Meta-analytical methods to identify who benefits most from treatments: daft, deluded, or deft approach?

Identifying which individuals benefit most from particular treatments or other interventions underpins so-called personalised or stratified medicine. However, single trials are typically underpowered for exploring whether participant characteristics, such as age or disease severity, determine an individual’s response to treatment. A meta-analysis of multiple trials, particularly one where individual participant data (IPD) are available, provides greater power to investigate interactions between participant characteristics (covariates) and treatment effects. We use a published IPD meta-analysis to illustrate three broad approaches used for testing such interactions. Based on another systematic review of recently published IPD meta-analyses, we also show that all three approaches can be applied to aggregate data as well as IPD. We also summarise which methods of analysing and presenting interactions are in current use, and describe their advantages and disadvantages. We recommend that testing for interactions using within-trials information alone (the deft approach) becomes standard practice, alongside graphical presentation that directly visualises this

Non-inferiority trials: are they inferior? A systematic review of reporting in major medical journals

OBJECTIVE: To assess the adequacy of reporting of non-inferiority trials alongside the consistency and utility of current recommended analyses and guidelines. DESIGN: Review of randomised clinical trials that used a non-inferiority design published between January 2010 and May 2015 in medical journals that had an impact factor >10 (JAMA Internal Medicine, Archives Internal Medicine, PLOS Medicine, Annals of Internal Medicine, BMJ, JAMA, Lancet and New England Journal of Medicine). DATA SOURCES: Ovid (MEDLINE). METHODS: We searched for non-inferiority trials and assessed the following: choice of non-inferiority margin and justification of margin; power and significance level for sample size; patient population used and how this was defined; any missing data methods used and assumptions declared and any sensitivity analyses used. RESULTS: A total of 168 trial publications were included. Most trials concluded non-inferiority (132; 79%). The non-inferiority margin was reported for 98% (164), but less than half reported any justification for the margin (77; 46%). While most chose two different analyses (91; 54%) the most common being intention-to-treat (ITT) or modified ITT and per-protocol, a large number of articles only chose to conduct and report one analysis (65; 39%), most commonly the ITT analysis. There was lack of clarity or inconsistency between the type I error rate and corresponding CIs for 73 (43%) articles. Missing data were rarely considered with (99; 59%) not declaring whether imputation techniques were used. CONCLUSIONS: Reporting and conduct of non-inferiority trials is inconsistent and does not follow the recommendations in available statistical guidelines, which are not wholly consistent themselves. Authors should clearly describe the methods used and provide clear descriptions of and justifications for their design and primary analysis. Failure to do this risks misleading conclusions being drawn, with consequent effects on clinical practice

Estimands: bringing clarity and focus to research questions in clinical trials

Precise specification of the research question and associated treatment effect of interest is essential in clinical research, yet recent work shows that they are often incompletely specified. The ICH E9 (R1) Addendum on Estimands and Sensitivity Analysis in Clinical Trials introduces a framework that supports researchers in precisely and transparently specifying the treatment effect they aim to estimate in their clinical trial. In this paper, we present practical examples to demonstrate to all researchers involved in clinical trials how estimands can help them to specify the research question, lead to a better understanding of the treatment effect to be estimated and hence increase the probability of success of the trial

Reference based sensitivity analysis for longitudinal trials with protocol deviation via multiple imputation

Randomised controlled trials provide essential evidence for the evaluation of new and existing medical treatments. Unfortunately the statistical analysis is often complicated by the occurrence of protocol deviations, which mean we cannot always measure the intended outcomes for individuals who deviate, resulting in a missing data problem. In such settings, however one approaches the analysis, an untestable assumption about the distribution of the unobserved data must be made. To understand how far the results depend on these assumptions, the primary analysis should be supplemented by a range of sensitivity analyses, which explore how the conclusions vary over a range of different credible assumptions for the missing data. In this article we describe a new command, mimix, that can be used to perform reference based sensitivity analyses for randomised controlled trials with longitudinal quantitative outcome data, using the approach proposed by Carpenter, Roger, and Kenward (2013). Under this approach, we make qualitative assumptions about how individuals' missing outcomes relate to those observed in relevant groups in the trial, based on plausible clinical scenarios. Statistical analysis then proceeds using the method of multiple imputation

Population-calibrated Multiple Imputation for a Binary/categorical Covariate in Categorical Regression Models

Multiple imputation (MI) has become popular for analyses with missing data in medical research. The standard implementation of MI is based on the assumption of data being missing at random (MAR). However, for missing data generated by missing not at random mechanisms, MI performed assuming MAR might not be satisfactory. For an incomplete variable in a given data set, its corresponding population marginal distribution might also be available in an external data source. We show how this information can be readily utilised in the imputation model to calibrate inference to the population by incorporating an appropriately calculated offset termed the "calibrated-δ adjustment." We describe the derivation of this offset from the population distribution of the incomplete variable and show how, in applications, it can be used to closely (and often exactly) match the post-imputation distribution to the population level. Through analytic and simulation studies, we show that our proposed calibrated-δ adjustment MI method can give the same inference as standard MI when data are MAR, and can produce more accurate inference under two general missing not at random missingness mechanisms. The method is used to impute missing ethnicity data in a type 2 diabetes prevalence case study using UK primary care electronic health records, where it results in scientifically relevant changes in inference for non-White ethnic groups compared with standard MI. Calibrated-δ adjustment MI represents a pragmatic approach for utilising available population-level information in a sensitivity analysis to explore potential departures from the MAR assumption

Making Associativity Operational

The purpose of this paper is to propose an operational idea for developing algebraic thinking in the absence of alphanumeric symbols. The paper reports on a design experiment encouraging preschool children to use the associative property algebraically. We describe the theoretical basis of the design, the tasks used, and examples of algebraic thinking in 5–6-year-old children. Theoretically, the paper makes a critical distinction between operational and structural meanings of the notion of equality. We argue that mathematical thinking involving equality among young learners can comprise both an operational and a structural conception and that the operational conception has a side that is productively linked to the structural conception. Using carefully designed hands-on tasks, the crux of the paper is the realization of algebraic thinking (in verbal mathematics) as operationally experienced in the ability to transform one number structure, with a quantity that is subject to change, into another through equality-preserving transformations

Effects of local hypothermia-rewarming on physiology, metabolism and inflammation of acutely injured human spinal cord.

In five patients with acute, severe thoracic traumatic spinal cord injuries (TSCIs), American spinal injuries association Impairment Scale (AIS) grades A-C, we induced cord hypothermia (33 °C) then rewarming (37 °C). A pressure probe and a microdialysis catheter were placed intradurally at the injury site to monitor intraspinal pressure (ISP), spinal cord perfusion pressure (SCPP), tissue metabolism and inflammation. Cord hypothermia-rewarming, applied to awake patients, did not cause discomfort or neurological deterioration. Cooling did not affect cord physiology (ISP, SCPP), but markedly altered cord metabolism (increased glucose, lactate, lactate/pyruvate ratio (LPR), glutamate; decreased glycerol) and markedly reduced cord inflammation (reduced IL1β, IL8, MCP, MIP1α, MIP1β). Compared with pre-cooling baseline, rewarming was associated with significantly worse cord physiology (increased ICP, decreased SCPP), cord metabolism (increased lactate, LPR; decreased glucose, glycerol) and cord inflammation (increased IL1β, IL8, IL4, IL10, MCP, MIP1α). The study was terminated because three patients developed delayed wound infections. At 18-months, two patients improved and three stayed the same. We conclude that, after TSCI, hypothermia is potentially beneficial by reducing cord inflammation, though after rewarming these benefits are lost due to increases in cord swelling, ischemia and inflammation. We thus urge caution when using hypothermia-rewarming therapeutically in TSCI

Doom and Boom on a Resilient Reef: Climate Change, Algal Overgrowth and Coral Recovery

Background: Coral reefs around the world are experiencing large-scale degradation, largely due to global climate change, overfishing, diseases and eutrophication. Climate change models suggest increasing frequency and severity of warming-induced coral bleaching events, with consequent increases in coral mortality and algal overgrowth. Critically, the recovery of damaged reefs will depend on the reversibility of seaweed blooms, generally considered to depend on grazing of the seaweed, and replenishment of corals by larvae that successfully recruit to damaged reefs. These processes usually take years to decades to bring a reef back to coral dominance

Herbivory, Connectivity, and Ecosystem Resilience: Response of a Coral Reef to a Large-Scale Perturbation

Coral reefs world-wide are threatened by escalating local and global impacts, and some impacted reefs have shifted from coral dominance to a state dominated by macroalgae. Therefore, there is a growing need to understand the processes that affect the capacity of these ecosystems to return to coral dominance following disturbances, including those that prevent the establishment of persistent stands of macroalgae. Unlike many reefs in the Caribbean, over the last several decades, reefs around the Indo-Pacific island of Moorea, French Polynesia have consistently returned to coral dominance following major perturbations without shifting to a macroalgae-dominated state. Here, we present evidence of a rapid increase in populations of herbivorous fishes following the most recent perturbation, and show that grazing by these herbivores has prevented the establishment of macroalgae following near complete loss of coral on offshore reefs. Importantly, we found the positive response of herbivorous fishes to increased benthic primary productivity associated with coral loss was driven largely by parrotfishes that initially recruit to stable nursery habitat within the lagoons before moving to offshore reefs later in life. These results underscore the importance of connectivity between the lagoon and offshore reefs for preventing the establishment of macroalgae following disturbances, and indicate that protecting nearshore nursery habitat of herbivorous fishes is critical for maintaining reef resilience

Listening In on the Past: What Can Otolith δ18O Values Really Tell Us about the Environmental History of Fishes?

Oxygen isotope ratios from fish otoliths are used to discriminate marine stocks and reconstruct past climate, assuming that variations in otolith δ18O values closely reflect differences in temperature history of fish when accounting for salinity induced variability in water δ18O. To investigate this, we exploited the environmental and migratory data gathered from a decade using archival tags to study the behaviour of adult plaice (Pleuronectes platessa L.) in the North Sea. Based on the tag-derived monthly distributions of the fish and corresponding temperature and salinity estimates modelled across three consecutive years, we first predicted annual otolith δ18O values for three geographically discrete offshore sub-stocks, using three alternative plausible scenarios for otolith growth. Comparison of predicted vs. measured annual δ18O values demonstrated >96% correct prediction of sub-stock membership, irrespective of the otolith growth scenario. Pronounced inter-stock differences in δ18O values, notably in summer, provide a robust marker for reconstructing broad-scale plaice distribution in the North Sea. However, although largely congruent, measured and predicted annual δ18O values of did not fully match. Small, but consistent, offsets were also observed between individual high-resolution otolith δ18O values measured during tag recording time and corresponding δ18O predictions using concomitant tag-recorded temperatures and location-specific salinity estimates. The nature of the shifts differed among sub-stocks, suggesting specific vital effects linked to variation in physiological response to temperature. Therefore, although otolith δ18O in free-ranging fish largely reflects environmental temperature and salinity, we counsel prudence when interpreting otolith δ18O data for stock discrimination or temperature reconstruction until the mechanisms underpinning otolith δ18O signature acquisition, and associated variation, are clarified