Time-varying Treatment Effects Research Articles

Estimating curvilinear time-varying treatment effects: Combining g-estimation of structural nested mean models with time-varying effect models for longitudinal causal inference.

Longitudinal designs can fortify causal inquiries of a focal predictor (i.e., treatment) on an outcome. But valid causal inferences are complicated by causal feedback between confounders and treatment over time. G-estimation of a structural nested mean model (SNMM) is designed to handle the complexities beset by measured time-varying or treatment-dependent confounding in longitudinal data. But valid inference requires correctly specifying the functional form of the SNMM, such as how the effects stay constant or change over time. In this article, we develop a g-estimation strategy for linear structural nested mean models whose causal parameters adopt the form of time-varying coefficient functions. These time-varying coefficient functions are smooth semiparametric functions of time that permit probing how the treatment effects may change curvilinearly. Further effect modification by time-invariant and time-varying covariates can be readily postulated in the SNMM to test fine-grained effect heterogeneity. We then describe a g-estimation strategy for estimating such an SNMM. We utilize the established time-varying effect model (TVEM) approach from the prevention and psychotherapy research literature for modeling flexible changes in covariate-outcome associations over time. Moreover, we exploit a known benefit of g-estimation over routine regression methods: its double robustness conferring protection against biases induced by certain forms of model misspecification. We encourage psychology researchers seeking correct causal conclusions from longitudinal data to use an SNMM with time-varying coefficient functions to assess curvilinear causal effects over time, and to use g-estimation with TVEM to resolve measured treatment-dependent confounding. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Impact of a complex health services intervention in long-term care nursing homes on 3-year overall survival: results from the CoCare study

BackgroundThe Coordinated medical Care (CoCare) project aimed to improve the quality of medical care in nursing homes by optimizing collaboration between nurses and physicians. We analyze the impact of the CoCare intervention on overall survival.MethodsThe effect of time-varying treatment on 3-year overall survival was analyzed with treatment as time-varying covariate within the entire cohort. To reduce bias due to non-random assignment to treatment groups, regression adjustment was applied. Therefore, age, sex, and level of care were used as potential confounders.ResultsThe study population consisted of 8,893 nursing home residents (NHRs), of which 1,330 participated in the CoCare intervention. The three-year overall survival was 49.8% in the entire cohort. NHRs receiving the intervention were associated with a higher survival probability compared to NHRs of the control group. In a univariable cox model with time-dependent treatment, the intervention was associated with a hazard ratio of 0.70 [95%CI 0.56–0.87, p = 0.002]. After adjustment for age, sex and level of care, the hazard ratio increased to 0.82 but was still significant [95%CI 0.71–0.96, p = 0.011].ConclusionThe analysis shows that optimizing collaboration between nurses and physicians leads to better survival of NHRs in Germany. This adds to the already published favorable cost-benefit ratio of the CoCare intervention and shows that a routine implementation of optimized collaboration between nurses and physicians is highly recommended.

Estimation of the causal effects of time-varying treatments in nested case-control studies using marginal structural Cox models.

When estimating the causal effects of time-varying treatments on survival in nested case-control (NCC) studies, marginal structural Cox models (Cox-MSMs) with inverse probability weights (IPWs) are a natural approach. However, calculating IPWs from the cases and controls is difficult because they are not random samples from the full cohort, and the number of subjects may be insufficient for calculation. To overcome these difficulties, we propose a method for calculating IPWs to fit Cox-MSMs to NCC sampling data. We estimate the IPWs using a pseudo-likelihood estimation method with an inverse probability of sampling weight using NCC samples, and additional samples of subjects who experience treatment changes and subjects whose follow-up is censored are required to calculate the weights. Our method only requires covariate histories for the samples. The confidence intervals are calculated from the robust variance estimator for the NCC sampling data. We also derive the asymptotic properties of the estimator of Cox-MSM under NCC sampling. The proposed methods will allow researchers to apply several case-control matching methods to improve statistical efficiency. A simulation study was conducted to evaluate the finite sample performance of the proposed method. We also applied our method to a motivating pharmacoepidemiological study examining the effect of statins on the incidence of coronary heart disease. The proposed method may be useful for estimating the causal effects of time-varying treatments in NCC studies.

Weighted Hazard Ratio Estimation for Delayed and Diminishing Treatment Effect

Nonproportional hazards (NPH) have been observed in confirmatory clinical trials with time to event outcomes. Under NPH, the hazard ratio does not stay constant over time and the log rank test is no longer the most powerful test. The weighted log rank test (WLRT) has been introduced to deal with the presence of nonproportionality. We focus our attention on the WLRT and the complementary Cox model based on time varying treatment effect proposed by Lin and León. We investigate whether the proposed weighted hazard ratio (WHR) approach is unbiased in scenarios where the WLRT statistic is the most powerful test. In the diminishing treatment effect scenario where the WLRT statistic would be most optimal, the time varying treatment effect estimated by the Cox model estimates the treatment effect very close to the true one. However, when the true hazard ratio is large the proposed model overestimates the treatment effect and the treatment profile over time. In the delayed treatment scenario, the estimated treatment effect profile over time is typically close to the true profile. For both scenarios, we have demonstrated analytically that the hazard ratio functions are approximately equal under small treatment effects. When the assumed rate of how quickly the treatment effect profile is diminishing or delaying differs in the analysis from that in the true data generating mechanism, the estimated hazard ratio profile from the WHR approach is biased. Since in practice the true HR time profile may differ from that assumed in the WHR analysis, it may be preferable to use alternative approaches for effect estimation.

Time-varying treatment effect modification of oral analgesic effectiveness by depressive symptoms in knee osteoarthritis: an application of structural nested mean models in a prospective cohort.

Depressive symptoms are common in knee osteoarthritis (OA), exacerbate knee pain severity and may influence outcomes of oral analgesic treatments. The aim was to assess whether oral analgesic effectiveness in knee OA varies by fluctuations in depressive symptoms. The sample included Osteoarthritis Initiative (OAI) participants not treated with oral analgesics at enrolment (n = 1477), with radiographic disease at the first follow-up visit (defined as the index date). Oral analgesic treatment and depressive symptoms, assessed with the Center for Epidemiological Studies Depression [(CES-D) score ≥16] Scale, were measured over three annual visits. Knee pain severity was measured at visits adjacent to treatment and modifier using the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) pain subscale (rescaled range = 0-100). Structural nested mean models (SNMMs) estimated causal mean differences in knee pain severity comparing treatment versus no treatment. The average causal effects of treated versus not treated for observations without depressive symptoms showed negligible differences in knee pain severity. However, causal mean differences in knee pain severity comparing treatment versus no treatment among observations with depressive symptoms increased over time from -0.10 [95% confidence interval (CI): -9.94, 9.74] to -16.67 (95% CI: -26.33, -7.01). Accordingly, the difference in average causal effects regarding oral analgesic treatment for knee pain severity between person-time with and without depressive symptoms was largest (-16.53; 95% CI: -26.75, -6.31) at the last time point. Cumulative treatment for 2 or 3 years did not yield larger causal mean differences. Knee OA patients with persistent depressive symptoms and chronic pain may derive more analgesic treatment benefit than those without depressive symptoms and less pain.

The air quality and well-being effects of low emission zones

This study provides the first evidence of the subjective well-being impacts of low emission zones (LEZs) while also undertaking a comprehensive analysis of their air quality effects. We identify causal impacts by exploiting the zones’ introduction date with difference-in-differences designs robust to staggered implementations and time-varying treatment effects. Results show air quality improvements through reductions in traffic-related pollutants despite ground-level ozone increases and harmful spatial pollution spillovers. We further find that the zones cause transitory yet long-lasting reductions in individuals’ life satisfaction despite health benefits, suggesting that the subjective well-being effects of restricting mobility potentially outweigh those of improved health.

Sample Size Calculations for Stepped Wedge Designs with Treatment Effects that May Change with the Duration of Time under Intervention.

The stepped wedge design is often used to evaluate interventions as they are rolled out across schools, health clinics, communities, or other clusters. Most models used in the design and analysis of stepped wedge trials assume that the intervention effect is immediate and constant over time following implementation of the intervention (the "exposure time"). This is known as the IT (immediate treatment effect) assumption. However, recent research has shown that using methods based on the IT assumption when the treatment effect varies over exposure time can give extremely misleading results. In this manuscript, we discuss the need to carefully specify an appropriate measure of the treatment effect when the IT assumption is violated and we show how a stepped wedge trial can be powered when it is anticipated that the treatment effect will vary as a function of the exposure time. Specifically, we describe how to power a trial when the exposure time indicator (ETI) model of Kenny et al. (Statistics in Medicine, 41, 4311-4339, 2022) is used and the estimand of interest is a weighted average of the time-varying treatment effects. We apply these methods to the ADDRESS-BP trial, a type 3 hybrid implementation study designed to address racial disparities in health care by evaluating a practice-based implementation strategy to reduce hypertension in African American communities.

An application programming interface implementing Bayesian approaches for evaluating effect of time-varying treatment with R and Python

IntroductionMethods and tools evaluating treatment effect have been primarily developed for binary type of treatment. Yet, treatment is rarely binary outside the experimental setting, varies by dosage, frequency and time. Treatment is routinely adjusted, initiated or stopped when being administered over a period of time.MethodsBoth Gaussian Process (GP) regression and Bayesian additive regression tree (BART) have been used successfully for handling complex setting involving time-varying treatments that is either adaptive or non-adaptive. Here, we introduce an application programming interface (API) that implements both BART and GP for estimating averaged treatment effect (ATE) and conditional averaged treatment (CATE) for the two-stage time-varying treatment strategies.ResultsWe provide two real applications for evaluating comparative effectiveness of time-varying treatment strategies. The first example evaluates an early aggressive treatment strategies for caring children with newly diagnosed Juvenile Idiopathic Arthritis (JIA). The second evaluates the persistent per-protocol treatment effectiveness in a large randomized pragmatic trial. The examples demonstrate the use of the API calling from R and Python, for handling both non-adaptive or adaptive treatments, with presences of partially observed or missing data issues. Summary tables and interactive figures of the results are downloadable.

High-deductible Health Plans and Nonfatal Opioid Overdose.

Opioid-related overdose is a public health emergency in the United States. Meanwhile, high-deductible health plans (HDHPs) have become more prevalent in the United States over the last 2 decades, raising concern about their potential for discouraging high-need populations, like those with opioid use disorder (OUD), from engaging in care that may mitigate the probability of overdose. This study assesses the impact of an employer offering an HDHP on nonfatal opioid overdose among commercially insured individuals with OUD in the United States. We used deidentified insurance claims data from 2007 to 2017 with 97,788 person-years. We used an intent-to-treat, difference-in-differences regression framework to estimate the change in the probability of a nonfatal opioid overdose among enrollees with OUD whose employers began offering an HDHP insurance option during the study period compared with the change among those whose employer never offered an HDHP. We also used an event-study model to account for dynamic time-varying treatment effects. Across both comparison and treatment groups, 2% of the sample experienced a nonfatal opioid overdose during the study period. Our primary model and robustness checks revealed no impact of HDHP offer on the probability of a nonfatal overdose. Our study suggests that HDHP offer was not associated with an observed increase in the probability of nonfatal opioid overdose among commercially insured person-years with OUD. However, given the strong evidence that medications for OUD (MOUD) can reduce the risk of overdose, research should explore which facets of insurance design may impact MOUD use.

Cost-effectiveness analysis of later-line therapies for metastatic colorectal cancer (mCRC) based on a novel methodology of network meta-analysis (NMA) of survival curves.

3605 Background: With advances in the management of mCRC, survival outcomes of patients have improved. While some patients still progress after first and second lines of treatment, there remain options for third or later-line treatment. This study aimed to determine the cost-effectiveness of later-line (>3) treatments for patients with mCRC in the US, based on a NMA of survival curves. Unlike conventional NMA using constant hazard ratios, this method is not constrained by the proportional hazard assumption and uses parametric fitting that incorporates the shape and scale parameters to provide time-varying treatment effects. Methods: The NMA compared the efficacy of 6 treatments, atezolizumab+/-cobimetinib (ATE+/-COB), fruquintinib (FRU), regorafenib (REG), TAS-102+/-bevacizumab (TAS+/-BEV), including biosimilar, to placebo (PBO). The study used a 3-state partitioned survival model over a 5-year time horizon incorporating drug acquisition, administration, adverse events, monitoring, and end of life costs, and utilities sourced from literature. Total costs, life-years (LY) and quality-adjusted LYs (QALY) for each treatment were determined. Incremental cost-effectiveness (ICER) and incremental cost-utility ratios (ICUR) were estimated using PBO as a common comparator. Results: Over the 5-year period and across the 6 therapies, survival ranged from 0.62 LYs for PBO to 1.15 LYs for TAS+BEV, translating to QALYs ranging from 0.44 for PBO to 0.85 for TAS+BEV. Total costs of treatment ranged from 278,877 for PBO to 417,495 for TAS+BEV (405,002 with biosimilar). TAS+BEV yielded the lowest ICER of an additional 261,421 (237,860 with biosimilar)/LY gained (g) and ICUR of an additional 343,458 (312,504 with biosimilar)/QALYg; while ATE presented the least favorable ICER and ICUR of an additional $522,602/LYg and $701,381/QALYg, respectively (Table). Conclusions: Among the 6 treatments evaluated, TAS+BEV emerged as the most cost-effective later-line treatment for mCRC while atezolizumab was the least cost-effective. Additionally, replacing BEV with a biosimilar reduces costs and enhances cost-effectiveness, improving access for patients. [Table: see text]

Estimating time-varying treatment effects in longitudinal studies.

Longitudinal study designs are frequently used to investigate the effects of a naturally observed predictor (treatment) on an outcome over time. Because the treatment at each time point or wave is not randomly assigned, valid inferences of its causal effects require adjusting for covariates that confound each treatment-outcome association. But adjusting for covariates which are inevitably time-varying is fraught with difficulties. On the one hand, standard regression adjustment for variables affected by treatment can lead to severe bias. On the other hand, omitting time-varying covariates from confounding adjustment precipitates spurious associations that can lead to severe bias. Thus, either including or omitting time-varying covariates for confounding adjustment can lead to incorrect inferences. In this article, we introduce an estimation strategy from the causal inference literature for evaluating the causal effects of time-varying treatments in the presence of time-varying confounding. G-estimation of the treatment effect at a particular wave proceeds by carefully adjusting for only pre-treatment instances of all variables while dispensing with any post-treatment instances. The introduced approach has various appealing features. Effect modification by time-varying covariates can be investigated using covariate-treatment interactions. Treatment may be either continuous or noncontinuous with any mean model permitted. Unbiased estimation requires correctly specifying a mean model for either the treatment or the outcome, but not necessarily both. The treatment and outcome models can be fitted with standard regression functions. In summary, g-estimation is effective, flexible, robust, and relatively straightforward to implement. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Causal inference in survival analysis using longitudinal observational data: Sequential trials and marginal structural models.

Longitudinal observational data on patients can be used to investigate causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for estimating such effects by controlling for the time-dependent confounding that typically occurs. The most commonly used is marginal structural models (MSM) estimated using inverse probability of treatment weights (IPTW) (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, and involves creating a sequence of "trials" from new time origins and comparing treatment initiators and non-initiators. Individuals are censored when they deviate from their treatment assignment at the start of each "trial" (initiator or noninitiator), which is accounted for using inverse probability of censoring weights. The analysis uses data combined across trials. We show that the sequential trials approach can estimate the parameters of a particular MSM. The causal estimand that we focus on is the marginal risk difference between the sustained treatment strategies of "always treat" vs "never treat." We compare how the sequential trials approach and MSM-IPTW estimate this estimand, and discuss their assumptions and how data are used differently. The performance of the two approaches is compared in a simulation study. The sequential trials approach, which tends to involve less extreme weights than MSM-IPTW, results in greater efficiency for estimating the marginal risk difference at most follow-up times, but this can, in certain scenarios, be reversed at later time points and relies on modelling assumptions. We apply the methods to longitudinal observational data from the UK Cystic Fibrosis Registry to estimate the effect of dornase alfa on survival.

Comparative Safety Analysis of Opioid Agonist Treatment in Pregnant Women with Opioid Use Disorder: A Population-Based Study.

Receipt of opioid agonist treatment during early and late pregnancy for opioid use disorder may relate to varying perinatal risks.Weaimed to assess the effect of time-varying prenatal exposure toopioid agonist treatment using buprenorphine or methadone on adverse neonatal and pregnancy outcomes. We conducted a retrospective cohort study of pregnant women with opioid use disorder using Rhode Island Medicaid claims data and vital statistics during 2008-16. Time-varying exposure was evaluated in early (0-20 weeks) and late (≥21 weeks) pregnancy. Marginal structural models with inverse probability of treatment weighting were applied. Of 400 eligible pregnancies, 85 and 137 individuals received buprenorphine and methadone, respectively, during early pregnancy. Compared with 152 untreated pregnancieswith opioid use disorders, methadone exposure in both periods was associated with an increased risk of preterm birth (adjusted odds ratio [aOR]: 2.52; 95% confidence interval [CI] 1.07-5.95), low birth weight (aOR: 2.99; 95% CI 1.34-6.66), neonatal intensive care unit admission (aOR, 5.04; 95% CI 2.49-10.21), neonatal abstinence syndrome (aOR: 11.36; 95% CI 5.65-22.82), respiratory symptoms (aOR, 2.71; 95% CI 1.17-6.24), and maternal hospital stay > 7 days (aOR, 14.51; 95% CI 7.23-29.12). Similar patterns emerged for buprenorphine regarding neonatal abstinence syndrome (aOR: 10.27; 95% CI 4.91-21.47) and extended maternal hospital stay (aOR: 3.84; 95% CI 1.83-8.07). However, differences were found favoring the use of buprenorphine for preterm birth versus untreated pregnancies (aOR: 0.17; 95% CI 0.04-0.77), and for several outcomes versus methadone. Methadone and buprenorphine prescribed for the treatment of opioid use disorder during pregnancy are associated with varying perinatal risks. However, buprenorphine may be preferred in the setting of pregnancy opioid agonist treatment. Further research is necessary to confirm our findings and minimize residual confounding.

Clinical biostatistics in the 2020s

Clinical biostatistics in the 2020s

Long-Term Exposure to Neighborhood Policing and the Racial/Ethnic Gap in High School Graduation.

Researchers are increasingly exploring the consequences of policing for the educational outcomes of minority youth. This study contributes to this literature by asking three questions. First, what are racial/ethnic disparities in long-term exposure to neighborhood policing? Second, how does this exposure affect high school graduation? Third, how much of the ethnoracial gap in high school graduation would remain if neighborhood policing was equalized? To address these questions, we use data from the New York City Department of Education and follow five cohorts of NYC public school students from middle to high school. Our findings reveal starkly different experiences with neighborhood policing across racial/ethnic groups. Using novel methods for time-varying treatment effects, we find that long-term exposure to neighborhood policing has negative effects on high school graduation, with important differences across racial/ethnic groups. Using gap-closing estimands, we show that assigning a sample of Black and Latino students to the same level of neighborhood policing as White students would close the Black-White gap in high school graduation by more than one quarter and the Latino-White gap by almost one fifth. Alternatively, we explore interventions where policing is solely a function of violent crime, which close the Black-White gap by as much as one tenth. Our study advances previous research by focusing on cumulative, long-term exposure to neighborhood policing and by assessing various counterfactual scenarios that inform research and policy.

Within-Person Variability Score-Based Causal Inference: A Two-Step Estimation for Joint Effects of Time-Varying Treatments

Behavioral science researchers have shown strong interest in disaggregating within-person relations from between-person differences (stable traits) using longitudinal data. In this paper, we propose a method of within-person variability score-based causal inference for estimating joint effects of time-varying continuous treatments by controlling for stable traits of persons. After explaining the assumed data-generating process and providing formal definitions of stable trait factors, within-person variability scores, and joint effects of time-varying treatments at the within-person level, we introduce the proposed method, which consists of a two-step analysis. Within-person variability scores for each person, which are disaggregated from stable traits of that person, are first calculated using weights based on a best linear correlation preserving predictor through structural equation modeling (SEM). Causal parameters are then estimated via a potential outcome approach, either marginal structural models (MSMs) or structural nested mean models (SNMMs), using calculated within-person variability scores. Unlike the approach that relies entirely on SEM, the present method does not assume linearity for observed time-varying confounders at the within-person level. We emphasize the use of SNMMs with G-estimation because of its property of being doubly robust to model misspecifications in how observed time-varying confounders are functionally related to treatments/predictors and outcomes at the within-person level. Through simulation, we show that the proposed method can recover causal parameters well and that causal estimates might be severely biased if one does not properly account for stable traits. An empirical application using data regarding sleep habits and mental health status from the Tokyo Teen Cohort study is also provided.

Analysis of stepped wedge cluster randomized trials in the presence of a time-varying treatment effect.

Stepped wedge cluster randomized controlled trials are typically analyzed using models that assume the full effect of the treatment is achieved instantaneously. We provide an analytical framework for scenarios in which the treatment effect varies as a function of exposure time (time since the start of treatment) and define the "effect curve" as the magnitude of the treatment effect on the linear predictor scale as a function of exposure time. The "time-averaged treatment effect" (TATE) and "long-term treatment effect" (LTE) are summaries of this curve. We analytically derive the expectation of the estimator resulting from a model that assumes an immediate treatment effect and show that it can be expressed as a weighted sum of the time-specific treatment effects corresponding to the observed exposure times. Surprisingly, although the weights sum to one, some of the weights can be negative. This implies that may be severely misleading and can even converge to a value of the opposite sign of the true TATE or LTE. We describe several models, some of which make assumptions about the shape of the effect curve, that can be used to simultaneously estimate the entire effect curve, the TATE, and the LTE. We evaluate these models in a simulation study to examine the operating characteristics of the resulting estimators and apply them to two real datasets.

Bias amplification in the g-computation algorithm for time-varying treatments: a case study of industry payments and prescription of opioid products

BackgroundIt is often challenging to determine which variables need to be included in the g-computation algorithm under the time-varying setting. Conditioning on instrumental variables (IVs) is known to introduce greater bias when there is unmeasured confounding in the point-treatment settings, and this is also true for near-IVs which are weakly associated with the outcome not through the treatment. However, it is unknown whether adjusting for (near-)IVs amplifies bias in the g-computation algorithm estimators for time-varying treatments compared to the estimators ignoring such variables. We thus aimed to compare the magnitude of bias by adjusting for (near-)IVs across their different relationships with treatments in the time-varying settings.MethodsAfter showing a case study of the association between the receipt of industry payments and physicians’ opioid prescribing rate in the US, we demonstrated Monte Carlo simulation to investigate the extent to which the bias due to unmeasured confounders is amplified by adjusting for (near-)IV across several g-computation algorithms.ResultsIn our simulation study, adjusting for a perfect IV of time-varying treatments in the g-computation algorithm increased bias due to unmeasured confounding, particularly when the IV had a strong relationship with the treatment. We also found the increase in bias even adjusting for near-IV when such variable had a very weak association with unmeasured confounders between the treatment and the outcome compared to its association with the time-varying treatments. Instead, this bias amplifying feature was not observed (i.e., bias due to unmeasured confounders decreased) by adjusting for near-IV when it had a stronger association with the unmeasured confounders (≥0.1 correlation coefficient in our multivariate normal setting).ConclusionIt would be recommended to avoid adjusting for perfect IV in the g-computation algorithm to obtain a less biased estimate of the time-varying treatment effect. On the other hand, it may be recommended to include near-IV in the algorithm unless their association with unmeasured confounders is very weak. These findings would help researchers to consider the magnitude of bias when adjusting for (near-)IVs and select variables in the g-computation algorithm for the time-varying setting when they are aware of the presence of unmeasured confounding.

IDF21-0454 Time-varying associations of long-term use of RASi use and all-site Cancers and mortality in type 2 diabetes (2002-2019)

Background: Cancer has replaced cardiovascular disease (CVD) as the leading cause of death in many countries. Type 2 diabetes (T2D) is associated with increased risk of cancer. Renin-angiotensin system inhibitors (RASi) are prescribed for hypertension and organ-protection, but may have pluripotent, anti-cancer effects. Evidence for a link between RASi and cancer remains inconclusive and prior studies did not account for time-varying and cumulative treatment effects.

Information Delay in Hiring: Ban-the-Box and Time-Varying Treatment Effects

Information Delay in Hiring: Ban-the-Box and Time-Varying Treatment Effects