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 We also provide a description of some of Marshall's unpublished work, which is accompanied by a bonus anecdote.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.

Doubly robust nonparametric instrumental variable estimators for survival outcomes.

Instrumental variable (IV) methods allow us the opportunity to address unmeasured confounding in causal inference. However, most IV methods are only applicable to discrete or continuous outcomes with very few IV methods for censored survival outcomes. In this article, we propose nonparametric estimators for the local average treatment effect on survival probabilities under both covariate-dependent and outcome-dependent censoring. We provide an efficient influence function-based estimator and a simple estimation procedure when the IV is either binary or continuous. The proposed estimators possess double-robustness properties and can easily incorporate nonparametric estimation using machine learning tools. In simulation studies, we demonstrate the flexibility and double robustness of our proposed estimators under various plausible scenarios. We apply our method to the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial for estimating the causal effect of screening on survival probabilities and investigate the causal contrasts between the two interventions under different censoring assumptions.

Estimation of the Time-Varying Incremental Effect of Low-dose Aspirin on Incidence of Pregnancy.

BACKGROUND: In many research settings, the intervention implied by the average causal effect of a time-varying exposure is impractical or unrealistic, and we might instead prefer a more realistic target estimand. Instead of requiring all individuals to be always exposed versus unexposed, incremental effects quantify the impact of merely shifting each individual's probability of being exposed. METHODS: We demonstrate the estimation of incremental effects in the time-varying setting, using data from the Effects of Aspirin in Gestation and Reproduction trial, which assessed the effect of preconception low-dose aspirin on pregnancy outcomes. Compliance to aspirin or placebo was summarized weekly and was affected by time-varying confounders such as bleeding or nausea. We sought to estimate what the incidence of pregnancy by 26 weeks postrandomization would have been if we shifted each participant's probability of taking aspirin or placebo each week by odds ratios (OR) between 0.30 and 3.00. RESULTS: Under no intervention (OR = 1), the incidence of pregnancy was 77% (95% CI: 74%, 80%). Decreasing women's probability of complying with aspirin had little estimated effect on pregnancy incidence. When we increased women's probability of taking aspirin, estimated incidence of pregnancy increased, from 83% (95% confidence interval [CI] = 79%, 87%) for OR = 2 to 89% (95% CI = 84%, 93%) for OR=3. We observed similar results when we shifted women's probability of complying with a placebo. CONCLUSIONS: These results estimated that realistic interventions to increase women's probability of taking aspirin would have yielded little to no impact on the incidence of pregnancy, relative to similar interventions on placebo.

Estimation of the Average Causal Effect in Longitudinal Data With Time-Varying Exposures: The Challenge of Nonpositivity and the Impact of Model Flexibility.

There are important challenges to the estimation and identification of average causal effects in longitudinal data with time-varying exposures. Here, we discuss the difficulty in meeting the positivity condition. Our motivating example is the per-protocol analysis of the Effects of Aspirin in Gestation and Reproduction (EAGeR) Trial. We estimated the average causal effect comparing the incidence of pregnancy by 26 weeks that would have occurred if all women had been assigned to aspirin and complied versus the incidence if all women had been assigned to placebo and complied. Using flexible targeted minimum loss-based estimation, we estimated a risk difference of 1.27% (95% CI: -9.83, 12.38). Using a less flexible inverse probability weighting approach, the risk difference was 5.77% (95% CI: -1.13, 13.05). However, the cumulative probability of compliance conditional on covariates approached 0 as follow-up accrued, indicating a practical violation of the positivity assumption, which limited our ability to make causal interpretations. The effects of nonpositivity were more apparent when using a more flexible estimator, as indicated by the greater imprecision. When faced with nonpositivity, one can use a flexible approach and be transparent about the uncertainty, use a parametric approach and smooth over gaps in the data, or target a different estimand that will be less vulnerable to positivity violations.

Performance Evaluation of Parametric and Nonparametric Methods When Assessing Effect Measure Modification.

Effect measure modification is often evaluated using parametric models. These models, although efficient when correctly specified, make strong parametric assumptions. While nonparametric models avoid important functional form assumptions, they often require larger samples to achieve a given accuracy. We conducted a simulation study to evaluate performance tradeoffs between correctly specified parametric and nonparametric models to detect effect modification of a binary exposure by both binary and continuous modifiers. We evaluated generalized linear models and doubly robust (DR) estimators, with and without sample splitting. Continuous modifiers were modeled with cubic splines, fractional polynomials, and nonparametric DR-learner. For binary modifiers, generalized linear models showed the greatest power to detect effect modification, ranging from 0.42 to 1.00 in the worst and best scenario, respectively. Augmented inverse probability weighting had the lowest power, with an increase of 23% when using sample splitting. For continuous modifiers, the DR-learner was comparable to flexible parametric models in capturing quadratic and nonlinear monotonic functions. However, for nonlinear, nonmonotonic functions, the DR-learner had lower integrated bias than splines and fractional polynomials, with values of 141.3, 251.7, and 209.0, respectively. Our findings suggest comparable performance between nonparametric and correctly specified parametric models in evaluating effect modification.

Use of a Doubly Robust Machine-Learning-Based Approach to Evaluate Body Mass Index as a Modifier of the Association Between Fruit and Vegetable Intake and Preeclampsia.

The Dietary Guidelines for Americans rely on summaries of the effect of dietary pattern on disease risk, independent of other population characteristics. We explored the modifying effect of prepregnancy body mass index (BMI; weight (kg)/height (m)2) on the relationship between fruit and vegetable density (cup-equivalents/1,000 kcal) and preeclampsia using data from a pregnancy cohort study conducted at 8 US medical centers (n = 9,412; 2010-2013). Usual daily periconceptional intake of total fruits and total vegetables was estimated from a food frequency questionnaire. We quantified the effects of diets with a high density of fruits (≥1.2 cups/1,000 kcal/day vs. <1.2 cups/1,000 kcal/day) and vegetables (≥1.3 cups/1,000 kcal/day vs. <1.3 cups/1,000 kcal/day) on preeclampsia risk, conditional on BMI, using a doubly robust estimator implemented in 2 stages. We found that the protective association of higher fruit density declined approximately linearly from a BMI of 20 to a BMI of 32, by 0.25 cases per 100 women per each BMI unit, and then flattened. The protective association of higher vegetable density strengthened in a linear fashion, by 0.3 cases per 100 women for every unit increase in BMI, up to a BMI of 30, where it plateaued. Dietary patterns with a high periconceptional density of fruits and vegetables appear more protective against preeclampsia for women with higher BMI than for leaner women.

Challenges in Obtaining Valid Causal Effect Estimates with Machine Learning Algorithms.

Unlike parametric regression, machine learning (ML) methods do not generally require precise knowledge of the true data generating mechanisms. As such, numerous authors have advocated for ML methods to estimate causal effects. Unfortunately, ML algorithmscan perform worse than parametric regression. We demonstrate the performance of ML-based single- and double-robust estimators. We use 100 Monte Carlo samples with sample sizes of 200, 1200, and 5000 to investigate bias and confidence interval coverage under several scenarios. In a simple confounding scenario, confounders were related to the treatment and the outcome via parametric models. In a complex confounding scenario, the simple confounders were transformed to induce complicated nonlinear relationships. In the simple scenario, when ML algorithms were used, double-robust estimators were superior to single-robust estimators. In the complex scenario, single-robust estimators with ML algorithms were at least as biased as estimators using misspecified parametric models. Double-robust estimators were less biased, but coverage was well below nominal. The use of sample splitting, inclusion of confounder interactions, reliance on a richly specified ML algorithm, and use of doubly robust estimators was the only explored approach that yielded negligible bias and nominal coverage. Our results suggest that ML based singly robust methods should be avoided.

AIPW: An R Package for Augmented Inverse Probability-Weighted Estimation of Average Causal Effects.

An increasing number of recent studies have suggested that doubly robust estimators with cross-fitting should be used when estimating causal effects with machine learning methods. However, not all existing programs that implement doubly robust estimators support machine learning methods and cross-fitting, or provide estimates on multiplicative scales. To address these needs, we developed AIPW, a software package implementing augmented inverse probability weighting (AIPW) estimation of average causal effects in R (R Foundation for Statistical Computing, Vienna, Austria). Key features of the AIPW package include cross-fitting and flexible covariate adjustment for observational studies and randomized controlled trials (RCTs). In this paper, we use a simulated RCT to illustrate implementation of the AIPW estimator. We also perform a simulation study to evaluate the performance of the AIPW package compared with other doubly robust implementations, including CausalGAM, npcausal, tmle, and tmle3. Our simulation showed that the AIPW package yields performance comparable to that of other programs. Furthermore, we also found that cross-fitting substantively decreases the bias and improves the confidence interval coverage for doubly robust estimators fitted with machine learning algorithms. Our findings suggest that the AIPW package can be a useful tool for estimating average causal effects with machine learning methods in RCTs and observational studies.

Incremental Propensity Score Effects for Time-fixed Exposures.

When causal inference is of primary interest, a range of target parameters can be chosen to define the causal effect, such as average treatment effects (ATEs). However, ATEs may not always align with the research question at hand. Furthermore, the assumptions needed to interpret estimates as ATEs, such as exchangeability, consistency, and positivity, are often not met. Here, we present the incremental propensity score (PS) approach to quantify the effect of shifting each person's exposure propensity by some predetermined amount. Compared with the ATE, incremental PS may better reflect the impact of certain policy interventions and do not require that positivity hold. Using the Nulliparous Pregnancy Outcomes Study: monitoring mothers-to-be (nuMoM2b), we quantified the relationship between total vegetable intake and the risk of preeclampsia and compared it to average treatment effect estimates. The ATE estimates suggested a reduction of between two and three preeclampsia cases per 100 pregnancies for consuming at least half a cup of vegetables per 1,000 kcal. However, positivity violations obfuscate the interpretation of these results. In contrast, shifting each woman's exposure propensity by odds ratios ranging from 0.20 to 5.0 yielded no difference in the risk of preeclampsia. Our analyses show the utility of the incremental PS effects in addressing public health questions with fewer assumptions.

Defining and Identifying Per-protocol Effects in Randomized Trials.

In trials with noncompliance to assigned treatment, researchers might be interested in estimating a per-protocol effect-a comparison of two counterfactual outcomes defined by treatment assignment and (often time-varying) compliance with a well-defined treatment protocol. Here, we provide a general counterfactual definition of a per-protocol effect and discuss examples of per-protocol effects that are of either substantive or methodologic interest. In doing so, we seek to make more concrete what per-protocol effects are and highlight that one can estimate per-protocol effects that are more than just a comparison of always taking treatment in two distinct treatment arms. We then discuss one set of identifiability conditions that allow for identification of a causal per-protocol effect, highlighting some potential violations of those conditions that might arise when estimating per-protocol effects.

Rate of false conviction of criminal defendants who are sentenced to death.

The rate of erroneous conviction of innocent criminal defendants is often described as not merely unknown but unknowable. There is no systematic method to determine the accuracy of a criminal conviction; if there were, these errors would not occur in the first place. As a result, very few false convictions are ever discovered, and those that are discovered are not representative of the group as a whole. In the United States, however, a high proportion of false convictions that do come to light and produce exonerations are concentrated among the tiny minority of cases in which defendants are sentenced to death. This makes it possible to use data on death row exonerations to estimate the overall rate of false conviction among death sentences. The high rate of exoneration among death-sentenced defendants appears to be driven by the threat of execution, but most death-sentenced defendants are removed from death row and resentenced to life imprisonment, after which the likelihood of exoneration drops sharply. We use survival analysis to model this effect, and estimate that if all death-sentenced defendants remained under sentence of death indefinitely, at least 4.1% would be exonerated. We conclude that this is a conservative estimate of the proportion of false conviction among death sentences in the United States.

Preoperative Metyrosine Improves Cardiovascular Outcomes for Patients Undergoing Surgery for Pheochromocytoma and Paraganglioma.

BACKGROUND: The goal of preoperative pharmacotherapy for pheochromocytoma (PCC) and paraganglioma (PGL) resection is to minimize intraoperative hemodynamic instability and perioperative cardiovascular complications, but no standard preoperative regimen exists. Historically, treatment used metyrosine and phenoxybenzamine (MP). The recent metyrosine shortage required that phenoxybenzamine alone (PA) be used for treatment. The authors examined their experience to determine the impact of preoperative metyrosine treatment on patient outcomes. METHODS: A retrospective cohort study investigated patients who underwent initial PCC/PGL resection (2000-2014). The primary outcome was intraoperative hemodynamics, measured by heart rate (HR) and systolic blood pressure (SBP). The secondary outcomes included perioperative complications and cardiovascular-specific complications (CVC). Univariate analysis was performed, and adjusted risk differences were estimated after confounding was taken into account. RESULTS: Of 174 patients, 142 (81.6 %) were in the MP group. The MP and PA patients had comparable intraoperative use of antihypertensives (83.9 vs 78.1 %; p = 0.443), vasopressors (74.6 vs 87.5 %; p = 0.120), and fluid resuscitation (mean, 24.4 vs 24.8 ml/min; p = 0.761). Although the perioperative complication rate did not differ significantly between the MP and PA groups (respectively 23.4 vs 34.4 %; p = 0.198), the PA patients had a 15.8 % higher rate of CVC even after controlling for confounders (p = 0.034). Compared with the MP patients, the PA patients had significantly more hemodynamic instability intraoperatively, with a greater range in HR (7.4 bpm; p = 0.034) and SBP (14.8 mmHg; p = 0.020). CONCLUSIONS: In this study, preoperative metyrosine improved intraoperative hemodynamic stability and decreased CVC rates in patients undergoing PCC/PGLresection. These data suggest that the addition of preoperative metyrosine may improve operative outcomes.

Surrogate markers for time-varying treatments and outcomes.

BACKGROUND: A surrogate marker is a variable commonly used in clinical trials to guide treatment decisions when the outcome of ultimate interest is not available. A good surrogate marker is one where the treatment effect on the surrogate is a strong predictor of the effect of treatment on the outcome. We review the situation when there is one treatment delivered at baseline, one surrogate measured at one later time point, and one ultimate outcome of interest and discuss new issues arising when variables are time-varying. METHODS: Most of the literature on surrogate markers has only considered simple settings with one treatment, one surrogate, and one outcome of interest at a fixed time point. However, more complicated time-varying settings are common in practice. In this article, we describe the unique challenges in two settings, time-varying treatments and time-varying surrogates, while relating the ideas back to the causal-effects and causal-association paradigms. CONCLUSION: In addition to discussing and extending popular notions of surrogacy to time-varying settings, we give examples illustrating that one can be misled by not taking into account time-varying information about the surrogate or treatment. We hope this article has provided some motivation for future work on estimation and inference in such settings.

Optimal restricted estimation for more efficient longitudinal causal inference.

Efficient semiparametric estimation of longitudinal causal effects is often analytically or computationally intractable. We propose a novel restricted estimation approach for increasing efficiency, which can be used with other techniques, is straightforward to implement, and requires no additional modeling assumptions.

Comparison of methods for estimating the effect of salvage therapy in prostate cancer when treatment is given by indication.

For patients who were previously treated for prostate cancer, salvage hormone therapy is frequently given when the longitudinal marker prostate-specific antigen begins to rise during follow-up. Because the treatment is given by indication, estimating the effect of the hormone therapy is challenging. In a previous paper we described two methods for estimating the treatment effect, called two-stage and sequential stratification. The two-stage method involved modeling the longitudinal and survival data. The sequential stratification method involves contrasts within matched sets of people, where each matched set includes people who did and did not receive hormone therapy. In this paper, we evaluate the properties of these two methods and compare and contrast them with the marginal structural model methodology. The marginal structural model methodology involves a weighted survival analysis, where the weights are derived from models for the time of hormone therapy. We highlight the different conditional and marginal interpretations of the quantities being estimated by the three methods. Using simulations that mimic the prostate cancer setting, we evaluate bias, efficiency, and accuracy of estimated standard errors and robustness to modeling assumptions. The results show differences between the methods in terms of the quantities being estimated and in efficiency. We also demonstrate how the results of a randomized trial of salvage hormone therapy are strongly influenced by the design of the study and discuss how the findings from using the three methodologies can be used to infer the results of a trial.

The impact of aggressive and conservative propensity for initiation of neuromuscular blockade in mechanically ventilated patients with hypoxemic respiratory failure.

INTRODUCTION: Neuromuscular blockade (NMB) in ventilated patients may cause benefit or harm. We applied "incremental interventions" to determine the impact of altering NMB initiation aggressiveness. METHODS: Retrospective cohort study of ventilated patients with PaO2/FiO2 ratio < 150 mmHg and PEEP≥ 8cmH2O from the Medical Information Mart of Intensive Care IV database (MIMIC-IV version 1.0) estimating the effect of incremental interventions on in-hospital mortality and ventilator-free days, modifying hourly propensity for NMB initiation to be aggressive or conservative relative to usual care, adjusting for confounding with inverse probability weighting. RESULTS: 5221 patients were included (13.3% initiated on NMB). Incremental interventions estimated a strong effect on NMB usage: 5-fold higher hourly odds of initiation increased usage to 36.5% (CI = [34.3%,38.7%]) and 5-fold lower odds decreased usage to 3.8% (CI = [3.3%,4.3%]). Aggressive and conservative strategies demonstrated a U-shaped mortality relationship. 5-fold higher or lower propensity increased in-hospital mortality by 2.6% (0.95 CI = [1.5%,3.7%]) or 1.3% (0.95 CI = [0.1%,2.5%]) respectively. In secondary analysis of a healthier patient cohort, results were similar, however conservative strategies also improved ventilator-free days. INTERPRETATION: Aggressive or conservative initiation of NMB may worsen mortality. In healthier populations, marginally conservative NMB initiation strategies may lead to increased ventilator free days with minimal impact on mortality.

Improved cardiovascular risk prediction using nonparametric regression and electronic health record data.

BACKGROUND: Use of the electronic health record (EHR) is expected to increase rapidly in the near future, yet little research exists on whether analyzing internal EHR data using flexible, adaptive statistical methods could improve clinical risk prediction. Extensive implementation of EHR in the Veterans Health Administration provides an opportunity for exploration. OBJECTIVES: To compare the performance of various approaches for predicting risk of cerebrovascular and cardiovascular (CCV) death, using traditional risk predictors versus more comprehensive EHR data. RESEARCH DESIGN: Retrospective cohort study. We identified all Veterans Health Administration patients without recent CCV events treated at 12 facilities from 2003 to 2007, and predicted risk using the Framingham risk score, logistic regression, generalized additive modeling, and gradient tree boosting. MEASURES: The outcome was CCV-related death within 5 years. We assessed each method's predictive performance with the area under the receiver operating characteristic curve (AUC), the Hosmer-Lemeshow goodness-of-fit test, plots of estimated risk, and reclassification tables, using cross-validation to penalize overfitting. RESULTS: Regression methods outperformed the Framingham risk score, even with the same predictors (AUC increased from 71% to 73% and calibration also improved). Even better performance was attained in models using additional EHR-derived predictor variables (AUC increased to 78% and net reclassification improvement was as large as 0.29). Nonparametric regression further improved calibration and discrimination compared with logistic regression. CONCLUSIONS: Despite the EHR lacking some risk factors and its imperfect data quality, health care systems may be able to substantially improve risk prediction for their patients by using internally developed EHR-derived models and flexible statistical methodology.

Marginal structural models for estimating the longitudinal effects of community violence exposure on youths' internalizing and externalizing symptoms.

OBJECTIVE: Longitudinal observational data pose a challenge for causal inference when the exposure of interest varies over time alongside time-dependent confounders, which often occurs in trauma research. We describe marginal structural models (MSMs) using inverse probability weighting as a useful solution under several assumptions that are well-suited to estimating causal effects in trauma research. METHOD: We illustrate the application of MSMs by estimating the joint effects of community violence exposure across time on youths' internalizing and externalizing symptoms. Our sample included 4,327 youth (50% female, 50% male; 1.4% Asian American or Pacific Islander, 34.7% Black, 46.9% Hispanic, .8% Native American, 14.3%, White, 1.5%, Other race/ethnicity; Mage at baseline = 8.62, range = 3-15) from the Project on Human Development in Chicago Neighborhoods. RESULTS: Wave 3 internalizing symptoms increased linearly with increases in Wave 2 and Wave 3 community violence exposure, whereas effects on externalizing symptoms were quadratic for Wave 2 community violence exposure and linear for Wave 3. These results fail to provide support for the desensitization model of community violence exposure. CONCLUSION: MSMs are a useful tool for researchers who rely on longitudinal observational data to estimate causal effects of time-varying exposures, as is often the case in the study of psychological trauma. (PsycInfo Database Record (c) 2023 APA, all rights reserved).