Continuous response variables are often transformed to meet modeling assumptions, but the choice of the transformation can be challenging. Two transformation models have recently been proposed: semiparametric cumulative probability models (CPMs) and parametric most likely transformation models (MLTs). Both approaches model the cumulative distribution function and require specifying a link function, which implicitly assumes that the responses follow a known distribution after some monotonic transformation. However, the two approaches estimate the transformation differently. With CPMs, an ordinal regression model is fit, which essentially treats each continuous response as a unique category and therefore nonparametrically estimates the transformation; CPMs are semiparametric linear transformation models. In contrast, with MLTs, the transformation is parameterized using flexible basis functions. Conditional expectations and quantiles are readily derived from both methods on the response variable's original scale. We compare the two methods with extensive simulations. We find that both methods generally have good performance with moderate and large sample sizes. MLTs slightly outperformed CPMs in small sample sizes under correct models. CPMs tended to be somewhat more robust to model misspecification and outcome rounding. Except in the simplest situations, both methods outperform basic transformation approaches commonly used in practice. We apply both methods to an HIV biomarker study. KEYWORDSHIV, nonparametric maximum likelihood estimation, ordinal regression model, transformation model 562

Across rural sub-Saharan Africa, people living with HIV (PLHIV) commonly seek out treatment from traditional healers. We report on the clinical outcomes of a community health worker intervention adapted for traditional healers with insight into our results from qualitative interviews. We employed a pre-post intervention study design and used sequential mixed methods to assess the impact of a traditional healer support worker intervention in Zambézia province, Mozambique. After receiving a positive test result, 276 participants who were newly enrolled in HIV treatment and were interested in receiving home-based support from a traditional healer were recruited into the study. Those who enrolled from February 2016 to August 2016 received standard of care services, while those who enrolled from June 2017 to May 2018 received support from a traditional healer. We conducted interviews among healers and participants to gain insight into fidelity of study activities, barriers to support, and program improvement. Medication possession ratio at home (based on pharmacy pick-up dates) was not significantly different between pre- and post-intervention participants (0.80 in the pre-intervention group compared to 0.79 in the post-intervention group; p = 0.96). Participants reported receiving educational and psychosocial support from healers. Healers adapted their support protocol to initiate directly observed therapy among participants with poor adherence. Traditional healers can provide community-based psychosocial support, education, directly observed therapy, and disclosure assistance for PLHIV. Multiple factors may hinder patients’ desire and ability to remain adherent to treatment, including poverty, confusion about medication side effects, and frustration with wait times at the health facility.

Continuous response data are regularly transformed to meet regression modeling assumptions. However, approaches taken to identify the appropriate transformation can be ad hoc and can increase model uncertainty. Further, the resulting transformations often vary across studies leading to difficulties with synthesizing and interpreting results. When a continuous response variable is measured repeatedly within individuals or when continuous responses arise from clusters, analyses have the additional challenge caused by within‐individual or within‐cluster correlations. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered, continuous response data using generalized estimating equations for ordinal responses. With the proposed approach, estimates of marginal model parameters, cumulative distribution functions , expectations, and quantiles conditional on covariates can be obtained without pretransformation of the response data. While computational challenges arise with large numbers of distinct values of the continuous response variable, we propose feasible and computationally efficient approaches to fit CPMs under commonly used working correlation structures. We study finite sample operating characteristics of the estimators via simulation and illustrate their implementation with two data examples. One studies predictors of CD4:CD8 ratios in a cohort living with HIV, and the other investigates the association of a single nucleotide polymorphism and lung function decline in a cohort with early chronic obstructive pulmonary disease.

Objectives: To explore whether tai chi can improve lung function, exercise capacity, and health-related outcomes in patients with chronic obstructive pulmonary disease (COPD). Methods: The PubMed, Embase, Cochrane Central Register of Controlled Trials, Chinese National Knowledge Infrastructure (CNKI), Wanfang, and China Science and Technology Journal Database (VIP) databases were searched from inception to January 5, 2023. The methodological quality of the included studies was evaluated according to the Cochrane Handbook for Systematic Reviews of Interventions criteria. Results: A total of 1430 participants from 20 randomized controlled trials were included in this review. The results indicated significant effects of tai chi on FEV1, 6WMD, anxiety, and quality of life ( p < 0.01), but not on FEV1%, FEVI/FVC, depression, and social support. Conclusions: Tai chi might be a potential alternative therapy to improve FEV1, 6WMD, anxiety, and quality of life for patients with COPD.