Notes on testing noninferiority in ordinal data under the parallel groups design

A novel approach to assess dynamic treatment regimes embedded in a SMART with an ordinal outcome

Sequential multiple assignment randomized trials (SMARTs) are used to construct data-driven optimal intervention strategies for subjects based on their intervention and covariate histories in different branches of health and behavioral sciences where a sequence of interventions is given to a participant. Sequential intervention strategies are often called dynamic treatment regimes (DTR). In the existing literature, the majority of the analysis methodologies for SMART data assume a continuous primary outcome. However, ordinal outcomes are also quite common in clinical practice. In this work, first, we introduce the notion of generalized odds ratio ( G O R $$ GOR $$ ) to compare two DTRs embedded in a SMART with an ordinal outcome and discuss some combinatorial properties of this measure. Next, we propose a likelihood-based approach to estimate G O R $$ GOR $$ from SMART data, and derive the asymptotic properties of its estimate. We discuss alternative ways to estimate G O R $$ GOR $$ using concordant-discordant pairs and two-sample U $$ U $$ -statistic. We derive the required sample size formula for designing SMARTs with ordinal outcomes based on G O R $$ GOR $$ . A simulation study shows the performance of the estimated G O R $$ GOR $$ in terms of the estimated power corresponding to the derived sample size. The methodology is applied to analyze data from the SMART+ study, conducted in the UK, to improve carbohydrate periodization behavior in athletes using a menu planner mobile application, Hexis Performance. A freely available Shiny web app using R is provided to make the proposed methodology accessible to other researchers and practitioners.

Noninferiority testing for matched-pair ordinal data with misclassification

New treatments that are noninferior or equivalent to-but not necessarily superior to-the reference treatment may still be beneficial to patients because they have fewer side effects, are more convenient, take less time, or cost less. The noninferiority test is widely used in medical research to provide guidance in such situation. In addition, categorical variables are frequently encountered in medical research, such as in studies involving patient-reported outcomes. In this paper, we develop a noninferiority testing procedure for correlated ordinal categorical variables based on a paired design with a latent normal distribution approach. Misclassification is frequently encountered in the collection of ordinal categorical data; therefore, we further extend the procedure to account for misclassification using information in the partially validated data. Simulation studies are conducted to investigate the accuracy of the estimates, the type I error rates, and the power of the proposed procedure. Finally, we analyze one substantive example to demonstrate the utility of the proposed approach.

Shared Care for Patients with Diabetes at Risk of Retinopathy: A Feasibility Trial

Purpose:

While diabetes is a chronic disease, in many health care systems patients with diabetes at risk of diabetic retinopathy (DR) are managed in hospital settings. Aim of this feasibility study is to assess the quality of care and economic benefits of a shared care model managing patients at risk of DR in a primary eye care clinic (PEC) compared with a current tertiary specialist outpatient clinic (SOC).

Methods:

A randomized trial was performed, to compare a PEC with a SOC in Singapore. The trial patients included those previously seen at the SOC, and having no DR or stable mild non proliferative (NPDR) with no macular edema, no visual and DR deterioration. Primary outcomes were clinical management. Secondary outcomes were patient satisfaction and cost of consultation. Differences analysis used equivalence testing and generalized odds ratios (GOR).

Results:

The trial included 231 patients, 83.1% classified as no DR (PEC: 79.1%; SOC: 87.1%) and 16.9% as stable mild NPDR (PEC: 20.9%; SOC: 12.9%). DR management at PEC was significantly equivalent to that received at the SOC (rate difference 2.56%; CI: (–1.61% to 6.74%)) and 4.29%; CI: (0.14%–8.45%), respectively. Patient satisfaction at the PEC was equally high when compared to SOC (GOR: 1.71; CI: (0.50–2.00)). Direct costs per patient visit was 45% lower at PEC compared to SOC.

Conclusions:

Our feasibility trial showed that patients with diabetes with no or stable DR receive similar clinical care and management at a lower-cost PEC setting, are equally satisfied with the service compared to tertiary eye care. A follow-up study is necessary to validate these findings. Managing patients with diabetes at risk of DR at a PEC may be a safe and effective shared care model to improve accessibility for patients while enhancing professional collaboration between hospital and community settings.

Shared Cared for Stable Glaucoma Patients: Economic Benefits and Patient-centered Outcomes of a Feasibility Trial

PURPOSE

The purpose of this article is to assess the quality of care and economic benefits of a shared care model managing patients with stable glaucoma in a primary eye care (PEC) clinic compared with a tertiary specialist outpatient clinic (SOC) in Singapore.

PATIENTS AND METHODS

A randomized equivalence feasibility trial was preformed comparing the PEC with SOC models. Participants recruited from the SOC had no visual field progression or change in management for at least 3 years, were on a maximum of a single glaucoma medication, had no previous tube-shunt implant and were at least 3-year posttrabeculectomy surgery.Primary outcomes were clinical assessment and management, economic benefits, and patient satisfaction. Differences were analyzed using equivalence testing and generalized odds ratios.

RESULTS

The trial included 233 patients, consisting of 42.1% glaucoma disc suspects (PEC: 47.4%; SOC: 36.8%), 27.5% primary angle closure suspects (PEC: 25.0%; SOC: 29.9%), 13.7% with ocular hypertension (PEC: 13.8%; SOC: 13.7%), 3.9% with primary angle closure glaucoma (PEC: 4.3%; SOC: 3.4%), and 3.0% with primary open angle glaucoma (PEC: 1.7%; SOC: 4.3%). Glaucoma clinical care for patients at PEC was as good as SOC [rate difference, 6.83%; 95% confidence interval (CI), 2.84-11.12) and management (rate difference, 7.69%; 95% CI, 3.21-12.17). In 23 cases (9.9%), 5.2% at PEC and 14.5% at SOC, there was disconcordance with the gold standard of senior consultant. Patient satisfaction at the PEC was equally high when compared with SOC (generalized odds ratio, 1.43; CI, 0.50-2.00). Direct costs per patient visit were 43% lower at PEC compared with SOC.

CONCLUSION

Managing stable glaucoma patients at a primary care setting is a cost saving, safe, and effective shared care while enhancing professional collaboration between hospital and community settings.

Testing Equality in Ordinal Data with Repeated Measurements: A Model-Free Approach

In randomized clinical trials, we often encounter ordinal categorical responses with repeated measurements. We propose a model-free approach with using the generalized odds ratio (GOR) to measure the relative treatment effect. We develop procedures for testing equality of treatment effects and derive interval estimators for the GOR. We further develop a simple procedure for testing the treatment-by-period interaction. To illustrate the use of test procedures and interval estimators developed here, we consider two real-life data sets, one studying the gender effect on pain scores on an ordinal scale after hip joint resurfacing surgeries, and the other investigating the effect of an active hypnotic drug in insomnia patients on ordinal categories of time to falling asleep.

Testing equality and interval estimation of the generalized odds ratio in ordinal data under a three-period crossover design

The crossover design can be of use to save the number of patients or improve power of a parallel groups design in studying treatments to noncurable chronic diseases. We propose using the generalized odds ratio for paired sample data to measure the relative effects in ordinal data between treatments and between periods. We show that one can apply the commonly used asymptotic and exact test procedures for stratified analysis in epidemiology to test non-equality of treatments in ordinal data, as well as obtain asymptotic and exact interval estimators for the generalized odds ratio under a three-period crossover design. We further show that one can apply procedures for testing the homogeneity of the odds ratio under stratified sampling to examine whether there are treatment-by-period interactions. We use the data taken from a three-period crossover trial studying the effects of low and high doses of an analgesic versus a placebo for the relief of pain in primary dysmenorrhea to illustrate the use of these test procedures and estimators proposed here.

Test Statistics and Confidence Intervals to Establish Noninferiority between Treatments with Ordinal Categorical Data

The problem for establishing noninferiority is discussed between a new treatment and a standard (control) treatment with ordinal categorical data. A measure of treatment effect is used and a method of specifying noninferiority margin for the measure is provided. Two Z-type test statistics are proposed where the estimation of variance is constructed under the shifted null hypothesis using U-statistics. Furthermore, the confidence interval and the sample size formula are given based on the proposed test statistics. The proposed procedure is applied to a dataset from a clinical trial. A simulation study is conducted to compare the performance of the proposed test statistics with that of the existing ones, and the results show that the proposed test statistics are better in terms of the deviation from nominal level and the power.