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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Restricted mean survival time is an alternative measure of treatment effect to hazard ratio in clinical trials with time-to-event outcome. The current methods have been focused on one-stage designs. ...In this article, we propose optimal two-stage designs for a single-arm study with the smallest expected sample size. We compare the performance of the new optimal two-stage designs with the existing one-stage design with regards to the expected sample size and the expected total study length. The simulation results indicate that the new two-stage designs can save the expected sample size substantially as compared to the one-stage design. We use a non-small cell lung cancer trial to illustrate the application of the proposed designs. The proposed optimal two-stage designs are recommended for use when time for patient accrual is longer than the pre-specified follow-up time.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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