Marshall Joffe's Contributions to Causal Inference, Biostatistics, and Epidemiology.

We pay tribute to Marshall Joffe, PhD, and his substantial contributions to the field of causal inference with focus in biostatistics and epidemiology. By compiling narratives written by us, his colleagues, we not only present highlights of Marshall's research and their significance for causal inference but also offer a portrayal of Marshall's personal accomplishments and character. Our discussion of Marshall's research notably includes (but is not limited to) handling of posttreatment variables such as noncompliance, employing G-estimation for treatment effects on failure-time outcomes, estimating effects of time-varying exposures subject to time-dependent confounding, and developing a causal framework for case-control studies. We also provide a description of some of Marshall's unpublished work, which is accompanied by a bonus anecdote. We discuss future research directions related to Marshall's research. While Marshall's impact in causal inference and the world outside of it cannot be wholly captured by our words, we hope nonetheless to present some of what he has done for our field and what he has meant to us and to his loved ones.

Comparison of the Test-negative Design and Cohort Design With Explicit Target Trial Emulation for Evaluating COVID-19 Vaccine Effectiveness.

BACKGROUND: Observational studies are used for estimating vaccine effectiveness under real-world conditions. The practical performance of two common approaches-cohort and test-negative designs-need to be compared for COVID-19 vaccines. METHODS: We compared the cohort and test-negative designs to estimate the effectiveness of the BNT162b2 vaccine against COVID-19 outcomes using nationwide data from the United States Department of Veterans Affairs. Specifically, we (1) explicitly emulated a target trial using follow-up data and evaluated the potential for confounding using negative controls and benchmarking to a randomized trial, (2) performed case-control sampling of the cohort to confirm empirically that the same estimate is obtained, (3) further restricted the sampling to person-days with a test, and (4) implemented additional features of a test-negative design. We also compared their performance in limited datasets. RESULTS: Estimated BNT162b2 vaccine effectiveness was similar under all four designs. Empirical results suggested limited residual confounding by healthcare-seeking behavior. Analyses in limited datasets showed evidence of residual confounding, with estimates biased downward in the cohort design and upward in the test-negative design. CONCLUSION: Vaccine effectiveness estimates under a cohort design with explicit target trial emulation and a test-negative design were similar when using rich information from the VA healthcare system, but diverged in opposite directions when using a limited dataset. In settings like ours with sufficient information on confounders and other key variables, the cohort design with explicit target trial emulation may be preferable as a principled approach that allows estimation of absolute risks and facilitates interpretation of effect estimates.

Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators.

The class of doubly robust (DR) functionals studied by Rotnitzky et al. (2021) is of central importance in economics and biostatistics. It strictly includes both (i) the class of mean-square continuous functionals that can be written as an expectation of an affine functional of a conditional expectation studied by Chernozhukov et al. (2022b) and the class of functionals studied by Robins et al. (2008). The present state-of-the-art estimators for DR functionals ψ are double-machine-learning (DML) estimators (Chernozhukov et al., 2018). A DML estimator ψ^1 of ψ depends on estimates p^(x) and b^x of a pair of nuisance functions p(x) and bx, and is said to satisfy "rate double-robustness" if the Cauchy-Schwarz upper bound of its bias is o(n-1/2). Were it achievable, our scientific goal would have been to construct valid, assumption-lean (i.e. no complexity-reducing assumptions on b or p) tests of the validity of a nominal (1-α) Wald confidence interval (CI) centered at ψ^1. But this would require a test of the bias to be o(n-1/2), which can be shown not to exist. We therefore adopt the less ambitious goal of falsifying, when possible, an analyst's justification for her claim that the reported (1-α) Wald CI is valid. In many instances, an analyst justifies her claim by imposing complexity-reducing assumptions on b and p to ensure "rate double-robustness". Here we exhibit valid, assumption-lean tests of H0: "rate double-robustness holds", with non-trivial power against certain alternatives. If H0 is rejected, we will have falsified her justification. However, no assumption-lean test of H0, including ours, can be a consistent test. Thus, the failure of our test to reject is not meaningful evidence in favor of H0.

A formal causal interpretation of the case-crossover design.

The case-crossover design of Maclure is widely used in epidemiology and other fields to study causal effects of transient treatments on acute outcomes. However, its validity and causal interpretation have only been justified under informal conditions. Here, we place the design in a formal counterfactual framework for the first time. Doing so helps to clarify its assumptions and interpretation. In particular, when the treatment effect is nonnull, we identify a previously unnoticed bias arising from strong common causes of the outcome at different person-times. We analyze this bias and demonstrate its potential importance with simulations. We also use our derivation of the limit of the case-crossover estimator to analyze its sensitivity to treatment effect heterogeneity, a violation of one of the informal criteria for validity. The upshot of this work for practitioners is that, while the case-crossover design can be useful for testing the causal null hypothesis in the presence of baseline confounders, extra caution is warranted when using the case-crossover design for point estimation of causal effects.

Rejoinder: A formal causal interpretation of the case-crossover design.

We thank the discussants for their insightful commentary and questions. In our rejoinder, we extend our analysis to additional settings, control strategies, and sources of bias relevant to how case-crossover is often used in practice, as suggested by multiple discussants. In particular, we consider: control exposures that follow occurrence of events, settings with shared exposure trajectories (which are common in case-crossover studies of effects of air pollution), bias due to non-transient treatment effects, removing bias due to time trends in treatment using control subjects, and extending our results to the continuous time setting. We also take the opportunity to clarify an easily misinterpreted comment we made about collapsibility, which we thank Andersen and Martinussen for highlighting. Throughout, in the spirit of the discussants. contributions, we iterate between general bias formulas and simulations and numerical studies from illustrative simplified scenarios to build insight.

Coherent modeling of longitudinal causal effects on binary outcomes.

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Toward this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the noncausal nuisance parameters. This leads to a series of difficulties in interpretation, estimation, and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparameterization of the noncausal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parameterization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parameterization, thereby justifying the restriction to multiplicative SNMMs.

Sensitivity analysis using bias functions for studies extending inferences from a randomized trial to a target population.

Extending (i.e., generalizing or transporting) causal inferences from a randomized trial to a target population requires assumptions that randomized and nonrandomized individuals are exchangeable conditional on baseline covariates. These assumptions are made on the basis of background knowledge, which is often uncertain or controversial, and need to be subjected to sensitivity analysis. We present simple methods for sensitivity analyses that directly parameterize violations of the assumptions using bias functions and do not require detailed background knowledge about specific unknown or unmeasured determinants of the outcome or modifiers of the treatment effect. We show how the methods can be applied to non-nested trial designs, where the trial data are combined with a separately obtained sample of nonrandomized individuals, as well as to nested trial designs, where the trial is embedded within a cohort sampled from the target population.

Video article: the subtemporal extradural approach to cavernous sinus tumour.

OBJECTIVE: Here we demonstrate via operative video the subtemporal extradural approach to a tumour in the cavernous sinus. METHODS: The extradural approach is performed here in a paediatric patient (a 15-year-old child) via a right extended pterional osteoplastic craniotomy with removal of the zygomatic arch. The operative microscope is introduced, and the dura is divided at the superior orbital fissure into endosteal and meningeal layers using a diamond knife. The middle cranial fossa floor is drilled flat to increase access, and the plane is further developed towards the cavernous sinus. The tumour is seen bulging from within the cavernous sinus, and the cavernous sinus is opened in the anteromedial triangle between cranial nerves Vi and Vii. After biopsy, the tumour is debulked with an ultrasonic aspirator. Doppler is used to identify the internal carotid artery and preserve it. The bone flap is replaced, and the wound is closed in layers in standard fashion. RESULTS: The patient recovered well and was discharged on post-operative day 3. Persistent sixth nerve palsy (present pre-operatively) was present; however, otherwise, there was good recovery from surgery. Good resection of tumour is demonstrated on post-operative MR imaging. CONCLUSIONS: This approach is uncommon but important as it enables extradural access to the cavernous sinus, minimising the complications associated with an intradural approach such as cortical injury. In this video, we also demonstrate the fundamental anatomy using annotation and cadaveric images to enhance understanding required for the neurosurgeon to successfully complete this approach. The patient consented to the procedure in the standard fashion.

Quantitative and functional visual field outcomes after endoscopic trans-sphenoidal pituitary adenectomy.

OBJECTIVE: Quantitative data on visual outcomes after trans-sphenoidal surgery is lacking in the literature. This study aims to address this by quantitatively assessing visual field outcomes after endoscopic trans-sphenoidal pituitary adenectomy using the capabilities of modern semi-automated kinetic perimetry. METHODS: Visual field area (deg2) calculated on perimetry performed before and after surgery was statistically analysed. Functional improvement was assessed against UK driving standards. RESULTS: Sixty-four patients (128 eyes) were analysed (May 2016-Nov 2019). I4e and I3e isopter area significantly increased after surgery (p < 0.0001). Of eyes with pre-operative deficits: 80.7% improved and 7.9% worsened; the median amount of improvement was 60% (IQR 6-246%). Median increase in I4e isopter was 2213deg2 (IQR 595-4271deg2) and in I3e isopter 1034 deg2 (IQR 180-2001 deg2). Thirteen out of fifteen (87%) patients with III4e data regained driving eligibility after surgery. Age and extent of resection (EOR) did not correlate with visual improvement. Better pre-operative visual field area correlated with a better post-operative area (p < 0.0001). However, the rate of improvement in the visual field area increased with poorer pre-operative vision (p < 0.0001). CONCLUSIONS: A median visual field improvement of 60% may be expected in over 80% of patients. Functionally, a significant proportion of patients can expect to regain driving eligibility. EOR did not impact on visual recovery. When the primary goal of surgery is alleviating visual impairment, optic apparatus decompression without the aim for gross total resection appears a valid strategy. Patients with the worst pre-operative visual field often experience the greatest improvement, and therefore, poor pre-operative vision alone should not preclude surgical intervention.

Potential Biases Arising From Epidemic Dynamics in Observational Seroprotection Studies.

The extent and duration of immunity following infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are critical outstanding questions about the epidemiology of this novel virus, and studies are needed to evaluate the effects of serostatus on reinfection. Understanding the potential sources of bias and methods for alleviating biases in these studies is important for informing their design and analysis. Confounding by individual-level risk factors in observational studies like these is relatively well appreciated. Here, we show how geographic structure and the underlying, natural dynamics of epidemics can also induce noncausal associations. We take the approach of simulating serological studies in the context of an uncontrolled or controlled epidemic, under different assumptions about whether prior infection does or does not protect an individual against subsequent infection, and using various designs and analytical approaches to analyze the simulated data. We find that in studies assessing whether seropositivity confers protection against future infection, comparing seropositive persons with seronegative persons with similar time-dependent patterns of exposure to infection by stratifying or matching on geographic location and time of enrollment is essential in order to prevent bias.

Study Designs for Extending Causal Inferences From a Randomized Trial to a Target Population.

In this article, we examine study designs for extending (generalizing or transporting) causal inferences from a randomized trial to a target population. Specifically, we consider nested trial designs, where randomized individuals are nested within a sample from the target population, and nonnested trial designs, including composite data-set designs, where observations from a randomized trial are combined with those from a separately obtained sample of nonrandomized individuals from the target population. We show that the counterfactual quantities that can be identified in each study design depend on what is known about the probability of sampling nonrandomized individuals. For each study design, we examine identification of counterfactual outcome means via the g-formula and inverse probability weighting. Last, we explore the implications of the sampling properties underlying the designs for the identification and estimation of the probability of trial participation.

Parametric g-formula implementations for causal survival analyses.

The g-formula can be used to estimate the survival curve under a sustained treatment strategy. Two available estimators of the g-formula are noniterative conditional expectation and iterative conditional expectation. We propose a version of the iterative conditional expectation estimator and describe its procedures for deterministic and random treatment strategies. Also, because little is known about the comparative performance of noniterative and iterative conditional expectation estimators, we explore their relative efficiency via simulation studies. Our simulations show that, in the absence of model misspecification and unmeasured confounding, our proposed iterative conditional expectation estimator and the noniterative conditional expectation estimator are similarly efficient, and that both are at least as efficient as the classical iterative conditional expectation estimator. We describe an application of both noniterative and iterative conditional expectation to answer "when to start" treatment questions using data from the HIV-CAUSAL Collaboration.

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.

Hypothetical Lifestyle Strategies in Middle-Aged Women and the Long-Term Risk of Stroke.

Background and Purpose- Long-term effect of lifestyle changes on stroke incidence has not been estimated in randomized trials. We used observational data to estimate the incidence of stroke under hypothetical lifestyle strategies in the NHS (Nurses' Health Study). Methods- We considered 3 nondietary strategies (smoking cessation, exercising ≥30 min/d, gradual body mass index reduction if overweight/obese) and several dietary strategies (eating ≥3 servings/wk of fish, ≤3 servings/wk of unprocessed red meat, no processed red meat, ≥1 servings/d of nuts, etc). We used the parametric g-formula to estimate the 26-year risk of stroke under these strategies. Results- In 59 727 women, mean age 52 years at baseline in 1986, the estimated 26-year risks under no lifestyle interventions were 4.7% for total stroke, 2.4% for ischemic stroke, and 0.7% for hemorrhagic stroke. Under the combined nondietary interventions, the estimated 26-year risk of total stroke was 3.5% (95% CI, 2.6%-4.3%) and ischemic stroke was 1.6% (95% CI, 1.1%-2.1%). Smaller reductions in total stroke risk were estimated under isolated dietary strategies of increased intake of fish and nuts and reduced intake of unprocessed red meat. Ischemic stroke risk was lower under reduced intake of unprocessed and processed red meat, and hemorrhagic stroke risk was lower under a strategy of increased fish consumption. Conclusions- In this population of middle-aged women, sustained, lifestyle modifications were estimated to reduce the 26-year risk of total stroke by 25% and ischemic stroke by 36%. Sustained dietary modifications were estimated to reduce the 26-year risk of total stroke by 23%.

Weight Gain After Smoking Cessation and Lifestyle Strategies to Reduce it.

BACKGROUND: Weight gain following smoking cessation reduces the incentive to quit, especially among women. Exercise and diet interventions may reduce postcessation weight gain, but their long-term effect has not been estimated in randomized trials. METHODS: We estimated the long-term reduction in postcessation weight gain among women under smoking cessation alone or combined with (1) moderate-to-vigorous exercise (15, 30, 45, 60 minutes/day), and (2) exercise and diet modification (≤2 servings/week of unprocessed red meat; ≥5 servings/day of fruits and vegetables; minimal sugar-sweetened beverages, sweets and desserts, potato chips or fried potatoes, and processed red meat). RESULTS: Among 10,087 eligible smokers in the Nurses' Health Study and 9,271 in the Nurses' Health Study II, the estimated 10-year mean weights under smoking cessation were 75.0 (95% CI = 74.7, 75.5) kg and 79.0 (78.2, 79.6) kg, respectively. Pooling both cohorts, the estimated postcessation mean weight gain was 4.9 (7.3, 2.6) kg lower under a hypothetical strategy of exercising at least 30 minutes/day and diet modification, and 5.9 (8.0, 3.8) kg lower under exercising at least 60 minutes/day and diet modification, compared with smoking cessation without exercising. CONCLUSIONS: In this study, substantial weight gain occurred in women after smoking cessation, but we estimate that exercise and dietary modifications could have averted most of it.

Quality of life after selective dorsal rhizotomy: an assessment of family-reported outcomes using the CPQoL questionnaire.

BACKGROUND: Selective dorsal rhizotomy (SDR) is widely accepted as an effective procedure for management of lower limb spasticity in children with cerebral palsy. However, effects of the procedure on quality of life are not widely reported and less so using a structured and validated quality of life tool such as Cerebral Palsy Quality of Life Questionnaire (CPQoL). Here, we present complete data for CPQoL outcomes for SDR patients operated in a single institution at 2 years follow-up. METHODS: Patients were operated over a 5-year period by the same surgeon using the same technique in a single institution. CPQoL questionnaires were completed by patients and families pre-operatively and at 6 months, 1 year and 2 years post-operatively. Data was collected prospectively. RESULTS: A total of 78 patients (58 male, 20 female), age range 2.6-13.8 years (median 6.33) were included whom underwent SDR between October 2012-November 2017. All had complete follow-up up to 2 years post-procedure (most recent November 2019). Four patients were excluded due to incomplete follow-up data. Statistically significant improvement was seen across five out of seven CPQoL domains and this was sustained to 2 years post-SDR. CONCLUSIONS: We demonstrate using a validated Quality of Life Tool that SDR has a beneficial effect on the quality of life for patients with cerebral palsy at this length of follow-up.

Fronto-orbital advancement and reconstruction using reverse frontal bone graft without the use of orbital bar: a technical note.

INTRODUCTION: We describe our technique of using reverse frontal bone graft for FOAR for patients with metopic or coronal synostosis and present our complications using the Leeds classification system for complications in craniosynostosis surgery. METHODS: Since April 2015, seventeen patients have been operated using this technique. We perform a frontal bone graft that is then reversed, and supraorbital margins are drilled out. The orbital bar is then removed and drilled down to make bone dust and on-lay bone grafts which are then used to fill gaps on exposed dura and fill in around the temporal region. RESULTS: All 17 patients who underwent this technique have good cosmetic results. We report 5 (29%) complications and 8 (47%) blood transfusions (7 exposures, 1 cell salvage).

Emulating a trial of joint dynamic strategies: An application to monitoring and treatment of HIV-positive individuals.

Decisions about when to start or switch a therapy often depend on the frequency with which individuals are monitored or tested. For example, the optimal time to switch antiretroviral therapy depends on the frequency with which HIV-positive individuals have HIV RNA measured. This paper describes an approach to use observational data for the comparison of joint monitoring and treatment strategies and applies the method to a clinically relevant question in HIV research: when can monitoring frequency be decreased and when should individuals switch from a first-line treatment regimen to a new regimen? We outline the target trial that would compare the dynamic strategies of interest and then describe how to emulate it using data from HIV-positive individuals included in the HIV-CAUSAL Collaboration and the Centers for AIDS Research Network of Integrated Clinical Systems. When, as in our example, few individuals follow the dynamic strategies of interest over long periods of follow-up, we describe how to leverage an additional assumption: no direct effect of monitoring on the outcome of interest. We compare our results with and without the "no direct effect" assumption. We found little differences on survival and AIDS-free survival between strategies where monitoring frequency was decreased at a CD4 threshold of 350 cells/µl compared with 500 cells/µl and where treatment was switched at an HIV-RNA threshold of 1000 copies/ml compared with 200 copies/ml. The "no direct effect" assumption resulted in efficiency improvements for the risk difference estimates ranging from an 7- to 53-fold increase in the effective sample size.

The learning curve for endoscopic trans-sphenoidal resection of pituitary macroadenomas. A single institution experience, Leeds, UK.

BACKGROUND: The object of this study was to assess whether increasing operative experience results in greater endoscopic trans-sphenoidal resection of pituitary macroadenomas and lower complications. METHODS: A retrospective single institution cohort study was performed. Subjects underwent endoscopic trans-sphenoidal resection of pituitary macroadenoma between July 2009 and July 2016 by three neurosurgeons. Following data collection, statistical analysis compared percentage of tumor resection and length of hospital stay (LOS) with experience. Complications including CSF leak are reported. RESULTS: In total, 142 patients (87 male, 55 female) mean age 55.1 were included. Surgeon 1 performed 106 cases; surgeon 2 performed 23 cases; and surgeon 3 performed 13 cases. Mean pre-operative tumor volumes were 8.18 cm3, 6.52 cm3, and 3.47 cm3 and post-operative volumes were 2.21, 1.74, and 1.93 cm3 for surgeons 1, 2, and 3, respectively. Respective percentage resections were 74.3, 77.2, and 52.1%. Analysis demonstrated no difference in tumor resection with increasing experience for all three surgeons (p = 0.11, p = 0.17, and p = 0.26). Tumor consistency and cavernous sinus involvement did not appear to affect tumor resection. Mean LOS was 5 days, 4 days, and 3 days, respectively, with no significant correlation with experience for all three surgeons. Intraoperative CSF leak incidence was 19/106 (18%) for surgeon 1, 6/23(26%) for surgeon 2, and 2/13(15%) for surgeon 3. Primary closure rate was 96.3% and only three other complications occurred. CONCLUSIONS: This study demonstrates that in our institution there is no statistically significant learning curve for the endoscopic resection of pituitary macroadenoma. However, there is a trend of improvement in tumor resection with experience for one surgeon. These findings suggest that the surgeons in our institution were capable of performing this procedure effectively with a low complication rate since adoption of the endoscopic technique in 2009.

A Comparison of Agent-Based Models and the Parametric G-Formula for Causal Inference.

Decision-making requires choosing from treatments on the basis of correctly estimated outcome distributions under each treatment. In the absence of randomized trials, 2 possible approaches are the parametric g-formula and agent-based models (ABMs). The g-formula has been used exclusively to estimate effects in the population from which data were collected, whereas ABMs are commonly used to estimate effects in multiple populations, necessitating stronger assumptions. Here, we describe potential biases that arise when ABM assumptions do not hold. To do so, we estimated 12-month mortality risk in simulated populations differing in prevalence of an unknown common cause of mortality and a time-varying confounder. The ABM and g-formula correctly estimated mortality and causal effects when all inputs were from the target population. However, whenever any inputs came from another population, the ABM gave biased estimates of mortality-and often of causal effects even when the true effect was null. In the absence of unmeasured confounding and model misspecification, both methods produce valid causal inferences for a given population when all inputs are from that population. However, ABMs may result in bias when extrapolated to populations that differ on the distribution of unmeasured outcome determinants, even when the causal network linking variables is identical.