Multiple assessments of non-inferiority trials with ordinal endpoints.

Non-inferiority (NI) trials are implemented when there is a practical demand to search for alternatives to standard therapies, such as to reduce side effects. An experimental treatment is considered non-inferior to the standard treatment when it exhibits clinically non-significant loss of efficacy. Ordinal categorical responses are frequently observed in clinical trials. It has been reported that responses measured using an ordinal scale produce more informative analysis than when responses collapse into binary outcomes. We study the NI trials using ordinal endpoints. We propose a latent variable model for ordinal categorical responses. Based on the proposed latent variable model, the mean efficacy of the different treatments is denoted by the corresponding mean parameter of the underlying continuous distributions. A two-step procedure is proposed for model identification and parameter estimation. A non-inferiority analysis can then be conducted based on the latent variable model and the corresponding estimation procedure. We also develop a method and an algorithm to produce an optimal sample size configuration based on the proposed testing procedure. Two clinical examples are provided for demonstrative purposes.

Response-adaptive treatment allocation for clinical studies with ordinal responses.

Ordinal responses are common in clinical studies. Although the proportional odds model is a popular option for analyzing ordered-categorical data, it cannot control the type I error rate when the proportional odds assumption fails to hold. The latent Weibull model was recently shown to be a superior candidate for modeling ordinal data, with remarkably better performance than the latent normal model when the data are highly skewed. In clinical trials with ordinal responses, a balanced design is common, with equal sample allocation for each treatment. However, a more ethical approach is to adopt a response-adaptive allocation scheme in which more patients receive the better treatment. In this paper, we propose the use of the doubly adaptive biased coin design to generate treatment allocations that benefit the trial participants. The proposed treatment allocation scheme not only allows more patients to receive the better treatment, it also maintains compatible test power for the comparison of treatment efficiencies. A clinical example is used to illustrate the proposed procedure.

Patterns of Failure and Survival Trends Of 720 Patients with Stage I Nasopharyngeal Carcinoma Diagnosed from 1990-2012: A Large-scale Retrospective Cohort Study.

Objectives: To evaluate the patterns of failure and survival trends of patients with stage I nasopharyngeal carcinoma (NPC) treated with radiotherapy alone over the last 20 years. Materials and Methods: A retrospective cohort study was conducted on 720 patients with stage I NPC who were treated with curative two-dimensional radiotherapy (2DRT), three-dimensional conformal radiotherapy (3DRT), or intensity-modulated radiotherapy (IMRT) between January 1990 and December 2012. The patients were categorized into four calendar periods (1990-1996, 1997-2002, 2003-2007, and 2008-2012) and four age subgroups (18-39, 40-49, 50-59, and >60). We computed overall survival (OS), progression free survival (PFS), locoregional relapse free survival (LRFS) and distant metastasis free survival (DMFS) as measures of patient survival. Results: After a median follow-up period of 105 months (range 1-280 months), we observed the increasing trends in survival and disease control. The 3-, 5-, and 7-year OS rates increased from 97.0%, 86.7%, and 81.7% in the first calendar period (1990-1996) to 100%, 99.3%, and 98.0% in the last calendar period (2008-2012), respectively (P<0.001). Additionally, significant increasing trends could be seen in the PFS and LRFS during the four calendar periods. In the subgroup analysis, the OS, PFS and LRFS in patients diagnosed older than 40 years had greater improvement than the younger patients. However, the rate of distant metastasis was stable and relatively low, as the 5-year distant metastasis rate ranged from 0.2%-2.5% among the four calendar periods. Conclusion: The survival rates in patients with stage I NPC showed increasing trends from 1990 to 2012. The advances of radiotherapy provided excellent locoregional control and enhanced overall survival, and in particular, the IMRT decreased locoregional relapse.

Combination of Tumor Volume and Epstein-Barr Virus DNA Improved Prognostic Stratification of Stage II Nasopharyngeal Carcinoma in the Intensity Modulated Radiotherapy Era: A Large-Scale Cohort Study.

PURPOSE: Little is known about combination of the circulating Epstein-Barr viral (EBV) DNA and tumor volume in prognosis of stage II nasopharyngeal carcinoma (NPC) patients in the intensity modulated radiotherapy (IMRT) era. We conducted this cohort study to evaluate the prognostic values of combining these two factors. MATERIALS AND METHODS: By Kaplan-Meier, we compare the differences of survival curves between 385 patients with different EBV DNA or tumor volume levels, or with the combination of two biomarkers mentioned above. RESULTS: Gross tumor volume of cervical lymph nodes (GTVnd, p < 0.001) and total tumor volume (GTVtotal, p < 0.001) were both closely related to pretreatment EBV DNA, while gross tumor volume of nasopharynx (GTVnx, p=0.047) was weakly related to EBV DNA. EBV DNA was significantly correlated with progress-free survival (PFS, p=0.005), locoregional-free survival (LRFS, p=0.039), and distant metastasis-free survival (DMFS, p=0.017), while GTVtotal, regardless of GTVnx and GTVnd, had a significant correlation with PFS and LRFS. The p-values of GTVtotal for PFS and LRFS were 0.008 and 0.001, respectively. According to GTVtotal and pretreatment EBV DNA level, patients were divided into a low-risk group (EBV DNA 0 copy/mL, GTVtotal < 30 cm3; EBV DNA 0 copy/mL, GTVtotal ≥ 30 cm3; or EBV DNA > 0 copy/mL, GTVtotal < 30 cm3) and a high-risk group (EBV DNA > 0 copy/mL, GTVtotal ≥ 30 cm3). When patients in the low-risk group were compared with those in the high-risk group, 3-year PFS (p=0.003), LRFS (p=0.010), and DMFS (p=0.031) rates were statistically significant. CONCLUSION: Pretreatment plasma EBV DNA and tumor volume were both closely correlated with prognosis of stage II NPC patients in the IMRT era. Combination of EBV DNA and tumor volume can refine prognosis and indicate for clinical therapy.

Comparison of two treatments with skewed ordinal responses.

In clinical studies, the proportional odds model is widely used to compare treatment efficacies when the responses are categorically ordered. However, this model has been shown to be inappropriate when the proportional odds assumption is invalid, mainly because it is unable to control the type I error rate in such circumstances. To remedy this problem, the latent normal model was recently promoted and has been demonstrated to be superior to the proportional odds model. However, the application of the latent normal model is limited to compare treatments with similar underlying distributions except possibly their means and variances. When the underlying distributions are very different in skewness, both of the aforementioned procedures suffer from the undesirable inflation of the type I error rate. To solve the problem for clinical studies with ordinal responses, we provide a viable solution that relies on the use of the latent Weibull distribution, which is a member of the log-location-scale family. The proposed model is able to control the type I error rate regardless of the degree of skewness of the treatment responses. In addition, the power of the test also outperforms that of the latent normal model. The testing procedure draws on newly developed theoretical results related to latent distributions from the location-scale family. The testing procedure is illustrated with two clinical examples.

Multiple comparisons with a control for a latent variable model with ordered categorical responses.

Ordered categorical data are frequently encountered in clinical studies. A popular method for comparing the efficacy of treatments is to use logistic regression with the proportional odds assumption. The test statistic is based on the Wilcoxon-Mann-Whitney test. However, the proportional odds assumption may not be appropriate. In such cases, the probability of rejecting the null hypothesis is much inflated even though the treatments have the same mean efficacy. An alternative approach that does not rely on the proportional odds assumption is to conceptualize the responses as manifestations of some underlying continuous variables. However, statistical procedures were developed only for the comparison of two treatments. In this article, we derive testing procedures that compare several treatments to a control, utilizing a latent normal distribution with the latent variable model. The proposed procedure is useful because multiple comparisons with a control is very frequently an objective of a clinical study. Data from clinical trials are used to illustrate the proposed procedures.

A unified framework for the comparison of treatments with ordinal responses.

Different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable. In this paper, we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses. The latent variable model is built upon the location-scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables, including the proportional odds model, the ordered probit-type model, and the proportional hazards model. A flexible estimation procedure is proposed for the identification and estimation of the general latent variable model, which allows for the location and scale parameters to be freely estimated. The framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data, thus allowing for important statistical inferences such as location and/or dispersion comparisons among treatments to be conveniently drawn. Analysis on real data sets is used to illustrate the proposed methods.

Pairwise comparisons with ordered categorical data.

Clinical trials frequently involve pairwise comparisons of different treatments to evaluate their relative efficacy. In this study, we examine methods for conducting pairwise tests of treatments with ordered categorical responses. A modified version of the Wilcoxon-Mann-Whitney test based on a logistic regression model assuming proportional odds is a popular choice for comparing two treatments. This paper discusses the extension of this test to pairwise comparisons involving more than two treatments. However, when the proportional odds assumption is not valid, the Wilcoxon-Mann-Whitney-type test procedure cannot control the overall type I error rate at the prespecified level of significance. We therefore propose a better strategy in which a latent normal model is employed. We presented a simulated comparative study of power and the overall type I error rate to illustrate the superiority of the latent normal model. Examples are also given for illustrative purposes.