Propensity score methods for time-dependent cluster confounding

In observational studies, subjects are often nested within clusters. In medical studies, patients are often treated by doctors and therefore patients are regarded as nested or clustered within doctors. A concern that arises with clustered data is that cluster-level characteristics (e.g., characteristics of the doctor) are associated with both treatment selection and patient outcomes, resulting in cluster-level confounding. Measuring and modeling cluster attributes can be difficult and statistical methods exist to control for all unmeasured cluster characteristics. An assumption of these methods however is that characteristics of the cluster and the effects of those characteristics on the outcome (as well as probability of treatment assignment when using covariate balancing methods) are constant over time. In this paper, we consider methods that relax this assumption and allow for estimation of treatment effects in the presence of unmeasured time-dependent cluster confounding. The methods are based on matching with the propensity score and incorporate unmeasured time-specific cluster effects by performing matching within clusters or using fixed- or random-cluster effects in the propensity score model. The methods are illustrated using data to compare the effectiveness of two total hip devices with respect to survival of the device and a simulation study is performed that compares the proposed methods. One method that was found to perform well is matching within surgeon clusters partitioned by time. Considerations in implementing the proposed methods are discussed.     

THE EFFECT OF UNMEASURED CONFOUNDERS ON THE ABILITY TO ESTIMATE A TRUE PERFORMANCE OR SELECTION GRADIENT (AND OTHER PARTIAL REGRESSION COEFFICIENTS)

Multiple regression of observational data is frequently used to infer causal effects. Partial regression coefficients are biased estimates of causal effects if unmeasured confounders are not in the regression model. The sensitivity of partial regression coefficients to omitted confounders is investigated with a Monte‐Carlo simulation. A subset of causal traits is “measured” and their effects are estimated using ordinary least squares regression and compared to their expected values. Three major results are: (1) the error due to confounding is much larger than that due to sampling, especially with large samples, (2) confounding error shrinks trivially with sample size, and (3) small true effects are frequently estimated as large effects. Consequently, confidence intervals from regression are poor guides to the true intervals, especially with large sample sizes. The addition of a confounder to the model improves estimates only 55% of the time. Results are improved with complete knowledge of the rank order of causal effects but even with this omniscience, measured intervals are poor proxies for true intervals if there are many unmeasured confounders. The results suggest that only under very limited conditions can we have much confidence in the magnitude of partial regression coefficients as estimates of causal effects.     

The Sign of the Unmeasured Confounding Bias under Various Standard Populations

Unmeasured confounders are a common problem in drawing causal inferences in observational studies. VanderWeele (Biometrics 2008, 64, 702–706) presented a theorem that allows researchers to determine the sign of the unmeasured confounding bias when monotonic relationships hold between the unmeasured confounder and the treatment, and between the unmeasured confounder and the outcome. He showed that his theorem can be applied to causal effects with the total group as the standard population, but he did not mention the causal effects with treated and untreated groups as the standard population. Here, we extend his results to these causal effects, and apply our theorems to an observational study. When researchers have a sense of what the unmeasured confounder may be, conclusions can be drawn about the sign of the bias.     

Impact of Time to Start Treatment Following Infection with Application to Initiating HAART in HIV-Positive Patients

Summary We estimate how the effect of antiretroviral treatment depends on the time from HIV-infection to initiation of treatment, using observational data. A major challenge in making inferences from such observational data arises from biases associated with the nonrandom assignment of treatment, for example bias induced by dependence of time of initiation on disease status. To address this concern, we develop a new class of Structural Nested Mean Models (SNMMs) to estimate the impact of time of initiation of treatment after infection on an outcome measured a fixed duration after initiation, compared to the effect of not initiating treatment. This leads to a SNMM that models the effect of multiple dosages of treatment on a time-dependent outcome, in contrast to most existing SNNMs, which focus on the effect of one dosage of treatment on an outcome measured at the end of the study. Our identifying assumption is that there are no unmeasured confounders. We illustrate our methods using the observational Acute Infection and Early Disease Research Program (AIEDRP) Core01 database on HIV. The current standard of care in HIV-infected patients is Highly Active Anti-Retroviral Treatment (HAART); however, the optimal time to start HAART has not yet been identified. The new class of SNNMs allows estimation of the dependence of the effect of 1 year of HAART on the time between estimated date of infection and treatment initiation, and on patient characteristics. Results of fitting this model imply that early use of HAART substantially improves immune reconstitution in the early and acute phase of HIV-infection.     

Local failure after primary radiotherapy in lung cancer: Is there a role for SBRT?

AimOur purpose is to construe the role of stereotactic body radiation therapy (SBRT) in the management of lung cancer from our early experience with SBRT for salvage treatment in patients with recurrent lung cancer after initial radiation therapy.BackgroundLocoregional recurrences are a frequent challenge in patients treated with radio-chemotherapy for locally advanced NSCLC. Conventional external beam radiation therapy (EBRT) is rarely given as salvage treatment because of the risk of toxicity. There is a paucity of published studies evaluating the role of SBRT in this clinical setting.Materials and methodsBetween 2008 and present, 10 patients with biopsy proven non-small cell lung cancer (NSCLC) underwent 14 radiosurgical procedures for salvage therapy after failing initial radiation treatment. Patients’ age ranged from 54 to 88 years with a median of 74 years in 6 males and 4 females. Intervals from initial radiation treatment to salvage SBRT were 3–33 months with a median of 13 months. SBRT treatments were delivered using Intensity Modulated Volumetric Arc Therapy (VMAT). All patients received concomitant chemotherapy.ResultsOverall survival after salvage radiosurgery ranged from 6 to 41 months (mean 20 months, median 18 months). Four of the ten patients are alive with disease locally controlled. Of the remaining 6 patients, 4 had distant progression of disease with brain metastases and one had both brain and lung metastases. The other patient had a regional failure. Toxicities were found in three of the ten (30%) patients with grade I pneumonitis.ConclusionIn our early experience, salvage SBRT is an effective modality of treating patients who failed after conventional irradiation, achieving excellent results in terms of local control with acceptable toxicity. Further prospective studies are needed to determine optimal fractionation schemes.     

A systematic review of instrumental variable analyses using geographic region as an instrument

BackgroundInstrumental variables analysis is a methodology to mitigate the effects of measured and unmeasured confounding in observational studies of treatment effects. Geographic area is increasingly used as an instrument.MethodsWe conducted a literature review to determine the properties of geographic area in studies of cancer treatments. We identified cancer studies performed in the United States which incorporated instrumental variable analysis with area-wide treatment rate within a geographic region as the instrument. We assessed the degree of treatment variability between geographic regions, assessed balance of measured confounders afforded by geographic area and compared the results of instrumental variable analysis to those of multivariable methods.ResultsGeographic region as an instrument was relatively common, with 22 eligible studies identified, many of which were published in high-impact journals. Treatment rates did not vary greatly by geographic region. Covariates were not balanced by the instrument in the majority of studies. Eight out of eleven studies found statistically significant effects of treatment on multivariable analysis but not for instrumental variables, with the central estimates of the instrumental variables analysis generally being closer to the null.ConclusionsWe recommend caution and an investigation of IV assumptions when considering the use of geographic region as an instrument in observational studies of cancer treatments. The value of geographic region as an instrument should be critically evaluated in other areas of medicine.     

Does Clustering Affect the Usual Test Statistics of no Treatment Effect in a Randomized Clinical Trial?

In many clinical trials, such as those undertaken by large cooperative cancer groups (CALGB, ECOG, SWOG, EORTC), patients are randomized to one of two treatments within an institution (a hospital or clinic). In such clinical trials, it has often occurred that outcomes of patients within institutions tend to be similar (correlated), due, possibly, to unmeasured variables such as quality of staff or quality of hospital equipment. We discuss when, in the presence of random hospital effects, the usual test statistics for no treatment effect, which do not take these hospital effects into account, are (asymptotically) unbiased.     

Analysis of longitudinal marginal structural models

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), proposed by Robins (2000), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator of Robins et al. (2000) is used as an initial estimator and forms the basis for an improved, one-step estimator that is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County. A simulation study demonstrates the bias of naive estimators in the presence of time-dependent confounders and also shows the efficiency gain of the IPTW estimator, even in the absence such confounding. The efficiency gain of the improved, one-step estimator is demonstrated through simulation.     

Bounds on controlled direct effects under monotonic assumptions about mediators and confounders

Adjusting for intermediate variables is a common analytic strategy for estimating a direct effect. Even if the total effect is unconfounded, the direct effect is not identified when unmeasured variables affect the intermediate and outcome variables. Therefore, some researchers presented bounds on the controlled direct effects via linear programming. They applied a monotonic assumption about treatment and intermediate variables and a no-interaction assumption to derive narrower bounds. Here, we improve their bounds without using linear programming and hence derive a bound under the monotonic assumption about an intermediate variable only. To improve the bounds, we further introduce the monotonic assumption about confounders. While previous studies assumed that an outcome is a binary variable, we do not make that assumption. The proposed bounds are illustrated using two examples from randomized trials.     

Increasing efficiency and reducing bias when assessing HPV vaccination efficacy by using nontargeted HPV strains

Studies of vaccine efficacy often record both the incidence of vaccine-targeted virus strains (primary outcome) and the incidence of nontargeted strains (secondary outcome). However, standard estimates of vaccine efficacy on targeted strains ignore the data on nontargeted strains. Assuming nontargeted strains are unaffected by vaccination, we regard the secondary outcome as a negative control outcome and show how using such data can (i) increase the precision of the estimated vaccine efficacy against targeted strains in randomized trials and (ii) reduce confounding bias of that same estimate in observational studies. For objective (i), we augment the primary outcome estimating equation with a function of the secondary outcome that is unbiased for zero. For objective (ii), we jointly estimate the treatment effects on the primary and secondary outcomes. If the bias induced by the unmeasured confounders is similar for both types of outcomes, as is plausible for factors that influence the general risk of infection, then we can use the estimated efficacy against the secondary outcomes to remove the bias from estimated efficacy against the primary outcome. We demonstrate the utility of these approaches in studies of HPV vaccines that only target a few highly carcinogenic strains. In this example, using nontargeted strains increased precision in randomized trials modestly but reduced bias in observational studies substantially.     

A Multivariate Model to Measure the Effect of Treatments in Survival to Breast Cancer

An homogeneous Markov process in continuous time with three states (no relapse, relapse, and death) to model the influence of treatments in relapse and survival times to breast cancer is considered. Different treatments such as chemotherapy, radiotherapy, and hormonal therapy, and combinations of these were applied to a cohort of 300 patients after surgery. All patients were seen longitudinally every month. The treatments are introduced as covariates by means of transition intensity, thus providing three covariates. The likelihood function is built from the data and the parameters estimated. Original computational programmes are constructed using the MATHEMATICA and MATLAB programmes, by means of which we estimate the parameters, calculate the transition probability functions, plot the graphs of the survival curves, and fit the survival curves to treatments obtained from the model with the corresponding empirical functions.     

Generalized propensity score approach to causal inference with spatial interference

Many spatial phenomena exhibit interference, where exposures at one location may affect the response at other locations. Because interference violates the stable unit treatment value assumption, standard methods for causal inference do not apply. We propose a new causal framework to recover direct and spill-over effects in the presence of spatial interference, taking into account that exposures at nearby locations are more influential than exposures at locations further apart. Under the no unmeasured confounding assumption, we show that a generalized propensity score is sufficient to remove all measured confounding. To reduce dimensionality issues, we propose a Bayesian spline-based regression model accounting for a sufficient set of variables for the generalized propensity score. A simulation study demonstrates the accuracy and coverage properties. We apply the method to estimate the causal effect of wildland fires on air pollution in the Western United States over 2005–2018.     

Bayesian propensity scores for high‐dimensional causal inference: A comparison of drug‐eluting to bare‐metal coronary stents

High‐dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high‐dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high‐dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem.     

Estimating causal treatment effects from longitudinal HIV natural history studies using marginal structural models

Several recently completed and ongoing studies of the natural history of HIV infection have generated a wealth of information about its clinical progression and how this progression is altered by therepeutic interventions and environmental factors. Natural history studies typically follow prospective cohort designs, and enroll large numbers of participants for long-term prospective follow-up (up to several years). Using data from the HIV Epidemiology Research Study (HERS), a six-year natural history study that enrolled 871 HIV-infected women starting in 1993, we investigate the therapeutic effect of highly active antiretroviral therapy regimens (HAART) on CD4 cell count using the marginal structural modeling framework and associated estimation procedures based on inverse-probability weighting (developed by Robins and colleagues). To evaluate treatment effects from a natural history study, specialized methods are needed because treatments are not randomly prescribed and, in particular, the treatment-response relationship can be confounded by variables that are time-varying. Our analysis uses CD4 data on all follow-up visits over a two-year period, and includes sensitivity analyses to investigate potential biases attributable to unmeasured confounding. Strategies for selecting ranges of a sensitivity parameter are given, as are intervals for treatment effect that reflect uncertainty attributable both to sampling and to lack of knowledge about the nature and existence of unmeasured confounding. To our knowledge, this is the first use in "real data" of Robins's sensitivity analysis for unmeasured confounding (Robins, 1999a, Synthese 121, 151-179). The findings from our analysis are consistent with recent treatment guidelines set by the U.S. Panel of the International AIDS Society (Carpenter et al., 2000, Journal of the American Medical Association 280, 381-391).     

Causal inference on the difference of the restricted mean lifetime between two groups

When comparing survival times between two treatment groups, it may be more appropriate to compare the restricted mean lifetime, i.e., the expectation of lifetime restricted to a time L, rather than mean lifetime in order to accommodate censoring. When the treatments are not assigned to patients randomly, as in observational studies, we also need to account for treatment imbalances in confounding factors. In this article, we propose estimators for the difference of the restricted mean lifetime between two groups that account for treatment imbalances in prognostic factors assuming a proportional hazards relationship. Large-sample properties of our estimators based on martingale theory for counting processes are also derived. Simulation studies were conducted to compare these estimators and to assess the adequacy of the large-sample approximations. Our methods are also applied to an observational database of acute coronary syndrome patients from Duke University Medical Center to estimate the treatment effect on the restricted mean lifetime over 5 years.     

Utilizing Propensity Scores to Estimate Causal Treatment Effects with Censored Time-Lagged Data

Observational studies frequently are conducted to compare long-term effects of treatments. Without randomization, patients receiving one treatment are not guaranteed to be prognostically comparable to those receiving another treatment. Furthermore, the response of interest may be right-censored because of incomplete follow-up. Statistical methods that do not account for censoring and confounding may lead to biased estimates. This article presents a method for estimating treatment effects in nonrandomized studies with right-censored responses. We review the assumptions required to estimate average causal effects and derive an estimator for comparing two treatments by applying inverse weights to the complete cases. The weights are determined according to the estimated probability of receiving treatment conditional on covariates and the estimated treatment-specific censoring distribution. By utilizing martingale representations, the estimator is shown to be asymptotically normal and an estimator for the asymptotic variance is derived. Simulation results are presented to evaluate the properties of the estimator. These methods are applied to an observational data set of acute coronary syndrome patients from Duke University Medical Center to estimate the effect of a treatment strategy on the mean 5-year medical cost.     

Sensitivity analyses for ecological regression

In many ecological regression studies investigating associations between environmental exposures and health outcomes, the observed relative risks are in the range 1.0-2.0. The interpretation of such small relative risks is difficult due to a variety of biases--some of which are unique to ecological data, since they arise from within-area variability in exposures/confounders. The potential for residual spatial dependence, due to unmeasured confounders and/or data anomalies with spatial structure, must also be considered, though it often will be of secondary importance when compared to the likely effects of unmeasured confounding and within-area variability in exposures/confounders. Methods for addressing sensitivity to these issues are described, along with an approach for assessing the implications of spatial dependence. An ecological study of the association between myocardial infarction and magnesium is critically reevaluated to determine potential sources of bias. It is argued that the sophistication of the statistical analysis should not outweigh the quality of the data, and that finessing models for spatial dependence will often not be merited in the context of ecological regression.     

Matching Methods for Obtaining Survival Functions to Estimate the Effect of a Time-Dependent Treatment

In observational studies of survival time featuring a binary time-dependent treatment, the hazard ratio (an instantaneous measure) is often used to represent the treatment effect. However, investigators are often more interested in the difference in survival functions. We propose semiparametric methods to estimate the causal effect of treatment among the treated with respect to survival probability. The objective is to compare post-treatment survival with the survival function that would have been observed in the absence of treatment. For each patient, we compute a prognostic score (based on the pre-treatment death hazard) and a propensity score (based on the treatment hazard). Each treated patient is then matched with an alive, uncensored and not-yet-treated patient with similar prognostic and/or propensity scores. The experience of each treated and matched patient is weighted using a variant of Inverse Probability of Censoring Weighting to account for the impact of censoring. We propose estimators of the treatment-specific survival functions (and their difference), computed through weighted Nelson–Aalen estimators. Closed-form variance estimators are proposed which take into consideration the potential replication of subjects across matched sets. The proposed methods are evaluated through simulation, then applied to estimate the effect of kidney transplantation on survival among end-stage renal disease patients using data from a national organ failure registry.     

K‐Sample comparisons using propensity analysis

In this paper, we investigate K‐group comparisons on survival endpoints for observational studies. In clinical databases for observational studies, treatment for patients are chosen with probabilities varying depending on their baseline characteristics. This often results in noncomparable treatment groups because of imbalance in baseline characteristics of patients among treatment groups. In order to overcome this issue, we conduct propensity analysis and match the subjects with similar propensity scores across treatment groups or compare weighted group means (or weighted survival curves for censored outcome variables) using the inverse probability weighting (IPW). To this end, multinomial logistic regression has been a popular propensity analysis method to estimate the weights. We propose to use decision tree method as an alternative propensity analysis due to its simplicity and robustness. We also propose IPW rank statistics, called Dunnett‐type test and ANOVA‐type test, to compare 3 or more treatment groups on survival endpoints. Using simulations, we evaluate the finite sample performance of the weighted rank statistics combined with these propensity analysis methods. We demonstrate these methods with a real data example. The IPW method also allows us for unbiased estimation of population parameters of each treatment group. In this paper, we limit our discussions to survival outcomes, but all the methods can be easily modified for any type of outcomes, such as binary or continuous variables.