Efficient Study Design and Analysis of Longitudinal Dose-Response Data Using Fractional Polynomials.

Correctly characterising the dose-response relationship and taking the correct dose forward for further study is a critical part of the drug development process. We use optimal design theory to compare different designs and show that using longitudinal data from all available timepoints in a continuous-time dose-response model can substantially increase the efficiency of estimation of the dose-response compared to a single timepoint model. We give theoretical results to calculate the efficiency gains for a large class of these models. For example, a linearly growing Emax dose-response in a population with a between/within-patient variance ratio ranging from 0.1 to 1 measured at six visits can be estimated with between 1.43 and 2.22 times relative efficiency gain, or equivalently, with 30% to a 55% reduced sample size, compared to a single model of the final timepoint. Fractional polynomials are a flexible way to incorporate data from repeated measurements, increasing precision without imposing strong constraints. Longitudinal dose-response models using two fractional polynomial terms are robust to mis-specification of the true longitudinal process while maintaining, often large, efficiency gains. These models have applications for characterising the dose-response at interim or final analyses.

Subcortical grey matter volume and asymmetry in the long-term course of Rasmussen's encephalitis.

Rasmussen's encephalitis is characterized by drug-resistant focal seizures and chronic inflammation of one hemisphere leading to progressive loss of hemispheric volume. In this cohort study, we aimed to investigate subcortical grey matter volumes and asymmetries in Rasmussen's encephalitis longitudinally in clinically relevant subgroups. We retrospectively included all T1-weighted MRI scans of all people with Rasmussen's encephalitis who were treated at the University Hospital Bonn between 1995 and 2022 (n = 56, 345 scans, median onset 8 years, 36 female). All cases were classified as type 1 (onset ≤ 6 years) or type 2 (onset > 6 years). Subcortical segmentations were performed using FreeSurfer. Longitudinal trajectories of subcortical volumes and hemispheric ratios (ipsi-/contralesional) were assessed using linear mixed-effect models. Unihemispheric cortical degeneration was accompanied by ipsilesional atrophy of the nucleus accumbens, caudate nucleus, putamen, thalamus and contralesional atrophy of the nucleus accumbens and caudate nucleus both in type 1 (all P ≤ 0.014) and type 2 (all P < 0.001). In type 1, however, contralesional volume increase of the amygdala, hippocampus, pallidum and thalamus was found (all P ≤ 0.013). Both ipsilesional and contralesional subcortical atrophies, like cortical atrophy, are most probably caused by neurodegeneration following chronic neuroinflammation. We speculate that contralesional volume increase in type 1 could be related to either neuroplasticity or ongoing acute neuroinflammation, which needs to be investigated in further studies.

Longitudinal changes in hippocampal texture from healthy aging to Alzheimer's disease.

Early detection of Alzheimer's disease is essential to develop preventive treatment strategies. Detectible change in brain volume emerges relatively late in the pathogenic progression of disease, but microstructural changes caused by early neuropathology may cause subtle changes in the MR signal, quantifiable using texture analysis. Texture analysis quantifies spatial patterns in an image, such as smoothness, randomness and heterogeneity. We investigated whether the MRI texture of the hippocampus, an early site of Alzheimer's disease pathology, is sensitive to changes in brain microstructure before the onset of cognitive impairment. We also explored the longitudinal trajectories of hippocampal texture across the Alzheimer's continuum in relation to hippocampal volume and other biomarkers. Finally, we assessed the ability of texture to predict future cognitive decline, over and above hippocampal volume. Data were acquired from the Alzheimer's Disease Neuroimaging Initiative. Texture was calculated for bilateral hippocampi on 3T T1-weighted MRI scans. Two hundred and ninety-three texture features were reduced to five principal components that described 88% of total variance within cognitively unimpaired participants. We assessed cross-sectional differences in these texture components and hippocampal volume between four diagnostic groups: cognitively unimpaired amyloid-ß- (n = 406); cognitively unimpaired amyloid-ß+ (n = 213); mild cognitive impairment amyloid-ß+ (n = 347); and Alzheimer's disease dementia amyloid-ß+ (n = 202). To assess longitudinal texture change across the Alzheimer's continuum, we used a multivariate mixed-effects spline model to calculate a 'disease time' for all timepoints based on amyloid PET and cognitive scores. This was used as a scale on which to compare the trajectories of biomarkers, including volume and texture of the hippocampus. The trajectories were modelled in a subset of the data: cognitively unimpaired amyloid-ß- (n = 345); cognitively unimpaired amyloid-ß+ (n = 173); mild cognitive impairment amyloid-ß+ (n = 301); and Alzheimer's disease dementia amyloid-ß+ (n = 161). We identified a difference in texture component 4 at the earliest stage of Alzheimer's disease, between cognitively unimpaired amyloid-ß- and cognitively unimpaired amyloid-ß+ older adults (Cohen's d = 0.23, Padj = 0.014). Differences in additional texture components and hippocampal volume emerged later in the disease continuum alongside the onset of cognitive impairment (d = 0.30-1.22, Padj < 0.002). Longitudinal modelling of the texture trajectories revealed that, while most elements of texture developed over the course of the disease, noise reduced sensitivity for tracking individual textural change over time. Critically, however, texture provided additional information than was provided by volume alone to more accurately predict future cognitive change (d = 0.32-0.63, Padj < 0.0001). Our results support the use of texture as a measure of brain health, sensitive to Alzheimer's disease pathology, at a time when therapeutic intervention may be most effective.

Comparison of Seven Non-Linear Mixed Effect Model-Based Approaches to Test for Treatment Effect.

Analyses of longitudinal data with non-linear mixed-effects models (NLMEM) are typically associated with high power, but sometimes at the cost of inflated type I error. Approaches to overcome this problem were published recently, such as model-averaging across drug models (MAD), individual model-averaging (IMA), and combined Likelihood Ratio Test (cLRT). This work aimed to assess seven NLMEM approaches in the same framework: treatment effect assessment in balanced two-armed designs using real natural history data with or without the addition of simulated treatment effect. The approaches are MAD, IMA, cLRT, standard model selection (STDs), structural similarity selection (SSs), randomized cLRT (rcLRT), and model-averaging across placebo and drug models (MAPD). The assessment included type I error, using Alzheimer's Disease Assessment Scale-cognitive (ADAS-cog) scores from 817 untreated patients and power and accuracy in the treatment effect estimates after the addition of simulated treatment effects. The model selection and averaging among a set of pre-selected candidate models were driven by the Akaike information criteria (AIC). The type I error rate was controlled only for IMA and rcLRT; the inflation observed otherwise was explained by the placebo model misspecification and selection bias. Both IMA and rcLRT had reasonable power and accuracy except under a low typical treatment effect.

Joint longitudinal and time-to-event modelling compared with standard Cox modelling in patients with type 2 diabetes with and without established cardiovascular disease: An analysis of the EXSCEL trial.

AIM: To demonstrate the gain in predictive performance when cardiovascular disease (CVD) risk prediction tools (RPTs) incorporate repeated rather than only single measurements of risk factors. MATERIALS AND METHODS: We used data from the Exenatide Study of Cardiovascular Event Lowering (EXSCEL) trial to compare the quality of predictions of future major adverse cardiovascular events (MACE) with the Cox proportional hazards model (using single values of risk factors) compared to the Bayesian joint model (using repeated measures of risk factors). The risk of MACE was calculated in patients with type 2 diabetes with and without established CVD. We assessed the predictive ability of the following cardiovascular risk factors: glycated haemoglobin, high-density lipoprotein cholesterol (HDL-C), non-HDL-C, triglycerides, estimated glomerular filtration rate, low-density lipoprotein cholesterol (LDL-C), total cholesterol, and systolic blood pressure (SBP) using the time-dependent area under the receiver-operating characteristic curve (aROC) for discrimination and the time-dependent Brier score for calibration. RESULTS: In participants without history of CVD, the aROC of SBP increased from 0.62 to 0.69 when repeated rather than only single measurements of SBP were incorporated into the predictive model. Similarly, the aROC increased from 0.67 to 0.80 when repeated rather than only single measurements of both SBP and LDL-C were incorporated into the predictive model. For all other investigated cardiovascular risk factors, the measures of discrimination and calibration both improved when using the joint model as compared to the Cox proportional hazards model. The improvement was evident in participants with and without history of CVD but was more pronounced in the latter group. CONCLUSIONS: The analysis demonstrates that the joint modelling approach, considering trajectories of cardiovascular risk factors, provides superior predictive performance compared to standard RPTs that use only a single timepoint.

Modelling item scores of Unified Parkinson's Disease Rating Scale Part III for greater trial efficiency.

AIMS: The multipart Unified Parkinson's Disease Rating Scale is the standard instrument in clinical trials. A sum of scores for all items in 1 or more parts of the instrument is usually analysed. Without accounting for relative importance of individual items, this sum of scores conceivably does not optimize the power of the instrument. The aim was to compare the ability to detect drug effect in slowing down motor function deterioration, as measured by Part III of the Scale-motor examinations-between the item scores and the sum of scores. METHODS: We used data from 423 patients in a Parkinson's disease progression trial to estimate the symptom severity by item response modelling; modelled symptom progression using the severity and the sum of scores; and conducted simulations to compare the sensitivity of detecting a broad range of hypothetical drug effects on progression using the severity and the sum of scores. RESULTS: The severity endpoint was far more sensitive than the sum of scores for detecting treatment effects, e.g. requiring 275 vs. 625 patients per arm to achieve 60% probability of trial success for detecting a range of potential effects in a 2-year trial. Nontremor items related to the left side of the body seemed most informative. The domain relevance of tremor items appeared questionable. CONCLUSION: This analysis generated clear evidence that longitudinal modelling of item scores can enhance trial efficiency and success. It also called for reassessing the placement of the tremor items in the instrument.

Modelling disease course in amyotrophic lateral Sclerosis: pseudo-longitudinal insights from cross-sectional health-related quality of life data.

BACKGROUND: Amyotrophic Lateral Sclerosis (ALS) is a rapidly progressive neurodegenerative disorder with limited robust disease-modifying therapies presently available. While several treatments are aimed at improving health-related quality of life (HRQoL), longitudinal data on how QoL changes across the disease course are rare. OBJECTIVES: To explore longitudinal changes in emotional well-being and HRQoL in ALS. METHODS: Of the 161 subjects initially recruited, 39 received 2 subsequent follow-up assessments at 6 and 12 months after baseline. The ALS Functional Rating Scale-Revised (ALSFRS-R) was used to assess physical impairment. HRQoL was assessed using the ALS Assessment Questionnaire (ALSAQ-40). The D50 disease progression model was applied to explore longitudinal changes in HRQoL. RESULTS: Patients were primarily in the early semi-stable and early progressive model-derived disease phases. Non-linear correlation analyses showed that the ALSAQ-40 summary index and emotional well-being subdomain behaved differently across disease phases, indicating that the response shift occurs early in disease. Both the ALSFRS-R and ALSAQ-40 significantly declined at 6- and 12-monthly follow-ups. CONCLUSION: ALSAQ-40 summary index and emotional well-being change comparably over both actual time and model-derived phases, indicating that the D50 model enables pseudo-longitudinal interpretations of cross-sectional data in ALS.

Impact of shortened dental arch on oral health-related quality of life over a period of 10 years - A randomized controlled trial.

OBJECTIVES: To compare oral health-related quality of life (OHRQoL) in patients with either molar replacement by partial removable dental prostheses (PRDP) or with restored shortened dental arches (SDA) over a period of 10 years. METHODS: In this multi-center RCT, a consecutive sample of 215 patients with bilateral molar loss in at least one jaw was initially recruited in 14 prosthodontic departments. Of those patients, 150 could be randomly allocated to the treatment groups (SDA: n = 71; PRDP: n = 79), received the allocated treatment, and were available for follow-up assessments. OHRQoL was assessed using the 49-item version of the Oral Health Impact Profile (OHIP) before treatment (baseline) and at follow-ups after treatment (4-8 weeks and 6, 12, 24, 36, 48, 60, 96, and 120 months). To investigate the course of OHRQoL over time, we longitudinally modelled treatment and time effects using mixed-effects models. RESULTS: OHRQoL substantially improved from baseline to first follow-up in both groups indicated by a mean decrease in OHIP scores of 20.0 points (95%-CI: 12.5-27.5). When compared to the SDA group, OHRQoL in the PRDP group was not significantly different (-0.6 OHIP points; 95%-CI: -7.1 to 5.9) during the study period when assuming a constant time effect. OHRQoL remained stable over the 10 years with a statistically insignificant time effect (p = 0.848). CONCLUSIONS: For patients requesting prosthodontic treatment for their lost molars, treatments with SDA or PRDP improve clinically relevantly OHRQoL and maintain it over a period of 10 years with no option being superior to the other. CLINICAL SIGNIFICANCE: Since there was no significant difference between the two treatment options over the observation period of 10 years, and since results have stayed stable over time, patients can be informed that both treatment concepts are equivalent concerning OHRQoL.

Foetal ultrasound measurement imputations based on growth curves versus multiple imputation chained equation (MICE).

BACKGROUND: Ultrasound measures are valuable for epidemiologic studies of risk factors for growth restriction. Longitudinal measurements enable investigation of rates of change and identification of windows where growth is impacted more acutely. However, missing data can be problematic in these studies, limiting sample size, ability to characterise windows of vulnerability, and in some instances creating bias. We sought to compare a parametric linear mixed model (LMM) approach to multiple imputation in this setting with multiple imputation by chained equation (MICE) methodology. METHODS: Ultrasound scans performed for clinical purposes were abstracted from women in the LIFECODES birth cohort (n = 1003) if they were close in time to three study visits (median 18, 26, and 35 weeks' gestation). We created imputed datasets using LMM and MICE and calculated associations between demographic factors and ultrasound parameters cross-sectionally and longitudinally. Results were compared with a complete-case analysis. RESULTS: Most participants had ultrasounds at 18 weeks' gestation, and ~50% had measurements at 26 and 35 weeks; 100% had birthweight. Associations between demographic factors and ultrasound measures were similar in magnitude, but more precise, when either imputed datasets were used, compared with a complete-case analysis, in both the cross-sectional or longitudinal analyses. CONCLUSIONS: MICE, though ignoring the non-linear features of the trajectory and within subject correlation, is able to provide reasonable imputation of foetal growth data when compared to LMM. Because it simultaneously imputes missing covariate data and does not require specification of variance structure as in LMM, MICE may be preferable for imputation in this setting.

Developmental cognitive neuroscience using latent change score models: A tutorial and applications.

Assessing and analysing individual differences in change over time is of central scientific importance to developmental neuroscience. However, the literature is based largely on cross-sectional comparisons, which reflect a variety of influences and cannot directly represent change. We advocate using latent change score (LCS) models in longitudinal samples as a statistical framework to tease apart the complex processes underlying lifespan development in brain and behaviour using longitudinal data. LCS models provide a flexible framework that naturally accommodates key developmental questions as model parameters and can even be used, with some limitations, in cases with only two measurement occasions. We illustrate the use of LCS models with two empirical examples. In a lifespan cognitive training study (COGITO, N = 204 (N = 32 imaging) on two waves) we observe correlated change in brain and behaviour in the context of a high-intensity training intervention. In an adolescent development cohort (NSPN, N = 176, two waves) we find greater variability in cortical thinning in males than in females. To facilitate the adoption of LCS by the developmental community, we provide analysis code that can be adapted by other researchers and basic primers in two freely available SEM software packages (lavaan and Ωnyx).

Informative Observation in Health Data: Association of Past Level and Trend with Time to Next Measurement.

In routine health data, risk factors and biomarkers are typically measured irregularly in time, with the frequency of their measurement depending on a range of factors - for example, sicker patients are measured more often. This is termed informative observation. Failure to account for this in subsequent modelling can lead to bias. Here, we illustrate this issue using body mass index measurements taken on patients with type 2 diabetes in Salford, UK. We modelled the observation process (time to next measurement) as a recurrent event Cox model, and studied whether previous measurements in BMI, and trends in the BMI, were associated with changes in the frequency of measurement. Interestingly, we found that increasing BMI led to a lower propensity for future measurements. More broadly, this illustrates the need and opportunity to develop and apply models that account for, and exploit, informative observation.

Fast and accurate modelling of longitudinal and repeated measures neuroimaging data.

Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions (e.g., assumption of Compound Symmetry--the state of all equal variances and equal correlations--or spatially homogeneous longitudinal correlations). While some new methods have been proposed to more accurately account for such data, these methods are based on iterative algorithms that are slow and failure-prone. In this article, we propose the use of the Sandwich Estimator method which first estimates the parameters of interest with a simple Ordinary Least Square model and second estimates variances/covariances with the "so-called" Sandwich Estimator (SwE) which accounts for the within-subject correlation existing in longitudinal data. Here, we introduce the SwE method in its classic form, and we review and propose several adjustments to improve its behaviour, specifically in small samples. We use intensive Monte Carlo simulations to compare all considered adjustments and isolate the best combination for neuroimaging data. We also compare the SwE method to other popular methods and demonstrate its strengths and weaknesses. Finally, we analyse a highly unbalanced longitudinal dataset from the Alzheimer's Disease Neuroimaging Initiative and demonstrate the flexibility of the SwE method to fit within- and between-subject effects in a single model. Software implementing this SwE method has been made freely available at http://warwick.ac.uk/tenichols/SwE.