Identification and estimation of survivor average causal effects

A mixed model approach to estimate the survivor average causal effect in cluster-randomized trials

In many medical studies, the outcome measure (such as quality of life, QOL) for some study participants becomes informatively truncated (censored, missing, or unobserved) due to death or other forms of dropout, creating a nonignorable missing data problem. In such cases, the use of a composite outcome or imputation methods that fill in unmeasurable QOL values for those who died rely on strong and untestable assumptions and may be conceptually unappealing to certain stakeholders when estimating a treatment effect. The survivor average causal effect (SACE) is an alternative causal estimand that surmounts some of these issues. While principal stratification has been applied to estimate the SACE in individually randomized trials, methods for estimating the SACE in cluster-randomized trials are currently limited. To address this gap, we develop a mixed model approach along with an expectation-maximization algorithm to estimate the SACE in cluster-randomized trials. We model the continuous outcome measure with a random intercept to account for intracluster correlations due to cluster-level randomization, and model the principal strata membership both with and without a random intercept. In simulations, we compare the performance of our approaches with an existing fixed-effects approach to illustrate the importance of accounting for clustering in cluster-randomized trials. The methodology is then illustrated using a cluster-randomized trial of telecare and assistive technology on health-related QOL in the elderly.

The survival-incorporated median vs the median in the survivors or in the always-survivors: What are we measuring? and Why?

Many clinical studies evaluate the benefit of a treatment based on both survival and other continuous/ordinal clinical outcomes, such as quality of life scores. In these studies, when subjects die before the follow-up assessment, the clinical outcomes become undefined and are truncated by death. Treating outcomes as "missing" or "censored" due to death can be misleading for treatment effect evaluation. We show that if we use the median in the survivors or in the always-survivors as estimands to summarize clinical outcomes, we may conclude that a trade-off exists between the probability of survival and good clinical outcomes, even in settings where both the probability of survival and the probability of any good clinical outcome are better for one treatment. Therefore, we advocate not always treating death as a mechanism through which clinical outcomes are missing, but rather as part of the outcome measure. To account for the survival status, we describe the survival-incorporated median as an alternative summary measure for outcomes in the presence of death. The survival-incorporated median is the threshold such that 50% of the population is alive with an outcome above that threshold. Through conceptual examples and an application to a prostate cancer treatment study, we show that the survival-incorporated median provides a simple and useful summary measure to inform clinical practice.

Unified semicompeting risks analysis of hepatitis natural history through mediation modeling

Natural history of hepatitis B or C is comprised of multiple milestones such as liver cirrhosis and liver cancer. To fully characterize its natural course, semicompeting risks represent a common problem where liver cirrhosis and liver cancer are both of interest, but only the former may be censored by the latter. Copula, frailty and multistate models serve as well-established analytics for semicompeting risks. Here, we cast the semicompeting risks in a mediation framework, with liver cirrhosis as a mediator and liver cancer as an outcome. We define the indirect and direct effects as the effects of an exposure on the liver cancer incidence mediated and not mediated through liver cirrhosis, respectively. With the estimands derived as conditional probabilities, we derive respective expressions under the copula, frailty, and multistate models. Next, we propose estimators based on nonparametric maximum likelihood or U-statistics and establish their asymptotic results. Numerical studies demonstrate that the efficiency of copula models leads to potential bias due to model misspecification. Moreover, the robustness of frailty models is accompanied by a loss in efficiency, and multistate models balance the efficiency and robustness. We demonstrate the utility of the proposed methods by a hepatitis study, showing that hepatitis B and C lead to a higher incidence of liver cancer by increasing liver cirrhosis incidence. Thus, mediation modeling provides a unified framework that accommodates various semicompeting risks models.

Considering Questions Before Methods in Dementia Research With Competing Events and Causal Goals

Studying causal exposure effects on dementia is challenging when death is a competing event. Researchers often interpret death as a potential source of bias, although bias cannot be defined or assessed if the causal question is not explicitly specified. Here we discuss 2 possible notions of a causal effect on dementia risk: the "controlled direct effect" and the "total effect." We provide definitions and discuss the "censoring" assumptions needed for identification in either case and their link to familiar statistical methods. We illustrate concepts in a hypothetical randomized trial on smoking cessation in late midlife, and emulate such a trial using observational data from the Rotterdam Study, the Netherlands, 1990-2015. We estimated a total effect of smoking cessation (compared with continued smoking) on 20-year dementia risk of 2.1 (95% confidence interval: -0.1, 4.2) percentage points and a controlled direct effect of smoking cessation on 20-year dementia risk had death been prevented of -2.7 (95% confidence interval: -6.1, 0.8) percentage points. Our study highlights how analyses corresponding to different causal questions can have different results, here with point estimates on opposite sides of the null. Having a clear causal question in view of the competing event and transparent and explicit assumptions are essential to interpreting results and potential bias.

Biomarker-guided duration of antibiotic treatment in children hospitalised with confirmed or suspected bacterial infection: statistical analysis plan for the BATCH trial and PRECISE sub-study

INTRODUCTION

The BATCH trial is a multi-centre randomised controlled trial to compare procalcitonin-guided management of severe bacterial infection in children with current management. PRECISE is a mechanistic sub-study embedded into the BATCH trial. This paper describes the statistical analysis plan for the BATCH trial and PRECISE sub-study.

METHODS

The BATCH trial will assess the effectiveness of an additional procalcitonin test in children (aged 72 h to 18 years) hospitalised with suspected or confirmed bacterial infection to guide antimicrobial prescribing decisions. Participants will be enrolled in the trial from randomisation until day 28 follow-up. The co-primary outcomes are duration of intravenous antibiotic use and a composite safety outcome. Target sample size is 1942 patients, based on detecting a 1-day reduction in intravenous antibiotic use (90% power, two-sided) and on a non-inferiority margin of 5% risk difference in the composite safety outcome (90% power, one-sided), while allowing for up to 10% loss to follow-up.

RESULTS

Baseline characteristics will be summarised overall, by trial arm, and by whether patients were recruited before or after the pause in recruitment due to the COVID-19 pandemic. In the primary analysis, duration of intravenous antibiotic use will be tested for superiority using Cox regression, and the composite safety outcome will be tested for non-inferiority using logistic regression. The intervention will be judged successful if it reduces the duration of intravenous antibiotic use without compromising safety. Secondary analyses will include sensitivity analyses, pre-specified subgroup analyses, and analysis of secondary outcomes. Two sub-studies, including PRECISE, involve additional pre-specified subgroup analyses. All analyses will be adjusted for the balancing factors used in the randomisation, namely centre and patient age.

CONCLUSION

We describe the statistical analysis plan for the BATCH trial and PRECISE sub-study, including definitions of clinical outcomes, reporting guidelines, statistical principles, and analysis methods. The trial uses a design with co-primary superiority and non-inferiority endpoints. The analysis plan has been written prior to the completion of follow-up.

TRIAL REGISTRATION

BATCH: ISRCTN11369832, registered 20 September 2017, doi.org/10.1186/ISRCTN11369832.

PRECISE

ISRCTN14945050, registered 17 December 2020, doi.org/10.1186/ISRCTN14945050.

Causal inference with outcomes truncated by death in multiarm studies

It is challenging to evaluate causal effects when the outcomes of interest suffer from truncation-by-death in many clinical studies; that is, outcomes cannot be observed if patients die before the time of measurement. To address this problem, it is common to consider average treatment effects by principal stratification, for which, the identifiability results and estimation methods with a binary treatment have been established in previous literature. However, in multiarm studies with more than two treatment options, estimation of causal effects becomes more complicated and requires additional techniques. In this article, we consider identification, estimation, and bounds of causal effects with multivalued ordinal treatments and the outcomes subject to truncation-by-death. We define causal parameters of interest in this setting and show that they are identifiable either using some auxiliary variable or based on linear model assumption. We then propose a semiparametric method for estimating the causal parameters and derive their asymptotic results. When the identification conditions are invalid, we derive sharp bounds of the causal effects by use of covariates adjustment. Simulation studies show good performance of the proposed estimator. We use the estimator to analyze the effects of a four-level chronic toxin on fetal developmental outcomes such as birth weight in rats and mice, with data from a developmental toxicity trial conducted by the National Toxicology Program. Data analyses demonstrate that a high dose of the toxin significantly reduces the weights of pups.

Doubly robust estimation of the hazard difference for competing risks data

We consider the conditional treatment effect for competing risks data in observational studies. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to (1) the assumed propensity score for treatment and the censoring model, and (2) the outcome models for the competing risks. An important property regarding the estimators is rate double robustness, in addition to the classical model double robustness. Rate double robustness enables the use of machine learning and nonparametric methods in order to estimate the nuisance parameters, while preserving the root-n $$ n $$ asymptotic normality of the estimated treatment effect for inferential purposes. We study the performance of the estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life drinking behavior on late life cognitive outcomes. The approaches developed in this article are implemented in the R package "HazardDiff".

Complete effect decomposition for an arbitrary number of multiple ordered mediators with time-varying confounders: A method for generalized causal multi-mediation analysis

Causal mediation analysis is advantageous for mechanism investigation. In settings with multiple causally ordered mediators, path-specific effects have been introduced to specify the effects of certain combinations of mediators. However, most path-specific effects are unidentifiable. An interventional analog of path-specific effects is adapted to address the non-identifiability problem. Moreover, previous studies only focused on cases with two or three mediators due to the complexity of the mediation formula in a large number of mediators. In this study, we provide a generalized definition of traditional path-specific effects and interventional path-specific effects with a recursive formula, along with the required assumptions for nonparametric identification. Subsequently, a general approach is developed with an arbitrary number of multiple ordered mediators and with time-varying confounders. All methods and software proposed in this study contribute to comprehensively decomposing a causal effect confirmed by data science and help disentangling causal mechanisms in the presence of complicated causal structures among multiple mediators.

Procalcitonin Evaluation of Antibiotic Use in COVID-19 Hospitalised Patients (PEACH): Protocol for a Retrospective Observational Study

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel virus responsible for the coronavirus disease 2019 (COVID-19) pandemic. Although COVID-19 is a viral illness, many patients admitted to hospital are prescribed antibiotics, based on concerns that COVID-19 patients may experience secondary bacterial infections, and the assumption that they may respond well to antibiotic therapy. This has led to an increase in antibiotic use for some hospitalised patients at a time when accumulating antibiotic resistance is a major global threat to health. Procalcitonin (PCT) is an inflammatory marker measured in blood samples and widely recommended to help diagnose bacterial infections and guide antibiotic treatment. The PEACH study will compare patient outcomes from English and Welsh hospitals that used PCT testing during the first wave of the COVID-19 pandemic with those from hospitals not using PCT. It will help to determine whether, and how, PCT testing should be used in the NHS in future waves of COVID-19 to protect patients from antibiotic overuse. PEACH is a retrospective observational cohort study using patient-level clinical data from acute hospital Trusts and Health Boards in England and Wales. The primary objective is to measure the difference in antibiotic use between COVID-19 patients who did or did not have PCT testing at the time of diagnosis. Secondary objectives include measuring differences in length of stay, mortality, intensive care unit admission, and resistant bacterial infections between these groups.

Statistical methods and graphical displays of quality of life with survival outcomes in oncology clinical trials for supporting the estimand framework

Background

Although there are discussions regarding standards of the analysis of patient-reported outcomes and quality of life (QOL) in oncology clinical trials, that of QOL with death events is not within their scope. For example, ignoring death can lead to bias in the QOL analysis for patients with moderate or high mortality rates in the palliative care setting. This is discussed in the estimand framework but is controversial. Information loss by summary measures under the estimand framework may make it challenging for clinicians to interpret the QOL analysis results. This study illustrated the use of graphical displays in the framework. They can be helpful for discussions between clinicians and statisticians and decision-making by stakeholders.

Methods

We reviewed the time-to-deterioration analysis, prioritized composite outcome approach, semi-competing risk analysis, survivor analysis, linear mixed model for repeated measures, and principal stratification approach. We summarized attributes of estimands and graphs in the statistical analysis and evaluated them in various hypothetical randomized controlled trials.

Results

Graphs for each analysis method provide different information and impressions. In the time-to-deterioration analysis, it was not easy to interpret the difference in the curves as an effect on QOL. The prioritized composite outcome approach provided new insights for QOL considering death by defining better conditions based on the distinction of OS and QOL. The semi-competing risk analysis provided different insights compared with the time-to-deterioration analysis and prioritized composite outcome approach. Due to the missing assumption, graphs by the linear mixed model for repeated measures should be carefully interpreted, even for descriptive purposes. The principal stratification approach provided pure comparison, but the interpretation was difficult because the target population was unknown.

Conclusions

Graphical displays can capture different aspects of treatment effects that should be described in the estimand framework.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01735-1.

The limitations of large-scale volunteer databases to address inequalities and global challenges in health and aging

Large-scale volunteer databanks (LSVD) have emerged from the recognized value of cohorts, attracting substantial funding and promising great scientific value. A major focus is their size, with the implicit and sometimes explicit assumption that large size (thus power) creates generalizability. We contend that this is open to challenge. In the context of aging and age-related disease research, LSVD typically have limitations such as healthy volunteer, white ethnicity and high-education biases, and they omit early and late life stages critical for understanding aging. Their outputs are heavily focused on biomedical pathways of single chronic diseases. LSVD outputs increasingly dominate the funding and the publication landscapes. This Perspective discusses LSVD limitations and calls for more transparent reporting in LSVD research, as well as a greater reflection on the value of LSVD in relation to resources consumed. We invite funders and researchers to examine whether LSVD do actually contribute knowledge needed for our acute global health challenges including inequalities.

Translating questions to estimands in randomized clinical trials with intercurrent events

Intercurrent (post‐treatment) events occur frequently in randomized trials, and investigators often express interest in treatment effects that suitably take account of these events. Contrasts that naively condition on intercurrent events do not have a straight‐forward causal interpretation, and the practical relevance of other commonly used approaches is debated. In this work, we discuss how to formulate and choose an estimand, beyond the marginal intention‐to‐treat effect, from the point of view of a decision maker and drug developer. In particular, we argue that careful articulation of a practically useful research question should either reflect decision making at this point in time or future drug development. Indeed, a substantially interesting estimand is simply a formalization of the (plain English) description of a research question. A common feature of estimands that are practically useful is that they correspond to possibly hypothetical but well‐defined interventions in identifiable (sub)populations. To illustrate our points, we consider five examples that were recently used to motivate consideration of principal stratum estimands in clinical trials. In all of these examples, we propose alternative causal estimands, such as conditional effects, sequential regime effects, and separable effects, that correspond to explicit research questions of substantial interest.

Hypothesis test for causal mediation of time-to-event mediator and outcome

Hepatitis B has been a well-documented risk factor of liver cancer and mortality. To what extent hepatitis B affects mortality through increasing liver cancer incidence is of research interest and remains to be studied. We formulate the research question as a hypothesis testing problem of causal mediation where both the mediator and the outcome are time-to-event variables. The problem is closely related to semicompeting risks because time to the intermediate event may be censored by an occurrence of the outcome. We propose two hypothesis testing methods: a weighted log-rank test (WLR) and an intersection-union test (IUT). A test statistic of the WLR is constructed by adapting a nonparametric estimator of the mediation effect; however, the test may be conservative regarding its Type I Error rate. To address this, we further propose the IUT, the test statistic of which is constructed under the composite null hypothesis. Asymptotic properties of the two tests are studied, showing that the IUT is a size α test with better statistical power than the WLR. The theoretical properties are supported by extensive simulation studies under finite samples. Applying the proposed methods to the motivating hepatitis study, both WLR and IUT provided strong evidence that hepatitis B had a significant mediation effect on mortality via liver cancer incidence.

A Bayesian nonparametric approach for evaluating the causal effect of treatment in randomized trials with semi-competing risks

We develop a Bayesian nonparametric (BNP) approach to evaluate the causal effect of treatment in a randomized trial where a nonterminal event may be censored by a terminal event, but not vice versa (i.e., semi-competing risks). Based on the idea of principal stratification, we define a novel estimand for the causal effect of treatment on the nonterminal event. We introduce identification assumptions, indexed by a sensitivity parameter, and show how to draw inference using our BNP approach. We conduct simulation studies and illustrate our methodology using data from a brain cancer trial. The R code implementing our model and algorithm is available for download at https://github.com/YanxunXu/BaySemiCompeting.

Causal inference for semi-competing risks data

The causal effects of Apolipoprotein E $\epsilon4$ allele (APOE) on late-onset Alzheimer's disease (AD) and death are complicated to define because AD may occur under one intervention but not under the other, and because AD occurrence may affect age of death. In this article, this dual outcome scenario is studied using the semi-competing risks framework for time-to-event data. Two event times are of interest: a nonterminal event time (age at AD diagnosis), and a terminal event time (age at death). AD diagnosis time is observed only if it precedes death, which may occur before or after AD. We propose new estimands for capturing the causal effect of APOE on AD and death. Our proposal is based on a stratification of the population with respect to the order of the two events. We present a novel assumption utilizing the time-to-event nature of the data, which is more flexible than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present and implement nonparametric and semiparametric estimation methods under right-censored semi-competing risks data for studying the complex effect of APOE on AD and death.

Bayesian G-Computation for Estimating Impacts of Interventions on Exposure Mixtures: Demonstration With Metals From Coal-Fired Power Plants and Birth Weight

The importance of studying the health impacts of exposure mixtures is increasingly being recognized, but such research presents many methodological and interpretation difficulties. We used Bayesian g-computation to estimate effects of a simulated public health action on exposure mixtures and birth weights in Milwaukee, Wisconsin, in 2011-2013. We linked data from birth records with census-tract-level air toxics data from the Environmental Protection Agency's National Air Toxics Assessment model. We estimated the difference between observed and expected birth weights that theoretically would have followed a hypothetical intervention to reduce exposure to 6 airborne metals by decommissioning 3 coal-fired power plants in Milwaukee County prior to 2010. Using Bayesian g-computation, we estimated a 68-g (95% credible interval: 25, 135) increase in birth weight following this hypothetical intervention. This example demonstrates the utility of our approach for using observational data to evaluate and contrast possible public health actions. Additionally, Bayesian g-computation offers a flexible strategy for estimating the effects of highly correlated exposures, addressing statistical issues such as variance inflation, and addressing conceptual issues such as the lack of interpretability of independent effects.

A generalized theory of separable effects in competing event settings

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects to define direct and indirect effects of the treatment on the event of interest. This definition was given in a simple setting, where the treatment was decomposed into two components acting along two separate causal pathways. Here we generalize the notion of separable effects, allowing for interpretation, identification and estimation in a wide variety of settings. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted as effects of modified treatments, even when they cannot be regarded as direct and indirect effects. For these settings we derive weaker conditions for identification of separable effects in studies where decomposed, or otherwise modified, treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. We also propose semi-parametric weighted estimators that are straightforward to implement. We stress that unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in future studies.

Causal Inference in Studying the Long-Term Health Effects of Disasters: Challenges and Potential Solutions

Two frequently encountered but underrecognized challenges for causal inference in studying the long-term health effects of disasters among survivors include 1) time-varying effects of disasters on a time-to-event outcome and 2) selection bias due to selective attrition. In this paper, we review approaches for overcoming these challenges and demonstrate application of the approaches to a real-world longitudinal data set of older adults who were directly affected by the 2011 Great East Japan Earthquake and Tsunami (n = 4,857). To illustrate the problem of time-varying effects of disasters, we examined the association between degree of damage due to the tsunami and all-cause mortality. We compared results from Cox regression analysis assuming proportional hazards with those derived using adjusted parametric survival curves allowing for time-varying hazard ratios. To illustrate the problem of selection bias, we examined the association between proximity to the coast (a proxy for housing damage from the tsunami) and depressive symptoms. We corrected for selection bias due to attrition in the 2 postdisaster follow-up surveys (conducted in 2013 and 2016) using multivariable adjustment, inverse probability of censoring weighting, and survivor average causal effect estimation. Our results demonstrate that analytical approaches which ignore time-varying effects on mortality and selection bias due to selective attrition may underestimate the long-term health effects of disasters.

The implications of outcome truncation in reproductive medicine RCTs: a simulation platform for trialists and simulation study

BACKGROUND

Randomised controlled trials in reproductive medicine are often subject to outcome truncation, where the study outcomes are only defined in a subset of the randomised cohort. Examples include birthweight (measurable only in the subgroup of participants who give birth) and miscarriage (which can only occur in participants who become pregnant). These outcomes are typically analysed by making a comparison between treatment arms within the subgroup (for example, comparing birthweights in the subgroup who gave birth or miscarriages in the subgroup who became pregnant). However, this approach does not represent a randomised comparison when treatment influences the probability of being observed (i.e. survival). The practical implications of this for the design and interpretation of reproductive trials are unclear however.

METHODS

We developed a simulation platform to investigate the implications of outcome truncation for reproductive medicine trials. We used this to perform a simulation study, in which we considered the bias, type 1 error, coverage, and precision of standard statistical analyses for truncated continuous and binary outcomes. Simulation settings were informed by published assisted reproduction trials.

RESULTS

Increasing treatment effect on the intermediate variable, strength of confounding between the intermediate and outcome variables, and the presence of an interaction between treatment and confounder were found to adversely affect performance. However, within parameter ranges we would consider to be more realistic, the adverse effects were generally not drastic. For binary outcomes, the study highlighted that outcome truncation could cause separation in smaller studies, where none or all of the participants in a study arm experience the outcome event. This was found to have severe consequences for inferences.

CONCLUSION

We have provided a simulation platform that can be used by researchers in the design and interpretation of reproductive medicine trials subject to outcome truncation and have used this to conduct a simulation study. The study highlights several key factors which trialists in the field should consider carefully to protect against erroneous inferences. Standard analyses of truncated binary outcomes in small studies may be highly biassed, and it remains to identify suitable approaches for analysing data in this context.

Survival mediation analysis with the death-truncated mediator: The completeness of the survival mediation parameter

In medical research, the development of mediation analysis with a survival outcome has facilitated investigation into causal mechanisms. However, studies have not discussed the death-truncation problem for mediators, the problem being that conventional mediation parameters cannot be well defined in the presence of a truncated mediator. In the present study, we systematically defined the completeness of causal effects to uncover the gap, in conventional causal definitions, between the survival and nonsurvival settings. We propose a novel approach to redefining natural direct and indirect effects, which are generalized forms of conventional causal effects for survival outcomes. Furthermore, we developed three statistical methods for the binary outcome of survival status and formulated a Cox model for survival time. We performed simulations to demonstrate that the proposed methods are unbiased and robust. We also applied the proposed method to explore the effect of hepatitis C virus infection on mortality, as mediated through hepatitis B viral load.

Addressing Competing Risks When Assessing the Impact of Health Services Interventions on Hospital Length of Stay

BACKGROUND

Although hospital length of stay is generally modeled continuously, it is increasingly recommended that length of stay should be considered a time-to-event outcome (i.e., time to discharge). Additionally, in-hospital mortality is a competing risk that makes it impossible for a patient to be discharged alive. We estimated the effect of trauma center accreditation on risk of being discharged alive while considering in-hospital mortality as a competing risk. We also compared these results with those from the "naive" approach, with length of stay modeled continuously.

METHODS

Data include admissions to a level I trauma center in Quebec, Canada, between 2008 and 2017. We computed standardized risk of being discharged alive at specific days by combining inverse probability weighting and the Aalen-Johansen estimator of the cumulative incidence function. We estimated effect of accreditation using pre-post, interrupted time series (ITS) analyses, and the "naive" approach.

RESULTS

Among 5,300 admissions, 12% died, and 83% were discharged alive within 60 days. Following accreditation, we observed increases in risk of discharge between the 7th day (4.5% [95% CI = 2.3, 6.6]) and 30th day since admission 3.8% (95% CI = 1.5, 6.2). We also observed a stable decrease in hospital mortality, -1.9% (95% CI = -3.6, -0.11) at the 14th day. Although pre-post and ITS produced similar results, we observed contradictory associations with the naive approach.

CONCLUSIONS

Treating length of stay as time to discharge allows for estimation of risk of being discharged alive at specific days after admission while accounting for competing risk of death.

Modeling semi-competing risks data as a longitudinal bivariate process

As individuals age, death is a competing risk for Alzheimer's disease (AD) but the reverse is not the case. As such, studies of AD can be placed within the semi-competing risks framework. Central to semi-competing risks, and in contrast to standard competing risks , is that one can learn about the dependence structure between the two events. To-date, however, most methods for semi-competing risks treat dependence as a nuisance and not a potential source of new clinical knowledge. We propose a novel regression-based framework that views the two time-to-event outcomes through the lens of a longitudinal bivariate process on a partition of the time scales of the two events. A key innovation of the framework is that dependence is represented in two distinct forms, local and global dependence, both of which have intuitive clinical interpretations. Estimation and inference are performed via penalized maximum likelihood, and can accommodate right censoring, left truncation, and time-varying covariates. An important consequence of the partitioning of the time scale is that an ambiguity regarding the specific form of the likelihood contribution may arise; a strategy for sensitivity analyses regarding this issue is described. The framework is then used to investigate the role of gender and having ≥1 apolipoprotein E (APOE) ε4 allele on the joint risk of AD and death using data from the Adult Changes in Thought study.

A structured methodology review showed analyses of functional outcomes are frequently limited to "survivors only" in trials enrolling patients at high risk of death

OBJECTIVE

This structured methodology review evaluated statistical approaches used in randomized controlled trials (RCTs) enrolling patients at high risk of death and makes recommendations for reporting future RCTs.

STUDY DESIGN AND SETTING

Using PubMed, we searched for RCTs published in five general medicine journals from January 2014 to August 2019 wherein mortality was ≥10% in at least one randomized group. We abstracted primary and secondary outcomes, statistical analysis methods, and patient samples evaluated (all randomized patients vs. "survivors only").

RESULTS

Of 1947 RCTs identified, 434 met eligibility criteria. Of the eligible RCTs, 91 (21%) and 351 (81%) had a primary or secondary functional outcome, respectively, of which 36 (40%) and 263 (75%) evaluated treatment effects among "survivors only". In RCTs that analyzed all randomized patients, the most common methods included use of ordinal outcomes (e.g., modified Rankin Scale) or creating composite outcomes (primary: 41 of 91 [45%]; secondary: 57 of 351 [16%]).

CONCLUSION

In RCTs enrolling patients at high risk of death, statistical analyses of functional outcomes are frequently conducted among "survivors only," for which conclusions might be misleading. Given the growing number of RCTs conducted among patients hospitalized with COVID-19 and other critical illnesses, standards for reporting should be created.

Bayesian semi-parametric G-computation for causal inference in a cohort study with MNAR dropout and death

Causal inference with observational longitudinal data and time-varying exposures is often complicated by time-dependent confounding and attrition. The G-computation formula is one approach for estimating a causal effect in this setting. The parametric modeling approach typically used in practice relies on strong modeling assumptions for valid inference, and moreover depends on an assumption of missing at random, which is not appropriate when the missingness is missing not at random (MNAR) or due to death. In this work we develop a flexible Bayesian semi-parametric G-computation approach for assessing the causal effect on the subpopulation that would survive irrespective of exposure, in a setting with MNAR dropout. The approach is to specify models for the observed data using Bayesian additive regression trees, and then use assumptions with embedded sensitivity parameters to identify and estimate the causal effect. The proposed approach is motivated by a longitudinal cohort study on cognition, health, and aging, and we apply our approach to study the effect of becoming a widow on memory. We also compare our approach to several standard methods.

Fitting a shared frailty illness-death model to left-truncated semi-competing risks data to examine the impact of education level on incident dementia

BACKGROUND

Semi-competing risks arise when interest lies in the time-to-event for some non-terminal event, the observation of which is subject to some terminal event. One approach to assessing the impact of covariates on semi-competing risks data is through the illness-death model with shared frailty, where hazard regression models are used to model the effect of covariates on the endpoints. The shared frailty term, which can be viewed as an individual-specific random effect, acknowledges dependence between the events that is not accounted for by covariates. Although methods exist for fitting such a model to right-censored semi-competing risks data, there is currently a gap in the literature for fitting such models when a flexible baseline hazard specification is desired and the data are left-truncated, for example when time is on the age scale. We provide a modeling framework and openly available code for implementation.

METHODS

We specified the model and the likelihood function that accounts for left-truncated data, and provided an approach to estimation and inference via maximum likelihood. Our model was fully parametric, specifying baseline hazards via Weibull or B-splines. Using simulated data we examined the operating characteristics of the implementation in terms of bias and coverage. We applied our methods to a dataset of 33,117 Kaiser Permanente Northern California members aged 65 or older examining the relationship between educational level (categorized as: high school or less; trade school, some college or college graduate; post-graduate) and incident dementia and death.

RESULTS

A simulation study showed that our implementation provided regression parameter estimates with negligible bias and good coverage. In our data application, we found higher levels of education are associated with a lower risk of incident dementia, after adjusting for sex and race/ethnicity.

CONCLUSIONS

As illustrated by our analysis of Kaiser data, our proposed modeling framework allows the analyst to assess the impact of covariates on semi-competing risks data, such as incident dementia and death, while accounting for dependence between the outcomes when data are left-truncated, as is common in studies of aging and dementia.

Missing not at random in end of life care studies: multiple imputation and sensitivity analysis on data from the ACTION study

Background

Missing data are common in end-of-life care studies, but there is still relatively little exploration of which is the best method to deal with them, and, in particular, if the missing at random (MAR) assumption is valid or missing not at random (MNAR) mechanisms should be assumed. In this paper we investigated this issue through a sensitivity analysis within the ACTION study, a multicenter cluster randomized controlled trial testing advance care planning in patients with advanced lung or colorectal cancer.

Methods

Multiple imputation procedures under MAR and MNAR assumptions were implemented. Possible violation of the MAR assumption was addressed with reference to variables measuring quality of life and symptoms. The MNAR model assumed that patients with worse health were more likely to have missing questionnaires, making a distinction between single missing items, which were assumed to satisfy the MAR assumption, and missing values due to completely missing questionnaire for which a MNAR mechanism was hypothesized. We explored the sensitivity to possible departures from MAR on gender differences between key indicators and on simple correlations.

Results

Up to 39% of follow-up data were missing. Results under MAR reflected that missingness was related to poorer health status. Correlations between variables, although very small, changed according to the imputation method, as well as the differences in scores by gender, indicating a certain sensitivity of the results to the violation of the MAR assumption.

Conclusions

The findings confirmed the importance of undertaking this kind of analysis in end-of-life care studies.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-020-01180-y.

Formulating causal questions and principled statistical answers

Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline ("point exposure") and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we describe principled definitions of causal effects and of estimation approaches classified according to whether they invoke the no unmeasured confounding assumption (including outcome regression and propensity score-based methods) or an instrumental variable with added assumptions. We mainly focus on continuous outcomes and causal average treatment effects. We discuss interpretation, challenges, and potential pitfalls and illustrate application using a "simulation learner," that mimics the effect of various breastfeeding interventions on a child's later development. This involves a typical simulation component with generated exposure, covariate, and outcome data inspired by a randomized intervention study. The simulation learner further generates various (linked) exposure types with a set of possible values per observation unit, from which observed as well as potential outcome data are generated. It thus provides true values of several causal effects. R code for data generation and analysis is available on www.ofcaus.org, where SAS and Stata code for analysis is also provided.

Quantile regression to estimate the survivor average causal effect of periodontal treatment effects on birthweight and gestational age

BACKGROUND

Survival average causal effect (SACE) can give valid estimates of the periodontal treatment effect on birth outcomes in randomized controlled trials when fetal losses are unequal across the treatment arms. A regression-based method to estimate SACE using ordinary least squares (OLS) regression can be biased if the treatment effect varies across the outcome distribution. In this case quantile regression may be a suitable alternative.

METHODS

We compared OLS and quantile regression models estimating SACE to calculate the effect of periodontal treatment on birthweight and gestational age in secondary analyses of publicly available Obstetrics and Periodontal Therapy (OPT) trial data.

RESULTS

Periodontal treatment tended to increase birthweight and gestational age at the lowest quantiles, remained flat in the middle quantiles, and trended to decrease both birthweight and gestational age in the highest quantiles. In quantile regression models estimating SACE the β-coefficients: 95% confidence intervals (CI) for the 5th, 50th, and 95th percentiles were 277.5:  -141.0 to 696.0 g, 1.4: -107 to 110.3 g, and -84: -344 to 175.3 g for birthweight, and 0.6: -1.0 to 2.2 weeks, -0.1: -0.5 to 0.2 weeks, and -0.6: -1.0 to -0.1 weeks for gestational age. Estimates from OLS models estimating SACE were close to the null, β: 95% CI -4.7: 132.3 to 123.0 g for birthweight, and 0.03: -0.72 to 0.78 weeks for gestational age.

CONCLUSIONS

OLS models to evaluate SACE for periodontal treatment effects on birthweight and gestational age may be biased towards the null. Quantile regression may be a preferable alternative.

Advance care planning in patients with advanced cancer: A 6-country, cluster-randomised clinical trial

BACKGROUND

Advance care planning (ACP) supports individuals to define, discuss, and record goals and preferences for future medical treatment and care. Despite being internationally recommended, randomised clinical trials of ACP in patients with advanced cancer are scarce.

METHODS AND FINDINGS

To test the implementation of ACP in patients with advanced cancer, we conducted a cluster-randomised trial in 23 hospitals across Belgium, Denmark, Italy, Netherlands, Slovenia, and United Kingdom in 2015-2018. Patients with advanced lung (stage III/IV) or colorectal (stage IV) cancer, WHO performance status 0-3, and at least 3 months life expectancy were eligible. The ACTION Respecting Choices ACP intervention as offered to patients in the intervention arm included scripted ACP conversations between patients, family members, and certified facilitators; standardised leaflets; and standardised advance directives. Control patients received care as usual. Main outcome measures were quality of life (operationalised as European Organisation for Research and Treatment of Cancer [EORTC] emotional functioning) and symptoms. Secondary outcomes were coping, patient satisfaction, shared decision-making, patient involvement in decision-making, inclusion of advance directives (ADs) in hospital files, and use of hospital care. In all, 1,117 patients were included (442 intervention; 675 control), and 809 (72%) completed the 12-week questionnaire. Patients' age ranged from 18 to 91 years, with a mean of 66; 39% were female. The mean number of ACP conversations per patient was 1.3. Fidelity was 86%. Sixteen percent of patients found ACP conversations distressing. Mean change in patients' quality of life did not differ between intervention and control groups (T-score -1.8 versus -0.8, p = 0.59), nor did changes in symptoms, coping, patient satisfaction, and shared decision-making. Specialist palliative care (37% versus 27%, p = 0.002) and AD inclusion in hospital files (10% versus 3%, p < 0.001) were more likely in the intervention group. A key limitation of the study is that recruitment rates were lower in intervention than in control hospitals.

CONCLUSIONS

Our results show that quality of life effects were not different between patients who had ACP conversations and those who received usual care. The increased use of specialist palliative care and AD inclusion in hospital files of intervention patients is meaningful and requires further study. Our findings suggest that alternative approaches to support patient-centred end-of-life care in this population are needed.

TRIAL REGISTRATION

ISRCTN registry ISRCTN63110516.

Post-randomization Biomarker Effect Modification Analysis in an HIV Vaccine Clinical Trial

While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, markers measuring immune response to vaccination were strongly correlated with infection. This finding generated the hypothesis that some marker-defined vaccinated subgroups were partially protected whereas others had their risk increased. This hypothesis can be assessed using the principal stratification framework (Frangakis and Rubin, 2002) for studying treatment effect modification by an intermediate response variable, using methods in the sub-field of principal surrogate (PS) analysis that studies multiple principal strata. Unfortunately, available methods for PS analysis require an augmented study design not available in HVTN 505, and make untestable structural risk assumptions, motivating a need for more robust PS methods. Fortunately, another sub-field of principal stratification, survivor average causal effect (SACE) analysis (Rubin, 2006) - which studies effects in a single principal stratum - provides many methods not requiring an augmented design and making fewer assumptions. We show how, for a binary intermediate response variable, methods developed for SACE analysis can be adapted to PS analysis, providing new and more robust PS methods. Application to HVTN 505 supports that the vaccine partially protected individuals with vaccine-induced T-cells expressing certain combinations of functions.

Estimation and inference for semi-competing risks based on data from a nested case-control study

In semi-competing risks, the occurrence of some non-terminal event is subject to a terminal event, usually death. While existing methods for semi-competing risks data analysis assume complete information on all relevant covariates, data on at least one covariate are often not readily available in practice. In this setting, for standard univariate time-to-event analyses, researchers may choose from several strategies for sub-sampling patients on whom to collect complete data, including the nested case-control study design. Here, we consider a semi-competing risks analysis through the reuse of data from an existing nested case-control study for which risk sets were formed based on either the non-terminal or the terminal event. Additionally, we introduce the supplemented nested case-control design in which detailed data are collected on additional events of the other type. We propose estimation with respect to a frailty illness-death model through maximum weighted likelihood, specifying the baseline hazard functions either parametrically or semi-parametrically via B-splines. Two standard error estimators are proposed: (i) a computationally simple sandwich estimator and (ii) an estimator based on a perturbation resampling procedure. We derive the asymptotic properties of the proposed methods and evaluate their small-sample properties via simulation. The designs/methods are illustrated with an investigation of risk factors for acute graft-versus-host disease among N = 8838 patients undergoing hematopoietic stem cell transplantation, for which death is a significant competing risk.

A causal framework for classical statistical estimands in failure-time settings with competing events

In failure-time settings, a competing event is any event that makes it impossible for the event of interest to occur. For example, cardiovascular disease death is a competing event for prostate cancer death because an individual cannot die of prostate cancer once he has died of cardiovascular disease. Various statistical estimands have been defined as possible targets of inference in the classical competing risks literature. Many reviews have described these statistical estimands and their estimating procedures with recommendations about their use. However, this previous work has not used a formal framework for characterizing causal effects and their identifying conditions, which makes it difficult to interpret effect estimates and assess recommendations regarding analytic choices. Here we use a counterfactual framework to explicitly define each of these classical estimands. We clarify that, depending on whether competing events are defined as censoring events, contrasts of risks can define a total effect of the treatment on the event of interest or a direct effect of the treatment on the event of interest not mediated by the competing event. In contrast, regardless of whether competing events are defined as censoring events, counterfactual hazard contrasts cannot generally be interpreted as causal effects. We illustrate how identifying assumptions for all of these counterfactual estimands can be represented in causal diagrams, in which competing events are depicted as time-varying covariates. We present an application of these ideas to data from a randomized trial designed to estimate the effect of estrogen therapy on prostate cancer mortality.

A randomized trial of a specialist palliative care intervention for patients undergoing surgery for cancer: rationale and design of the Surgery for Cancer with Option of Palliative Care Expert (SCOPE) Trial

BACKGROUND

In medical oncology settings, early specialist palliative care interventions have demonstrated improvements in patient quality of life and survival compared with usual oncologic care. However, the effect of early specialist palliative care interventions in surgical oncology settings is not well studied.

METHODS

The Surgery for Cancer with Option for Palliative Care Expert (SCOPE) Trial is a single-center, prospective, single-blind, randomized controlled trial of a specialist palliative care intervention for cancer patients undergoing non-palliative surgery. It will enroll 236 patients scheduled for major abdominal operations for malignancy, who will be randomized 1:1 at enrollment to receive usual care (control arm) or specialist palliative care consultation (intervention arm). Intervention arm patients will receive consultations from a palliative care specialist (physician or nurse practitioner) preoperatively and postoperatively. The primary outcome is physical and functional wellbeing at 90 days postoperatively. Secondary outcomes are quality of life at 90 days postoperatively, posttraumatic stress disorder symptoms at 180 days postoperatively, days alive at home without an emergency room visit in the first 90 postoperative days, and overall survival at 1 year postoperatively. Participants will be followed for 3 years after surgery for exploratory analyses of their ongoing quality of life, healthcare utilization, and mortality.

DISCUSSION

SCOPE is an ongoing randomized controlled trial evaluating specialist palliative care interventions for cancer patients undergoing non-palliative oncologic surgery. Findings from the study will inform ways to identify and improve care of surgical patients who will likely benefit from specialist palliative care services.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT03436290 First Registered: 16 February 2018 Enrollment Began: 1 March 2018 Last Update: 20 December 2018.

A comparison of methods to estimate the survivor average causal effect in the presence of missing data: a simulation study

BACKGROUND

Attrition due to death and non-attendance are common sources of bias in studies of age-related diseases. A simulation study is presented to compare two methods for estimating the survivor average causal effect (SACE) of a binary exposure (sex-specific dietary iron intake) on a binary outcome (age-related macular degeneration, AMD) in this setting.

METHODS

A dataset of 10,000 participants was simulated 1200 times under each scenario with outcome data missing dependent on measured and unmeasured covariates and survival. Scenarios differed by the magnitude and direction of effect of an unmeasured confounder on both survival and the outcome, and whether participants who died following a protective exposure would also die if they had not received the exposure (validity of the monotonicity assumption). The performance of a marginal structural model (MSM, weighting for exposure, survival and missing data) was compared to a sensitivity approach for estimating the SACE. As an illustrative example, the SACE of iron intake on AMD was estimated using data from 39,918 participants of the Melbourne Collaborative Cohort Study.

RESULTS

The MSM approach tended to underestimate the true magnitude of effect when the unmeasured confounder had opposing directions of effect on survival and the outcome. Overestimation was observed when the unmeasured confounder had the same direction of effect on survival and the outcome. Violation of the monotonicity assumption did not increase bias. The estimates were similar between the MSM approach and the sensitivity approach assessed at the sensitivity parameter of 1 (assuming no survival bias). In the illustrative example, high iron intake was found to be protective of AMD (adjusted OR 0.57, 95% CI 0.40-0.82) using complete case analysis via traditional logistic regression. The adjusted SACE odds ratio did not differ substantially from the complete case estimate, ranging from 0.54 to 0.58 for each of the SACE methods.

CONCLUSIONS

On average, MSMs with weighting for exposure, missing data and survival produced biased estimates of the SACE in the presence of an unmeasured survival-outcome confounder. The direction and magnitude of effect of unmeasured survival-outcome confounders should be considered when assessing exposure-outcome associations in the presence of attrition due to death.

Assessing the ratio of means as a causal estimand in clinical endpoint bioequivalence studies in the presence of intercurrent events

In clinical endpoint bioequivalence studies, the observed per-protocol (PP) population (compliers and completers in general) is usually used in the primary analysis for equivalence assessment. However, intercurrent events, ie, missingness and noncompliance, are not properly handled. The resulting estimand is not causal. Previously, we proposed the first causal framework to assess equivalence in the presence of missing data and noncompliance. We proposed a causal survivor average causal effect (SACE) estimand for the difference of means (DOM). In equivalence assessment, DOM is not as widely used as the ratio of means (ROM). However, no existing formula links the observed PP estimand to the SACE estimand for ROM as exists for DOM. Herein, we propose a similar causal framework for ROM using the principal stratification approach, one of the strategies recommended by the International Conference on Harmonisation (ICH) E9 R1 addendum. We quantify the bias of the observed ROM PP estimand for the SACE estimand, which provides a basis to identify three conditions under which the two estimands are equal. We propose a sensitivity analysis method to evaluate the robustness of the current PP estimator to estimate the SACE estimand. We extend Fieller's confidence interval for the SACE estimand using ROM, which can be applied to many settings. Simulation demonstrates that the PP estimator is biased in either directions and may inflate type 1 error and/or change power when the three identified conditions are violated. Our work can be applied to comparative clinical biosimilar studies.

Time-to-event analysis when the event is defined on a finite time interval

Acute graft-versus-host disease (GVHD) is a frequent complication following hematopoietic cell transplantation (HCT). Research on risk factors for acute GVHD has tended to ignore two important clinical issues. First, post-transplant mortality is high. In our motivating data, 100-day post-HCT mortality was 15.4%. Second, acute GVHD in its classic form is only diagnosed within 100 days of the transplant; beyond 100 days, a patient may be diagnosed with late onset acute or chronic GVHD. Standard modeling of time-to-event outcomes, however, generally conceive of patients being able to experience the event at any point on the time scale. In this paper, we propose a novel multi-state model that simultaneously: (i) accounts for mortality through joint modeling of acute GVHD and death, and (ii) explicitly acknowledges the finite time interval during which the event of interest can take place. The observed data likelihood is derived, with estimation and inference via maximum likelihood. Additionally, we provide methods for estimating the absolute risk of acute GVHD and death simultaneously. The proposed framework is compared via comprehensive simulations to a number of alternative approaches that each acknowledge some but not all aspects of acute GVHD, and illustrated with an analysis of HCT data that motivated this work.

SemiCompRisks: An R Package for the Analysis of Independent and Cluster-correlated Semi-competing Risks Data

Semi-competing risks refer to the setting where primary scientific interest lies in estimation and inference with respect to a non-terminal event, the occurrence of which is subject to a terminal event. In this paper, we present the R package SemiCompRisks that provides functions to perform the analysis of independent/clustered semi-competing risks data under the illness-death multi-state model. The package allows the user to choose the specification for model components from a range of options giving users substantial flexibility, including: accelerated failure time or proportional hazards regression models; parametric or non-parametric specifications for baseline survival functions; parametric or non-parametric specifications for random effects distributions when the data are cluster-correlated; and, a Markov or semi-Markov specification for terminal event following non-terminal event. While estimation is mainly performed within the Bayesian paradigm, the package also provides the maximum likelihood estimation for select parametric models. The package also includes functions for univariate survival analysis as complementary analysis tools.

Does selective survival before study enrolment attenuate estimated effects of education on rate of cognitive decline in older adults? A simulation approach for quantifying survival bias in life course epidemiology

Background

The relationship between education and late-life cognitive decline is controversial. Selective survival between early life, when education is typically completed, and late life, when cognitive ageing studies take place, could attenuate effect estimates.

Methods

We quantified potential survival bias (collider-stratification bias) in estimation of the effect of education on late-life cognitive decline by simulating hypothetical cohorts of 20-year-olds and applying cumulative mortality from US life tables. For each of four causal scenarios (2000 replications each), we compared the estimated versus causal effect of education on cognitive decline over 9 years, starting at age 60, 75 or 90 in random samples of n = 2000 people who survived to each age.

Results

Effects of education on cognitive decline were underestimated when both education and U, another determinant of cognitive decline, influenced mortality (collider-stratification bias). The magnitude of bias was sensitive to the magnitude of the effect of U on cognitive decline and whether there was a multiplicative interaction between education and U on mortality. For example, when there was a multiplicative interaction between education and U on mortality, 95% confidence interval coverage of the causal effect ranged from 83.4% to 50.4% at age 60 and 25.8% to 0.2% at age 90.

Conclusions

Selective survival could lead to underestimation of effects of education on late-life cognitive decline. Our simulations map survival bias to testable assumptions about underlying causal structures.

Methods for the assessment of selection bias in drug safety during pregnancy studies using electronic medical data

Electronic health data are routinely used for population drug studies. Due to the ethical dilemma in carrying out experimental drug studies on pregnant women, the effects of medication usage during pregnancy on fetal and maternal outcomes are largely evaluated using this data collection medium. One major limitation in this type of study is the delayed inclusion of pregnancies in the cohort. For example, in the province of Quebec, Canada, a major pregnancy cohort only captured pregnancies after 20 weeks gestation. The purpose of this study was to demonstrate three methods that can be used to assess the extent of selection bias due to the delayed inclusion of pregnancies. We use causal directed acyclic graphs to explain the source of this selection bias. In an example involving a cohort of pregnant asthmatic women reconstructed from the linkage of administrative health databases from the province of Quebec, we use numerical derivations, a simulation study and a sensitivity analysis to investigate the potential for bias and loss of power due to the delayed inclusion. We find that this selection bias can be partially mitigated by controlling for variables related to (spontaneous or therapeutic) abortion and the outcome of interest. The three proposed methods allow for the pre and post hoc ascertainment of the bias. While delayed pregnancy inclusion selection bias (which includes "live birth bias") can produce substantial bias in pregnancy drug studies, all three methods are effective at producing estimates of the size of the bias.

Eliminating Survivor Bias in Two-stage Instrumental Variable Estimators

Mendelian randomization studies commonly focus on elderly populations. This makes the instrumental variables analysis of such studies sensitive to survivor bias, a type of selection bias. A particular concern is that the instrumental variable conditions, even when valid for the source population, may be violated for the selective population of individuals who survive the onset of the study. This is potentially very damaging because Mendelian randomization studies are known to be sensitive to bias due to even minor violations of the instrumental variable conditions. Interestingly, the instrumental variable conditions continue to hold within certain risk sets of individuals who are still alive at a given age when the instrument and unmeasured confounders exert additive effects on the exposure, and moreover, the exposure and unmeasured confounders exert additive effects on the hazard of death. In this article, we will exploit this property to derive a two-stage instrumental variable estimator for the effect of exposure on mortality, which is insulated against the above described selection bias under these additivity assumptions.

Parametric Mediational g-Formula Approach to Mediation Analysis with Time-varying Exposures, Mediators, and Confounders

The assessment of direct and indirect effects with time-varying mediators and confounders is a common but challenging problem, and standard mediation analysis approaches are generally not applicable in this context. The mediational g-formula was recently proposed to address this problem, paired with a semiparametric estimation approach to evaluate longitudinal mediation effects empirically. In this article, we develop a parametric estimation approach to the mediational g-formula, including a feasible algorithm implemented in a freely available SAS macro. In the Framingham Heart Study data, we apply this method to estimate the interventional analogues of natural direct and indirect effects of smoking behaviors sustained over a 10-year period on blood pressure when considering weight change as a time-varying mediator. Compared with not smoking, smoking 20 cigarettes per day for 10 years was estimated to increase blood pressure by 1.2 mm Hg (95% CI: -0.7, 2.7). The direct effect was estimated to increase blood pressure by 1.5 mm Hg (95% CI: -0.3, 2.9), and the indirect effect was -0.3 mm Hg (95% CI: -0.5, -0.1), which is negative because smoking which is associated with lower weight is associated in turn with lower blood pressure. These results provide evidence that weight change in fact partially conceals the detrimental effects of cigarette smoking on blood pressure. Our study represents, to our knowledge, the first application of the parametric mediational g-formula in an epidemiologic cohort study (see video abstract at, http://links.lww.com/EDE/B159.).

Statistical methods to compare functional outcomes in randomized controlled trials with high mortality

Mortality is a common primary endpoint in randomized controlled trials of patients with a high severity of illness, such as critically ill patients. However, researchers are increasingly evaluating functional outcomes, such as quality of life. Importantly, in such trials some patients may die before the assessment of a functional outcome, resulting in the functional outcome being “truncated due to death.” As described in this paper, defining and testing treatment effects on functional outcomes in this setting requires careful consideration. Data from a completed trial of critically ill patients are used to highlight key differences among three statistical approaches used when analyzing such trials.

Mediation analysis for a survival outcome with time-varying exposures, mediators, and confounders

We propose an approach to conduct mediation analysis for survival data with time-varying exposures, mediators, and confounders. We identify certain interventional direct and indirect effects through a survival mediational g-formula and describe the required assumptions. We also provide a feasible parametric approach along with an algorithm and software to estimate these effects. We apply this method to analyze the Framingham Heart Study data to investigate the causal mechanism of smoking on mortality through coronary artery disease. The estimated overall 10-year all-cause mortality risk difference comparing "always smoke 30 cigarettes per day" versus "never smoke" was 4.3 (95% CI = (1.37, 6.30)). Of the overall effect, we estimated 7.91% (95% CI: = 1.36%, 19.32%) was mediated by the incidence and timing of coronary artery disease. The survival mediational g-formula constitutes a powerful tool for conducting mediation analysis with longitudinal data.

Assessing the Potential for Bias From Nonresponse to a Study Follow-up Interview: An Example From the Agricultural Health Study

Prospective cohort studies are important tools for identifying causes of disease. However, these studies are susceptible to attrition. When information collected after enrollment is through interview or exam, attrition leads to missing information for nonrespondents. The Agricultural Health Study enrolled 52,394 farmers in 1993-1997 and collected additional information during subsequent interviews. Forty-six percent of enrolled farmers responded to the 2005-2010 interview; 7% of farmers died prior to the interview. We examined whether response was related to attributes measured at enrollment. To characterize potential bias from attrition, we evaluated differences in associations between smoking and incidence of 3 cancer types between the enrolled cohort and the subcohort of 2005-2010 respondents, using cancer registry information. In the subcohort we evaluated the ability of inverse probability weighting (IPW) to reduce bias. Response was related to age, state, race/ethnicity, education, marital status, smoking, and alcohol consumption. When exposure and outcome were associated and case response was differential by exposure, some bias was observed; IPW conditional on exposure and covariates failed to correct estimates. When response was nondifferential, subcohort and full-cohort estimates were similar, making IPW unnecessary. This example provides a demonstration of investigating the influence of attrition in cohort studies using information that has been self-reported after enrollment.