Hypothetical Estimands in Clinical Trials: A Unification of Causal Inference and Missing Data Methods.

The ICH E9 addendum introduces the term intercurrent event to refer to events that happen after treatment initiation and that can either preclude observation of the outcome of interest or affect its interpretation. It proposes five strategies for handling intercurrent events to form an estimand but does not suggest statistical methods for estimation. In this article we focus on the hypothetical strategy, where the treatment effect is defined under the hypothetical scenario in which the intercurrent event is prevented. For its estimation, we consider causal inference and missing data methods. We establish that certain "causal inference estimators" are identical to certain "missing data estimators." These links may help those familiar with one set of methods but not the other. Moreover, using potential outcome notation allows us to state more clearly the assumptions on which missing data methods rely to estimate hypothetical estimands. This helps to indicate whether estimating a hypothetical estimand is reasonable, and what data should be used in the analysis. We show that hypothetical estimands can be estimated by exploiting data after intercurrent event occurrence, which is typically not used. Supplementary materials for this article are available online.

Non-thermal disruption of ß-adrenergic receptor-activated Ca2+ signalling and apoptosis in human ES-derived cardiomyocytes by microwave electric fields at 2.4 GHz.

The ubiquity of wireless electronic-device connectivity has seen microwaves emerge as one of the fastest growing forms of electromagnetic exposure. A growing evidence-base refutes the claim that wireless technologies pose no risk to human health at current safety levels designed to limit thermal (heating) effects. The potential impact of non-thermal effects of microwave exposure, especially in electrically-excitable tissues (e.g., heart), remains controversial. We exposed human embryonic stem-cell derived cardiomyocytes (CM), under baseline and beta-adrenergic receptor (ß-AR)-stimulated conditions, to microwaves at 2.4 GHz, a frequency used extensively in wireless communication (e.g., 4G, Bluetooth™ and WiFi). To control for any effect of sample heating, experiments were done in CM subjected to matched rates of direct heating or CM maintained at 37 °C. Detailed profiling of the temporal and amplitude features of Ca2+ signalling in CM under these experimental conditions was reconciled with the extent and spatial clustering of apoptosis. The data show that exposure of CM to 2.4 GHz EMF eliminated the normal Ca2+ signalling response to ß-AR stimulation and provoked spatially-clustered apoptosis. This is first evidence that non-thermal effects of 2.4 GHz microwaves might have profound effects on human CM function, responsiveness to activation, and survival.

Mediation of the total effect of cystic fibrosis-related diabetes on mortality: A UK Cystic Fibrosis Registry cohort study.

AIM: To investigate whether the effect of cystic fibrosis-related diabetes (CFRD) on the composite outcome of mortality or transplant could act through lung function, pulmonary exacerbations and/or nutritional status. METHODS: A retrospective cohort of adult cystic fibrosis (CF) patients who had not been diagnosed with CFRD were identified from the UK Cystic Fibrosis Registry (n = 2750). Rate of death or transplant was compared between patients who did and did not develop CFRD (with insulin use) during follow-up using Poisson regression, separately by sex. Causal mediation methods were used to investigate whether lung function, pulmonary exacerbations and nutritional status lie on the causal pathway between insulin-treated CFRD and mortality/transplant. RESULTS: At all ages, the mortality/transplant rate was higher in both men and women diagnosed with CFRD. Pulmonary exacerbations were the strongest mediator of the effect of CFRD on mortality/transplant, with an estimated 15% [95% CI: 7%, 28%] of the effect at 2 years post-CFRD diagnosis attributed to exacerbations, growing to 24% [95% CI: 9%, 46%] at 4 years post-diagnosis. Neither lung function nor nutritional status were found to be significant mediators of this effect. Estimates were similar but with wider confidence intervals in a cohort that additionally included people with CFRD but not using insulin. CONCLUSION: There is evidence that pulmonary exacerbations mediate the effect of CFRD on mortality but, as they are estimated to mediate less than one-quarter of the total effect, the mechanism through which CFRD influences survival may involve other factors.

Methods of analysis for survival outcomes with time-updated mediators, with application to longitudinal disease registry data.

Mediation analysis is a useful tool to illuminate the mechanisms through which an exposure affects an outcome but statistical challenges exist with time-to-event outcomes and longitudinal observational data. Natural direct and indirect effects cannot be identified when there are exposure-induced confounders of the mediator-outcome relationship. Previous measurements of a repeatedly-measured mediator may themselves confound the relationship between the mediator and the outcome. To overcome these obstacles, two recent methods have been proposed, one based on path-specific effects and one based on an additive hazards model and the concept of exposure splitting. We investigate these techniques, focusing on their application to observational datasets. We apply both methods to an analysis of the UK Cystic Fibrosis Registry dataset to identify how much of the relationship between onset of cystic fibrosis-related diabetes and subsequent survival acts through pulmonary function. Statistical properties of the methods are investigated using simulation. Both methods produce unbiased estimates of indirect and direct effects in scenarios consistent with their stated assumptions but, if the data are measured infrequently, estimates may be biased. Findings are used to highlight considerations in the interpretation of the observational data analysis.

Using Negative Control Outcomes and Difference-in-Differences Analysis to Estimate Treatment Effects in an Entirely Treated Cohort: The Effect of Ivacaftor in Cystic Fibrosis.

When an entire cohort of patients receives a treatment, it is difficult to estimate the treatment effect in the treated because there are no directly comparable untreated patients. Attempts can be made to find a suitable control group (e.g., historical controls), but underlying differences between the treated and untreated can result in bias. Here we show how negative control outcomes combined with difference-in-differences analysis can be used to assess bias in treatment effect estimates and obtain unbiased estimates under certain assumptions. Causal diagrams and potential outcomes are used to explain the methods and assumptions. We apply the methods to UK Cystic Fibrosis Registry data to investigate the effect of ivacaftor, introduced in 2012 for a subset of the cystic fibrosis population with a particular genotype, on lung function and annual rate (days/year) of receiving intravenous (IV) antibiotics (i.e., IV days). We consider 2 negative control outcomes: outcomes measured in the pre-ivacaftor period and outcomes among persons ineligible for ivacaftor because of their genotype. Ivacaftor was found to improve lung function in year 1 (an approximately 6.5-percentage-point increase in ppFEV1), was associated with reduced lung function decline (an approximately 0.5-percentage-point decrease in annual ppFEV1 decline, though confidence intervals included 0), and reduced the annual rate of IV days (approximately 60% over 3 years).

CATS II Long-term Anthropometric and Metabolic Effects of Maternal Sub-optimal Thyroid Function in Offspring and Mothers.

CONTEXT AND OBJECTIVES: The Controlled Antenatal Thyroid Screening Study I (CATS-I) was a randomized controlled trial investigating the effects of levothyroxine therapy for suboptimal gestational thyroid function (SGTF), comparing outcomes in children of treated (SGTF-T) with untreated (SGTF-U) women during pregnancy. This follow-up study, CATS-II, reports the long-term effects on anthropometric, bone, and cardiometabolic outcomes in mothers and offspring and includes a group with normal gestational thyroid function (NGTF). DESIGN & PARTICIPANTS: 332 mothers (197 NGTF, 56 SGTF-U, 79 SGTF-T) aged 41.2±5.3 years (mean±SD) and 326 paired children assessed 9.3±1.0 years after birth for (i) body mass index (BMI); (ii) lean, fat, and bone mass by dual-energy X-ray absorptiometry; (iii) blood pressure, augmentation index, and aortic pulse-wave-velocity; and (iv) thyroid function, lipids, insulin, and adiponectin. The difference between group means was compared using linear regression. RESULTS: Offspring's measurements were similar between groups. Although maternal BMI was similar between groups at CATS-I, after 9 years (at CATS-II) SGTF-U mothers showed higher BMI (median [interquartile ratio] 28.3 [24.6-32.6] kg/m2) compared with NGTF (25.8 [22.9-30.0] kg/m2; P = 0.029), driven by fat mass increase. At CATS-II SGTF-U mothers also had higher thyroid-stimulating hormone (TSH) values (2.45 [1.43-3.50] mU/L) than NGTF (1.54 [1.12-2.07] mU/L; P = 0.015), since 64% had never received levothyroxine. At CATS-II, SGTF-T mothers had BMI (25.8 [23.1-29.8] kg/m2, P = 0.672) and TSH (1.68 [0.89-2.96] mU/L; P = 0.474) values similar to NGTF mothers. CONCLUSIONS: Levothyroxine supplementation of women with SGTF did not affect long-term offspring anthropometric, bone, and cardiometabolic measurements. However, absence of treatment was associated with sustained long-term increase in BMI and fat mass in women with SGTF.

Maternal Prepregnancy Weight Status and Adolescent Eating Disorder Behaviors: A Longitudinal Study of Risk Pathways.

BACKGROUND: Maternal characteristics and childhood growth have been identified as risk factors for eating disorders. Most studies to date have been unable to investigate these factors prospectively while accounting for their interdependencies. We address this by investigating whether the association of maternal prepregnancy body mass index (ppBMI) with adolescent eating disorder behaviors can be explained by childhood growth and/or a concurrent environmental pathway captured by maternal eating habits. METHODS: We analyzed data from girls participating in the Avon Longitudinal Study of Parents and Children (ALSPAC), a prospective UK cohort. The study had information on parentally and self-reported eating disorder behaviors at age 13/14 years (n = 3,529), maternal ppBMI and eating habits at age 8, child's birth weight, BMI from age 7 to 12, pubertal development at 11, and relevant confounders. We quantified contributions of childhood growth and concomitant maternal eating habits to the association of maternal ppBMI with eating disorder behaviors in terms of interventional disparity effects for multiple mediators. RESULTS: Maternal prepregnancy underweight was negatively associated with eating disorder behaviors (-0.18; 95% confidence interval: -0.29, -0.06), whereas overweight/obesity had the opposite relationship (0.25; 0.18, 0.32). Both were nearly fully explained by childhood growth. CONCLUSIONS: Although maternal ppBMI is associated with developing eating disorders, its role needs to be understood in the context of childhood factors, in particular childhood growth. The relatively small size of the remaining associations, once growth factors are hypothetically equalized across levels of maternal ppBMI, suggests that childhood growth is a potential area for prevention.

Estimating long-term treatment effects in observational data: A comparison of the performance of different methods under real-world uncertainty.

In the presence of time-dependent confounding, there are several methods available to estimate treatment effects. With correctly specified models and appropriate structural assumptions, any of these methods could provide consistent effect estimates, but with real-world data, all models will be misspecified and it is difficult to know if assumptions are violated. In this paper, we investigate five methods: inverse probability weighting of marginal structural models, history-adjusted marginal structural models, sequential conditional mean models, g-computation formula, and g-estimation of structural nested models. This work is motivated by an investigation of the effects of treatments in cystic fibrosis using the UK Cystic Fibrosis Registry data focussing on two outcomes: lung function (continuous outcome) and annual number of days receiving intravenous antibiotics (count outcome). We identified five features of this data that may affect the performance of the methods: misspecification of the causal null, long-term treatment effects, effect modification by time-varying covariates, misspecification of the direction of causal pathways, and censoring. In simulation studies, under ideal settings, all five methods provide consistent estimates of the treatment effect with little difference between methods. However, all methods performed poorly under some settings, highlighting the importance of using appropriate methods based on the data available. Furthermore, with the count outcome, the issue of non-collapsibility makes comparison between methods delivering marginal and conditional effects difficult. In many situations, we would recommend using more than one of the available methods for analysis, as if the effect estimates are very different, this would indicate potential issues with the analyses.

Socioeconomic determinants of growth in a longitudinal study in Nepal.

Socioeconomic status (SES) is associated with childhood anthropometry, but little is known about how it is associated with tissue growth and body composition. To investigate this, we looked at components of SES at birth with growth in early and mid-childhood, and body composition in a longitudinal study in Nepal. The exposure variables (material assets, land ownership, and maternal education) were quantified from questionnaire data before birth. Anthropometry data at birth, 2.5 and 8.5 years, were normalized using WHO reference ranges and conditional growth calculated. Associations with child growth and body composition were explored using multiple regression analysis. Complete anthropometry data were available for 793 children. There was a positive association between SES and height-for-age and weight-for-age, and a reduction in odds of stunting and underweight for each increase in rank of SES variable. Associations tended to be significant when moving from the lower to the upper asset score, from none to secondary education, and no land to >30 dhur (~500 m2 ). The strongest associations were for maternal secondary education, showing an increase of 0.6-0.7 z scores in height-for-age and weight-for-age at 2.5 and 8.5 years and 0.3 kg/m2 in fat and lean mass compared to no education. There was a positive association with conditional growth in the highest asset score group and secondary maternal education, and generally no association with land ownership. Our results show that SES at birth is important for the growth of children, with a greater association with fat mass. The greatest influence was maternal secondary education.

Analysis of Longitudinal Studies With Repeated Outcome Measures: Adjusting for Time-Dependent Confounding Using Conventional Methods.

Estimation of causal effects of time-varying exposures using longitudinal data is a common problem in epidemiology. When there are time-varying confounders, which may include past outcomes, affected by prior exposure, standard regression methods can lead to bias. Methods such as inverse probability weighted estimation of marginal structural models have been developed to address this problem. However, in this paper we show how standard regression methods can be used, even in the presence of time-dependent confounding, to estimate the total effect of an exposure on a subsequent outcome by controlling appropriately for prior exposures, outcomes, and time-varying covariates. We refer to the resulting estimation approach as sequential conditional mean models (SCMMs), which can be fitted using generalized estimating equations. We outline this approach and describe how including propensity score adjustment is advantageous. We compare the causal effects being estimated using SCMMs and marginal structural models, and we compare the two approaches using simulations. SCMMs enable more precise inferences, with greater robustness against model misspecification via propensity score adjustment, and easily accommodate continuous exposures and interactions. A new test for direct effects of past exposures on a subsequent outcome is described.

An Assessment and Extension of the Mechanism-Based Approach to the Identification of Age-Period-Cohort Models.

Many methods have been proposed to solve the age-period-cohort (APC) linear identification problem, but most are not theoretically informed and may lead to biased estimators of APC effects. One exception is the mechanism-based approach recently proposed and based on Pearl's front-door criterion; this approach ensures consistent APC effect estimators in the presence of a complete set of intermediate variables between one of age, period, cohort, and the outcome of interest, as long as the assumed parametric models for all the relevant causal pathways are correct. Through a simulation study mimicking APC data on cardiovascular mortality, we demonstrate possible pitfalls that users of the mechanism-based approach may encounter under realistic conditions: namely, when (1) the set of available intermediate variables is incomplete, (2) intermediate variables are affected by two or more of the APC variables (while this feature is not acknowledged in the analysis), and (3) unaccounted confounding is present between intermediate variables and the outcome. Furthermore, we show how the mechanism-based approach can be extended beyond the originally proposed linear and probit regression models to incorporate all generalized linear models, as well as nonlinearities in the predictors, using Monte Carlo simulation. Based on the observed biases resulting from departures from underlying assumptions, we formulate guidelines for the application of the mechanism-based approach (extended or not).

Interventional Effects for Mediation Analysis with Multiple Mediators.

The mediation formula for the identification of natural (in)direct effects has facilitated mediation analyses that better respect the nature of the data, with greater consideration of the need for confounding control. The default assumptions on which it relies are strong, however. In particular, they are known to be violated when confounders of the mediator-outcome association are affected by the exposure. This complicates extensions of counterfactual-based mediation analysis to settings that involve repeatedly measured mediators, or multiple correlated mediators. VanderWeele, Vansteelandt, and Robins introduced so-called interventional (in)direct effects. These can be identified under much weaker conditions than natural (in)direct effects, but have the drawback of not adding up to the total effect. In this article, we adapt their proposal to achieve an exact decomposition of the total effect, and extend it to the multiple mediator setting. Interestingly, the proposed effects capture the path-specific effects of an exposure on an outcome that are mediated by distinct mediators, even when-as often-the structural dependence between the multiple mediators is unknown, for instance, when the direction of the causal effects between the mediators is unknown, or there may be unmeasured common causes of the mediators.

A comparison of methods to adjust for continuous covariates in the analysis of randomised trials.

BACKGROUND: Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. METHODS: We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets. RESULTS: Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall. CONCLUSIONS: For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt.

Medication Use in Early-HD Participants in Track-HD: an Investigation of its Effects on Clinical Performance.

 Insufficient evidence exists to guide the long-term pharmacological management of Huntington's disease (HD) although most current interventions rely on symptomatic management. The effect of many frontline treatments on potential endpoints for HD clinical trials remains unknown. Our objective was to investigate how therapies widely used to manage HD affect the symptom for which they are prescribed and other endpoints using data from TRACK-HD. We used longitudinal models to estimate effects of medication use on performance on tests of motor, cognitive and neuropsychiatric function using data from 123 TRACK-HD stage 1/2 participants across four study visits. Adjustment for confounding by prior medication use, prior clinical performance, concomitant use of other medications, and baseline variables (sex, disease group, age, CAG, study site, education) enabled a closer-to-causal interpretation of the associations. Adjusting for baseline variables only, medication use was typically associated with worse clinical performance, reflecting greater medication use in more advanced patients. After additional adjustment for longitudinal confounders such "inverse" associations were generally eliminated and in the expected directions: participants taking neuroleptics tended to have better motor performance, improved affect and poorer cognitive performance, and those taking SSRI/SNRIs had less apathy, less affect and better total behaviour scores. However, we uncovered few statistically significant associations. Limitations include sample size and unmeasured confounding. In conclusion, adjustment for confounding by prior measurements largely eliminated associations between medication use and poorer clinical performance from simple analyses. However, there was little convincing evidence of causal effects of medication on clinical performance and larger cohorts or trials are needed.

Network Mendelian randomization: using genetic variants as instrumental variables to investigate mediation in causal pathways.

BACKGROUND: Mendelian randomization uses genetic variants, assumed to be instrumental variables for a particular exposure, to estimate the causal effect of that exposure on an outcome. If the instrumental variable criteria are satisfied, the resulting estimator is consistent even in the presence of unmeasured confounding and reverse causation. METHODS: We extend the Mendelian randomization paradigm to investigate more complex networks of relationships between variables, in particular where some of the effect of an exposure on the outcome may operate through an intermediate variable (a mediator). If instrumental variables for the exposure and mediator are available, direct and indirect effects of the exposure on the outcome can be estimated, for example using either a regression-based method or structural equation models. The direction of effect between the exposure and a possible mediator can also be assessed. Methods are illustrated in an applied example considering causal relationships between body mass index, C-reactive protein and uric acid. RESULTS: These estimators are consistent in the presence of unmeasured confounding if, in addition to the instrumental variable assumptions, the effects of both the exposure on the mediator and the mediator on the outcome are homogeneous across individuals and linear without interactions. Nevertheless, a simulation study demonstrates that even considerable heterogeneity in these effects does not lead to bias in the estimates. CONCLUSIONS: These methods can be used to estimate direct and indirect causal effects in a mediation setting, and have potential for the investigation of more complex networks between multiple interrelated exposures and disease outcomes.

Mediation analysis with intermediate confounding: structural equation modeling viewed through the causal inference lens.

The study of mediation has a long tradition in the social sciences and a relatively more recent one in epidemiology. The first school is linked to path analysis and structural equation models (SEMs), while the second is related mostly to methods developed within the potential outcomes approach to causal inference. By giving model-free definitions of direct and indirect effects and clear assumptions for their identification, the latter school has formalized notions intuitively developed in the former and has greatly increased the flexibility of the models involved. However, through its predominant focus on nonparametric identification, the causal inference approach to effect decomposition via natural effects is limited to settings that exclude intermediate confounders. Such confounders are naturally dealt with (albeit with the caveats of informality and modeling inflexibility) in the SEM framework. Therefore, it seems pertinent to revisit SEMs with intermediate confounders, armed with the formal definitions and (parametric) identification assumptions from causal inference. Here we investigate: 1) how identification assumptions affect the specification of SEMs, 2) whether the more restrictive SEM assumptions can be relaxed, and 3) whether existing sensitivity analyses can be extended to this setting. Data from the Avon Longitudinal Study of Parents and Children (1990-2005) are used for illustration.