Leveraging baseline covariates to analyze small cluster-randomized trials with a rare binary outcome.

Cluster-randomized trials (CRTs) involve randomizing entire groups of participants-called clusters-to treatment arms but are often comprised of a limited or fixed number of available clusters. While covariate adjustment can account for chance imbalances between treatment arms and increase statistical efficiency in individually randomized trials, analytical methods for individual-level covariate adjustment in small CRTs have received little attention to date. In this paper, we systematically investigate, through extensive simulations, the operating characteristics of propensity score weighting and multivariable regression as two individual-level covariate adjustment strategies for estimating the participant-average causal effect in small CRTs with a rare binary outcome and identify scenarios where each adjustment strategy has a relative efficiency advantage over the other to make practical recommendations. We also examine the finite-sample performance of the bias-corrected sandwich variance estimators associated with propensity score weighting and multivariable regression for quantifying the uncertainty in estimating the participant-average treatment effect. To illustrate the methods for individual-level covariate adjustment, we reanalyze a recent CRT testing a sedation protocol in 31 pediatric intensive care units.

Transportability of causal inference under random dynamic treatment regimes for kidney-pancreas transplantation.

A difficult decision for patients in need of kidney-pancreas transplant is whether to seek a living kidney donor or wait to receive both organs from one deceased donor. The framework of dynamic treatment regimes (DTRs) can inform this choice, but a patient-relevant strategy such as "wait for deceased-donor transplant" is ill-defined because there are multiple versions of treatment (i.e., wait times, organ qualities). Existing DTR methods average over the distribution of treatment versions in the data, estimating survival under a "representative intervention." This is undesirable if transporting inferences to a target population such as patients today, who experience shorter wait times thanks to evolutions in allocation policy. We, therefore, propose the concept of a generalized representative intervention (GRI): a random DTR that assigns treatment version by drawing from the distribution among strategy compliers in the target population (e.g., patients today). We describe an inverse-probability-weighted product-limit estimator of survival under a GRI that performs well in simulations and can be implemented in standard statistical software. For continuous treatments (e.g., organ quality), weights are reformulated to depend on probabilities only, not densities. We apply our method to a national database of kidney-pancreas transplant candidates from 2001-2020 to illustrate that variability in transplant rate across years and centers results in qualitative differences in the optimal strategy for patient survival.

Two-phase designs with current status data.

We consider the design and analysis of two-phase studies aiming to assess the relation between a fixed (eg, genetic) marker and an event time under current status observation. We consider a common setting in which a phase I sample is comprised of a large cohort of individuals with outcome (ie, current status) data and a vector of inexpensive covariates. Stored biospecimens for individuals in the phase I sample can be assayed to record the marker of interest for individuals selected in a phase II sub-sample. The design challenge is then to select the phase II sub-sample in order to maximize the precision of the marker effect on the time of interest under a proportional hazards model. This problem has not been examined before for current status data and the role of the assessment time is highlighted. Inference based on likelihood and inverse probability weighted estimating functions are considered, with designs centered on score-based residuals, extreme current status observations, or stratified sampling schemes. Data from a registry of patients with psoriatic arthritis is used in an illustration where we study the risk of diabetes as a comorbidity.

The impact of correlated exposures and missing data on multiple informant models used to identify critical exposure windows.

There has been heightened interest in identifying critical windows of exposure for adverse health outcomes; that is, time points during which exposures have the greatest impact on a person's health. Multiple informant models implemented using generalized estimating equations (MIM GEEs) have been applied to address this research question because they enable statistical comparisons of differences in associations across exposure windows. As interest rises in using MIMs, the feasibility and appropriateness of their application under settings of correlated exposures and partially missing exposure measurements requires further examination. We evaluated the impact of correlation between exposure measurements and missing exposure data on the power and differences in association estimated by the MIM GEE and an inverse probability weighted extension to account for informatively missing exposures. We assessed these operating characteristics under a variety of correlation structures, sample sizes, and missing data mechanisms considering various exposure-outcome scenarios. We showed that applying MIM GEEs maintains higher power when there is a single critical window of exposure and exposure measures are not highly correlated, but may result in low power and bias under other settings. We applied these methods to a study of pregnant women living with HIV to explore differences in association between trimester-specific viral load and infant neurodevelopment.

Developing non-response weights to account for attrition-related bias in a longitudinal pregnancy cohort.

BACKGROUND: Prospective cohorts may be vulnerable to bias due to attrition. Inverse probability weights have been proposed as a method to help mitigate this bias. The current study used the "All Our Families" longitudinal pregnancy cohort of 3351 maternal-infant pairs and aimed to develop inverse probability weights using logistic regression models to predict study continuation versus drop-out from baseline to the three-year data collection wave. METHODS: Two methods of variable selection took place. One method was a knowledge-based a priori variable selection approach, while the second used Least Absolute Shrinkage and Selection Operator (LASSO). The ability of each model to predict continuing participation through discrimination and calibration for both approaches were evaluated by examining area under the receiver operating curve (AUROC) and calibration plots, respectively. Stabilized inverse probability weights were generated using predicted probabilities. Weight performance was assessed using standardized differences of baseline characteristics for those who continue in study and those that do not, with and without weights (unadjusted estimates). RESULTS: The a priori and LASSO variable selection method prediction models had good and fair discrimination with AUROC of 0.69 (95% Confidence Interval [CI]: 0.67-0.71) and 0.73 (95% CI: 0.71-0.75), respectively. Calibration plots and non-significant Hosmer-Lemeshow Goodness of Fit Tests indicated that both the a priori (p = 0.329) and LASSO model (p = 0.242) were well-calibrated. Unweighted results indicated large (> 10%) standardized differences in 15 demographic variables (range: 11 - 29%), when comparing those who continued in the study with those that did not. Weights derived from the a priori and LASSO models reduced standardized differences relative to unadjusted estimates, with the largest differences of 13% and 5%, respectively. Additionally, when applying the same LASSO variable selection method to develop weights in future data collection waves, standardized differences remained below 10% for each demographic variable. CONCLUSION: The LASSO variable selection approach produced robust weights that addressed non-response bias more than the knowledge-driven approach. These weights can be applied to analyses across multiple longitudinal waves of data collection to reduce bias.

Weighted expectile regression for right-censored data.

Expectile regression can be used to analyze the entire conditional distribution of a response, omitting all distributional assumptions. Among its benefits are computational simplicity, efficiency, and the possibility to incorporate a semiparametric predictor. Due to its advantages in full data settings, we propose an extension to right-censored data situations, where conventional methods typically focus only on mean effects. We propose to extend expectile regression with inverse probability weights. Estimates are easy to implement and computationally simple. Expectiles can be converted to more easily interpreted tail expectations, that is, the expected residual life. It provides a meaningful effect measure, similar to the hazard rate. The results from an extensive simulation study are presented, evaluating consistency and sensitivity to violations of assumptions. We use the proposed method to analyze survival times of colorectal cancer patients from a regional certified high volume cancer center.

Balancing vs modeling approaches to weighting in practice.

There are two seemingly unrelated approaches to weighting in observational studies. One of them maximizes the fit of a model for treatment assignment to then derive weights-we call this the modeling approach. The other directly optimizes certain features of the weights-we call this the balancing approach. The implementations of these two approaches are related: the balancing approach implicitly models the propensity score, while instances of the modeling approach impose balance conditions on the covariates used to estimate the propensity score. In this article, we review and compare these two approaches to weighting. Previous review papers have focused on the modeling approach, emphasizing the importance of checking covariate balance. However, as we discuss, the dispersion of the weights is another important aspect of the weights to consider, in addition to the representativeness of the weighted sample and the sample boundedness of the weighted estimator. In particular, the dispersion of the weights is important because it translates into a measure of effective sample size, which can be used to select between alternative weighting schemes. In this article, we examine the balancing approach to weighting, discuss recent methodological developments, and compare instances of the balancing and modeling approaches in a simulation study and an empirical study. In practice, unless the treatment assignment model is known, we recommend using the balancing approach to weighting, as it systematically results in better covariate balance with weights that are minimally dispersed. As a result, effect estimates tend to be more accurate and stable.

An Investigation of Selection Bias in Estimating Racial Disparity in Stroke Risk Factors.

Selection due to survival or attrition might bias estimates of racial disparities in health, but few studies quantify the likely magnitude of such bias. In a large national cohort with moderate loss to follow-up, we contrasted racial differences in 2 stroke risk factors, incident hypertension and incident left ventricular hypertrophy, estimated by complete-case analyses, inverse probability of attrition weighting, and the survivor average causal effect. We used data on 12,497 black and 17,660 white participants enrolled in the United States (2003-2007) and collected incident risk factor data approximately 10 years after baseline. At follow-up, 21.0% of white participants and 23.0% of black participants had died; additionally 22.0% of white participants and 28.4% of black participants had withdrawn. Individual probabilities of completing the follow-up visit were estimated using baseline demographic and health characteristics. Adjusted risk ratio estimates of racial disparities from complete-case analyses in both incident hypertension (1.11, 95% confidence interval: 1.02, 1.21) and incident left ventricular hypertrophy (1.02, 95% confidence interval: 0.84, 1.24) were virtually identical to estimates from inverse probability of attrition weighting and survivor average causal effect. Despite racial differences in mortality and attrition, we found little evidence of selection bias in the estimation of racial differences for these incident risk factors.

Treating loss-to-follow-up as a missing data problem: a case study using a longitudinal cohort of HIV-infected patients in Haiti.

BACKGROUND: HIV programs are often assessed by the proportion of patients who are alive and retained in care; however some patients are categorized as lost to follow-up (LTF) and have unknown vital status. LTF is not an outcome but a mixed category of patients who have undocumented death, transfer and disengagement from care. Estimating vital status (dead versus alive) among this category is critical for survival analyses and program evaluation. METHODS: We used three methods to estimate survival in the cohort and to ascertain factors associated with death among the first cohort of HIV positive patients to receive antiretroviral therapy in Haiti: complete case (CC) (drops missing), Inverse Probability Weights (IPW) (uses tracking data) and Multiple Imputation with Chained Equations (MICE) (imputes missing data). Logistic regression was used to calculate odds ratios and 95% confidence intervals for adjusted models for death at 10 years. The logistic regression models controlled for sex, age, severe poverty (living on <$1 USD per day), Port-au-Prince residence and baseline clinical characteristics of weight, CD4, WHO stage and tuberculosis diagnosis. RESULTS: Age, severe poverty, baseline weight and WHO stage were statistically significant predictors of AIDS related mortality across all models. Gender was only statistically significant in the MICE model but had at least a 10% difference in odds ratios across all models. CONCLUSION: Each of these methods had different assumptions and differed in the number of observations included due to how missing values were addressed. We found MICE to be most robust in predicting survival status as it allowed us to impute missing data so that we had the maximum number of observations to perform regression analyses. MICE also provides a complementary alternative for estimating survival among patients with unassigned vital status. Additionally, the results were easier to interpret, less likely to be biased and provided an alternative to a problem that is often commented upon in the extant literature.

Assessing the Potential for Bias From Nonresponse to a Study Follow-up Interview: An Example From the Agricultural Health Study.

Prospective cohort studies are important tools for identifying causes of disease. However, these studies are susceptible to attrition. When information collected after enrollment is through interview or exam, attrition leads to missing information for nonrespondents. The Agricultural Health Study enrolled 52,394 farmers in 1993-1997 and collected additional information during subsequent interviews. Forty-six percent of enrolled farmers responded to the 2005-2010 interview; 7% of farmers died prior to the interview. We examined whether response was related to attributes measured at enrollment. To characterize potential bias from attrition, we evaluated differences in associations between smoking and incidence of 3 cancer types between the enrolled cohort and the subcohort of 2005-2010 respondents, using cancer registry information. In the subcohort we evaluated the ability of inverse probability weighting (IPW) to reduce bias. Response was related to age, state, race/ethnicity, education, marital status, smoking, and alcohol consumption. When exposure and outcome were associated and case response was differential by exposure, some bias was observed; IPW conditional on exposure and covariates failed to correct estimates. When response was nondifferential, subcohort and full-cohort estimates were similar, making IPW unnecessary. This example provides a demonstration of investigating the influence of attrition in cohort studies using information that has been self-reported after enrollment.

Estimating inverse-probability weights for longitudinal data with dropout or truncation: The xtrccipw command.

Individuals may drop out of a longitudinal study, rendering their outcomes unobserved but still well defined. However, they may also undergo truncation (for example, death), beyond which their outcomes are no longer meaningful. Kurland and Heagerty (2005, Biostatistics 6: 241-258) developed a method to conduct regression conditioning on nontruncation, that is, regression conditioning on continuation (RCC), for longitudinal outcomes that are monotonically missing at random (for example, because of dropout). This method first estimates the probability of dropout among continuing individuals to construct inverse-probability weights (IPWs), then fits generalized estimating equations (GEE) with these IPWs. In this article, we present the xtrccipw command, which can both estimate the IPWs required by RCC and then use these IPWs in a GEE estimator by calling the glm command from within xtrccipw. In the absence of truncation, the xtrccipw command can also be used to run a weighted GEE analysis. We demonstrate the xtrccipw command by analyzing an example dataset and the original Kurland and Heagerty (2005) data. We also use xtrccipw to illustrate some empirical properties of RCC through a simulation study.

Estimating causal effects for multivalued treatments: a comparison of approaches.

Interventions with multivalued treatments are common in medical and health research, such as when comparing the efficacy of competing drugs or interventions, or comparing between various doses of a particular drug. In recent years, there has been a growing interest in the development of multivalued treatment effect estimators using observational data. In this paper, we compare the performance of commonly used regression-based methods that estimate multivalued treatment effects based on the unconfoundedness assumption. These estimation methods fall into three general categories: (i) estimators based on a model for the outcome variable using conventional regression adjustment; (ii) weighted estimators based on a model for the treatment assignment; and (iii) 'doubly-robust' estimators that model both the treatment assignment and outcome variable within the same framework. We assess the performance of these models using Monte Carlo simulation and demonstrate their application with empirical data. Our results show that (i) when models estimating both the treatment and outcome are correctly specified, all adjustment methods provide similar unbiased estimates; (ii) when the outcome model is misspecified, regression adjustment performs poorly, while all the weighting methods provide unbiased estimates; (iii) when the treatment model is misspecified, methods based solely on modeling the treatment perform poorly, while regression adjustment and the doubly robust models provide unbiased estimates; and (iv) when both the treatment and outcome models are misspecified, all methods perform poorly. Given that researchers will rarely know which of the two models is misspecified, our results support the use of doubly robust estimation.

A weighted cumulative sum (WCUSUM) to monitor medical outcomes with dependent censoring.

We develop a weighted cumulative sum (WCUSUM) to evaluate and monitor pre-transplant waitlist mortality of facilities in the context where transplantation is considered to be dependent censoring. Waitlist patients are evaluated multiple times in order to update their current medical condition as reflected in a time-dependent variable called the Model for End-Stage Liver Disease (MELD) score. Higher MELD scores are indicative of higher pre-transplant death risk. Moreover, under the current liver allocation system, patients with higher MELD scores receive higher priority for liver transplantation. To evaluate the waitlist mortality of transplant centers, it is important to take this dependent censoring into consideration. We assume a 'standard' transplant practice through a transplant model and utilize inverse probability censoring weights to construct a WCUSUM. We evaluate the properties of a weighted zero-mean process as the basis of the proposed WCUSUM. We then discuss a resampling technique to obtain control limits. The proposed WCUSUM is illustrated through the analysis of national transplant registry data.

Estimating Causal Effects of HIV Prevention Interventions with Interference in Network-based Studies among People Who Inject Drugs.

Evaluating causal effects in the presence of interference is challenging in network-based studies of hard-to-reach populations. Like many such populations, people who inject drugs (PWID) are embedded in social networks and often exert influence on others in their network. In our setting, the study design is observational with a non-randomized network-based HIV prevention intervention. Information is available on each participant and their connections that confer possible HIV risk through injection and sexual behaviors. We considered two inverse probability weighted (IPW) estimators to quantify the population-level spillover effects of non-randomized interventions on subsequent health outcomes. We demonstrated that these two IPW estimators are consistent, asymptotically normal, and derived a closed-form estimator for the asymptotic variance, while allowing for overlapping interference sets (groups of individuals in which the interference is assumed possible). A simulation study was conducted to evaluate the finite-sample performance of the estimators. We analyzed data from the Transmission Reduction Intervention Project, which ascertained a network of PWID and their contacts in Athens, Greece, from 2013 to 2015. We evaluated the effects of community alerts on subsequent HIV risk behavior in this observed network, where the connections or links between participants were defined by using substances or having unprotected sex together. In the study, community alerts were distributed to inform people of recent HIV infections among individuals in close proximity in the observed network. The estimates of the risk differences for spillover using either IPW estimator demonstrated a protective effect. The results suggest that HIV risk behavior could be mitigated by exposure to a community alert when an increased risk of HIV is detected in the network.

Reflection on modern methods: combining weights for confounding and missing data.

Inverse probability weights are increasingly used in epidemiological analysis, and estimation and application of weights to address a single bias are well discussed in the literature. Weights to address multiple biases simultaneously (i.e. a combination of weights) have almost exclusively been discussed related to marginal structural models in longitudinal settings where treatment weights (estimated first) are combined with censoring weights (estimated second). In this work, we examine two examples of combined weights for confounding and missingness in a time-fixed setting in which outcome or confounder data are missing, and the estimand is the marginal expectation of the outcome under a time-fixed treatment. We discuss the identification conditions, construction of combined weights and how assumptions of the missing data mechanisms affect this construction. We use a simulation to illustrate the estimation and application of the weights in the two examples. Notably, when only outcome data are missing, construction of combined weights is straightforward; however, when confounder data are missing, we show that in general we must follow a specific estimation procedure which entails first estimating missingness weights and then estimating treatment probabilities from data with missingness weights applied. However, if treatment and missingness are conditionally independent, then treatment probabilities can be estimated among the complete cases.

Flexible semiparametric mode regression for time-to-event data.

The distribution of time-to-event outcomes is usually right-skewed. While for symmetric and moderately skewed data the mean and median are appropriate location measures, the mode is preferable for heavily skewed data as it better represents the center of the distribution. Mode regression has been introduced for uncensored data to model the relationship between covariates and the mode of the outcome. Starting from nonparametric kernel density based mode regression, we examine the use of inverse probability of censoring weights to extend mode regression to handle right-censored data. We add a semiparametric predictor to add further flexibility to the model and we construct a pseudo Akaike's information criterion to select the bandwidth and smoothing parameters. We use simulations to evaluate the performance of our proposed approach. We demonstrate the benefit of adding mode regression to one's toolbox for analyzing survival data on a pancreatic cancer data set from a prospectively maintained cancer registry.

Triple-negative metaplastic breast cancer: treatment and prognosis by type of surgery.

BACKGROUND: The role of surgery type in the prognosis of triple-negative metaplastic breast cancer (TN-MBC) patients remains controversial. Our study was designed to assess the role of surgery type in patient outcomes. MATERIALS AND METHODS: Data from the Surveillance, Epidemiology, and End Results database were extracted to analyze patients with TN-MBC between 2010 and 2016. Kaplan-Meier analyses and multivariate Cox proportional models were used to estimate the prognoses. RESULTS: We included 1,146 patients with a median follow-up time of 26 months (range 1-83 months). 470 (41.0%), 369 (32.2%), 244 (21.3%), and 63 (5.5%) patients underwent breast-conserving surgery (BCS), total mastectomy (TM), radical mastectomy, or no surgery. With the multivariate Cox analysis, the prognosis was related to age, TNM stage, and surgery type. With the Kaplan-Meier analysis, the more radical the operation, the worse the prognosis for the patients in the entire cohort. Within stage I-III disease, the best prognoses were observed in the patients undergoing BCS, followed by TM and radical mastectomy. The adjusted survival analysis showed that the prognoses of the patients undergoing BCS were better than the prognoses of the patients undergoing TM. Within stage IV disease, the patients who underwent an operation had a better prognosis regardless of the mode. CONCLUSION: Patients undergoing BCS had the best prognoses among the patients with early and locally advanced TN-MBC. This improves our understanding of the clinicopathological and prognostic features of this rare entity but also provides more convincing therapeutic guidelines for TN-MBC.

Properties and pitfalls of weighting as an alternative to multilevel multiple imputation in cluster randomized trials with missing binary outcomes under covariate-dependent missingness.

The generalized estimating equation (GEE) approach can be used to analyze cluster randomized trial data to obtain population-averaged intervention effects. However, most cluster randomized trials have some missing outcome data and a GEE analysis of available data may be biased when outcome data are not missing completely at random. Although multilevel multiple imputation for GEE (MMI-GEE) has been widely used, alternative approaches such as weighted GEE are less common in practice. Using both simulations and a real data example, we evaluate the performance of inverse probability weighted GEE vs. MMI-GEE for binary outcomes. Simulated data are generated assuming a covariate-dependent missing data pattern across a range of missingness clustering (from none to high), where all covariates are measured at baseline and are fully observed (i.e. a type of missing-at-random mechanism). Two types of weights are estimated and used in the weighted GEE: (1) assuming no clustering of missingness (W-GEE) and (2) accounting for such clustering (CW-GEE). Results show that, even in settings with high missingness clustering, CW-GEE can lead to more bias and lower coverage than W-GEE, whereas W-GEE and MMI-GEE provide comparable results. W-GEE should be considered a viable strategy to account for missing outcomes in cluster randomized trials.

Propensity score weighting under limited overlap and model misspecification.

Propensity score weighting methods are often used in non-randomized studies to adjust for confounding and assess treatment effects. The most popular among them, the inverse probability weighting, assigns weights that are proportional to the inverse of the conditional probability of a specific treatment assignment, given observed covariates. A key requirement for inverse probability weighting estimation is the positivity assumption, i.e. the propensity score must be bounded away from 0 and 1. In practice, violations of the positivity assumption often manifest by the presence of limited overlap in the propensity score distributions between treatment groups. When these practical violations occur, a small number of highly influential inverse probability weights may lead to unstable inverse probability weighting estimators, with biased estimates and large variances. To mitigate these issues, a number of alternative methods have been proposed, including inverse probability weighting trimming, overlap weights, matching weights, and entropy weights. Because overlap weights, matching weights, and entropy weights target the population for whom there is equipoise (and with adequate overlap) and their estimands depend on the true propensity score, a common criticism is that these estimators may be more sensitive to misspecifications of the propensity score model. In this paper, we conduct extensive simulation studies to compare the performances of inverse probability weighting and inverse probability weighting trimming against those of overlap weights, matching weights, and entropy weights under limited overlap and misspecified propensity score models. Across the wide range of scenarios we considered, overlap weights, matching weights, and entropy weights consistently outperform inverse probability weighting in terms of bias, root mean squared error, and coverage probability.

Long-term exposure to PM2.5 and ozone and hospital admissions of Medicare participants in the Southeast USA.

We examined the association between average annual fine particulate matter (PM2.5) and ozone and first hospital admissions of Medicare participants for stroke, chronic obstructive pulmonary disease (COPD), pneumonia, myocardial infarction (MI), lung cancer, and heart failure (HF). Annual average PM2.5 and ozone levels were estimated using high-resolution spatio-temporal models. We fit a marginal structural Cox proportional hazards model, using stabilized inverse probability weights (IPWs) to account for the competing risk of death and confounding. Analyses were then repeated after restricting to exposure levels below the current U.S. standards. The results showed that PM2.5 was significantly associated with an increased hazard of admissions for all studied outcomes; the highest observed being a 6.1% (95% CI: 5.9%-6.2%) increase in the hazard of admissions with pneumonia for each µg/m3 increase in particulate levels. Ozone was also significantly associated with an increase in the risk of first hospital admissions of all outcomes. The hazard of pneumonia increased by 3.0% (95% CI: 2.9%-3.1%) for each ppb increase in the ozone level. Our results reveal a need to regulate long-term ozone exposure, and that associations persist below current PM2.5 standards.