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In recent years, adaptive randomization methods have gained significant popularity in clinical research and trial design due to their ability to provide both efficiency and flexibility in adjusting the statistical procedures of ongoing clinical trials. For a study to compare multiple treatments, a multi-arm two-stage design could be utilized to select the best treatment from the first stage and further compare that treatment with control in the second stage. The traditional design used equal randomization in both stages. To better utilize the interim results from the first stage, we propose to develop response adaptive randomization two-stage designs for a multi-arm clinical trial with binary outcome. Two allocation methods are considered: (1) an optimal allocation based on a sequential design; (2) the play-the-winner rule. Optimal multi-arm two-stage designs are obtained under three criteria: minimizing the expected number of failures, minimizing the average expected sample size, and minimizing the expected sample size under the null hypothesis. Simulation studies show that the proposed adaptive design based on the play-the-winner rule has good performance. A phase II trial for patients with pancreas adenocarcinoma and a germline BRCA $/$ / PALB2 mutation was used to illustrate the application of the proposed response adaptive randomization designs. [ABSTRACT FROM AUTHOR]

When multiple influential covariates need to be balanced during a clinical trial, stratified blocked randomization and covariate-adaptive randomization procedures are frequently used in trials to prevent bias and enhance the validity of data analysis results. The latter approach is increasingly used in practice for a study with multiple covariates and limited sample sizes. Among a group of these approaches, the covariate-adaptive procedures proposed by Pocock and Simon are straightforward to be utilized in practice. We aim to investigate the optimal design parameters for the patient treatment assignment probability of their developed three methods. In addition, we seek to answer the question related to the randomization performance when additional covariates are added to the existing randomization procedure. We conducted extensive simulation studies to address these practically important questions. [ABSTRACT FROM AUTHOR]

Background: It is unknown if fluid biomarkers reflective of brain pathologies are useful in detecting and following a neurodegenerative process in individuals exposed to repetitive head impacts. This study explores the relationship between blood biomarkers and longitudinal change in cognitive function and regional brain volumes in a cohort of professional fighters. Methods: Participants are drawn from a convenience sample of active and retired professional boxers and Mixed Martial Arts fighters and a control group with no prior exposure to head impacts. 3 T MRI brain imaging, plasma samples, and computerized cognitive testing were obtained at baseline and, for a subset, annually. MRI regional volumes were extracted, along with plasma levels of neurofilament light chain (NfL), glial fibrillary acidic protein (GFAP), p-tau231, and N-terminal tau (NTA). Statistical analyses were performed to assess the relationship between plasma levels and regional brain volumes and cognitive performance at baseline and longitudinally. Results: One hundred forty active boxers (mean age: 31 with standard deviation (SD) of 8), 211 active MMA (mean age of 30 with SD of 5), 69 retired boxers (mean age 49 with SD of 9), and 52 control participants (mean age 36 with SD of 12) were included in the analyses. Baseline GFAP levels were highest in the retired boxers (retired boxers v. active MMA: p = 0.0191), whereas active boxers had higher levels of NfL (active boxers v. MMA: p = 0.047). GFAP showed an increase longitudinally in retired boxers that was associated with decreasing volumes of multiple cortical and subcortical structures (e.g., hippocampus: B = − 1.25, 95% CI, − 1.65 to − 0.85) and increase in lateral ventricle size (B = 1.75, 95% CI, 1.46 to 2.04). Furthermore, performance on cognitive domains including memory, processing speed, psychomotor speed, and reaction time declined over time with increasing GFAP (e.g., processing speed: B = − 0.04, 95% CI, − 0.07 to − 0.02; reaction time: B = 0.52, 95% CI, 0.28 to 0.76). Among active fighters, increasing levels of GFAP were correlated with lower thalamic (B = − 1.42, 95% CI, − 2.34 to -0.49) and corpus callosum volumes, along with worsening scores on psychomotor speed (B = 0.14, 95% CI, 0.01 to 0.27). Conclusion: Longitudinal plasma GFAP levels may have a role in identifying individuals exposed to repetitive head impacts who are at risk of showing progressive regional atrophy and cognitive decline. [ABSTRACT FROM AUTHOR]

Response adaptive randomization has the potential to treat more participants in better treatments in a trial to benefit participants. We propose optimal response adaptive randomization designs for a two-stage study with binary response, having the smallest expected sample size or the fewest expected number of failures. Equal randomization is used in the first stage, and data from the first stage is used to determine the adaptive sample size ratio in the second stage. In the proposed optimal designs, the type I error rate and the statistical power are calculated from the asymptotic normal distributions. The new designs that minimize the expected number of failures have the advantage over the existing optimal randomized designs to substantially reduce the number of failures. [ABSTRACT FROM AUTHOR]

Adaptive designs are increasingly used in clinical trials to assess the effectiveness of new drugs. For a single-arm study with a binary outcome, several adaptive designs were developed by using numerical search algorithms and the conditional power approach. The design based on numerical search algorithms is able to identify the global optimal design, but the computational intensity limits the usage of these designs. The conditional power approach searches for the optimal design without expensive computing time. In addition, promising zone strategy was proposed to move on drug development to the follow-up stages when the interim results are promising. We propose to develop two adaptive designs: One based on the conditional power approach, and the other based on the promising zone strategy. These two designs preserve types I and II error rates. It is preferable to satisfy the monotonic property for adaptive designs: The second stage sample size decreases as the first stage responses go up. We theoretically prove this important property for the two proposed designs. The proposed designs can be easily applied to real trials with limited computing resources. [ABSTRACT FROM AUTHOR]

Objectives: Gallbladder cancer (GBC) is a rare, poor‐prognosis cancer with unique demographics, comorbidities and a paucity of research. This study investigated inpatient palliative care and its associations with demographics, comorbidities (e.g., obesity), length of stay and hospital charges in GBC in US hospitals (2007–2016). Methods: Data were extracted from the National Inpatient Sample (NIS) database that contains deidentified clinical and nonclinical information for each hospitalisation. Inpatient palliative care utilisation was identified using the International Classification of Diseases (ICD‐9 and ICD‐10) codes (V66.7 and Z51.5). Generalised regression analysis was conducted with adjustment for variations in predictors. Results: Of the 4921 reported GBC hospitalizations, only 10.3% encountered palliative care. Palliative care was associated with reduced hospital charges by $12,405 per hospitalisation (P < 0.0001) with no change in length of stay. Palliative care utilisation increased over time (P = 0.004). It was associated with age >80 years, with more severe disease, and in‐hospital death (P < 0.0001). Obesity had a negative association with palliative care utilisation (P = 0.0029). Discussion Our novel study found that obese people were less likely to use palliative care services in GBC. Interventions are needed to increase palliative care consultation in GBC patients, particularly in obese patients. [ABSTRACT FROM AUTHOR]

Intraclass correlation coefficient for data in a clustered study is traditionally estimated from a one-way random-effects model. This model assumes normality for the random cluster effect and the residual effect. When the normality assumption is questionable, we find that the estimated correlation could be much below the nominal level when data are highly skewed or data have low kurtosis. We develop a bias-corrected estimator based on the approach by Thomas and Hultquist for a study with unbalanced cluster sizes. For multivariate normal data or non-normal data with moderate skewness, we compare the performance of the new bias-corrected estimator with two existing estimators with regards to accuracy and precision. When correlation is small, the existing ANOVA estimator works well. When correlation is medium to large, the proposed new estimator has the correlation close to the nominal level, and its mean squared error is smaller than others. [ABSTRACT FROM AUTHOR]

Cross-validation (CV) is a resampling approach to evaluate machine learning models when sample size is limited. The number of all possible combinations of folds for the training data, known as CV rounds, are often very small in leave-one-out CV. Alternatively, Monte Carlo cross-validation (MCCV) can be performed with a flexible number of simulations when computational resources are feasible for a study with limited sample size. We conduct extensive simulation studies to compare accuracy between MCCV and CV with the same number of simulations for a study with binary outcome (e.g., disease progression or not). Accuracy of MCCV is generally higher than CV although the gain is small. They have similar performance when sample size is large. Meanwhile, MCCV is going to provide reliable performance metrics as the number of simulations increases. Two real examples are used to illustrate the comparison between MCCV and CV. [ABSTRACT FROM AUTHOR]

Asymptotic approaches are traditionally used to calculate confidence intervals for intraclass correlation coefficient in a clustered binary study. When sample size is small to medium, or correlation or response rate is near the boundary, asymptotic intervals often do not have satisfactory performance with regard to coverage. We propose using the importance sampling method to construct the profile confidence limits for the intraclass correlation coefficient. Importance sampling is a simulation based approach to reduce the variance of the estimated parameter. Four existing asymptotic limits are used as statistical quantities for sample space ordering in the importance sampling method. Simulation studies are performed to evaluate the performance of the proposed accurate intervals with regard to coverage and interval width. Simulation results indicate that the accurate intervals based on the asymptotic limits by Fleiss and Cuzick generally have shorter width than others in many cases, while the accurate intervals based on Zou and Donner asymptotic limits outperform others when correlation and response rate are close to their boundaries. [ABSTRACT FROM AUTHOR]

Interval-censored data occur in a study where the exact event time of each participant is not observed but it is known to be within a certain time interval. Multiple tests were proposed for such data, including the logrank test by Sun, the proportional hazard test by Finkelstein, and the Wilcoxon-type test by Peto and Peto. We propose sample size calculations based on these tests for a parallel one-stage or two-stage design. When the proportional hazard assumption is met, the proportional hazard test and the logrank test need smaller sample sizes than the Wilcoxon-type test, and the sample size savings are substantial. But this trend is reversed when the proportional hazard assumption does not hold, and the sample size savings using the Wilcoxon-type test are sizable. An example from a lung cancer clinical trial is used to illustrate the application of the proposed sample size calculations. [ABSTRACT FROM AUTHOR]

Repeated data are increasingly collected in studies to investigate the trajectory of change in measurements over time. Determining a link between one repeated measurement with another that is considered as the biomarker for disease progression, may provide a new target for drug development. When a third variable is associated with one of the two measurements, partial correlation after eliminating the effect of that variable is able to provide reliable estimate for association as compared to the existing raw correlation for repeated data. We propose using linear regression models to compute residuals by modeling a relationship between each measurement and a third variable. The computed residuals are then used in a linear mixed model (implemented by SAS Proc Mixed) to compute partial correlation for repeated data. Alternatively, the partial correlation may be computed as the average of partial correlations at each visit. We provide two real examples to illustrate the application of the proposed partial correlation and conduct extensive numerical studies to evaluate the proposed partial correlation coefficients. [ABSTRACT FROM AUTHOR]

Amyloid- β (A β ) is the target in many clinical trials for Alzheimer's disease (AD). Preclinical AD patients are heterogeneous with regards to different backgrounds and diagnosis. Accurately predicting A β status of participants by using machine learning (ML) models based on easily accessible data, could improve the effectiveness of AD clinical trials. We will develop optimal ML models for each subpopulation stratified by sex and disease stages using sub scores from screening neurological tests. Data from the AD Neuroimaging Initiative (ADNI) were used to build the ML models, for three groups: individuals with significant memory concern, early mild cognitive impairment (MCI), and late MCI. Data were further separated into 6 groups by disease stage (3 levels) and sex (2 categories). The outcome was defined as the A β status confirmed by the PET imaging, and the features include demographic data, newly identified risk factors, screening tests, and the domain scores from screening tests. Monte Carlo simulation studies were used together with k-fold cross-validation technique to compute model performance metric. We also develop a new feature selection method based on the stochastic ordering to avoiding searching all possible combinations of features. Accuracy of the identified optimal model for SMC male was over 90% by using domain scores, and accuracy for LMCI female was above 86%. Domain scores can improve the ML model prediction as compared to the total scores. Accurate ML prediction models can identify the proper population for AD clinical trials. [ABSTRACT FROM AUTHOR]

Clustered binary data are commonly encountered in many medical research studies with several binary outcomes from each cluster. Asymptotic methods are traditionally used for confidence interval calculations. However, these intervals often have unsatisfactory performance with regards to coverage for a study with a small sample size or the actual proportion near the boundary. To improve the coverage probability, exact Buehler's one-sided intervals may be utilized, but they are computationally intensive in this setting. Therefore, we propose using importance sampling to calculate confidence intervals that almost always guarantee the coverage. We conduct extensive simulation studies to compare the performance of the existing asymptotic intervals and the new accurate intervals using importance sampling. The new intervals based on the asymptotic Wilson score for sample space ordering perform better than others, and they are recommended for use in practice. [ABSTRACT FROM AUTHOR]

Sample size calculation based on normal approximations is often associated with the loss of statistical power for a single-arm trial with a time-to-event endpoint. Recently, Wu (2015) derived the exact variance for the one-sample log-rank test under the alternative and showed that a single-arm one-stage study based on exact variance often has power above the nominal level while the type I error rate is controlled. We extend this approach to a single-arm two-stage design by using exact variances of the one-sample log-rank test for the first stage and the two stages combined. The empirical power of the proposed two-stage optimal designs is often not guaranteed under a two-stage design setting, which could be due to the asymptotic bi-variate normal distribution used to estimate the joint distribution of the test statistics. We adjust the nominal power level in the design search to guarantee the simulated power of the identified optimal design being above the nominal level. The sample size and the study time savings of the proposed two-stage designs are substantial as compared to the one-stage design. [ABSTRACT FROM AUTHOR]

Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlation calculation are compared: (1) Pearson correlation; (2) correlation of subject means; (3) partial correlation for subject effect; (4) partial correlation for visit effect; and (5) a mixed model approach. Pearson correlation coefficient is traditionally used in a cross-sectional study. Pearson correlation is close to the correlations computed from mixed-effects models that consider the correlation structure, but Pearson correlation may not be theoretically appropriate in a repeated-measure study as it ignores the correlation of the outcomes from multiple visits within the same subject. We compare these methods with regard to the average of correlation and the mean squared error. In general, correlation under the mixed-effects model with the compound symmetric structure is recommended as its correlation is close to the nominal level with small mean square error. [ABSTRACT FROM AUTHOR]

To estimate the disease prevalence, a gold standard test is the best choice for accurate estimation. The gold standard could be very expensive or time consuming for use in practice. For this reason, a screening test may be used together with the gold standard to improve the test results, although the new test may not be as accurate as the gold standard. When some subjects in the study are tested by both tests and the remaining subjects are only tested by the screening test, this is a so-called double-sampling scheme. Data from such studies are partially validated. The prevalence of disease is often the parameter of interest from such studies. The traditionally used asymptotic approach based on limiting distributions of test statistics generally has unacceptable Type I error control. The approximate unconditional approach based on estimation was applied to this problem and shown to have a better performance than the asymptotic approach with regard to Type I error control. These approaches do not guarantee the Type I error rate. For this reason, we consider two exact approaches for testing the prevalence of disease for data from a double-sampling scheme. One is the exact approach based on maximization, and the other is the approach based on estimation and maximization. The approach based on estimation and maximization needs more computational cost than the approach based on maximization. The former approach is generally more powerful than the maximization approach, although the gain is negligible to small. We found that exact approaches based on the Wald-type test statistic with variance estimate using the restricted parameter estimates have a satisfactory performance as compared to exact approaches based on other test statistics. [ABSTRACT FROM AUTHOR]

More than half of the patients with Alzheimer's disease (AD) have comorbidities including TDP-43 and Lewy bodies, which are also associated with frontotemporal lobar degeneration and dementia with Lewy bodies, respectively. These comorbidities may help explain the overlapping neuropsychiatric symptoms between AD and other dementias. Data on 221 AD patients with Neuropsychiatric Inventory-Questionnaire were obtained from the National Alzheimer's Coordinating Center. TDP-43 was associated with aberrant motor activity, whereas Lewy bodies were associated with anxiety, irritability, sleep behavior, and appetite problems. The associations between these comorbidities and neuropsychiatric symptoms were more significant for patients with sparse diffuse plaques. [ABSTRACT FROM AUTHOR]

In a parallel group study comparing a new treatment with a standard of care, missing data often occur for various reasons. When the outcome is binary, the data from such studies can be summarized into a 2 × 3 contingency table, with the missing observations in the last column. When the missingness is neither related to the outcome of interest nor related to other outcomes from the study but it is covariate dependent with the sole covariate being treatment, this type of missing data mechanism is considered as missing at random. In 2016, Tian et al. proposed three statistics to test the hypothesis that the response rate is equivalent for a parallel group study with missing data. The asymptotic limiting distributions of these test statistics were used for statistical inference. However, asymptotic approaches for testing proportions generally do not have satisfactory performance with regard to type I error rate control for a clinical trial with the sample size from small to medium. For this reason, we consider an exact approach based on maximization to provide valid and efficient statistical inference for a parallel group study with missing data. Exact approaches can guarantee the type I error rate and they are computationally feasible in this setting. We conduct extensive numerical studies to compare the performance of the exact approach based on the three statistics for a one-sided hypothesis testing problem. We conclude that the exact approach based on the likelihood ratio statistic is more powerful than the exact approach based on the other two statistics. Two real clinical trial data sets are used to illustrate the application of the proposed exact approach. [ABSTRACT FROM AUTHOR]

Adaptive designs play an important role in contemporary clinical trials to make designs flexible and efficient. In cancer clinical trials, given a relatively small sample size, it is important to obtain as much information as possible during this phase. We propose a new adaptive optimal design that stops for futility only in the first stage as Simon's two-stage design. The existing adaptive two-stage designs are often allowed to be stopped for futility or efficacy due to computational advantage. It is difficult to search for an optimal design with futility stopping only in the first stage by using efficient search algorithms; for example, the branch-and-bound algorithm. We have to use multiple computational techniques to search for the optimal design. The proposed adaptive design meets the important property of the monotonic property that the second stage sample size is a nonincreasing function of the number of responses from the first stage. In this article, we show that the proposed adaptive design always has a smaller expected sample size than Simon's optimal design. We recommend it for use in practice as an alternative to the commonly used Simon's design. [ABSTRACT FROM AUTHOR]

To compare a new binary diagnostic test with the gold standard, sensitivity and specificity are the two common measurements used to evaluate the new test. When not all the patients are verified by the gold standard due to time, budget, or cost considerations, several approaches have been proposed to compute sample size for such studies under the assumption of missing completely at random. However, the majority of them are based on asymptotic approaches that generally do not guarantee the type I and II error rates, and the remaining approaches use exact binomial distributions in sample size calculation but only the verified samples are used. In this article, for a study with verification bias, we propose computing exact sample sizes by using all the samples. The proposed approach is compared with the existing exact approach that compute sample size by using verified samples only, and the results show that the proposed approach requires fewer participants than the competitor. [ABSTRACT FROM AUTHOR]

In addition to point estimate for the probability of response in a two-stage design (e.g. Simon's two-stage design for binary endpoints), confidence limits should be computed and reported. The current method of inverting the p-value function to compute the confidence interval does not guarantee coverage probability in a two-stage setting. The existing exact approach to calculate one-sided limits is based on the overall number of responses to order the sample space. This approach could be conservative because many sample points have the same limits. We propose a new exact one-sided interval based on p-value for the sample space ordering. Exact intervals are computed by using binomial distributions directly, instead of a normal approximation. Both exact intervals preserve the nominal confidence level. The proposed exact interval based on the p-value generally performs better than the other exact interval with regard to expected length and simple average length of confidence intervals. [ABSTRACT FROM AUTHOR]

In an agreement test between two raters with binary endpoints, existing methods for sample size calculation are always based on asymptotic approaches that use limiting distributions of a test statistic under null and alternative hypotheses. These calculated sample sizes may be not reliable due to the unsatisfactory type I error control of asymptotic approaches. We propose a new sample size calculation based on exact approaches which control for the type I error rate. The two exact approaches are considered: one approach based on maximization and the other based on estimation and maximization. We found that the latter approach is generally more powerful than the one based on maximization. Therefore, we present the sample size calculation based on estimation and maximization. A real example from a clinical trial to diagnose low back pain of patients is used to illustrate the two exact testing procedures and sample size determination. [ABSTRACT FROM AUTHOR]

Simon's two-stage designs are widely used in clinical trials to assess the activity of a new treatment. In practice, it is often the case that the second stage sample size is different from the planned one. For this reason, the critical value for the second stage is no longer valid for statistical inference. Existing approaches for making statistical inference are either based on asymptotic methods or not optimal. We propose an approach to maximize the power of a study while maintaining the type I error rate, where the type I error rate and power are calculated exactly from binomial distributions. The critical values of the proposed approach are numerically searched by an intelligent algorithm over the complete parameter space. It is guaranteed that the proposed approach is at least as powerful as the conditional power approach which is a valid but non-optimal approach. The power gain of the proposed approach can be substantial as compared to the conditional power approach. We apply the proposed approach to a real Phase II clinical trial. [ABSTRACT FROM AUTHOR]

Unconditional exact tests are increasingly used in practice for categorical data to increase the power of a study and to make the data analysis approach being consistent with the study design. In a two-arm study with a binary endpoint,p-value based on the exact unconditional Barnard test is computed by maximizing the tail probability over a nuisance parameter with a range from 0 to 1. The traditional grid search method is able to find an approximate maximum with a partition of the parameter space, but it is not accurate and this approach becomes computationally intensive for a study beyond two groups. We propose using a polynomial method to rewrite the tail probability as a polynomial. The solutions from the derivative of the polynomial contain the solution for the global maximum of the tail probability. We use an example from a double-blind randomized Phase II cancer clinical trial to illustrate the application of the proposed polynomial method to achieve an accuratep-value. We also compare the performance of the proposed method and the traditional grid search method under various conditions. We would recommend using this new polynomial method in computing accurate exact unconditionalp-values. [ABSTRACT FROM AUTHOR]

Simon's two-stage design has been widely used in early phase clinical trials to assess the activity of a new investigated treatment. In practice, the actual sample sizes do not always follow the study design precisely, especially in the second stage. When over- or under-enrollment occurs in a study, the original critical values for the study design are no longer valid for making proper statistical inference in a clinical trial. The hypothesis for such studies is always one-sided, and the null hypothesis is rejected when only a few responses are observed. Therefore, a one-sided lower interval is suitable to test the hypothesis. The commonly used approaches for confidence interval construction are based on asymptotic approaches. These approaches generally do not guarantee the coverage probability. For this reason, Clopper-Pearson approach can be used to compute exact confidence intervals. This approach has to be used in conjunction with a method to order the sample space. The frequently used method is based on point estimates for the response rate, but this ordering has too many ties which lead to conservativeness of the exact intervals. We propose developing exact one-sided intervals based on the p-value to order the sample space. The proposed approach outperforms the existing asymptotic and exact approaches. Therefore, it is recommended for use in practice. [ABSTRACT FROM AUTHOR]

This research was motivated by a clinical trial design for a cognitive study. The pilot study was a matched-pairs design where some data are missing, specifically the missing data coming at the end of the study. Existing approaches to determine sample size are all based on asymptotic approaches (e.g., the generalized estimating equation (GEE) approach). When the sample size in a clinical trial is small to medium, these asymptotic approaches may not be appropriate for use due to the unsatisfactory Type I and II error rates. For this reason, we consider the exact unconditional approach to compute the sample size for a matched-pairs study with incomplete data. Recommendations are made for each possible missingness pattern by comparing the exact sample sizes based on three commonly used test statistics, with the existing sample size calculation based on the GEE approach. An example from a real surgeon-reviewers study is used to illustrate the application of the exact sample size calculation in study designs. [ABSTRACT FROM AUTHOR]

This research is motivated by one of our survey studies to assess the potential influence of introducing zebra mussels to the Lake Mead National Recreation Area, Nevada. One research question in this study is to investigate the association between the boating activity type and the awareness of zebra mussels. A chi-squared test is often used for testing independence between two factors with nominal levels. When the null hypothesis of independence between two factors is rejected, we are often left wondering where does the significance come from. Cell residuals, including standardized residuals and adjusted residuals, are traditionally used in testing for cell significance, which is often known as a post hoc test after a statistically significant chi-squared test. In practice, the limiting distributions of these residuals are utilized for statistical inference. However, they may lead to different conclusions based on the calculated p-values, and their p-values could be over- o6r under-estimated due to the unsatisfactory performance of asymptotic approaches with regards to type I error control. In this article, we propose new exact p-values by using Fisher’s approach based on three commonly used test statistics to order the sample space. We theoretically prove that the proposed new exact p-values based on these test statistics are the same. Based on our extensive simulation studies, we show that the existing asymptotic approach based on adjusted residual is often more likely to reject the null hypothesis as compared to the exact approach due to the inflated family-wise error rates as observed. We would recommend the proposed exact p-value for use in practice as a valuable post hoc analysis technique for chi-squared analysis. [ABSTRACT FROM AUTHOR]

We consider four exact procedures to test the homogeneity of proportions for correlated multiple clustered data. Exact procedures are compared with the asymptotic approach based on the score statistic. We use a real example from a double-blind clinical trial studying the treatment of otitis media to illustrate the various test procedures and provide extensive numerical studies to compare procedures with regards to Type I error rates and powers under the unconditional framework. The exact unconditional procedure based on estimation followed by maximization is generally more powerful than other procedures. [ABSTRACT FROM AUTHOR]

In randomized complete block designs, a monotonic relationship among treatment groups may already be established from prior information, e.g., a study with different dose levels of a drug. The test statistic developed by Page and another from Jonckheere and Terpstra are two unweighted rank based tests used to detect ordered alternatives when the assumptions in the traditional two-way analysis of variance are not satisfied. We consider a new weighted rank based test by utilizing a weight for each subject based on the sample variance in computing the new test statistic. The new weighted rank based test is compared with the two commonly used unweighted tests with regard to power under various conditions. The weighted test is generally more powerful than the two unweighted tests when the number of treatment groups is small to moderate. [ABSTRACT FROM AUTHOR]

Cohen's kappa coefficient, κ, is a statistical measure of inter-rater agreement or inter-annotator agreement for qualitative items. In this paper, we focus on interval estimation of κ in the case of two raters and binary items. So far, only asymptotic and bootstrap intervals are available for κ due to its complexity. However, there is no guarantee that such intervals will capture κ with the desired nominal level 1- α. In other words, the statistical inferences based on these intervals are not reliable. We apply the Buehler method to obtain exact confidence intervals based on four widely used asymptotic intervals, three Wald-type confidence intervals and one interval constructed from a profile variance. These exact intervals are compared with regard to coverage probability and length for small to medium sample sizes. The exact intervals based on the Garner interval and the Lee and Tu interval are generally recommended for use in practice due to good performance in both coverage probability and length. [ABSTRACT FROM AUTHOR]

For a diagnostic test with continuous measurement, it is often important to construct confidence intervals for the sensitivity at a fixed level of specificity. Bootstrap-based confidence intervals were shown to have good performance as compared to others, and the one by Zhou and Qin (2005) was recommended as the best existing confidence interval, named the BTII interval. We propose two new confidence intervals based on the profile variance method and conduct extensive simulation studies to compare the proposed intervals and the BTII intervals under a wide range of conditions. An example from a medical study on severe head trauma is used to illustrate application of the new intervals. The new proposed intervals generally have better performance than the BTII interval. [ABSTRACT FROM AUTHOR]

The activity of a new treatment in clinical trials with binary endpoints can be assessed by comparing the observed response rate to the target response rate. Traditionally, a one-sided hypothesis is used to make statistical inference, and the actual Type I error rate has to be computed over the parameter space of the null hypothesis. The monotonicity property is a fundamental property that guarantees the actual Type I error rate occurring at the boundary. One-arm two-stage designs are considered in this article. We theoretically proved this important property when the final threshold value of a design is less than the first-stage sample size together with another weak condition being satisfied. The method used in this article may finally lead to the final complete proof of this property in the future. We also numerically proved that the monotonicity property is satisfied for designs with the first-stage and the second-stage sample sizes from 10 to 100. [ABSTRACT FROM PUBLISHER]

We present sample size determination using exact approaches for testing the ratio of incidence rates from a two-arm non-inferiority trial. The first approach is the exact conditional approach by treating the total number of events from two groups fixed, and the other is the exact unconditional approach based on maximization. Exact approaches guarantee the type I error rate which is often not satisfied in the commonly used asymptotic approaches on the basis of the corresponding limiting distributions of test statistics. We provide tables for sample size determination in commonly used cases in practice, and an example is used to show the application of these exact approaches. Sample size comparison using different exact approaches concludes that the exact unconditional approach based on the Wald-type test statistic has good performance in balanced studies. [ABSTRACT FROM AUTHOR]

For surveys with sensitive questions, randomized response sampling strategies are often used to increase the response rate and encourage participants to provide the truth of the question while participants' privacy and confidentiality are protected. The proportion of responding ‘yes’ to the sensitive question is the parameter of interest. Asymptotic confidence intervals for this proportion are calculated from the limiting distribution of the test statistic, and are traditionally used in practice for statistical inference. It is well known that these intervals do not guarantee the coverage probability. For this reason, we apply the exact approach, adjusting the critical value as in [10], to construct the exact confidence interval of the proportion based on the likelihood ratio test and three Wilson-type tests. Two randomized response sampling strategies are studied: the Warner model and the unrelated model. The exact interval based on the likelihood ratio test has shorter average length than others when the probability of the sensitive question is low. Exact Wilson intervals have good performance in other cases. A real example from a survey study is utilized to illustrate the application of these exact intervals. [ABSTRACT FROM PUBLISHER]

Simon's optimal two-stage design has been widely used in early phase clinical trials for Oncology and AIDS studies with binary endpoints. With this approach, the second-stage sample size is fixed when the trial passes the first stage with sufficient activity. Adaptive designs, such as those due to Banerjee and Tsiatis (2006) and Englert and Kieser (2013), are flexible in the sense that the second-stage sample size depends on the response from the first stage, and these designs are often seen to reduce the expected sample size under the null hypothesis as compared with Simon's approach. An unappealing trait of the existing designs is that they are not associated with a second-stage sample size, which is a non-increasing function of the first-stage response rate. In this paper, an efficient intelligent process, the branch-and-bound algorithm, is used in extensively searching for the optimal adaptive design with the smallest expected sample size under the null, while the type I and II error rates are maintained and the aforementioned monotonicity characteristic is respected. The proposed optimal design is observed to have smaller expected sample sizes compared to Simon's optimal design, and the maximum total sample size of the proposed adaptive design is very close to that from Simon's method. The proposed optimal adaptive two-stage design is recommended for use in practice to improve the flexibility and efficiency of early phase therapeutic development. [ABSTRACT FROM AUTHOR]

In historical clinical trials, the sample size and the number of success in the control group are often considered as given. The traditional method for sample size calculation is based on an asymptotic approach developed by Makuch and Simon (1980). Exact unconditional approaches may be considered as alternative to control for the type I error rate where the asymptotic approach may fail to do so. We provide the sample size calculation using an efficient exact unconditional testing procedure based on estimation and maximization. The sample size using the exact unconditional approach based on estimation and maximization is generally smaller than those based on the other approaches. [ABSTRACT FROM PUBLISHER]

We consider two exact unconditional procedures to test the difference between two multinomials with ordered categorical data. Exact unconditional procedures are compared to other approaches based on the Wilcoxon mid-rank test and the proportional odds model. We use a real example from an arthritis pain study to illustrate the various test procedures and provide an extensive numerical study to compare procedures with regards to type I error rates and power under the unconditional framework. The exact unconditional procedure based on estimation followed by maximization is generally more powerful than other procedures, and is therefore recommended for use in practice. [ABSTRACT FROM AUTHOR]

For comparison of proportions, there are three commonly used measurements: the difference, the relative risk, and the odds ratio. Significant effort has been spent on exact confidence intervals for the difference. In this article, we focus on the relative risk and the odds ratio when data are collected from a matched-pairs design or a two-arm independent binomial experiment. Exact one-sided and two-sided confidence intervals are proposed for each configuration of two measurements and two types of data. The one-sided intervals are constructed using an inductive order, they are the smallest under the order, and are admissible under the set inclusion criterion. The two-sided intervals are the intersection of two one-sided intervals. R codes are developed to implement the intervals. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The Youden Index is a summary measurement of the receiver operating characteristic (ROC) curve for the accuracy of a diagnostic test with ordinal or continuous endpoints. The bootstrap confidence interval based on the adjusted proportion estimate was shown to have satisfactory performance among the existing confidence intervals, including the parametric interval via the delta method. In this article, we propose two confidence intervals using the square-and-add limits based on the Wilson score method. We compare the two proposed intervals with the existing interval with extensive simulation studies. The new interval based on the empirical proportion estimate generally has better performance than that based on the adjusted proportion estimate. A real example from a clinical trial of prostate cancer is illustrated for the application of the new intervals. [ABSTRACT FROM AUTHOR]

In ophthalmologic studies, measurements obtained from both eyes of an individual are often highly correlated. Ignoring the correlation could lead to incorrect inferences. An asymptotic method was proposed by Tang and others (2008) for testing equality of proportions between two groups under Rosner's model. In this article, we investigate three testing procedures for general g ≥ 2 groups. Our simulation results show the score testing procedure usually produces satisfactory type I error control and has reasonable power. The three test procedures get closer when sample size becomes larger. Examples from ophthalmologic studies are used to illustrate our proposed methods. [ABSTRACT FROM AUTHOR]

We consider seven exact unconditional testing procedures for comparing adjusted incidence rates between two groups from a Poisson process. Exact tests are always preferable due to the guarantee of test size in small to medium sample settings. Han [Comparing two independent incidence rates using conditional and unconditional exact tests. Pharm Stat. 2008;7(3):195–201] compared the performance of partial maximizationp-values based on the Wald test statistic, the likelihood ratio test statistic, the score test statistic, and the conditionalp-value. These four testing procedures do not perform consistently, as the results depend on the choice of test statistics for general alternatives. We consider the approach based on estimation and partial maximization, and compare these to the ones studied by Han (2008) for testing superiority. The procedures are compared with regard to the actual type I error rate and power under various conditions. An example from a biomedical research study is provided to illustrate the testing procedures. The approach based on partial maximization using the score test is recommended due to the comparable performance and computational advantage in large sample settings. Additionally, the approach based on estimation and partial maximization performs consistently for all the three test statistics, and is also recommended for use in practice. [ABSTRACT FROM AUTHOR]

The asymptotic approach and Fisher's exact approach have often been used for testing the association between two dichotomous variables. The asymptotic approach may be appropriate to use in large samples but is often criticized for being associated with unacceptable high actual type I error rates for small to medium sample sizes. Fisher's exact approach suffers from conservative type I error rates and low power. For these reasons, a number of exact unconditional approaches have been proposed, which have been seen to be generally more powerful than exact conditional counterparts. We consider the traditional unconditional approach based on maximization and compare it to our presented approach, which is based on estimation and maximization. We extend the unconditional approach based on estimation and maximization to designs with the total sum fixed. The procedures based on the Pearson chi-square, Yates's corrected, and likelihood ratio test statistics are evaluated with regard to actual type I error rates and powers. A real example is used to illustrate the various testing procedures. The unconditional approach based on estimation and maximization performs well, having an actual level much closer to the nominal level. The Pearson chi-square and likelihood ratio test statistics work well with this efficient unconditional approach. This approach is generally more powerful than the other p-value calculation methods in the scenarios considered. [ABSTRACT FROM AUTHOR]

We propose a new nonparametric test for ordered alternative problem based on the rank difference between two observations from different groups. These groups are assumed to be independent from each other. The exact mean and variance of the test statistic under the null distribution are derived, and its asymptotic distribution is proven to be normal. Furthermore, an extensive power comparison between the new test and other commonly used tests shows that the new test is generally more powerful than others under various conditions, including the same type of distribution, and mixed distributions. A real example from an anti-hypertensive drug trial is provided to illustrate the application of the tests. The new test is therefore recommended for use in practice due to easy calculation and substantial power gain. [ABSTRACT FROM AUTHOR]

Asymptotic and exact conditional approaches have often been used for testing agreement between two raters with binary outcomes. The exact conditional approach is guaranteed to respect the test size as compared to the traditionally used asymptotic approach based on the standardized Cohen's kappa coefficient. An alternative to the conditional approach is an unconditional strategy which relaxes the restriction of fixed marginal totals as in the conditional approach. Three exact unconditional hypothesis testing procedures are considered in this article: an approach based on maximization, an approach based on the conditional p-value and maximization, and an approach based on estimation and maximization. We compared these testing procedures based on the commonly used Cohen's kappa with regards to test size and power. We recommend the following two exact approaches for use in practice due to power advantages: the approach based on conditional p-value and maximization and the approach based on estimation and maximization. [ABSTRACT FROM AUTHOR]

In areas such as oncology, two-stage designs are often preferred as compared to one-stage designs due to the ability to stop the trial early when faced with evidence of lack of sufficient efficacy and the associated sample size savings. We present exact two-stage designs based on Barnard's exact test for differences in proportions and compare the designs to those proposed by Kepner (2010) and Jung (2010). In addition, we present tables of decision rules under a variety of assumed realities for use in trial planning. The procedure is recommended for use due to the substantial sample size savings experienced. [ABSTRACT FROM PUBLISHER]

In preclinical studies and clinical dose-ranging trials, the Jonckheere-Terpstra test is widely used in the assessment of dose-response relationships. Hewett and Spurrier (1979) presented a two-stage analog of the test in the context of large sample sizes. In this paper, we propose an exact test based on Simon's minimax and optimal design criteria originally used in one-arm phase II designs based on binary endpoints. The convergence rate of the joint distribution of the first and second stage test statistics to the limiting distribution is studied, and design parameters are provided for a variety of assumed alternatives. The behavior of the test is also examined in the presence of ties, and the proposed designs are illustrated through application in the planning of a hypercholesterolemia clinical trial. The minimax and optimal two-stage procedures are shown to be preferable as compared with the one-stage procedure because of the associated reduction in expected sample size for given error constraints. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Features common to phase II clinical trials include limited knowledge of the experimental treatment being evaluated, design components reflecting ethical considerations, and small to moderate sample sizes as a result of resource constraints. It is for these reasons that there exist many two-stage designs proposed in the literature for use in this context. The majority of these designs are for binary endpoints and based on exact probability calculations, or are for continuous endpoints and rooted in asymptotic approximations to the null distribution. We present exact two-stage Mann–Whitney designs in the context of two-arm randomized clinical trials. In addition to describing the designs, we present tables of decision rules under a variety of assumed realities for use in trial planning. [Copyright &y& Elsevier]

Lloyd ( Aust. Nz. J. Stat., 50, 329-345, 2008) developed an exact testing approach to control for nuisance parameters, which was shown to be advantageous in testing for differences between two population proportions. We utilized this approach to obtain unconditional tests for trends in 2 × K contingency tables. We compare the unconditional procedure with other unconditional and conditional approaches based on the well-known Cochran-Armitage test statistic. We give an example to illustrate the approach, and provide a comparison between the methods with regards to type I error and power. The proposed procedure is preferable because it is less conservative and has superior power properties. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The Inverse Gaussian (IG) distribution is commonly introduced to model and examine right skewed data having positive support. When applying the IG model, it is critical to develop efficient goodness-of-fit tests. In this article, we propose a new test statistic for examining the IG goodness-of-fit based on approximating parametric likelihood ratios. The parametric likelihood ratio methodology is well-known to provide powerful likelihood ratio tests. In the nonparametric context, the classical empirical likelihood (EL) ratio method is often applied in order to efficiently approximate properties of parametric likelihoods, using an approach based on substituting empirical distribution functions for their population counterparts. The optimal parametric likelihood ratio approach is however based on density functions. We develop and analyze the EL ratio approach based on densities in order to test the IG model fit. We show that the proposed test is an improvement over the entropy-based goodness-of-fit test for IG presented by . Theoretical support is obtained by proving consistency of the new test and an asymptotic proposition regarding the null distribution of the proposed test statistic. Monte Carlo simulations confirm the powerful properties of the proposed method. Real data examples demonstrate the applicability of the density-based EL ratio goodness-of-fit test for an IG assumption in practice. [Copyright &y& Elsevier]