Estimation Of Marginal Effects Research Articles

Transportability of model‐based estimands in evidence synthesis

In evidence synthesis, effect modifiers are typically described as variables that induce treatment effect heterogeneity at the individual level, through treatment‐covariate interactions in an outcome model parametrized at such level. As such, effect modification is defined with respect to a conditional measure, but marginal effect estimates are required for population‐level decisions in health technology assessment. For noncollapsible measures, purely prognostic variables that are not determinants of treatment response at the individual level may modify marginal effects, even where there is individual‐level treatment effect homogeneity. With heterogeneity, marginal effects for measures that are not directly collapsible cannot be expressed in terms of marginal covariate moments, and generally depend on the joint distribution of conditional effect measure modifiers and purely prognostic variables. There are implications for recommended practices in evidence synthesis. Unadjusted anchored indirect comparisons can be biased in the absence of individual‐level treatment effect heterogeneity, or when marginal covariate moments are balanced across studies. Covariate adjustment may be necessary to account for cross‐study imbalances in joint covariate distributions involving purely prognostic variables. In the absence of individual patient data for the target, covariate adjustment approaches are inherently limited in their ability to remove bias for measures that are not directly collapsible. Directly collapsible measures would facilitate the transportability of marginal effects between studies by: (1) reducing dependence on model‐based covariate adjustment where there is individual‐level treatment effect homogeneity or marginal covariate moments are balanced; and (2) facilitating the selection of baseline covariates for adjustment where there is individual‐level treatment effect heterogeneity.

Lactated Ringer vs Normal Saline Solution During Sickle Cell Vaso-Occlusive Episodes.

Sickle cell disease (SCD), a clinically heterogenous genetic hemoglobinopathy, is characterized by painful vaso-occlusive episodes (VOEs) that can require hospitalization. Patients admitted with VOEs are often initially resuscitated with normal saline (NS) to improve concurrent hypovolemia, despite preclinical evidence that NS may promote erythrocyte sickling. The comparative effectiveness of alternative volume-expanding fluids (eg, lactated Ringer [LR]) for resuscitation during VOEs is unclear. To compare the effectiveness of LR to NS fluid resuscitation in patients with SCD and VOEs. This multicenter cohort study and target trial emulation included inpatient adults with SCD VOEs who received either LR or NS on hospital day 1. The Premier PINC AI database (2016-2022), a multicenter clinical database including approximately 25% of US hospitalizations was used. The analysis took place between October 6, 2023, and June 20, 2024. Receipt of LR (intervention) or NS (control) on hospital day 1. The primary outcome was hospital-free days (HFDs) by day 30. Targeted maximum likelihood estimation was used to calculate marginal effect estimates. Heterogeneity of treatment effect was explored in subgroups. A total of 55 574 patient encounters where LR (n = 3495) or NS (n = 52 079) was administered on hospital day 1 were included; the median (IQR) age was 30 (25-37) years. Patients who received LR had more HFDs compared with those who received NS (marginal mean difference, 0.4; 95% CI, 0.1-0.6 days). Patients who received LR also had shorter hospital lengths of stay (marginal mean difference, -0.4; 95% CI, -0.7 to -0.1 days) and lower risk of 30-day readmission (marginal risk difference, -5.8%; 95% CI, -9.8% to -1.8%). Differences in HFDs between LR and NS were heterogenous based on fluid volume received: among patients who received less than 2 L, there was no difference in LR vs NS; among those who received 2 or more L, LR was superior to NS. This cohort study found that, compared with NS, LR had a small but significant improvement in HFDs and secondary outcomes including 30-day readmission. These results suggest that, among patients with VOEs in whom clinicians plan to give volume resuscitation fluids on hospital admission, LR should be preferred over NS.

Effect of a correlated competing risk on marginal survival estimation in an accelerated failure time model

In problems with a time to event outcome, subjects may experience competing events, which censor the outcome of interest. Cox’s partial likelihood estimator treating competing events as independent censoring is commonly used to examine group differences in clinical trials but fails to adjust for omitted covariates and can bias the assessment of marginal benefit. A bivariate normal linear model generating latent data with dependent censoring is used to assess this bias. Our R-package bnc provides maximum penalized likelihood (MPL) parameter estimation using a novel EM algorithm. Using bnc, we study the properties of such MPL estimation. Simulation results for two-sample survival comparisons of time to an event of interest, with independent censoring accompanied by censoring from a correlated competing risk, are presented. Key parameters—means, hazard ratios, and correlation—are estimated. These results demonstrated that, despite ill-conditioning in models generating correlated competing risks, estimates of marginal effects are reliable. Bivariate normal models were fitted in a trial of head and neck cancer. Model fits help with clinical interpretation while also supplementing other standard methods for follow-up that are terminated by intervening risks.

Estimating multinomial logit models with endogenous variables: Control function versus two adapted approaches

It is shown that the control function (CF) method’s estimates of the modal constants in a multinomial logit model (MNL) with endogenous explanatory variables are biased. This has not previously been reported in the literature, and has consequences in demand analysis, transportation policy design and project evaluation. Two adaptations of existing approaches are proposed as alternatives to CF for deriving estimators of parameters in MNL models with endogenous explanatory variables that evidence good consistency properties. The first approach is based on moment conditions while the second one combines parameters obtained in two consecutive estimation stages. Both approaches employ instrumental variables. These two adapted approaches are implemented using simulated data from a transport mode choice problem. The results are compared with those obtained using the classic control-function method, typically used by practitioners for estimating transport demand models with endogenous variables and making quantitative evaluations of transport policies and projects. All three approaches generate similar estimates for the parameters of the explanatory variables, but the two proposed adaptations produce considerably more accurate estimates of the modal constants. This greater accuracy has potentially significant consequences for multinomial logit models’ predictive ability and estimates of marginal effects, elasticities and the social benefits of projects based on consumer surplus calculations.

Analisis Ekonomi Pekerja Migran Indonesia dalam Memilih Jenis Pekerjaan pada BP3MI Provinsi Jawa Barat

This article presents the results of economic research on Indonesian migrant workers in choosing the type of work. Primary data were obtained through a survey of prospective migrant workers managed by the Indonesian Migrant Workers Protection Agency of West Java Province. The data explored represent the economic, social, demographic, and institutional aspects of migration, with mixed data properties, namely nominal, ordinal and multinomial. The qualitative limited dependent variable (QLDV) econometric method was used to estimate the multinomial logit equation. The results of the marginal effects estimation found that education level, wage level in the destination country, lack of job opportunities in the place of residence, experience working as a migrant worker, domestic wages, and the existence of income from household members other than husband and wife explained the decision to choose the type of job to work. The probability of choosing the operator/factory occupation is 0.3954, which is greater than other occupations. With a high school education level and an overseas wage of IDR 15.26 million per month.

Impact of rural-urban energy equality on environmental sustainability and the role of governance

Globally, rural areas suffer from less infrastructure relative to urban areas. Political and development economists have mainly attributed this disparity in infrastructure distribution to governance. The literature has sufficiently discussed the role that rural-urban infrastructure inequality plays in development outcomes such as poverty. However, not much is known about the effect of the rural-urban infrastructure gap on the environment. To contribute to knowledge and policy discussions, we investigate the impact of rural-urban energy access (in)equality on environmental degradation and the role governance plays using data from 47 sub-Saharan African countries from 2000–2020. Evidence from the heteroskedasticity-based instrumental variable regression consistent with Driscoll and Kraay's estimation revealed that bridging rural-urban energy access inequality is associated with reduction in environmental degradation. We also documented that the direct effect of the governance-related variables used is mixed. The moderation and marginal effect estimates showed that improving governance quality conditions equality in rural-urban energy access to reduce environmental degradation. From a policy perspective, these findings suggest that the implementation of rural electrification policies supported by a good governance system would play a crucial role in mitigating environmental degradation in developing countries.

Stability of factors influencing walking-along-the-road pedestrian injury severity outcomes under different lighting conditions: A random parameters logit approach with heterogeneity in means and out-of-sample predictions

Pedestrians walking along the road’s edge are more exposed and vulnerable than those on designated crosswalks. Often, they remain oblivious to the imminent perils of potential collisions with vehicles, making crashes involving these pedestrians relatively unique compared to others. While previous research has recognized that the surrounding lighting conditions influence traffic crashes, the effect of different lighting conditions on walking-along-the-road pedestrian injury severity outcomes remains unexplored. This study examines the variations in the impact of risk factors on walking-along-the-road pedestrian-involved crash injury severity across various lighting conditions. Preliminary stability tests on the walking-along-the-road pedestrian-involved crash data obtained from Ghana revealed that the effect of most risk factors on injury severity outcomes is likely to differ under each lighting condition, warranting the estimation of separate models for each lighting condition. Thus, the data were grouped based on the lighting conditions, and different models were estimated employing the random parameter logit model with heterogeneity in the means approach to capture different levels of unobserved heterogeneity in the crash data. From the results, heavy vehicles, shoulder presence, and aged drivers were found to cause fatal pedestrian walking-along-the-road severity outcomes during daylight conditions, indicators for male pedestrians and speeding were identified to have stronger associations with fatalities on roads with no light at night, and crashes occurring on Tuesdays and Wednesdays were likely to be severe on lit roads at night. From the marginal effect estimates, although some explanatory variables showed consistent effects across various lighting conditions in pedestrian walking-along-the-road crashes, such as pedestrians aged < 25 years and between 25 and 44 years exhibited significant variations in their impact across different lighting conditions, supporting the finding that the effect of risk factors are unstable. Further, the out-of-sample simulations underscored the shifts in factor effects between different lighting conditions, highlighting that enhancing visibility could play a pivotal role in significantly reducing fatalities associated with pedestrians walking along the road. Targeted engineering, education, and enforcement countermeasures are proposed from the interesting insights drawn to improve pedestrian safety locally and internationally.

Adaptation to temperature extremes in Chinese agriculture, 1981 to 2010

Causal evidence for adaptation effects of specific agricultural instruments is scant but important for identifying potentially useful adaptive measures for climate change in the future. To address this gap, we leverage quasi-experimental variations in irrigation induced by a natural experiment for irrigation expansion started in 1996 and quantify the contribution of irrigation access to the overall adaptation effect. There are three primary findings. First, using a period-specific panel fixed effect model, the analysis shows a significant decline in the temperature-related yield loss in the post-1996 period compared to before, indicating a substantial overall adaptation effect. Second, estimation of marginal adaptation effects of inputs points to irrigation as the central input for adaptation among the inputs observed in the data. Third, using a difference-in-differences approach united with the panel methodology for identifying temperature effects, we show that the presence of the irrigation expansion experiment significantly mitigated the high temperature impacts on crop yields, with increased irrigation through the natural experiment accounting for about 40% of the overall adaptation effect.

Addressing Non-ignorable Panel Attrition Using External Population Data: Analysis of Demographic Events From Survey Data

Empirical analysis of variation in demographic events within the population is facilitated by using longitudinal survey data because of the richness of covariate measures in such data, but there is wave-on-wave dropout. When attrition is related to the event, it precludes consistent estimation of the impacts of covariates on the event and on event probabilities in the absence of additional assumptions. The paper introduces an adjustment procedure based on Bayes Theorem that directly addresses the problem of nonignorable dropout. It uses population information external to the survey sample to convert estimates of event probabilities and marginal effects of covariates on them that are conditional on retention in the longitudinal data to unconditional estimates of these quantities. In many plausible and verifiable circumstances, it produces estimates of the marginal effect of covariates closer to the true unconditional quantities than the conditional estimates obtained from estimation using the survey data alone.

Street and activity centre characteristics associated with the use of different transport modes

Streets play a vital role in cities, yet there is little understanding of how their characteristics influence the use of different transport modes, particularly in activity centres. Using measurements of people concentration (people/km) from 57 activity centre locations across Melbourne, Australia, this research significantly contributes to understanding how street and activity centre characteristics are associated with the use of each of the following: walking, cycling, buses, trams, cars, car parking, trucks and motorbikes. Fractional logit regression models including the estimation of marginal effects were developed. Street-related characteristics that were significant included: presence of bicycle lanes, exclusive general traffic lanes, clearways, car parking charges, public transport services, in addition to footpath width, public transport service frequency, and movement and place classifications. Activity centre-related characteristics found to be significant included: size of the activity centre, network distance to various facilities and the CBD, intersection density, employment density and car ownership. The findings from this research can be used to support activity centre planning to achieve broader transport and land use objectives, particularly those related to local living such as 20-minute neighbourhoods.

Semiparametric approach to estimation of marginal mean effects and marginal quantile effects

We consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance, and we apply the new tool to analyze a Swiss non-labor income data and discover a new interesting predictor.

Invited Perspective: The Potential of Potential Outcomes in Air Pollution Epidemiology.

Invited Perspective: The Potential of Potential Outcomes in Air Pollution Epidemiology.

Estimating the effect of brand beliefs on brand evaluations when beliefs are measured with error

We consider the internal validity of estimates of the effects of brand beliefs on brand evaluations when beliefs are measured with error. Consumer research suggests numerous errors that may impact belief measures. However, the literature has not determined precisely why and how myriad types of error matter for the evaluation-belief relationship. Furthermore, the literature has not explicitly considered what is necessary and sufficient to control for different types of belief error when using the latent general factor approach. We show that the important distinction for empirical research is not the origin of the error per se but its relationship to affective evaluation. Error related to brand evaluation has an inflationary effect on estimates of the evaluation-belief relationship while error unrelated to brand evaluation has an attenuating effect. We use a bifactor structural equations model to decompose belief measures into general and specific dimensions. The model uses bias free variation in specific beliefs to identify effects on brand evaluation while controlling for a general belief dimension correlated with evaluation. Compared to models that do not adjust for the bias, estimates of the bias corrected marginal effects are smaller but positive and significant.

Characterizing quantile-varying covariate effects under the accelerated failure time model.

An important task in survival analysis is choosing a structure for the relationship between covariates of interest and the time-to-event outcome. For example, the accelerated failure time (AFT) model structures each covariate effect as a constant multiplicative shift in the outcome distribution across all survival quantiles. Though parsimonious, this structure cannot detect or capture effects that differ across quantiles of the distribution, a limitation that is analogous to only permitting proportional hazards in the Cox model. To address this, we propose a general framework for quantile-varying multiplicative effects under the AFT model. Specifically, we embed flexible regression structures within the AFT model and derive a novel formula for interpretable effects on the quantile scale. A regression standardization scheme based on the g-formula is proposed to enable the estimation of both covariate-conditional and marginal effects for an exposure of interest. We implement a user-friendly Bayesian approach for the estimation and quantification of uncertainty while accounting for left truncation and complex censoring. We emphasize the intuitive interpretation of this model through numerical and graphical tools and illustrate its performance through simulation and application to a study of Alzheimer's disease and dementia.

A transformation perspective on marginal and conditional models.

Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multicenter trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal distributions are described by a linear transformation model and the correlations by a joint multivariate normal distribution. The joint model provides an analytic formula for the marginal distribution. Owing to the richness of transformation models, the techniques are applicable to any type of response variable, including bounded, skewed, binary, ordinal, or survival responses. We demonstrate how the common normal assumption for reaction times can be relaxed in the sleep deprivation benchmark data set and report marginal odds ratios for the notoriously difficult toe nail data. We furthermore discuss the analysis of two clinical trials aiming at the estimation of marginal treatment effects. In the first trial, pain was repeatedly assessed on a bounded visual analog scale and marginal proportional-odds models are presented. The second trial reported disease-free survival in rectal cancer patients, where the marginal hazard ratio from Weibull and Cox models is of special interest. An empirical evaluation compares the performance of the novel approach to general estimation equations for binary responses and to conditional mixed-effects models for continuous responses. An implementation is available in the tram add-on package to the R system and was benchmarked against established models in the literature.

A dynamic analysis of medication adherence.

BACKGROUND: Medication adherence is an important factor in maintaining and improving health, although adherence levels are often suboptimal. Previous studies have highlighted the importance of prior adherence behavior in understanding future adherence behaviors. OBJECTIVE: To improve understanding of adherence behavior and analyze the role of previous adherence in estimating the likelihood of future adherence for maintenance medications. METHODS: The adherence behaviors of 53,709 continuously enrolled individuals in employer-sponsored health plans were analyzed using a state-dependence framework (ie, adherence patterns in the past influence adherence in the future). This allowed for the estimation of the extent of carryover in adherence from one quarter to another while adjusting for observed and unobserved heterogeneity and enrollee characteristics. The role of the initial observation of adherence on the likelihood of future adherence was also analyzed. This study focuses on enrollee cohorts who filled prescriptions in 3 maintenance medication classes: lipid-lowering medications, antihypertensive medications, and oral antidiabetes medications. RESULTS: If an enrollee was adherent in the previous quarter, more than 80% of the time they remained adherent in the current quarter. Similarly, if they were nonadherent in the previous quarter, more than 75% of the time they remained nonadherent. Marginal effect estimates for prior adherence (previous quarter and initial quarter) showed increases in predicted adherence when adherent in the previous quarter (8.7 percentage points [pp] [95% CI = 8.0-9.3 pp] for lipid-lowering medications) and when adherent in the initial quarter (14.4 pp [13.8-15.1 pp] for lipid-lowering medications). Adherence in the initial and previous quarter increased predicted adherence considerably (22.7 pp [22.1-23.3 pp]). Similar patterns held for the antihypertensive medication cohort (antihypertensive medications) and the oral antidiabetes medication cohort (oral antidiabetes medications). The area under the curve (AUC) showed considerable improvement when moving from pooled probit models to dynamic random-effects probit models. AUC for the dynamic models exceeded 0.85 in the 3 medication cohorts, whereas the pooled probit models remained under 0.7. CONCLUSIONS: Adherence in the previous quarter is associated with adherence in the current quarter, after accounting for sources of observable and unobservable heterogeneity across enrollees. In addition, the initial value of adherence matters when explaining the likelihood of adherence.

Estimating Spillover Effects in Property and Casualty Insurance Consumption

The determinants of insurance consumption have been extensively studied, yet spatial correlations are rarely considered within this framework. In this article, we discuss several channels through which spatial dependence may arise and test for spatial dependence using six years (2009–2014) of province, city, and firm-level data from China. Results suggest that spatial spillover effects are large and have the potential to seriously bias marginal effect estimates if neglected. Specifically, when regions experience similar changes in determinants, marginal effect estimates in spatial models are nearly 1.5 times that implied by aspatial models. Additionally, we investigate the sources of the spatial dependence and find that cross-border spillovers occur within and between firms.

131-OR: Effect of a Value-Based Medication Benefit on Acute Preventable Diabetes Complications and Related Disparities

Employers are increasingly purchasing "preventive drug list" (PDL) insurance plans that make cardiometabolic medications $0. PDL designs improve adherence, but effects on health outcomes are unknown. We analyzed 2004-2017 commercial health insurance claims using a large, national data set. The intervention group included 12,853 commercially-insured diabetes patients aged 12-64 years who experienced employer-mandated PDL switches; the control group included 12,989 matched counterparts whose employers offered no PDL. We defined the index date as the day the intervention group received the PDL, and matched controls had a contemporaneous index date. Both groups had a 1-year baseline and 1-year follow-up study period. We measured monthly rates of aggregated acute preventable diabetes complication episodes (e.g, hyperglycemic coma, angina, and pneumonia) presenting to (1) the outpatient setting or (2) the emergency department, observation, or inpatient settings ("high acuity") . We constructed cumulative interrupted time series plots of these two measures and conducted segmented regression analysis and marginal effects estimation. Low-income members were a subgroup of interest. Annual outpatient and high-acuity complication episodes decreased by -13.5% (-15.2%, -11.7%) and -13.9% (-15.3%, -12.5%) , respectively, in the PDL group relative to controls. Low-income PDL members also experienced decreased outpatient (-27.2% [-32.1%, -22.4%]) and high-acuity complication episodes (-4.4% [-6.5%, -2.4%]) . This rigorous, quasi-experimental study is the first to demonstrate that a value-based medication benefit is associated with improved health outcomes and reduced disparities. Employer adoption of PDLs thus represents a relatively expedient approach to improving health and equity, and our results support a strategy of incentivizing such targeted cost sharing reductions for vulnerable diabetes populations. Disclosure J.Wharam: None. F.Zhang: Research Support; GlaxoSmithKline plc. M.Lakoma: None. L.F.Garabedian: None. S.Argetsinger: None. D.Ross-degnan: None. Funding CDC and NIDDK

Parametric G-computation for compatible indirect treatment comparisons with limited individual patient data.

Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is based on propensity score weighting, which is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the relevant population to recover a compatible marginal treatment effect. We propose a marginalization method based on parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. The approach views the covariate adjustment regression as a nuisance model and separates its estimation from the evaluation of the marginal treatment effect of interest. The method can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework. A simulation study provides proof-of-principle and benchmarks the method's performance against MAIC and the conventional outcome regression. Parametric G-computation achieves more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yields unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, the marginalized regression-adjusted estimates provide greater precision and accuracy than the conditional estimates produced by the conventional outcome regression, which are systematically biased because the measure of effect is non-collapsible.

Generalizability and effect measure modification in sibling comparison studies

Sibling comparison studies have the attractive feature of being able to control for unmeasured confounding by factors that are shared within families. However, there is sometimes a concern that these studies may have poor generalizability (external validity) due to the implicit restriction to families that are covariate-discordant, i.e., those families where at least two siblings have different levels of at least one of the covariates (exposure or confounders) under investigation. Even if this selection mechanism has been noted by many authors, previous accounts of the problem tend to be brief. The purpose of this paper is to provide a formal discussion of the implicit restriction to covariate-discordant families in sibling comparison studies. We discuss when and how this restriction may impair the generalizability of the study, and we show that a similar generalizability problem may in fact arise even when all families are covariate-discordant, e.g. even if the exposure is continuous so that all siblings have different exposure levels. We show how this problem can be solved by using a so-called marginal between-within model for estimation of marginal exposure effects. Finally, we illustrate the theoretical conclusions with a simulation study.