Under the missing at random assumption, we develop a robust estimator of treatment-selection rules under the direct-optimization paradigm. This estimator targets the maximum selection benefits to the population under correct specification of at least one mechanism from each of the two sets — missing data or conditional covariate distribution, and treatment assignment or disease outcome model. We evaluate and compare performance of the proposed estimator with alternative direct-optimization estimators through extensive simulation studies. We demonstrate the application of the proposed method through a real data example from an Alzheimer’s disease study for developing covariate combinations to guide the treatment of Alzheimer’s disease.

Subject noncompliance is a common problem in the analysis of randomized clinical trials (RCTs). With cognitive behavioral interventions, the addition of provider noncompliance further complicates making causal inference. As a motivating example, we consider an RCT of a motivational interviewing (MI)-based behavioral intervention for treating problem drug use. Treatment receipt depends on compliance of both a therapist (provider) and a patient (subject), where MI is received when the therapist adheres to the MI protocol and the patient actively participates in the intervention. However, therapists cannot be forced to follow protocol and patients cannot be forced to cooperate in an intervention. In this article, we (1) define a causal estimand of interest based on a principal stratification framework, the average causal effect of treatment among provider-subject pairs that comply with assignment or ACE(cc); (2) explore possible assumptions that identify ACE(cc); (3) develop novel estimators of ACE(cc); (4) evaluate estimators' statistical properties via simulation; and (5) apply our proposed methods for estimating ACE(cc) to data from our motivating example.

Statistical agencies are releasing statistical data to other agencies for research purposes or to inform public policy. Prior to data release, these agencies have a legal and ethical obligation to protect the confidentiality of individuals in the data. Agencies often release altered versions of the data, but there usually remains risks of disclosure. Many well-studied risk measures are available to assess risk; however, many agencies today continue to use subjective judgement, past experience, and ad hoc rules or checklists to assess disclosure risk. More recently, there has been a recognized demand for quantitative risk measures that provide a more objective criteria for data release. This tutorial provides an overview of the statistical disclosure control framework for microdata. We focus on the risk analysis stage within this framework by defining existing disclosure risk measures and how to estimate them with available software.

Mediation analysis is a standard approach to understanding how and why an intervention works in social and medical sciences. However, the presence of missing data, especially missing not at random data, poses a great challenge for the applicability of this approach in practice. Current methods for handling such missingness are still lacking in causal mediation analysis. In this article, we first show the identifiability of causal mediation effects with different types of missing outcomes under different missingness mechanisms. We then provide corresponding approaches for estimation and inference. Especially for missing not at random data, we develop an estimating equation-based approach to estimate causal mediation effects, which can easily handle different types of mediators and outcomes, and we also establish the asymptotic results of the estimators. Simulation results show good performance for the proposed estimators in finite samples. Finally, we use a real data set from the Clinical Antipsychotic Trials of Intervention Effectiveness Research for Alzheimer disease to illustrate our approach.

Prognostic studies are widely conducted to examine whether biomarkers are associated with patient's prognoses and play important roles in medical decisions. Because findings from one prognostic study may be very limited, meta-analyses may be useful to obtain sound evidence. However, prognostic studies are often analyzed by relying on a study-specific cut-off value, which can lead to difficulty in applying the standard meta-analysis techniques. In this paper, we propose two methods to estimate a time-dependent version of the summary receiver operating characteristics curve for meta-analyses of prognostic studies with a right-censored time-to-event outcome. We introduce a bivariate normal model for the pair of time-dependent sensitivity and specificity and propose a method to form inferences based on summary statistics reported in published papers. This method provides a valid inference asymptotically. In addition, we consider a bivariate binomial model. To draw inferences from this bivariate binomial model, we introduce a multiple imputation method. The multiple imputation is found to be approximately proper multiple imputation, and thus the standard Rubin's variance formula is justified from a Bayesian view point. Our simulation study and application to a real dataset revealed that both methods work well with a moderate or large number of studies and the bivariate binomial model coupled with the multiple imputation outperforms the bivariate normal model with a small number of studies. Copyright © 2016 John Wiley & Sons, Ltd.

The objective of diagnostic studies or prognostic studies is to evaluate and compare predictive capacities of biomarkers. Suppose we are interested in evaluation and comparison of predictive capacities of continuous biomarkers for a binary outcome based on research synthesis. In analysis of each study, subjects are often classified into two groups of the high-expression and low-expression groups according to a cut-off value, and statistical analysis is based on a 2 × 2 table defined by the response and the high expression or low expression of the biomarker. Because the cut-off is study specific, it is difficult to interpret a combined summary measure such as an odds ratio based on the standard meta-analysis techniques. The summary receiver operating characteristic curve is a useful method for meta-analysis of diagnostic studies in the presence of heterogeneity of cut-off values to examine discriminative capacities of biomarkers. We develop a method to estimate positive or negative predictive curves, which are alternative to the receiver operating characteristic curve based on information reported in published papers of each study. These predictive curves provide a useful graphical presentation of pairs of positive and negative predictive values and allow us to compare predictive capacities of biomarkers of different scales in the presence of heterogeneity in cut-off values among studies. Copyright © 2016 John Wiley & Sons, Ltd.

In observational studies, estimation of average causal treatment effect on a patient's response should adjust for confounders that are associated with both treatment exposure and response. In addition, the response, such as medical cost, may have incomplete follow-up. In this article, a double robust estimator is proposed for average causal treatment effect for right censored medical cost data. The estimator is double robust in the sense that it remains consistent when either the model for the treatment assignment or the regression model for the response is correctly specified. Double robust estimators increase the likelihood the results will represent a valid inference. Asymptotic normality is obtained for the proposed estimator, and an estimator for the asymptotic variance is also derived. Simulation studies show good finite sample performance of the proposed estimator and a real data analysis using the proposed method is provided as illustration. Copyright © 2016 John Wiley & Sons, Ltd.

Individualized coefficient alpha is defined. It is item and subject specific and is used to measure the quality of test score data with heterogenicity among the subjects and items. A regression model is developed based on 3 sets of generalized estimating equations. The first set of generalized estimating equation models the expectation of the responses, the second set models the response's variance, and the third set is proposed to estimate the individualized coefficient alpha, defined and used to measure individualized internal consistency of the responses. We also use different techniques to extend our method to handle missing data. Asymptotic property of the estimators is discussed, based on which inference on the coefficient alpha is derived. Performance of our method is evaluated through simulation study and real data analysis. The real data application is from a health literacy study in Hunan province of China.

Statistical agencies are releasing statistical data to other agencies for research purposes or to inform public policy. Prior to data release, these agencies have a legal and ethical obligation to protect the confidentiality of individuals in the data. Agencies often release altered versions of the data, but there usually remains risks of disclosure. Many well-studied risk measures are available to assess risk; however, many agencies today continue to use subjective judgement, past experience, and ad hoc rules or checklists to assess disclosure risk. More recently, there has been a recognized demand for quantitative risk measures that provide a more objective criteria for data release. This tutorial provides an overview of the statistical disclosure control framework for microdata. We focus on the risk analysis stage within this framework by defining existing disclosure risk measures and how to estimate them with available software.

Publication bias is one of the most important issues in meta-analysis. For standard meta-analyses to examine intervention effects, the funnel plot and the trim-and-fill method are simple and widely used techniques for assessing and adjusting for the influence of publication bias, respectively. However, their use may be subjective and can then produce misleading insights. To make a more objective inference for publication bias, various sensitivity analysis methods have been proposed, including the Copas selection model. For meta-analysis of diagnostic studies evaluating a continuous biomarker, the summary receiver operating characteristic (sROC) curve is a very useful method in the presence of heterogeneous cutoff values. To our best knowledge, no methods are available for evaluation of influence of publication bias on estimation of the sROC curve. In this paper, we introduce a Copas-type selection model for meta-analysis of diagnostic studies and propose a sensitivity analysis method for publication bias. Our method enables us to assess the influence of publication bias on the estimation of the sROC curve and then judge whether the result of the meta-analysis is sufficiently confident or should be interpreted with much caution. We illustrate our proposed method with real data.

For censored survival outcomes, it can be of great interest to evaluate the predictive power of individual markers or their functions. Compared with alternative evaluation approaches, the time-dependent ROC (receiver operating characteristics) based approaches rely on much weaker assumptions, can be more robust, and hence are preferred. In this article, we examine evaluation of markers’ predictive power using the time-dependent ROC curve and a concordance measure which can be viewed as a weighted area under the time-dependent AUC (area under the ROC curve) profile. This study significantly advances from existing time-dependent ROC studies by developing nonparametric estimators of the summary indexes and, more importantly, rigorously establishing their asymptotic properties. It reinforces the statistical foundation of the time-dependent ROC based evaluation approaches for censored survival outcomes. Numerical studies, including simulations and application to an HIV clinical trial, demonstrate the satisfactory finite-sample performance of the proposed approaches.

This paper proposes a general framework of marker validation designs, which includes most of existing validation designs. The sample size calculation formulas for the proposed general design are derived on the basis of the optimal allocation that minimizes the expected number of treatment failures. The optimal allocation is especially important in the targeted design which is often motivated by preliminary evidence that marker-positive patients respond to one treatment better than the other. Our sample size calculation also takes into account the classification error of a marker. The numerical studies are conducted to investigate the expected reduction on the treatment failures and the relative efficiency between the targeted design and the traditional design based on the optimal ratios. We illustrate the calculation of the optimal allocation and sample sizes through a hypothetical stage II colon cancer trial.

Incomplete multi-level data arise commonly in many clinical trials and observational studies. Because of multi-level variations in this type of data, appropriate data analysis should take these variations into account. A random effects model can allow for the multi-level variations by assuming random effects at each level, but the computation is intensive because high-dimensional integrations are often involved in fitting models. Marginal methods such as the inverse probability weighted generalized estimating equations can involve simple estimation computation, but it is hard to specify the working correlation matrix for multi-level data. In this paper, we introduce a latent variable method to deal with incomplete multi-level data when the missing mechanism is missing at random, which fills the gap between the random effects model and marginal models. Latent variable models are built for both the response and missing data processes to incorporate the variations that arise at each level. Simulation studies demonstrate that this method performs well in various situations. We apply the proposed method to an Alzheimer’s disease study.

Two common problems in assessing the accuracy of traditional Chinese medicine (TCM) doctors in detecting a particular symptom are the unknown true symptom status and the ordinal-scale of the symptom status. Wang et al. (Biostatistics 2011; DOI: 10.1093/biostatistics/kxq075) proposed a nonparametric maximum likelihood method for estimating the accuracy of different TCM doctors without a gold standard when the true symptom status is measured on an ordinal-scale. A key assumption of their work is that the diagnosis results are independent conditional on the gold standard. This assumption can be violated in many practical situations.In this paper, we propose a random effects modeling approach that extends their method to incorporate dependence structure among different tests or doctors. The proposed method is illustrated on a real data set from TCM, which contains the diagnostic results from five doctors for the same patients regarding symptoms related to Chills disease. The same data set was analyzed by Wang et al. under the conditional independence assumption. In addition, we also discuss an ad hoc test for the model fitting and a likelihood ratio test on the random effects.

For many medical conditions, several treatment options may be available for treating patients. We consider evaluating markers based on a simple treatment selection policy that incorporates information on the patient's marker value. For example, colon cancer patients may be treated by surgery alone or surgery plus chemotherapy. The c-myc gene expression level may be used as a biomarker for treatment selection. Although traditional regression methods may assess the effect of the marker and treatment on outcomes, it is more appealing to quantify directly the potential impact on the population of using the marker to select treatment. A useful tool is the selection impact (SI) curve proposed by Song and Pepe for binary outcomes (Biometrics 2004; 60:874–883). However, the current SI method does not deal with continuous outcomes, nor does it allow to adjust for other covariates that are important for treatment selection. In this paper, we extend the SI curve for general outcomes, with a specific focus on survival time. We further propose the covariate-specific SI curve to incorporate covariate information in treatment selection. Nonparametric and semiparametric estimators are developed accordingly. We show that the proposed estimators are consistent and asymptotically normal. The performance is assessed by simulation studies and illustrated through an application to data from a cancer clinical trial. Copyright © 2011 John Wiley & Sons, Ltd.

To investigate major methods of design and statistical analysis in controlled clinical acupuncture trials published in the West during the past six years (2003-2009) and, based on this analysis, to provide recommendations that address methodological issues and challenges in clinical acupuncture research.PubMed was searched for acupuncture RCTs published in Western journals in English between 2003 and 2009. The keyword used was acupuncture.One hundred and eight qualified reports of acupuncture trials that included more than 30 symptoms/conditions were identified, analyzed, and grouped into efficacy (explanatory), effectiveness (pragmatically beneficial), and other (unspecified) studies. All were randomized controlled clinical trials (RCTs). In spite of significant improvement in the quality of acupuncture RCTs in the last 30 years, these reports show that some methodological issues and shortcomings in design and analysis remain. Moreover, the quality of the efficacy studies was not superior to that of the other types of studies. Research design and reporting problems include unclear patient criteria and inadequate practitioner eligibility, inadequate randomization, and blinding, deficiencies in the selection of controls, and improper outcome measurements. The problems in statistical analysis included insufficient sample sizes and power calculations, inadequate handling of missing data and multiple comparisons, and inefficient methods for dealing with repeated measure and cluster data, baseline value adjustment, and confounding issues.Despite recent advancements in acupuncture research, acupuncture RCTs can be improved, and more rigorous research methods should be carefully considered.

In biomedical studies, there are multiple sources of information available of which only a small number of them are associated with the diseases. It is of importance to select and combine these factors that are associated with the disease in order to predict the disease status of a new subject. The receiving operating characteristic (ROC) technique has been widely used in disease classification, and the classification accuracy can be measured with area under the ROC curve (AUC). In this article, we combine recent variable selection methods with AUC methods to optimize diagnostic accuracy of multiple risk factors. We first describe one new and some recent AUC-based methods for effectively combining multiple risk factors for disease classification. We then apply them to analyze the data from a new clinical study, investigating whether a combination of traditional Chinese medicine symptoms and standard Western medicine risk factors can increase discriminative accuracy in diagnosing osteoporosis (OP). Based on the results, we conclude that we can make a better diagnosis of primary OP by combining traditional Chinese medicine symptoms with Western medicine risk factors.

To estimate the multivariate regression model from multiple individual studies, it would be challenging to obtain results if the input from individual studies only provide univariate or incomplete multivariate regression information. Samsa et al. (J. Biomed. Biotechnol. 2005; 2:113–123) proposed a simple method to combine coefficients from univariate linear regression models into a multivariate linear regression model, a method known as synthesis analysis. However, the validity of this method relies on the normality assumption of the data, and it does not provide variance estimates. In this paper we propose a new synthesis method that improves on the existing synthesis method by eliminating the normality assumption, reducing bias, and allowing for the variance estimation of the estimated parameters.

In this paper, we propose a new semi-parametric maximum likelihood (ML) estimate of a receiver operating characteristic (ROC) curve that satisfies the property of invariance of the ROC curve and is easy to compute. We show that our new estimator is sqrt[n]-consistent and has an asymptotically normal distribution. Our extensive simulation studies show that the proposed method is efficient and robust. Finally, we illustrate the application of the proposed estimator in a real data set.

Two-phase designs are common in epidemiological studies of dementia, and especially in Alzheimer research. In the first phase, all subjects are screened using a common screening test(s), while in the second phase, only a subset of these subjects is tested using a more definitive verification assessment, i.e. golden standard test. When comparing the accuracy of two screening tests in a two-phase study of dementia, inferences are commonly made using only the verified sample. It is well documented that in that case, there is a risk for bias, called verification bias. When the two screening tests have only two values (e.g. positive and negative) and we are trying to estimate the differences in sensitivities and specificities of the tests, one is actually estimating a confidence interval for differences of binomial proportions. Estimating this difference is not trivial even with complete data. It is well documented that it is a tricky task. In this paper, we suggest ways to apply imputation procedures in order to correct the verification bias. This procedure allows us to use well-established complete-data methods to deal with the difficulty of the estimation of the difference of two binomial proportions in addition to dealing with incomplete data. We compare different methods of estimation and evaluate the use of multiple imputation in this case. Our simulation results show that the use of multiple imputation is superior to other commonly used methods. We demonstrate our finding using Alzheimer data.

In observational studies, estimation of average causal treatment effect on a patient's response should adjust for confounders that are associated with both treatment exposure and response. In addition, the response, such as medical cost, may have incomplete follow-up. In this article, a double robust estimator is proposed for average causal treatment effect for right censored medical cost data. The estimator is double robust in the sense that it remains consistent when either the model for the treatment assignment or the regression model for the response is correctly specified. Double robust estimators increase the likelihood the results will represent a valid inference. Asymptotic normality is obtained for the proposed estimator, and an estimator for the asymptotic variance is also derived. Simulation studies show good finite sample performance of the proposed estimator and a real data analysis using the proposed method is provided as illustration. Copyright © 2016 John WileySons, Ltd.

The objective of diagnostic studies or prognostic studies is to evaluate and compare predictive capacities of biomarkers. Suppose we are interested in evaluation and comparison of predictive capacities of continuous biomarkers for a binary outcome based on research synthesis. In analysis of each study, subjects are often classified into two groups of the high-expression and low-expression groups according to a cut-off value, and statistical analysis is based on a 2 × 2 table defined by the response and the high expression or low expression of the biomarker. Because the cut-off is study specific, it is difficult to interpret a combined summary measure such as an odds ratio based on the standard meta-analysis techniques. The summary receiver operating characteristic curve is a useful method for meta-analysis of diagnostic studies in the presence of heterogeneity of cut-off values to examine discriminative capacities of biomarkers. We develop a method to estimate positive or negative predictive curves, which are alternative to the receiver operating characteristic curve based on information reported in published papers of each study. These predictive curves provide a useful graphical presentation of pairs of positive and negative predictive values and allow us to compare predictive capacities of biomarkers of different scales in the presence of heterogeneity in cut-off values among studies. Copyright © 2016 John WileySons, Ltd.

Prognostic studies are widely conducted to examine whether biomarkers are associated with patient's prognoses and play important roles in medical decisions. Because findings from one prognostic study may be very limited, meta-analyses may be useful to obtain sound evidence. However, prognostic studies are often analyzed by relying on a study-specific cut-off value, which can lead to difficulty in applying the standard meta-analysis techniques. In this paper, we propose two methods to estimate a time-dependent version of the summary receiver operating characteristics curve for meta-analyses of prognostic studies with a right-censored time-to-event outcome. We introduce a bivariate normal model for the pair of time-dependent sensitivity and specificity and propose a method to form inferences based on summary statistics reported in published papers. This method provides a valid inference asymptotically. In addition, we consider a bivariate binomial model. To draw inferences from this bivariate binomial model, we introduce a multiple imputation method. The multiple imputation is found to be approximately proper multiple imputation, and thus the standard Rubin's variance formula is justified from a Bayesian view point. Our simulation study and application to a real dataset revealed that both methods work well with a moderate or large number of studies and the bivariate binomial model coupled with the multiple imputation outperforms the bivariate normal model with a small number of studies. Copyright © 2016 John WileySons, Ltd.

In the case in which all subjects are screened using a common test and only a subset of these subjects are tested using a golden standard test, it is well documented that there is a risk for bias, called verification bias. When the test has only two levels (e.g. positive and negative) and we are trying to estimate the sensitivity and specificity of the test, we are actually constructing a confidence interval for a binomial proportion. Since it is well documented that this estimation is not trivial even with complete data, we adopt multiple imputation framework for verification bias problem. We propose several imputation procedures for this problem and compare different methods of estimation. We show that our imputation methods are better than the existing methods with regard to nominal coverage and confidence interval length.

For a continuous-scale diagnostic test, it is of interest to construct a confidence interval for the sensitivity of the diagnostic test at the cut-off that yields a predetermined level of its specificity (for example, 80, 90 or 95 per cent). In this paper we propose two new intervals for the sensitivity of a continuous-scale diagnostic test at a fixed level of specificity. We then conduct simulation studies to compare the relative performance of these two intervals with the best existing BCa bootstrap interval, proposed by Platt et al. Our simulation results show that the newly proposed intervals are better than the BCa bootstrap interval in terms of coverage accuracy and interval length. Copyright © 2005 John Wiley & Sons, Ltd.

Medical costs data with administratively censored observations often arise in cost-effectiveness studies of treatments for life-threatening diseases. Mean of medical costs incurred from the start of a treatment until death or a certain time point after the implementation of treatment is frequently of interest. In many situations, due to the skewed nature of the cost distribution and non-uniform rate of cost accumulation over time, the currently available normal approximation confidence interval has poor coverage accuracy. In this paper, we propose a bootstrap confidence interval for the mean of medical costs with censored observations. In simulation studies, we show that the proposed bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution. When there is light censoring on medical costs (or =25 per cent), we found that the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy. For heavily censored cost data (censoring rateor =30 per cent) with larger sample sizes (nor =200), the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy. We also illustrate the use of our methods in a real example.

Before adopting a new diagnostic procedure, which is more convenient and less expensive than the standard existing procedure, it is essentially important to assess whether the diagnostic accuracy of the new procedure is non-inferior (or equivalent) to that of the standard procedure. In this paper, we consider the situation where test responses are on an ordinal scale with more than two categories. We give two definitions of non-inferiority, one in terms of the probability of correctly identifying the case for a randomly selected pair of a case and a non-case over all possible cut-off points, and the other in terms of both the sensitivity and specificity directly. On the basis of large sample theory, we develop two simple test procedures for detecting non-inferiority. We further conduct Monte Carlo simulation to evaluate the finite sample performance of these test procedures. We note that the two asymptotic test procedures proposed here can actually perform reasonably well in a variety of situations even when the numbers of studied subjects from the diseased and non-diseased populations are not large. To illustrate the use of the proposed test procedures, we include an example of determining whether the diagnostic accuracy of using a digitized film is non-inferior to that of using a plain film for screening breast cancer. Finally, we note that the extension of these results to accommodate the case of detecting (two-sided) equivalence is simply straightforward.

In this paper we compared four non-parametric kernel smoothing methods for estimating an ROC curve based on a continuous-scale test. All four methods produced a smooth ROC curve of the test. The difference in these four methods lay with the way they chose their bandwidth parameters. To assess the relative performance of the four bandwidth selection methods, we conducted a simulation study using different underlying distributions, along with varied sample sizes. The results from our simulation study suggested that the kernel smoothing method originally proposed by Altman and Léger for estimation of the distribution function was the best choice for estimation of an ROC curve. We illustrated these methods with a real example.

The three-arm clinical trial design, which includes a test treatment, an active reference, and placebo control, is the gold standard for the assessment of non-inferiority. In the presence of non-compliance, one common concern is that an intent-to-treat (ITT) analysis (which is the standard approach to non-inferiority trials), tends to increase the chances of erroneously concluding non-inferiority, suggesting that the per-protocol (PP) analysis may be preferable for non-inferiority trials despite its inherent bias. The objective of this paper was to develop statistical methodology for dealing with non-compliance in three-arm non-inferiority trials for censored, time-to-event data. Changes in treatment were here considered the only form of non-compliance. An approach using a three-arm rank preserving structural failure time model and G-estimation analysis is here presented. Using simulations, the impact of non-compliance on non-inferiority trials was investigated in detail using ITT, PP analyses, and the present proposed method. Results indicate that the proposed method shows good characteristics, and that neither ITT nor PP analyses can always guarantee the validity of the non-inferiority conclusion. A Statistical Analysis System program for the implementation of the proposed test procedure is available from the authors upon request.

Publication bias is an inevitable problem in the systematic review and meta-analysis. It is also one of the main threats to the validity of meta-analysis. Although several statistical methods have been developed to detect and adjust for the publication bias since the beginning of 1980s, some of them are not well known and are not being used properly in both the statistical and clinical literature. In this paper, we provided a critical and extensive discussion on the methods for dealing with publication bias, including statistical principles, implementation, and software, as well as the advantages and limitations of these methods. We illustrated a practical application of these methods in a meta-analysis of continuous support for women during childbirth. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper we propose five new tests for the equality of paired means of health care costs. The first two tests are the parametric tests, a Z-score test and a likelihood ratio test, both derived under the bivariate normality assumption for the log-transformed costs. The third test (Z-score with jack-knife) is a semi-parametric Z-score method, which only requires marginal log-normal assumptions. The last two tests are the non-parametric bootstrap tests: one is based on a t-test statistic, and the other is based on Johnson's modified t-test statistic. We conduct a simulation study to compare the performance of these tests, along with some commonly used tests when the sample size is small to moderate. The simulation results demonstrate that the commonly used paired t-test on the log-scale and the Wilcoxon signed rank for differences of the two original scales can yield type I error rates larger than the preset nominal levels. The commonly used paired t-test on the original data performs well with slightly skewed data, but can yield inaccurate results when two populations have different skewness. The likelihood ratio test, the parametric and semi-parametric Z-score tests all have very good type I error control with the likelihood ratio test being the best. However, the semi-parametric Z-score test requires less distributional assumptions than the two parametric tests. The percentile-t bootstrap test and bootstrapped Johnson's modified t-test have better type I error control than the paired t-test on the original-scale and Johnson's modified t-test, respectively. Combining with the propensity-score method, we can also apply the proposed methods to test the mean equality of two cost outcomes in the presence of confounders. Our two applications are from health services research. In the first one, we want to know the effect of Medicaid reimbursement policy change on outpatient health care costs. The second one is to evaluate the effect of a hospitalist programme on health care costs in an observational study, and the imbalanced covariates between intervention and control patients are taken into account using a propensity score approach.

Epidemiological studies of dementia often use two-stage designs because of the relatively low prevalence of the disease and the high cost of ascertaining a diagnosis. The first stage of a two-stage design assesses a large sample with a screening instrument. Then, the subjects are grouped according to their performance on the screening instrument, such as poor, intermediate and good performers. The second stage involves a more extensive diagnostic procedure, such as a clinical assessment, for a particular subset of the study sample selected from each of these groups. However, not all selected subjects have the clinical diagnosis because some subjects may refuse and others are unable to be clinically assessed. Thus, some subjects screened do not have a clinical diagnosis. Furthermore, whether a subject has a clinical diagnosis depends not only on the screening test result but also on other factors, and the sampling fractions for the diagnosis are unknown and have to be estimated. One of the goals in these studies is to assess the relative accuracies of two screening tests. Any analysis using only verified cases may result in verification bias. In this paper, we propose the use of two bootstrap methods to construct confidence intervals for the difference in the accuracies of two screening tests in the presence of verification bias. We illustrate the application of the proposed methods to a simulated data set from a real two-stage study of dementia that has motivated this research.

Medical cost data often exhibit strong skewness and sometimes contain large proportions of zero values. Such characteristics prevent the analysis of variance (ANOVA) F-test and other frequently used standard tests from providing the correct inferences when the comparison of means is of interest. One solution to the problem is to introduce a parametric structure based on log-normal distributions with zero values and then construct a likelihood ratio test. While such a likelihood ratio test possesses excellent type I error control and power, its implementation requires a rather complicated iterative optimization program. In this paper, we propose a Wald test with simple computation. We then conduct a Monte Carlo simulation to compare the type I error rates and powers of the proposed Wald test with those of the likelihood ratio test. Our simulation study indicates that although the likelihood ratio test slightly outperforms the Wald test, the performance of the Wald test is also satisfactory, especially when the sample sizes are reasonably large. Finally, we illustrate the use of the proposed Wald test by analysing a clinical study assessing the effects of a computerized prospective drug utilization intervention on in-patient charges.

An epidemiological study often uses a two-phase design to estimate the prevalence rate of a mental disease. In a two-phase design study, the first phase assesses a large sample with an inexpensive screening test, and then the second phase selects a subsample for a more expensive diagnostic evaluation. Furthermore, disease status may not be ascertained for all subjects who are selected for disease verification because some subjects are unable to be clinically assessed, while others may refuse. Since not all screened subjects are selected for diagnostic assessments, there is potential for verification bias. In this paper, we propose the maximum likelihood (ML) and bootstrap methods to correct for verification bias for estimating and comparing the prevalence rates under the missing-at-random (MAR) assumption for the verification mechanism. We also propose a method to test this MAR assumption. Finally, we apply our methods to a large-scale prevalence study of dementia disorders.

When several independent groups have conducted studies to estimate a procedure's success rate, it is often of interest to combine the results of these studies in the hopes of obtaining a better estimate for the true unknown success rate of the procedure. In this paper we present two hierarchical methods for estimating the overall rate of success. Both methods take into account the within-study and between-study variation and assume in the first stage that the number of successes within each study follows a binomial distribution given each study's own success rate. They differ, however, in their second stage assumptions. The first method assumes in the second stage that the rates of success from individual studies form a random sample having a constant expected value and variance. Generalized estimating equations (GEE) are then used to estimate the overall rate of success and its variance. The second method assumes in the second stage that the success rates from different studies follow a beta distribution. Both methods use the maximum likelihood approach to derive an estimate for the overall success rate and to construct the corresponding confidence intervals. We also present a two-stage bootstrap approach to estimating a confidence interval for the success rate when the number of studies is small. We then perform a simulation study to compare the two methods. Finally, we illustrate these two methods and obtain bootstrap confidence intervals in a medical example analysing the effectiveness of hyperdynamic therapy for cerebral vasospasm.

The most commonly used estimator for a log-normal mean is the sample mean. In this paper, we show that this estimator can have a large mean square error, even for large samples. Then, we study three main alternative estimators: (i) a uniformly minimum variance unbiased (UMVU) estimator; (ii) a maximum likelihood (ML) estimator; (iii) a conditionally minimal mean square error (MSE) estimator. We find that the conditionally minimal MSE estimator has the smallest mean square error among the four estimators considered here, regardless of the sample size and the skewness of the log-normal population. However, for large samples (n > or = 200), the UMVU estimator, the ML estimator, and the conditionally minimal MSE estimators have very similar mean square errors. Since the ML estimator is the easiest to compute among these three estimators, for large samples we recommend the use of the ML estimator. For small to moderate samples, we recommend the use of the conditionally minimal MSE estimator.

We conducted a simulation study to compare two semi-parametric approaches for the estimation of covariate effects from multivariate failure time data. The first approach was developed by Wei, Lin and Weissfeld (WLW) and the second by Liang, Self and Chang (LSC). Based on the simulation results we recommend Wei, Lin and Weissfeld's method for the situations with identical covariates and high correlations between the failure times. When the covariates are independent, LSC produces smaller mean squared errors than WLW, although at the expense of larger bias. We also compared four computer programs for implementing Wei, Lin and Weissfeld's approach: a FORTRAN program, MULCOX2; a SAS macro; the coxph function in S-plus, and a specialized software package for complex survey data (SUDAAN). Our comparison indicates that for large data sets, the speeds of the SAS macro and coxph are comparable, while MULCOX2- and SUDAAN took longer to run. However, MULCOX2 and coxph function in S-plus have the advantage of allowing time-dependent covariates, and SUDAAN has the advantage of handling complex survey data.

In this paper we conduct a stimulation study to evaluate coverage error, interval width and relative bias of four main methods for the construction of confidence intervals of log-normal means: the naive method; Cox's method; a conservative method; and a parametric bootstrap method. The simulation study finds that the naive method is inappropriate, that Cox's method has the smallest coverage error for moderate and large sample sizes, and that the bootstrap method has the smallest coverage error for small sample sizes. In addition, Cox's method produces the smallest interval width among the three appropriate methods. We also apply the four methods to a real data set to contrast the differences.

Knee replacement is the most commonly used surgical treatment for knee arthritis. It has been reported that knee replacement rates vary across both regions and counties. This paper used data from Medicare patients to develop explanations for the variation. One problem with our data is that we do not have patient level information for Medicare patients who did not have a knee replacement during the study period. Therefore, even though our data have a natural hierarchical structure (region, county, patient), we cannot use a typical hierarchical model for the analysis due to missing patient level information. In this paper, we used a two-stage approach to analyse our data. In the first stage, we used an extra Poisson regression to model within-region variation of knee replacement rates while adjusting for the type of patient demographic information we had, and in the second stage, we used an empirical Bayes method to model between-region variation of knee replacement rates.

Synthesis analysis refers to a statistical method that integrates multiple univariate regression models and the correlation between each pair of predictors into a single multivariate regression model. The practical application of such a method could be developing a multivariate disease prediction model where a dataset containing the disease outcome and every predictor of interest is not available. In this study, we propose a new version of synthesis analysis that is specific to binary outcomes. We show that our proposed method possesses desirable statistical properties. We also conduct a simulation study to assess the robustness of the proposed method and compare it to a competing method.

Analysis of health care cost data is often complicated by a high level of skewness, heteroscedastic variances and the presence of missing data. Most of the existing literature on cost data analysis have been focused on modeling the conditional mean. In this paper, we study a weighted quantile regression approach for estimating the conditional quantiles health care cost data with missing covariates. The weighted quantile regression estimator is consistent, unlike the naive estimator, and asymptotically normal. Furthermore, we propose a modified BIC for variable selection in quantile regression when the covariates are missing at random. The quantile regression framework allows us to obtain a more complete picture of the effects of the covariates on the health care cost and is naturally adapted to the skewness and heterogeneity of the cost data. The method is semiparametric in the sense that it does not require to specify the likelihood function for the random error or the covariates. We investigate the weighted quantile regression procedure and the modified BIC via extensive simulations. We illustrate the application by analyzing a real data set from a health care cost study.

Diagnostic trials often require the use of a homogeneity test among several markers. Such a test may be necessary to determine the power both during the design phase and in the initial analysis stage. However, no formal method is available for the power and sample size calculation when the number of markers is greater than two and marker measurements are clustered in subjects. This article presents two procedures for testing the accuracy among clustered diagnostic markers. The first procedure is a test of homogeneity among continuous markers based on a global null hypothesis of the same accuracy. The result under the alternative provides the explicit distribution for the power and sample size calculation. The second procedure is a simultaneous pairwise comparison test based on weighted areas under the receiver operating characteristic curves. This test is particularly useful if a global difference among markers is found by the homogeneity test. We apply our procedures to the BioCycle Study designed to assess and compare the accuracy of hormone and oxidative stress markers in distinguishing women with ovulatory menstrual cycles from those without.