Efficient estimation of the distribution of time to composite endpoint when some endpoints are only partially observed.

Two common features of clinical trials, and other longitudinal studies, are (1) a primary interest in composite endpoints, and (2) the problem of subjects withdrawing prematurely from the study. In some settings, withdrawal may only affect observation of some components of the composite endpoint, for example when another component is death, information on which may be available from a national registry. In this paper, we use the theory of augmented inverse probability weighted estimating equations to show how such partial information on the composite endpoint for subjects who withdraw from the study can be incorporated in a principled way into the estimation of the distribution of time to composite endpoint, typically leading to increased efficiency without relying on additional assumptions above those that would be made by standard approaches. We describe our proposed approach theoretically, and demonstrate its properties in a simulation study

Making apples from oranges: Comparing noncollapsible effect estimators and their standard errors after adjustment for different covariate sets

We revisit the well‐known but often misunderstood issue of (non)collapsibility of effect measures in regression models for binary and time‐to‐event outcomes. We describe an existing simple but largely ignored procedure for marginalizing estimates of conditional odds ratios and propose a similar procedure for marginalizing estimates of conditional hazard ratios (allowing for right censoring), demonstrating its performance in simulation studies and in a reanalysis of data from a small randomized trial in primary biliary cirrhosis patients. In addition, we aim to provide an educational summary of issues surrounding (non)collapsibility from a causal inference perspective and to promote the idea that the words conditional and adjusted (likewise marginal and unadjusted) should not be used interchangeably

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

Outcome modelling strategies in epidemiology: traditional methods and basic alternatives.

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)

How much do tumor stage and treatment explain socioeconomic inequalities in breast cancer survival? Applying causal mediation analysis to population-based data

Substantial socioeconomic inequalities in breast cancer survival persist in England, possibly due to more advanced cancer at diagnosis and differential access to treatment. We aim to disentangle the contributions of differential stage at diagnosis and differential treatment to the socioeconomic inequalities in cancer survival. Information on 36,793 women diagnosed with breast cancer during 2000–2007 was routinely collected by an English population-based cancer registry. Deprivation was determined for each patient according to her area of residence at the time of diagnosis. A parametric implementation of the mediation formula using Monte Carlo simulation was used to estimate the proportion of the effect of deprivation on survival mediated by stage and by treatment. One-third (35 % [23–48 %]) of the higher mortality experienced by most deprived patients at 6 months after diagnosis, and one tenth (14 % [−3 to 31 %]) at 5 years, was mediated by adverse stage distribution. We initially found no evidence of mediation via differential surgical treatment. However, sensitivity analyses testing some of our study limitations showed in particular that up to thirty per cent of the higher mortality in most deprived patients could be mediated by differential surgical treatment. This study illustrates the importance of using causal inference methods with routine medical data and the need for testing key assumptions through sensitivity analyses. Our results suggest that, although effort for earlier diagnosis is important, this would reduce the cancer survival inequalities only by a third. Because of data limitations, role of differential surgical treatment may have been under-estimated

Data-adaptive doubly robust instrumental variable methods for treatment effect heterogeneity

We consider the estimation of the average treatment effect in the treated as a function of baseline covariates, where there is a valid (conditional) instrument. We describe two doubly-robust (DR) estimators: a g-estimator and a targeted minimum loss-based estimator (TMLE). These estimators can be viewed as generalisations of the two-stage least squares (TSLS) method to semiparametric models that make weaker assumptions. We exploit recent theoretical results and use data-adaptive estimation of the nuisance parameters for the g-estimator. A simulation study is used to compare standard TSLS with the two DR estimators’ finite-sample performance when using (1) parametric or (2) data-adaptive estimation of the nuisance parameters. Data-adaptive DR estimators have lower bias and improved coverage, when compared to incorrectly specified parametric DR estimators and TSLS. When the parametric model for the treatment effect curve is correctly specified, the g-estimator outperforms all others, but when this model is misspecified, TMLE performs best, while TSLS can result in large biases and zero coverage. The methods are also applied to the COPERS (COping with persistent Pain, Effectiveness Research in Selfmanagement) trial to make inferences about the causal effect of treatment actually received, and the extent to which this is modified by depression at baseline

Proposer of the vote of thanks and contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes

Vansteelandt and Dukes (henceforth VD) propose a practical resolution to an important tension between two philosophies of statistical inference. I summarise these aspects before discussing how we might revise our understanding of ‘bias–variance trade-off’ in statistical modelling in the light of VD’s work

Monotherapy with major antihypertensive drug classes and risk of hospital admissions for mood disorders

Major depressive and bipolar disorders predispose to atherosclerosis, and there is accruing data from animal model, epidemiological, and genomic studies that commonly used antihypertensive drugs may have a role in the pathogenesis or course of mood disorders. In this study, we propose to determine whether antihypertensive drugs have an impact on mood disorders through the analysis of patients on monotherapy with different classes of antihypertensive drugs from a large hospital database of 525 046 patients with follow-up for 5 years. There were 144 066 eligible patients fulfilling the inclusion criteria: age 40 to 80 years old at time of antihypertensive prescription and medication exposure >90 days. The burden of comorbidity assessed by Charlson and Elixhauser scores showed an independent linear association with mood disorder diagnosis. The median time to hospital admission with mood disorder was 847 days for the 299 admissions (641 685 person-years of follow-up). Patients on angiotensin-converting enzyme inhibitors or angiotensin receptor blockers had the lowest risk for mood disorder admissions, and compared with this group, those on β-blockers (hazard ratio=2.11; [95% confidence interval, 1.12–3.98]; P=0.02) and calcium antagonists (2.28 [95% confidence interval, 1.13–4.58]; P=0.02) showed higher risk, whereas those on no antihypertensives (1.63 [95% confidence interval, 0.94–2.82]; P=0.08) and thiazide diuretics (1.56 [95% confidence interval, 0.65–3.73]; P=0.32) showed no significant difference. Overall, our exploratory findings suggest possible differential effects of antihypertensive medications on mood that merits further study: calcium antagonists and β-blockers may be associated with increased risk, whereas angiotensin-converting enzyme inhibitors and angiotensin receptor blockers may be associated with a decreased risk of mood disorders