Rhian Daniel

Methods for dealing with time-dependent confounding.

Longitudinal studies, where data are repeatedly collected on subjects over a period, are common in medical research. When estimating the effect of a time-varying treatment or exposure on an outcome of interest measured at a later time, standard methods fail to give consistent estimators in the presence of time-varying confounders if those confounders are themselves affected by the treatment. Robins and colleagues have proposed several alternative methods that, provided certain assumptions hold, avoid the problems associated with standard approaches. They include the g-computation formula, inverse probability weighted estimation of marginal structural models and g-estimation of structural nested models. In this tutorial, we give a description of each of these methods, exploring the links and differences between them and the reasons for choosing one over the others in different settings.

Incidence of community-acquired lower respiratory tract infections and pneumonia among older adults in the United Kingdom: a population-based study

Community-acquired lower respiratory tract infections (LRTI) and pneumonia (CAP) are common causes of morbidity and mortality among those aged ≥65 years; a growing population in many countries. Detailed incidence estimates for these infections among older adults in the United Kingdom (UK) are lacking. We used electronic general practice records from the Clinical Practice Research Data link, linked to Hospital Episode Statistics inpatient data, to estimate incidence of community-acquired LRTI and CAP among UK older adults between April 1997-March 2011, by age, sex, region and deprivation quintile. Levels of antibiotic prescribing were also assessed. LRTI incidence increased with fluctuations over time, was higher in men than women aged ≥70 and increased with age from 92.21 episodes/1000 person-years (65-69 years) to 187.91/1000 (85-89 years). CAP incidence increased more markedly with age, from 2.81 to 21.81 episodes/1000 person-years respectively, and was higher among men. For both infection groups, increases over time were attenuated after age-standardisation, indicating that these rises were largely due to population aging. Rates among those in the most deprived quintile were around 70% higher than the least deprived and were generally higher in the North of England. GP antibiotic prescribing rates were high for LRTI but lower for CAP (mostly due to immediate hospitalisation). This is the first study to provide long-term detailed incidence estimates of community-acquired LRTI and CAP in UK older individuals, taking person-time at risk into account. The summary incidence commonly presented for the ≥65 age group considerably underestimates LRTI/CAP rates, particularly among older individuals within this group. Our methodology and findings are likely to be highly relevant to health planners and researchers in other countries with aging populations.

Using causal diagrams to guide analysis in missing data problems.

Estimating causal effects from incomplete data requires additional and inherently untestable assumptions regarding the mechanism giving rise to the missing data. We show that using causal diagrams to represent these additional assumptions both complements and clarifies some of the central issues in missing data theory, such as Rubins classification of missingness mechanisms (as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR)) and the circumstances in which causal effects can be estimated without bias by analysing only the subjects with complete data. In doing so, we formally extend the back-door criterion of Pearl and others for use in incomplete data examples. These ideas are illustrated with an example drawn from an occupational cohort study of the effect of cosmic radiation on skin cancer incidence.

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.

Causal mediation analysis with multiple mediators.

In diverse fields of empirical research—including many in the biological sciences—attempts are made to decompose the effect of an exposure on an outcome into its effects via a number of different pathways. For example, we may wish to separate the effect of heavy alcohol consumption on systolic blood pressure (SBP) into effects via body mass index (BMI), via gamma-glutamyl transpeptidase (GGT), and via other pathways. Much progress has been made, mainly due to contributions from the field of causal inference, in understanding the precise nature of statistical estimands that capture such intuitive effects, the assumptions under which they can be identified, and statistical methods for doing so. These contributions have focused almost entirely on settings with a single mediator, or a set of mediators considered en bloc; in many applications, however, researchers attempt a much more ambitious decomposition into numerous path-specific effects through many mediators. In this article, we give counterfactual definitions of such path-specific estimands in settings with multiple mediators, when earlier mediators may affect later ones, showing that there are many ways in which decomposition can be done. We discuss the strong assumptions under which the effects are identified, suggesting a sensitivity analysis approach when a particular subset of the assumptions cannot be justified. These ideas are illustrated using data on alcohol consumption, SBP, BMI, and GGT from the Izhevsk Family Study. We aim to bridge the gap from “single mediator theory” to “multiple mediator practice,” highlighting the ambitious nature of this endeavor and giving practical suggestions on how to proceed.

On regression adjustment for the propensity score

Propensity scores are widely adopted in observational research because they enable adjustment for high-dimensional confounders without requiring models for their association with the outcome of interest. The results of statistical analyses based on stratification, matching or inverse weighting by the propensity score are therefore less susceptible to model extrapolation than those based solely on outcome regression models. This is attractive because extrapolation in outcome regression models may be alarming, yet difficult to diagnose, when the exposed and unexposed individuals have very different covariate distributions. Standard regression adjustment for the propensity score forms an alternative to the aforementioned propensity score methods, but the benefits of this are less clear because it still involves modelling the outcome in addition to the propensity score. In this article, we develop novel insights into the properties of this adjustment method. We demonstrate that standard tests of the null hypothesis of no exposure effect (based on robust variance estimators), as well as particular standardised effects obtained from such adjusted regression models, are robust against misspecification of the outcome model when a propensity score model is correctly specified; they are thus not vulnerable to the aforementioned problem of extrapolation. We moreover propose efficient estimators for these standardised effects, which retain a useful causal interpretation even when the propensity score model is misspecified, provided the outcome regression model is correctly specified.

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.

Outcome modelling strategies in epidemiology: traditional methods and basic alternatives

Abstract Controlling for too many potential confounders can lead to or aggravate problems of data sparsity or multicollinearity, particularly when the number of covariates is large in relation to the study size. As a result, methods to reduce the number of modelled covariates are often deployed. We review several traditional modelling strategies, including stepwise regression and the ‘change-in-estimate’ (CIE) approach to deciding which potential confounders to include in an outcome-regression model for estimating effects of a targeted exposure. We discuss their shortcomings, and then provide some basic alternatives and refinements that do not require special macros or programming. Throughout, we assume the main goal is to derive the most accurate effect estimates obtainable from the data and commercial software. Allowing that most users must stay within standard software packages, this goal can be roughly approximated using basic methods to assess, and thereby minimize, mean squared error (MSE).

Prevalence of symptoms of childhood asthma, allergic rhinoconjunctivitis and eczema in the Pacific: The International Study of Asthma and Allergies in Childhood (ISAAC)

The International Study of Asthma and Allergies in Childhood (ISAAC) has provided valuable information regarding international prevalence patterns and potential risk factors for asthma, allergic rhinoconjunctivitis and eczema. However, the only Pacific countries that participated in ISAAC Phase I were Australia and New Zealand, and these included only a small number of Pacific children. Phase III has involved not only repeating the Phase I survey to examine time trends, but also to include centres and countries which are of interest but did not participate in Phase I. The ISAAC Phase III study was therefore conducted in the Pacific (in French Polynesia, New Caledonia, Tonga, Fiji Islands, Samoa, Cook Islands, Tokelau Islands and Niue). The overall prevalence rates of current symptoms (in the last 12 months) were 9.9% for asthma, 16.4% for allergic rhinoconjunctivitis and 10.7% for atopic eczema. The prevalence of current wheezing (9.9%) was generally much lower than that has been observed in Pacific children in New Zealand (31%), but there was considerable variation between the various Pacific centres: Tokelau Islands (19.7%), Tonga (16.2%), Niue (12.7%), French Polynesia (11.3%), Cook Islands (10.6%), Fiji Islands (10.4%), New Caledonia (8.2%) and Samoa (5.8%). The reasons for these differences in prevalence across the Pacific are unclear and require further research. The finding that prevalence levels are generally considerably lower than those in Pacific children in New Zealand adds to previous evidence that children who migrate experience an altered risk of asthma as a result of exposure to a new environment during childhood.

A method for increasing the robustness of multiple imputation

Missing data are common wherever statistical methods are applied in practice. They present a problem in that they require that additional assumptions be made about the mechanism leading to the incompleteness of the data. By incorporating two models for the missing data process, doubly robust (DR) weighting-based methods offer some protection against misspecification bias since inferences are valid when at least one of the two models is correctly specified. The balance between robustness, efficiency and analytical complexity is one which is difficult to strike, resulting in a split between the likelihood and multiple imputation (MI) school on one hand and the weighting and DR school on the other. An extension of MI is proposed that, in certain settings, can be shown to give rise to DR estimators. It is conjectured that this additional robustness holds more generally, as demonstrated using simulation studies. The method is applied to data from the RECORD study, a clinical trial comparing anti-glycaemic combination therapies in type II diabetes patients.