Targeted Minimum Loss-based Estimation Research Articles

The Causal Roadmap and Simulations to Improve the Rigor and Reproducibility of Real-data Applications.

The Causal Roadmap outlines a systematic approach to asking and answering questions of cause and effect: define the quantity of interest, evaluate needed assumptions, conduct statistical estimation, and carefully interpret results. To protect research integrity, it is essential that the algorithm for statistical estimation and inference be prespecified prior to conducting any effectiveness analyses. However, it is often unclear which algorithm will perform optimally for the real-data application. Instead, there is a temptation to simply implement one's favorite algorithm, recycling prior code or relying on the default settings of a computing package. Here, we call for the use of simulations that realistically reflect the application, including key characteristics such as strong confounding and dependent or missing outcomes, to objectively compare candidate estimators and facilitate full specification of the statistical analysis plan. Such simulations are informed by the Causal Roadmap and conducted after data collection but prior to effect estimation. We illustrate with two worked examples. First, in an observational longitudinal study, we use outcome-blind simulations to inform nuisance parameter estimation and variance estimation for longitudinal targeted minimum loss-based estimation. Second, in a cluster randomized trial with missing outcomes, we use treatment-blind simulations to examine type-I error control in two-stage targeted minimum loss-based estimation. In both examples, realistic simulations empower us to prespecify an estimation approach that is expected to have strong finite sample performance and also yield quality-controlled computing code for the actual analysis. Together, this process helps to improve the rigor and reproducibility of our research.

The effect of an intervention to promote isoniazid preventive therapy on leadership and management abilities

<sec><title>BACKGROUND</title>Across sub-Saharan Africa, mid-level healthcare managers oversee implementation of national guidelines. It remains unclear whether leadership and management training can improve population health outcomes.</sec><sec><title>METHODS</title>We sought to evaluate leadership/management skills among district-level health managers in Uganda participating in the SEARCH-IPT randomised trial to promote isoniazid preventive therapy (IPT) for persons with HIV (PWH). The intervention, which led to higher IPT rates, included annual leadership/management training of managers. We conducted a cross-sectional survey assessing leadership/management skills among managers at trial completion. The survey evaluated self-reported use of leadership/management tools and general leadership/management. We conducted a survey among a sample of providers to understand the intervention’s impact. Targeted minimum loss-based estimation (TMLE) was used to compare responses between trial arms.</sec><sec><title>RESULTS</title>Of 163 managers participating in the SEARCH-IPT trial, 119 (73%) completed the survey. Intervention managers reported more frequent use of leadership/management tools taught in the intervention curriculum than control managers (+3.64, 95% CI 1.98–5.30, P < 0.001). There were no significant differences in self-reported leadership skills in the intervention as compared to the control group. Among providers, the average reported quality of guidance and supervision was significantly higher in intervention vs control districts (+1.08, 95% CI 0.63–1.53, P = 0.001).</sec><sec><title>CONCLUSIONS</title>A leadership and management training intervention increased the use of leadership/management tools among mid-level managers and resulted in higher perceived quality of supervision among providers in intervention vs control districts in Uganda. These findings suggest improved leadership/management among managers contributed to increased IPT use among PWH in the intervention districts of the SEARCH-IPT trial.</sec>

Longitudinal patterns of natural hazard exposures and anxiety and depression symptoms among young adults in four low- and middle-income countries

We estimated the effect of community-level natural hazard exposure during prior developmental stages on later anxiety and depression symptoms among young adults and potential differences stratified by gender. We analyzed longitudinal data (2002–2020) on 5585 young adults between 19 and 26 years in Ethiopia, India, Peru, and Vietnam. A binary question identified community-level exposure, and psychometrically validated scales measured recent anxiety and depression symptoms. Young adults with three exposure histories (“time point 1,” “time point 2,” and “both time points”) were contrasted with their unexposed peers. We applied a longitudinal targeted minimum loss-based estimator with an ensemble of machine learning algorithms for estimation. Young adults living in exposed communities did not exhibit substantially different anxiety or depression symptoms from their unexposed peers, except for young women in Ethiopia who exhibited less anxiety symptoms (average causal effect [ACE] estimate = − 8.86 [95% CI: − 17.04, − 0.68] anxiety score). In this study, singular and repeated natural hazard exposures generally were not associated with later anxiety and depression symptoms. Further examination is needed to understand how distal natural hazard exposures affect lifelong mental health, which aspects of natural hazards are most salient, how disaster relief may modify symptoms, and gendered, age-specific, and contextual differences.

Targeted learning in observational studies with multi-valued treatments: An evaluation of antipsychotic drug treatment safety.

We investigate estimation of causal effects of multiple competing (multi-valued) treatments in the absence of randomization. Our work is motivated by an intention-to-treat study of the relative cardiometabolic risk of assignment to one of six commonly prescribed antipsychotic drugs in a cohort of nearly 39000 adults with serious mental illnesses. Doubly-robust estimators, such as targeted minimum loss-based estimation (TMLE), require correct specification of either the treatment model or outcome model to ensure consistent estimation; however, common TMLE implementations estimate treatment probabilities using multiple binomial regressions rather than multinomial regression. We implement a TMLE estimator that uses multinomial treatment assignment and ensemble machine learning to estimate average treatment effects. Our multinomial implementation improves coverage, but does not necessarily reduce bias, relative to the binomial implementation in simulation experiments with varying treatment propensity overlap and event rates. Evaluating the causal effects of the antipsychotics on 3-year diabetes risk or death, we find a safety benefit of moving from a second-generation drug considered among the safest of the second-generation drugs to an infrequently prescribed first-generation drug known for having low cardiometabolic risk.

Duration and timing of depression and risk of family dissolution: A register-based cohort study of newly-formed Danish families

BackgroundDepression is detrimental to partnership stability. However, it remains unclear if and how the duration and timing of depression affect the risk of family dissolution. MethodsWe conducted a Danish register-based cohort study of newly-formed cohabiting and married couples in 2008 and 2009, who were followed from the second year after family formation. Depressive episodes were defined by individual-level prescription patterns of antidepressant drugs (ATC codes N06A) in either partner. Family dissolution was characterized by the discontinuation of a shared residential address. Using Longitudinal Targeted Minimum Loss-based Estimation, we estimated the risk of family dissolution after 5 years of follow-up under various lengths and timings of depressive episodes. ResultsThere were 102,335 families included. The covariate-adjusted risk of family dissolution in families without depressive episodes was 30.0 % (95 % CI 29.6–30.4 %) and 35.5 % (95 % CI 29.5–41.5 %) in families with at least one depressive episode during follow-up. The risk of family dissolution increased with the duration of depressive episodes to 42.2 % (95 % CI 40.8–43.6 %) for five coherent years of depression. Depression shortly after family formation carried higher risk of family dissolution; this risk was 42.3 % (95 % CI 38.4–46.3 %) for depression experienced in the first year of family formation versus 32.9 % (95 % CI 31.8–34.0 %) in the fifth year of family formation. LimitationsProxy measures of depression by antidepressant prescriptions fails to identify milder depression. Annual measures of family dissolution precluded more fine-grained analyses of time-intervals. ConclusionsDepression is disruptive to family stability, particularly with longer duration and early onset after family formation.

All models are wrong, but which are useful? Comparing parametric and nonparametric estimation of causal effects in finite samples

Abstract There is a long-standing debate in the statistical, epidemiological, and econometric fields as to whether nonparametric estimation that uses machine learning in model fitting confers any meaningful advantage over simpler, parametric approaches in finite sample estimation of causal effects. We address the question: when estimating the effect of a treatment on an outcome, how much does the choice of nonparametric vs parametric estimation matter? Instead of answering this question with simulations that reflect a few chosen data scenarios, we propose a novel approach to compare estimators across a large number of data-generating mechanisms drawn from nonparametric models with semi-informative priors. We apply this proposed approach and compare the performance of two nonparametric estimators (Bayesian adaptive regression tree and a targeted minimum loss-based estimator) to two parametric estimators (a logistic regression-based plug-in estimator and a propensity score estimator) in terms of estimating the average treatment effect across thousands of data-generating mechanisms. We summarize performance in terms of bias, confidence interval coverage, and mean squared error. We find that the two nonparametric estimators can substantially reduce bias as compared to the two parametric estimators in large-sample settings characterized by interactions and nonlinearities while compromising very little in terms of performance even in simple, small-sample settings.

Evaluating a Targeted Minimum Loss-Based Estimator for Capture-Recapture Analysis: An Application to HIV Surveillance in San Francisco, California.

The capture-recapture method is a common tool used in epidemiology to estimate the size of "hidden" populations and correct the underascertainment of cases, based on incomplete and overlapping lists of the target population. Log-linear models are often used to estimate the population size yet may produce implausible and unreliable estimates due to model misspecification and small cell sizes. A novel targeted minimum loss-based estimation (TMLE) model developed for capture-recapture makes several notable improvements to conventional modeling: "targeting" the parameter of interest, flexibly fitting the data to alternative functional forms, and limiting bias from small cell sizes. Using simulations and empirical data from the San Francisco, California, Department of Public Health's human immunodeficiency virus (HIV) surveillance registry, we evaluated the performance of the TMLE model and compared results with those of other common models. Based on 2,584 people observed on 3 lists reportable to the surveillance registry, the TMLE model estimated the number of San Francisco residents living with HIV as of December 31, 2019, to be 13,523 (95% confidence interval: 12,222, 14,824). This estimate, compared with a "ground truth" of 12,507, was the most accurate and precise of all models examined. The TMLE model is a significant advancement in capture-recapture studies, leveraging modern statistical methods to improve estimation of the sizes of hidden populations.

Robust variance estimation and inference for causal effect estimation

Abstract We present two novel approaches to variance estimation of semi-parametric efficient point estimators of the treatment-specific mean: (i) a robust approach that directly targets the variance of the influence function (IF) as a counterfactual mean outcome and (ii) a modified non-parametric bootstrap-based approach. The performance of these approaches to variance estimation is compared to variance estimation based on the sample variance of the empirical IF in simulations across different levels of positivity violations and treatment effect sizes. In this article, we focus on estimation of the nuisance parameters using correctly specified parametric models for the treatment mechanism in order to highlight the challenges posed by violation of positivity assumptions (distinct from the challenges posed by non-parametric estimation of the nuisance parameters). Results demonstrate that (1) variance estimation based on the empirical IF may provide highly anti-conservative confidence interval coverage (as reported previously), (2) the proposed robust approach to variance estimation in this setting provides conservative coverage, and (3) the proposed modified bootstrap maintains close to nominal coverage and improves power. In the appendix, we (a) generalize the robust approach of estimating variance to marginal structural working models and (b) provide a proof of the consistency of the targeted minimum loss-based estimation bootstrap.

Blurring cluster randomized trials and observational studies: Two-Stage TMLE for subsampling, missingness, and few independent units.

Cluster randomized trials (CRTs) often enroll large numbers of participants; yet due to resource constraints, only a subset of participants may be selected for outcome assessment, and those sampled may not be representative of all cluster members. Missing data also present a challenge: if sampled individuals with measured outcomes are dissimilar from those with missing outcomes, unadjusted estimates of arm-specific endpoints and the intervention effect may be biased. Further, CRTs often enroll and randomize few clusters, limiting statistical power and raising concerns about finite sample performance. Motivated by SEARCH-TB, a CRT aimed at reducing incident tuberculosis infection, we demonstrate interlocking methods to handle these challenges. First, we extend Two-Stage targeted minimum loss-based estimation to account for three sources of missingness: (i) subsampling; (ii) measurement of baseline status among those sampled; and (iii) measurement of final status among those in the incidence cohort (persons known to be at risk at baseline). Second, we critically evaluate the assumptions under which subunits of the cluster can be considered the conditionally independent unit, improving precision and statistical power but also causing the CRT to behave like an observational study. Our application to SEARCH-TB highlights the real-world impact of different assumptions on measurement and dependence; estimates relying on unrealistic assumptions suggested the intervention increased the incidence of TB infection by 18% (risk ratio [RR]=1.18, 95% confidence interval [CI]: 0.85-1.63), while estimates accounting for the sampling scheme, missingness, and within community dependence found the intervention decreased the incident TB by 27% (RR=0.73, 95% CI: 0.57-0.92).

#4356 DYNAMIC EFFECT OF PROTEINURIA ON ADVERSE KIDNEY OUTCOMES WITH TARGETED MAXIMUM LIKELIHOOD ESTIMATION METHOD: RESULT FROM THE KNOW-CKD STUDY

Abstract Background and Aims Proteinuria is a risk factor for the progression of chronic kidney disease (CKD), but its causal inference may be challenging due to time varying exposure and confounding, the changing its degree, and loss to follow up. Method A total of 1,223 patients enrolled as part of The Korean Cohort Study for Outcome in Patients With Chronic Kidney Disease (KNOW-CKD) were analyzed at 3 observational points (baseline, 3-year; early, and 7-year; late) at which spot urine protein creatinine ratio (UPCR) was measured. We used longitudinal targeted minimum loss-based estimation (TMLE) and marginal structural models (MSM) to estimate the cumulative incidence of adverse kidney outcomes (eGFR halving and kidney failure requiring replacement therapy) of dynamic exposure to high proteinuria (UPCR≥1g/g) comparing counterfactuals (UPCR<1g/g) adjusted for time varying confounding (systolic blood pressure, estimated glomerular filtration rate, and renin-angiotensin-aldosterone blockers) and baseline covariates (age, sex, diabetes, cardiovascular disease, and smoking). Results Patients with sustained high proteinuria throughout 7-year follow-up had significant higher risk of renal events than those with counterfactuals (relative risk [RR], 3.120; 95% confidence interval, 2.150-4.528; P < 0.001). The RR were 0.168 (0.055-0.517; P = 0.002) and 0.613 (0.337-1.114; P = 0.108) for early and late proteinuria reduction comparing sustained high proteinuria, respectively. In MSM, hazard ratio (HR) of accumulative high proteinuria frequency were 1.612 (1.463-1.844; P <0.001) up to 3 years and 1.102 (0.877-1.387; P = 0.404) up to 7 years, respectively. Conclusion In CKD patients, sustained higher proteinuria is the main risk factor during the entire observation period. However, considering dynamic exposure, proteinuria reduction from the beginning has a protective effect on renal progression, but the effect weakens as the observation period becomes longer.

Effect of Tooth Loss on Cognitive Function among Older Adults in Singapore

Evidence suggests a longitudinal association between tooth loss and cognitive function. However, the temporality of this association is not well understood. We investigated the effect of several emulated tooth loss prevention scenarios on cognitive function. We used data from 3 waves (baseline: 2009, second wave: 2011–2012, and third wave: 2015) of the Panel on Health and Ageing of Singaporean Elderly (PHASE). PHASE targeted older adults, aged ≥60 y, in Singapore. Number of teeth was used as a time-varying exposure (baseline, second wave). Cognitive function (Short Portable Mental Status Questionnaire score) in the third wave was assessed as the outcome. Multiple time-invariant (baseline) and time-varying (baseline and second wave) covariates were included. The “longitudinal modified treatment policy approach” combined with targeted minimum loss–based estimation was used to define and estimate additive effects of emulated tooth loss prevention scenarios. Emulated scenarios were the following: what if edentate people retained 1 to 4 teeth (scenario 1), what if those with <5 teeth retained 5 to 9 teeth (scenario 2), what if those with <10 teeth retained 10 to 19 teeth (scenario 3), and what if everyone retained ≥20 teeth (scenario 4)? A total of 1,516 participants, excluding those with severe cognitive impairment, were included (male: 41.6%). The mean age at baseline was 70.6 y (SD = 7.1). The mean SPMSQ score at baseline was 2.06 (SD = 0.02) for edentulous, 1.55 (SD = 0.04) for 1 to 4 teeth, 1.61 (SD = 0.03) for 5 to 9 teeth, 1.73 (SD = 0.02) for 10 to 19 teeth, and 1.71 (SD = 0.02) for ≥20 teeth. Additive effect of hypothetical intervention gradually increased with intensity of prevention from scenario 1 to scenario 4 (scenario 1: −0.02 [95% CI, −0.08 to 0.04], scenario 2: −0.05 [95% CI, −0.11 to −0.00], scenario 3: −0.07 [95% CI, −0.14 to −0.00], scenario 4: −0.15 [95% CI, −0.23 to −0.06]). Emulated tooth loss prevention interventions were associated with better cognitive function score. Therefore, preventing tooth loss could potentially benefit maintenance of cognitive function among older adults.

Assessing the impacts of smoking cessation and resumption on back pain risk in later life.

This study aimed to assess the impacts of smoking cessation and resumption over 4 years on the risk of back pain at the 6-year follow-up among older adults in England. We analysed 6467 men and women aged ≥50 years in the English Longitudinal Study of Aging. Self-reported smoking status, assessed in waves 4 (2008-2009) and 6 (2012-2013), was used as exposure for the study, whereas self-reported back pain of moderate or severe intensity, assessed in wave 7 (2014-2015), was used as the outcome. A targeted minimum loss-based estimator was used with longitudinal modified treatment policies to adjust for baseline and time-varying covariates. Regarding the estimation of the effects of changes in smoking status on the risk of back pain, during the follow-up, individuals who resumed smoking within 4 years had a higher risk of back pain than those who avoided smoking for over 4 years, and the relative risk (RR) (95% confidence interval [CI]) was 1.536 (1.214-1.942). Regarding the estimation of effects of smoking cessation on the risk of back pain, smoking cessation over 4 years was associated with a significantly lower risk of back pain, as indicated by the originally observed data, and the RR (95% CI) was 0.955 (0.912-0.999). Older adults who avoided smoking for over 4 years had a lower risk of back pain. However, those who resumed smoking within 4 years had a higher risk of back pain. Older adults who avoided smoking for over 4 years had a lower risk of back pain. However, those who resumed smoking within 4 years had a higher risk of back pain. Our study data suggest the importance of maintaining smoking cessation to reduce the risk of back pain in the older population.

Impact of Teeth on Social Participation: Modified Treatment Policy Approach

Social participation prevents social isolation and loneliness among older adults while having numerous positive effects on their health and well-being in rapidly aging societies. We aimed to estimate the effect of retaining more natural teeth on social participation among older adults in Japan. The analysis used longitudinal data from 24,872 participants in the Japan Gerontological Evaluation Study (2010, 2013, and 2016). We employed a longitudinal modified treatment policy approach to determine the effect of several hypothetical scenarios (preventive scenarios and tooth loss scenarios) on frequent social participation (1 = at least once a week/0 = less than once a week) after a 6-y follow-up. The corresponding statistical parameters were estimated using targeted minimum loss-based estimation (TMLE) method. Number of teeth category (edentate/1–9/10–19/≥20) was treated as a time-varying exposure, and the outcome estimates were adjusted for time-varying (income, self-rated health, marital status, instrumental activities of daily living, vision loss, hearing loss, major comorbidities, and number of household members) and time-invariant covariates (age, sex, education, baseline social participation). Less frequent social participation was associated with older age, male sex, lower income, low educational attainment, and poor self-rated health at the baseline. Social participation improved when tooth loss prevention scenarios were emulated. The best preventive scenario (i.e., maintaining ≥20 teeth among each participant) improved social participation by 8% (risk ratio [RR] = 1.08; 95% confidence interval [CI], 1.05–1.11). Emulated tooth loss scenarios gradually decreased social participation. A hypothetical scenario in which all the participants were edentate throughout the follow-up period resulted in a 11% (RR = 0.89; 95% CI, 0.84–0.94) reduction in social participation. Subsequent tooth loss scenarios showed 8% (RR = 0.92; 95% CI, 0.88–0.95), 6% (RR = 0.94; 95% CI, 0.91–0.97), and 4% (RR = 0.96; 95% CI, 0.93–0.98) reductions, respectively. Thus, among Japanese older adults, retaining a higher number of teeth positively affects their social participation, whereas being edentate or having a relatively lower number of teeth negatively affects their social participation.

Effect of Sepsis on Death as Modified by Solid Organ Transplantation.

Patients who have undergone solid organ transplants (SOT) have an increased risk for sepsis compared with the general population. Paradoxically, studies suggest that SOT patients with sepsis may experience better outcomes compared with those without a SOT. However, these analyses used previous definitions of sepsis. It remains unknown whether the more recent definitions of sepsis and modern analytic approaches demonstrate a similar relationship. Using the Weill Cornell-Critical Care Database for Advanced Research, we analyzed granular physiologic, microbiologic, comorbidity, and therapeutic data in patients with and without SOT admitted to intensive care units (ICUs). We used a survival analysis with a targeted minimum loss-based estimation, adjusting for within-group (SOT and non-SOT) potential confounders to ascertain whether the effect of sepsis, defined by sepsis-3, on 28-day mortality was modified by SOT status. We performed additional analyses on restricted populations. We analyzed 28 431 patients: 439 with SOT and sepsis, 281 with SOT without sepsis, 6793 with sepsis and without SOT, and 20 918 with neither. The most common SOT types were kidney (475) and liver (163). Despite a higher severity of illness in both sepsis groups, the adjusted sepsis-attributable effect on 28-day mortality for non-SOT patients was 4.1% (95% confidence interval [CI], 3.8-4.5) and -14.4% (95% CI, -16.8 to -12) for SOT patients. The adjusted SOT effect modification was -18.5% (95% CI, -21.2 to -15.9). The adjusted sepsis-attributable effect for immunocompromised controls was -3.5% (95% CI, -4.5 to -2.6). Across a large database of patients admitted to ICUs, the sepsis-associated 28-day mortality effect was significantly lower in SOT patients compared with controls.

Health-related quality of life in various health conditions: two consecutive surveys of older Japanese adults.

Measuring health-related quality of life (HRQOL) in various health conditions in different countries is important given the regional differences. This study employed large-scale nationwide data targeting older adults in Japan to estimate the HRQOL in the key health conditions that are the major causes of disability. Our data were derived from two survey waves (2016 and 2019 surveys) of cross-sectional data from the Japan Gerontological Evaluation Study, an ongoing nationwide study targeting functionally independent older adults in Japan. A total of 28,345 individuals from 27 of the 47 Japanese provinces were analyzed. The EuroQoL 5-dimension 5-level instrument (EQ-5D-5L) was employed to assess the HRQOL utility scores. The targeted minimum loss-based estimator with sampling weighting methods was applied to estimate the utility score in eight major health conditions, including sensory organ disease, musculoskeletal disease, oral disorders, and depressive disorders. The estimated HRQOL utility score for those with the poorest health conditions in self-rated health, hearing loss, vision loss, number of remaining teeth (e.g., no teeth with no denture use), oral dysfunction, depressive symptoms, chronic low back pain, and chronic knee pain was 0.576 (95% confidence interval (CI) 0.555-0.598), 0.768 (95% CI 0.737-0.800), 0.680 (95% CI 0.662-0.699), 0.809 (95% CI 0.796-0.821), 0.776 (95% CI 0.764-0.788), 0.723 (95% CI 0.710-0.737), 0.715 (95% CI 0.690-0.739), and 0.742 (95% CI 0.722-0.763), respectively. We successfully provided a catalog for the HRQOL utility score in key health conditions that are the leading causes of disability among older adults.

Identifying HIV sequences that escape antibody neutralization using random forests and collaborative targeted learning

Abstract Recent studies have indicated that it is possible to protect individuals from HIV infection using passive infusion of monoclonal antibodies. However, in order for monoclonal antibodies to confer robust protection, the antibodies must be capable of neutralizing many possible strains of the virus. This is particularly challenging in the context of a highly diverse pathogen like HIV. It is therefore of great interest to leverage existing observational data sources to discover antibodies that are able to neutralize HIV viruses via residues where existing antibodies show modest protection. Such information feeds directly into the clinical trial pipeline for monoclonal antibody therapies by providing information on (i) whether and to what extent combinations of antibodies can generate superior protection and (ii) strategies for analyzing past clinical trials to identify in vivo evidence of antibody resistance. These observational data include genetic features of many diverse HIV genetic sequences, as well as in vitro measures of antibody resistance. The statistical learning problem we are interested in is developing statistical methodology that can be used to analyze these data to identify important genetic features that are significantly associated with antibody resistance. This is a challenging problem owing to the high-dimensional and strongly correlated nature of the genetic sequence data. To overcome these challenges, we propose an outcome-adaptive, collaborative targeted minimum loss-based estimation approach using random forests. We demonstrate via simulation that the approach enjoys important statistical benefits over existing approaches in terms of bias, mean squared error, and type I error. We apply the approach to the Compile, Analyze, and Tally Nab Panels database to identify AA positions that are potentially causally related to resistance to neutralization by several different antibodies.

Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes

This paper generalizes the targeted minimum loss-based estimation (TMLE) framework to allow for estimating the effects of time-varying interventions in settings where both interventions, covariates, and outcome can happen at subject-specific time-points on an arbitrarily fine time-scale. TMLE is a general template for constructing asymptotically linear substitution estimators for smooth low-dimensional parameters in infinite-dimensional models. Existing longitudinal TMLE methods are developed for data where observations are made on a discrete time-grid. We consider a continuous-time counting process model where intensity measures track the monitoring of subjects, and focus on a low-dimensional target parameter defined as the intervention-specific mean outcome at the end of follow-up. To construct our TMLE algorithm for the given statistical estimation problem, we derive an expression for the efficient influence curve and represent the target parameter as a functional of intensities and conditional expectations. The high-dimensional nuisance parameters of our model are estimated and updated in an iterative manner according to separate targeting steps for the involved intensities and conditional expectations. The resulting estimator solves the efficient influence curve equation. We state a general efficiency theorem and describe a highly adaptive lasso estimator for nuisance parameters that allows us to establish asymptotic linearity and efficiency of our estimator under minimal conditions on the underlying statistical model.

Developing a Targeted Learning-Based Statistical Analysis Plan

The Targeted Learning estimation roadmap provides a rigorous framework for developing a statistical analysis plan (SAP) for synthesizing evidence from randomized controlled trials and real world data. Learning from these data necessitates acknowledging potential sources of bias, and specifying appropriate mitigation strategies. This article demonstrates how Targeted Learning informs different aspects of SAP development, including explicit representation of intercurrent events. Guiding principles are to (a) define the target parameter of interest separately from the model or estimation procedure; and (b) use targeted minimum loss-based estimation (TMLE) and super learning for causal inference. These flexible methodologies can be entirely pre-specified while remaining data adaptive; and (c) carry out a nonparametric sensitivity analysis to evaluate the plausibility of a causal interpretation of the estimated treatment effect, and its stability with respect to violations of underlying casual assumptions. The roadmap promotes the principles and practices set forth in the International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use Guideline. An annotated SAP, checklists for pre-specifying the TMLE and super learning procedures, and sample R code are provided as supplementary materials.

Performance of LTMLE in the Presence of Missing Data in Control-Matched Longitudinal Studies

Conventional controlled trials employ randomization and blinding to ensure the balance of baseline covariates between study arms. Treatment effect is formally tested via a pre-specified hypothesis reflecting trial’s primary objective defined by the primary efficacy endpoint, such as, is experimental treatment effective in slowing cognitive decline at a pre-specified landmark time in a neurologic therapeutic development? To address the same clinical question, but, as a safety endpoint in an observational study post radiopharmaceutical imaging drug approval due to concerns of radiation retention in the brain after accumulated real-world use over time, the targeted minimum loss-based estimation (TMLE) method has been suggested. Overall, for a longitudinal control-matched cohort study, assessing treatment effect (efficacy or safety) in the presence of missingness can be very challenging, which depends also on trial duration and missingness pattern of outcome data between study arms. TMLE is a two-step procedure to estimate a target parameter and has been shown to be doubly robust. The objectives of our research are a few folds. First, we investigate the performance of the TMLE method using longitudinal structure (LTMLE) in a prospective control-matched longitudinal cohort study. Second, we evaluate the performance of LTMLE and a few methods that are often proposed in regulatory submissions for longitudinal data analysis or in the presence of missing data with various missing data mechanisms. Third, we assess the impacts of various missing data mechanisms to treatment effect estimation via extensive simulation studies. Finally, we discuss the results of the simulation studies and their implications to conducting a feasible real-world control-matched longitudinal cohort study.

Changes in Body Mass Index on the Risk of Back Pain: Estimating the Impacts of Weight Gain and Loss.

The relationship between obesity and back pain in older populations is poorly understood. This study aimed to examine (a) the impacts of changes in obesity status on back pain risk and (b) the heterogeneity in the influence of changes in obesity status according to muscle strength. We analyzed 6868 participants in waves 4 (2008-2009), 6 (2012-2013), and 7 (2014-2015) of the English Longitudinal Study of Ageing. The exposure comprised continuous body mass index (BMI) values, whereas the outcome comprised self-reported moderate or severe back pain. The targeted minimum loss-based estimator was used to estimate the impacts of hypothetical changes in BMI in each wave under 10 scenarios encompassing a 5%-25% hypothetical reduction/increase in BMI. We also performed stratified analysis using handgrip strength at the baseline. For the hypothetical reduction scenarios, a 10% (relative risk [RR]; 95% confidence interval [CI]=0.82 [0.73-0.92], p=.001) reduction in BMI estimated a significantly lower back pain risk compared to the observed data. For the hypothetical increase scenarios, a 5% (RR [95% CI]=1.11 [1.04-1.19], p=.002) increase in BMI estimated a significantly higher back pain risk. Increased BMI had a higher risk of back pain among those with weak strength when stratified by handgrip strength but not among those with strong strength. Our study confirmed that weight gain leads to a greater risk of back pain as well as heterogeneity in the influence of changes in obesity status according to the handgrip strength.