Response to: Simpson’s Paradox is suppression, but Lord’s Paradox is neither: clarification of and correction to Tu, Gunnell, and Gilthorpe (2008) by Nickerson CA & Brown NJL (https://doi.org/10.1186/1742-7622-5-2)

We commend Nickerson and Brown on their insightful exposition of the mathematical algebra behind Simpson’s paradox, suppression and Lord’s paradox; we also acknowledge there can be differences in how Lord’s paradox is approached analytically, compared to Simpson’s paradox and suppression, though not in every example of Lord’s paradox. Furthermore, Simpson’s paradox, suppression and Lord’s paradox ask the same contextual questions, seeking to understand if statistical adjustment is valid and meaningful, identifying which analytical option is correct. In our exposition of this, we focus on the perspective of context, which must invoke causal thinking. From a causal thinking perspective, Simpson’s paradox, suppression and Lord’s paradox present very similar analytical challenges

Intervention differential effects and regression to the mean in studies where sample selection is based on the initial value of the outcome variable: an evaluation of methods illustrated in weight-management studies

© 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Background: Intervention differential effects (IDEs) occur where changes in an outcome depend upon the initial values of that outcome. Although methods to identify IDEs are well documented, there remains a lack of understanding about the circumstances under which these methods are robust. One context that has not been explored is the identification of intervention differential effect in studies where sample selection is based on the initial value of the outcome being evaluated. We hypothesise that, in such settings, established methods for detecting IDEs will struggle to discriminate these from regression to the mean. Methods: Using simulated datasets of weight-loss intervention programmes that recruit according to initial body mass index, we explore the reliability of Oldham's method and multilevel modelling (MLM) to detect IDEs. Results: In datasets simulated with no IDE, Oldham's method and MLM yield Type I error rates >90%, confirming that threshold selection/truncation leads to bias due to regression to the mean. Type I error rates return close to 5% for both methods when a control group is introduced. Conclusions: Oldham's method and MLM can robustly detect IDEs in this setting, but only if analyses incorporate a control group for comparison

Placental blood transfusion in newborn babies reaches a plateau after 140 s: Further analysis of longitudinal survey of weight change

Objective: With the introduction of active management of the third stage of labour in the 1960s, it became usual practice to clamp and cut the umbilical cord immediately following birth. The timing of this cord clamping is controversial, as blood may beneficially be transferred to the baby if clamping of the cord is delayed slightly. There is no agreement, however, on how long the delay should be before clamping the cord. This study aimed to establish when blood ceased to flow in the umbilical cord to determine how long to delay clamping of the umbilical cord following delivery of the term newborn to maximise placental transfusion. Methods: This observational study collected longitudinal weight measurements set in a hospital labour ward. A total of 26 mothers at term and their singleton babies participated in the study. In this reanalysis, the velocity of weight change over the first minutes of life determined by functional data analysis was estimated. Results: We found that the flow velocity in the umbilical cord was on average 0 at 125 s after placing the baby on the scales, which was typically 140 s after birth. Conclusions: To maximise placental transfusion, cord clamping should be delayed for at least 140 s following birth of the baby

Advanced Modelling Strategies: Challenges and pitfalls in robust causal inference with observational data

Advanced Modelling Strategies: Challenges and pitfalls in robust causal inference with observational data summarises the lecture notes prepared for a four-day workshop sponsored by the Society for Social Medicine and hosted by the Leeds Institute for Data Analytics (LIDA) at the University of Leeds on 17th-20th July 2017

Theory and performance of substitution models for estimating relative causal effects in nutritional epidemiology.

BACKGROUND: Estimating relative causal effects (i.e., "substitution effects") is a common aim of nutritional research. In observational data, this is usually attempted using 1 of 2 statistical modeling approaches: the leave-one-out model and the energy partition model. Despite their widespread use, there are concerns that neither approach is well understood in practice. OBJECTIVES: We aimed to explore and illustrate the theory and performance of the leave-one-out and energy partition models for estimating substitution effects in nutritional epidemiology. METHODS: Monte Carlo data simulations were used to illustrate the theory and performance of both the leave-one-out model and energy partition model, by considering 3 broad types of causal effect estimands: 1) direct substitutions of the exposure with a single component, 2) inadvertent substitutions of the exposure with several components, and 3) average relative causal effects of the exposure instead of all other dietary sources. Models containing macronutrients, foods measured in calories, and foods measured in grams were all examined. RESULTS: The leave-one-out and energy partition models both performed equally well when the target estimand involved substituting a single exposure with a single component, provided all variables were measured in the same units. Bias occurred when the substitution involved >1 substituting component. Leave-one-out models that examined foods in mass while adjusting for total energy intake evaluated obscure estimands. CONCLUSIONS: Regardless of the approach, substitution models need to be constructed from clearly defined causal effect estimands. Estimands involving a single exposure and a single substituting component are typically estimated more accurately than estimands involving more complex substitutions. The practice of examining foods measured in grams or portions while adjusting for total energy intake is likely to deliver obscure relative effect estimands with unclear interpretations

Reflection on modern methods: generalized linear models for prognosis and intervention—theory, practice and implications for machine learning

Prediction and causal explanation are fundamentally distinct tasks of data analysis. In health applications, this difference can be understood in terms of the difference between prognosis (prediction) and prevention/treatment (causal explanation). Nevertheless, these two concepts are often conflated in practice. We use the framework of generalized linear models (GLMs) to illustrate that predictive and causal queries require distinct processes for their application and subsequent interpretation of results. In particular, we identify five primary ways in which GLMs for prediction differ from GLMs for causal inference: (i) the covariates that should be considered for inclusion in (and possibly exclusion from) the model; (ii) how a suitable set of covariates to include in the model is determined; (iii) which covariates are ultimately selected and what functional form (i.e. parameterization) they take; (iv) how the model is evaluated; and (v) how the model is interpreted. We outline some of the potential consequences of failing to acknowledge and respect these differences, and additionally consider the implications for machine learning (ML) methods. We then conclude with three recommendations that we hope will help ensure that both prediction and causal modelling are used appropriately and to greatest effect in health research

The impact of the Calman–Hine report on the processes and outcomes of care for Yorkshire's colorectal cancer patients

The 1995 Calman–Hine plan outlined radical reform of the UK's cancer services with the aim of improving outcomes and reducing inequalities in NHS cancer care. Its main recommendation was to concentrate care into the hands of site-specialist, multi-disciplinary teams. This study aimed to determine if the implementation of Calman–Hine cancer teams was associated with improved processes and outcomes of care for colorectal cancer patients. The design included longitudinal survey of 13 colorectal cancer teams in Yorkshire and retrospective study of population-based data collected by the Northern and Yorkshire Cancer Registry and Information Service. The population was all colorectal cancer patients diagnosed and treated in Yorkshire between 1995 and 2000. The main outcome measures were: variations in the use of anterior resection and preoperative radiotherapy in rectal cancer, chemotherapy in Dukes stage C and D patients, and five-year survival. Using multilevel models, these outcomes were assessed in relation to measures of the extent of Calman–Hine implementation throughout the study period, namely: (i) each team's degree of adherence to the Manual of Cancer Service Standards (which outlines the specification of the ‘ideal’ colorectal cancer team) and (ii) the extent of site specialisation of each team's surgeons. Variation was observed in the extent to which the colorectal cancer teams in Yorkshire had conformed to the Calman–Hine recommendations. An increase in surgical site specialisation was associated with increased use of preoperative radiotherapy (OR=1.43, 95% CI=1.04–1.98, P<0.04) and anterior resection (OR=1.43, 95% CI=1.16–1.76, P<0.01) in rectal cancer patients. Increases in adherence to the Manual of Cancer Service Standards was associated with improved five-year survival after adjustment for the casemix factors of age, stage of disease, socioeconomic status and year of diagnosis, especially for colon cancer (HR=0.97, 95% CI=0.94–0.99 P<0.01). There was a similar trend of improved survival in relation to increased surgical site specialisation for rectal cancer, although the effect was not statistically significant (HR=0.93, 95% CI=0.84–1.03, P=0.15). In conclusion, the extent of implementation of the Calman–Hine report has been variable and its recommendations are associated with improvements in processes and outcomes of care for colorectal cancer patients

The Authors Respond

Although the studies highlighted in Kinlen and Peto’s letter describe situations they take to be “national in scope”, none of these adopted the ‘region-wide’ analysis we recommend. Rather, these studies have focussed on rural areas with small populations experiencing extreme levels of inward-migration that had been selected from larger regions/nation states. To definitively avoid bias, our study points to the need for comparisons of areas with varying levels of inward migration, either by comparing all areas within an entire region/nation state or random subsets thereof

Simplifying the interpretation of continuous time models for spatio-temporal networks

Autoregressive and moving average models for temporally dynamic networks treat time as a series of discrete steps which assumes even intervals between data measurements and can introduce bias if this assumption is not met. Using real and simulated data from the London Underground network, this paper illustrates the use of continuous time multilevel models to capture temporal trajectories of edge properties without the need for simultaneous measurements, along with two methods for producing interpretable summaries of model results. These including extracting ‘features’ of temporal patterns (e.g. maxima, time of maxima) which have utility in understanding the network properties of each connection and summarising whole-network properties as a continuous function of time which allows estimation of network properties at any time without temporal aggregation of non-simultaneous measurements. Results for temporal pattern features in the response variable were captured with reasonable accuracy. Variation in the temporal pattern features for the exposure variable was underestimated by the models. The models showed some lack of precision. Both model summaries provided clear ‘real-world’ interpretations and could be applied to data from a range of spatio-temporal network structures (e.g. rivers, social networks). These models should be tested more extensively in a range of scenarios, with potential improvements such as random effects in the exposure variable dimension

Excess mortality and guideline-indicated care following non-ST-elevation myocardial infarction

BACKGROUND: Adherence to guideline-indicated care for the treatment of non-ST-elevation myocardial infarction (NSTEMI) is associated with improved outcomes. We investigated the extent and consequences of non-adherence to guideline-indicated care across a national health system. METHODS: A cohort study (ClinicalTrials.gov identifier: NCT02436187) was conducted using data from the Myocardial Ischaemia National Audit Project (n = 389,057 NSTEMI, n = 247 hospitals, England and Wales, 2003-2013). Accelerated failure time models were used to quantify the impact of non-adherence on survival according to dates of guideline publication. RESULTS: Over a period of 1,079,044 person-years (median 2.2 years of follow-up), 113,586 (29.2%) NSTEMI patients died. Of those eligible to receive care, 337,881 (86.9%) did not receive one or more guideline-indicated intervention; the most frequently missed were dietary advice (n = 254,869, 68.1%), smoking cessation advice (n = 245,357, 87.9%), P2Y12 inhibitors (n = 192,906, 66.3%) and coronary angiography (n = 161,853, 43.4%). Missed interventions with the strongest impact on reduced survival were coronary angiography (time ratio: 0.18, 95% confidence interval (CI): 0.17-0.18), cardiac rehabilitation (time ratio: 0.49, 95% CI: 0.48-0.50), smoking cessation advice (time ratio: 0.53, 95% CI: 0.51-0.57) and statins (time ratio: 0.56, 95% CI: 0.55-0.58). If all eligible patients in the study had received optimal care at the time of guideline publication, then 32,765 (28.9%) deaths (95% CI: 30,531-33,509) may have been prevented. CONCLUSION: The majority of patients hospitalised with NSTEMI missed at least one guideline-indicated intervention for which they were eligible. This was significantly associated with excess mortality. Greater attention to the provision of guideline-indicated care for the management of NSTEMI will reduce premature cardiovascular deaths