Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies

BACKGROUND: Longitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories. METHODS: This expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5–40 years. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts. RESULTS: Linear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence. CONCLUSIONS: LME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-022-01542-8

Developing decision support tools incorporating personalised predictions of likely visual benefit versus harm for cataract surgery:research programme

Background Surgery for established cataract is highly cost-effective and uncontroversial, yet uncertainty remains for individuals about when to proceed and when to delay surgery during the earlier stages of cataract. Objective We aimed to improve decision-making for cataract surgery through the development of evidence-based clinical tools that provide general information and personalised risk/benefit information. Design We used a mixed methodology consisting of four work packages. Work package 1 involved the development and psychometric validation of a brief, patient self-reported measure of visual difficulty from cataract and its relief from surgery, named Cataract Patient-Reported Outcome Measure, five items (Cat-PROM5). Work package 2 involved the review and refinement of risk models for adverse surgical events (posterior capsule rupture and visual acuity loss related to cataract surgery). Work package 3 involved the development of prediction models for the Cat-PROM5-based self-reported outcomes from a cohort study of 1500 patients; assessment of the validity of preference-based health economic indices for cataract surgery and the calibration of these to Cat-PROM5; assessment of patients’ and health-care professionals’ views on risk–benefit presentation formats, the perceived usefulness of Cat-PROM5, the value of personalised risk–benefit information, high-value information items and shared decision-making; development of cataract decision aid frequently asked questions, incorporation of personalised estimates of risks and benefits; and development of a cataract decision quality measure to assess the quality of decision-making. Work package 4 involved a mixed-methods feasibility study for a fully powered randomised controlled trial of the use of the cataract decision aid and a qualitative study of discordant or mismatching perceptions of outcome between patients and health-care professionals. Setting Four English NHS recruitment centres were involved: Bristol (lead centre), Brighton, Gloucestershire and Torbay. Multicentre NHS cataract surgery data were obtained from the National Ophthalmology Database. Participants Work package 1 – participants (n = 822) were from all four centres. Work package 2 – electronic medical record data were taken from the National Ophthalmology Database (final set > 1M operations). Work package 3 – cohort study participants were from Bristol (n = 1200) and Gloucestershire (n = 300); qualitative and development work was undertaken with patients and health-care professionals from all four centres. Work package 4 – Bristol, Brighton and Torbay participated in the recruitment of patients (n = 42) for the feasibility trial and recruitment of health-care professionals for the qualitative elements. Interventions For the feasibility trial, the intervention was the use of the cataract decision aid, incorporating frequently asked questions and personalised estimations of both adverse outcomes and self-reported benefit. Main outcome measures There was a range of quantitative and qualitative outcome measures: questionnaire psychometric performance metrics, risk indicators of adverse surgical events and visual outcome, predictors of self-reported outcome following cataract surgery, patient and health-care practitioner views, health economic calibration measures and randomised controlled trial feasibility measures. Data sources The data sources were patient self-reported questionnaire responses, study clinical data collection forms, recorded interviews with patients and health-care professionals, and anonymised National Ophthalmology Database data. Results Work package 1 – Cat-PROM5 was developed and validated with excellent to good psychometric properties (Rasch reliability 0.9, intraclass correlation repeatability 0.9, unidimensionality with residual eigenvalues ≤ 1.5) and excellent responsiveness to surgical intervention (Cohen delta –1.45). Work package 2 – earlier risk models for posterior capsule rupture and visual acuity loss were broadly affirmed (C-statistic for posterior capsule rupture 0.64; visual acuity loss 0.71). Work package 3 – the Cat-PROM5-based self-reported outcome regression models were derived based on 1181 participants with complete data (R2 ≈ 30% for each). Of the four preference-based health economic indices assessed, two demonstrated reasonable performance. Cat-PROM5 was successfully calibrated to health economic indices; adjusted limited dependent variable mixture models offered good to excellent fit (root-mean-square error 0.10–0.16). The personalised quantitative risk information was generally perceived as beneficial. A cataract decision aid and cataract decision quality measure were successfully developed based on the views of patients and health-care professionals. Work package 4 – data completeness was good for the feasibility study primary and secondary variables both before and after intervention/surgery (data completeness range 100–88%). Considering ability to recruit, the sample size required, instrumentation and availability of necessary health economic data, a fully powered randomised controlled trial (patients, n = 800, effect size 0.2 standard deviations, power 80%; p = 0.05) of the cataract decision aid would be feasible following psychometric refinement of the primary outcome (the cataract decision quality measure). The cataract decision aid was generally well-received by patients and health-care professionals, with cautions raised regarding perceived time and workload barriers. Discordant outcomes mostly related to patient dissatisfaction, with no clinical problem found. Limitations The National Ophthalmology Database data are expected to include some errors (mitigated by large multicentre data aggregations). The feasibility randomised controlled trial primary outcome (the cataract decision quality measure) displayed psychometric imperfections requiring refinement. The clinical occurrence of discordant outcomes is uncommon and the study team experienced difficulty identifying patients in this situation. Future work Future work could include regular review of the risk models for adverse outcomes to ensure currency, and the technical precision of complex-numbers analysis of refractive outcome to invite opportunities to improve post-operative spectacle-free vision. In addition, a fully powered randomised controlled trial of the cataract decision aid would be feasible, following psychometric refinement of the primary outcome (the cataract decision quality measure); this would clarify its potential role in routine service delivery. Conclusions In this research programme, evidence-based clinical tools have been successfully developed to improve pre-operative decision-making in cataract surgery. These include a psychometrically robust, patient-reported outcome measure (Cat-PROM5); prediction models for patient self-reported outcomes using Cat-PROM5; prediction models for clinically adverse surgical events and adverse visual acuity outcomes; and a cataract decision aid with relevant general information and personalised risk/benefit predictions. In addition, the successful mapping of Cat-PROM5 to existing health economic indices was achieved and the performances of indices were assessed in patients undergoing cataract surgery. A future full-powered randomised controlled trial of the cataract decision aid would be feasible (patients, n = 800, effect size 0.2 standard deviations, power 80%; p = 0.05). Trial registration This trial is registered as ISRCTN11309852. Funding This project was funded by the National Institute for Health and Care Research (NIHR) Programme Grants for Applied Research programme and will be published in full in Programme Grants for Applied Research; Vol. 10, No. 9. See the NIHR Journals Library website for further project information

Establishing tephrostratigraphic frameworks to aid the study of abrupt climatic and glacial transitions: a case study of the Last Glacial-Interglacial Transition in the British Isles (c. 16-8 ka BP)

Distally dispersed tephra layers have become an important tool in the investigation of palaeoenvironmental and archaeological records across the globe. They offer possibilities for the synchronisation and improved chronological control in those records to which they can be traced and hence contribute to an improved understanding of the pattern and timing of environmental and archaeological change during periods of rapid climatic adjustment. However, their use as robust isochronous markers for synchronising records is frequently compromised by uncertainties relating to stratigraphical context, precise chronology and chemical composition. Here we collate and review the tephrostratigraphical information dating to the Last Glacial-Interglacial Transition (LGIT; c. 16-8 ka BP) in the British Isles based on published and unpublished records obtained from 54 sites. Based on details of their stratigraphic position, chronology and chemical composition, we propose that 26 individual eruption events may be represented in this collective record which spans the LGIT. The great majority of these eruptives can be traced in origin to Iceland, but we also report on the recent discoveries of ultra-distal tephra from the North American Cascades range, including for the first time the Mount St Helens J Tephra at a site in southern Ireland. These particular ultra-distal discoveries have resulted from a reinterpretation of older data, demonstrating the potential importance of ‘unknown’ analyses in older tephra datasets. The outcome of this review is a comprehensive but provisional tephrostratigraphic framework for the LGIT in the British Isles, which helps to focus future research on parts of the scheme that are in need of further development or testing. The results, therefore, make an important contribution to the wider European tephrostratigraphic framework, while adding new discoveries of transcontinental isochronous tephra markers

Highly trifluoromethylated platinum compounds

The homoleptic, square-planar organoplatinum(II) compound [NBu 4]2[Pt(CF3)4] (1) undergoes oxidative addition of CF3I under mild conditions to give rise to the octahedral organoplatinum(IV) complex [NBu4]2[Pt(CF 3)5I] (2). This highly trifluoromethylated species reacts with Ag+ salts of weakly coordinating anions in Me2CO under a wet-air stream to afford the aquo derivative [NBu4] [Pt(CF3)5(OH2)] (4) in around 75% yield. When the reaction of 2 with the same Ag+ salts is carried out in MeCN, the solvento compound [NBu4][Pt(CF3)5(NCMe)] (5) is obtained in around 80% yield. The aquo ligand in 4 as well as the MeCN ligand in 5 are labile and can be cleanly replaced by neutral and anionic ligands to furnish a series of pentakis(trifluoromethyl)platinate(IV) compounds with formulae [NBu4][Pt(CF3)5(L)] (L=CO (6), pyridine (py; 7), tetrahydrothiophene (tht; 8)) and [NBu4] 2[Pt(CF3)5X] (X=Cl (9), Br (10)). The unusual carbonyl-platinum(IV) derivative [NBu4][Pt(CF3) 5(CO)] (6) is thermally stable and has a νCO of 2194 cm-1. The crystal structures of 2̇CH2Cl2, 5, [PPh4][Pt(CF3)5(CO)] (6'), and 7 have been established by X-ray diffraction methods. Compound 2 has shown itself to be a convenient entry to the chemistry of highly trifluoromethylated platinum compounds. To the best of our knowledge, compounds 2 and 4-10 are the organoelement compounds with the highest CF3 content to have been isolated and adequately characterized to date.This work was supported by the Spanish MICINN (DGPTC)/ FEDER (project CTQ2008-06669-C02-01/BQU) and the Gobier no de Aragón (Grupo Consolidado E21: Química Inorgánica y de los Compuestos Organometálicos).Peer Reviewe