crossover designs

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Please leave suggestions for studies using a crossover design.

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Consider O’Callaghan et al (2021; https://doi.org/10.1093/brain/awab142), Locus coeruleus integrity and the effect of atomoxetine on response inhibition in Parkinson’s disease. Their abstract reads:

Cognitive decline is a common feature of Parkinson’s disease, and many of these cognitive deficits fail to respond to dopaminergic therapy. Therefore, targeting other neuromodulatory systems represents an important therapeutic strategy. Among these, the locus coeruleus-noradrenaline system has been extensively implicated in response inhibition deficits. Restoring noradrenaline levels using the noradrenergic reuptake inhibitor atomoxetine can improve response inhibition in some patients with Parkinson’s disease, but there is considerable heterogeneity in treatment response. Accurately predicting the patients who would benefit from therapies targeting this neurotransmitter system remains a critical goal, in order to design the necessary clinical trials with stratified patient selection to establish the therapeutic potential of atomoxetine.

Here, we test the hypothesis that integrity of the noradrenergic locus coeruleus explains the variation in improvement of response inhibition following atomoxetine. In a double-blind placebo-controlled randomized crossover design, 19 patients with Parkinson’s disease completed an acute psychopharmacological challenge with 40 mg of oral atomoxetine or placebo. A stop-signal task was used to measure response inhibition, with stop-signal reaction times obtained through hierarchical Bayesian estimation of an ex-Gaussian race model. Twenty-six control subjects completed the same task without undergoing the drug manipulation. In a separate session, patients and controls underwent ultra-high field 7 T imaging of the locus coeruleus using a neuromelanin-sensitive magnetization transfer sequence.

The principal result was that atomoxetine improved stop-signal reaction times in those patients with lower locus coeruleus integrity. This was in the context of a general impairment in response inhibition, as patients on placebo had longer stop-signal reaction times compared to controls. We also found that the caudal portion of the locus coeruleus showed the largest neuromelanin signal decrease in the patients compared to controls.

Our results highlight a link between the integrity of the noradrenergic locus coeruleus and response inhibition in patients with Parkinson’s disease. Furthermore, they demonstrate the importance of baseline noradrenergic state in determining the response to atomoxetine. We suggest that locus coeruleus neuromelanin imaging offers a marker of noradrenergic capacity that could be used to stratify patients in trials of noradrenergic therapy and to ultimately inform personalized treatment approaches.

They used n = 19 persons with Parkinson’s and n = 26 controls in a crossover design, and their data and R code lives on the OSF at https://osf.io/tyka3/. In the paper, they used a hierarchical Bayesian ex-Gaussian race model, which may be of analytic interest.

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Consider Riedl et al (2022; https://doi.org/10.1016/j.schres.2022.06.009), Multimodal speech-gesture training in patients with schizophrenia spectrum disorder: Effects on quality of life and neural processing. From the abstract, we read:

Dysfunctional social communication is one of the most stable characteristics in patients with schizophrenia spectrum disorder (SSD) that severely affects quality of life. Interpreting abstract speech and integrating nonverbal information is particularly affected.

Considering the difficulty to treat communication dysfunctions with usual intervention, we investigated the possibility to apply a multimodal speech-gesture (MSG) training.

In the MSG training, we offered 8 sessions (60 min each) including perceptive and expressive tasks as well as meta-learning elements and transfer exercises to 29 patients with SSD. In a within-group crossover design, patients were randomized to a TAU-first (treatment as usual first, then MSG training) group (N = 20) or a MSG-first (MSG training first, then TAU only) group (N = 9), and were compared to healthy controls (N = 17). Outcomes were quality of life and related changes in the neural processing of abstract speech-gesture information, which were measured pre-post training through standardized psychological questionnaires and functional Magnetic Resonance Imaging, respectively.

Pre-training, patients showed reduced quality of life as compared to controls but improved significantly during the training. Strikingly, this improvement was correlated with neural activation changes in the middle temporal gyrus for the processing of abstract multimodal content. Improvement during training, self-report measures and ratings of relatives confirmed the MSG-related changes.

Together, we provide first promising results of a novel multimodal speech-gesture training for patients with schizophrenia. We could link training induced changes in speech-gesture processing to changes in quality of life, demonstrating the relevance of intact communication skills and gesture processing for well-being.

Their primary analyses are of n = 29 persons diagnosed with a schizophrenia spectrum disorder. "Main outcomes were measured through pre-post-fMRI and standardized psychological questionnaires [the SWLS]." Their data and code appear to live on the OSF at https://osf.io/uh4f9/.

Note.

On second look, this paper might not be the best candidate. Their measurement schedule indicates fMRI was clearly their primary outcome of interest. They did measure SWLS at a couple time points, but the schedule wasn't great from a cross-over perspective. It seems like it was more of an afterthought. See their schedule at https://osf.io/497hj.

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Cross-over and potential outcomes

It's not immediately obvious what the best notation might be for connecting the potential-outcomes framework with cross-over designs. Some papers to consider:

• Chapter 17 in Zhang et al (2019; https://doi.org/10.1007/978-3-030-15310-6), Contemporary Biostatistics with Biopharmaceutical Applications, has some notation, though it's not great for introductory purposes
• Poulson et al (2012; https://doi.org/10.1080/00031305.2012.671724) has some terrible notation in Section 3.3
• Ndum's (2009; link) dissertation has some unnecessarily complicated notation
• Basse et al (2019; link) is a preprint with some useful notation in Sections 2.1 and 2.2

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When discussing generalizations of the basic crossover design, consider mentioning Sundström et al (2023; https://doi.org/10.1001/jama.2023.3322). Though their data aren't really open, their design is a nice example of how a simple crossover can converge into a proper within-person ABA-type crossover design when you take many measurements within each person within each phase.

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Consider Carlson et al (2022; https://doi.org/10.1080/02701367.2022.2097625), The Effects of Training Load During Dietary Intervention Upon Fat Loss: A Randomized Crossover Trial. Their abstract reads:

Purpose: To date no studies have compared resistance training loading strategies combined with dietary intervention for fat loss. Methods: Thus, we performed a randomised crossover design comparing four weeks of heavier- (HL; ~80% 1RM) and lighter-load (LL; ~60% 1RM) resistance training, combined with calorie restriction and dietary guidance, including resistance trained participants (n=130; males=49, females=81). Both conditions performed low-volume, (single set of 9 exercises, 2x/week) effort matched (to momentary failure), but non-work-matched protocols. Testing was completed pre- and post-each intervention. Fat mass (kg) was the primary outcome, and a smallest effect size of interest (SESOI) was established at 3.3% loss of baseline bodyweight. Body fat percentage, lean mass, and strength (7-10RM) for chest press, leg press, and pull-down exercises were also measured. An 8-week washout period of traditional training with normal calorie interspersed each intervention. Results: Both interventions showed small statistically equivalent (within the SESOI) reductions in fat mass (HL: -0.67 kg [95%CI -0.91 to 0.42]; LL: -0.55 kg [95%CI -0.80 to -0.31]) which were also equivalent between conditions (HL – LL: -0.113 kg [95%CI -0.437 kg to 0.212 kg]). Changes in body fat percentage and lean mass were also minimal. Strength increases were small, similar between conditions, and within a previously determined SESOI for the population included (10.1%). Conclusions: Fat loss reductions are not impacted by resistance training load; both HL and LL produce similar, yet small, changes to body composition over a 4-week intervention. However, the maintenance of both lean mass and strength highlights the value of resistance training during dietary intervention.

They used N = 130 persons with some weight-training experience in a crossover design designed to compare relatively lighter and heavier lifting programs for losing weight. Their data and R code lives on the OSF at https://osf.io/prqew/. The fat data are approximately gamma distributed. Each person has up to 5 measurement occasions, and the dv (fat in lbs.) is correlated above 0.95 across waves, making this a well-powered study with a fairly intuitive appeal. Sex (male/female) could be a good additional covariate.