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Peter C Austin - One of the best experts on this subject based on the ideXlab platform.
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a review of the use of time varying Covariates in the fine gray subdistribution hazard competing risk regression model
Statistics in Medicine, 2020Co-Authors: Peter C Austin, Aurelien Latouche, Jason P FineAbstract:In survival analysis, time-varying Covariates are Covariates whose value can change during follow-up. Outcomes in medical research are frequently subject to competing risks (events precluding the occurrence of the primary outcome). We review the types of time-varying Covariates and highlight the effect of their inclusion in the subdistribution hazard model. External time-dependent Covariates are external to the subject, can effect the failure process, but are not otherwise involved in the failure mechanism. Internal time-varying Covariates are measured on the subject, can effect the failure process directly, and may also be impacted by the failure mechanism. In the absence of competing risks, a consequence of including internal time-dependent Covariates in the Cox model is that one cannot estimate the survival function or the effect of Covariates on the survival function. In the presence of competing risks, the inclusion of internal time-varying Covariates in a subdistribution hazard model results in the loss of the ability to estimate the cumulative incidence function (CIF) or the effect of Covariates on the CIF. Furthermore, the definition of the risk set for the subdistribution hazard function can make defining internal time-varying Covariates difficult or impossible. We conducted a review of the use of time-varying Covariates in subdistribution hazard models in articles published in the medical literature in 2015 and in the first 5 months of 2019. Seven percent of articles published included a time-varying Covariate. Several inappropriately described a time-varying Covariate as having an association with the risk of the outcome.
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generating survival times to simulate cox proportional hazards models with time varying Covariates
Statistics in Medicine, 2012Co-Authors: Peter C AustinAbstract:Simulations and Monte Carlo methods serve an important role in modern statistical research. They allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible. A key element in any statistical simulation is the existence of an appropriate data-generating process: one must be able to simulate data from a specified statistical model. We describe data-generating processes for the Cox proportional hazards model with time-varying Covariates when event times follow an exponential, Weibull, or Gompertz distribution. We consider three types of time-varying Covariates: first, a dichotomous time-varying Covariate that can change at most once from untreated to treated (e.g., organ transplant); second, a continuous time-varying Covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition; third, a dichotomous time-varying Covariate with a subject being able to move repeatedly between treatment states (e.g., current compliance or use of a medication). In each setting, we derive closed-form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time-invariant Covariates and to a single time-varying Covariate. We illustrate the utility of our closed-form expressions for simulating event times by using Monte Carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time-varying Covariates. This is compared with the statistical power to detect as statistically significant a binary time-invariant Covariate. Copyright © 2012 John Wiley & Sons, Ltd.
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goodness of fit diagnostics for the propensity score model when estimating treatment effects using Covariate adjustment with the propensity score
Pharmacoepidemiology and Drug Safety, 2008Co-Authors: Peter C AustinAbstract:The propensity score is defined to be a subject's probability of treatment selection, conditional on observed baseline Covariates. Conditional on the propensity score, treated and untreated subjects have similar distributions of observed baseline Covariates. In the medical literature, there are three commonly employed propensity-score methods: stratification (subclassification) on the propensity score, matching on the propensity score, and Covariate adjustment using the propensity score. Methods have been developed to assess the adequacy of the propensity score model in the context of stratification on the propensity score and propensity-score matching. However, no comparable methods have been developed for Covariate adjustment using the propensity score. Inferences about treatment effect made using propensity-score methods are only valid if, conditional on the propensity score, treated and untreated subjects have similar distributions of baseline Covariates. We develop both quantitative and qualitative methods to assess the balance in baseline Covariates between treated and untreated subjects. The quantitative method employs the weighted conditional standardized difference. This is the conditional difference in the mean of a Covariate between treated and untreated subjects, in units of the pooled standard deviation, integrated over the distribution of the propensity score. The qualitative method employs quantile regression models to determine whether, conditional on the propensity score, treated and untreated subjects have similar distributions of continuous Covariates. We illustrate our methods using a large dataset of patients discharged from hospital with a diagnosis of a heart attack (acute myocardial infarction). The exposure was receipt of a prescription for a beta-blocker at hospital discharge.
Aurelien Latouche - One of the best experts on this subject based on the ideXlab platform.
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a review of the use of time varying Covariates in the fine gray subdistribution hazard competing risk regression model
Statistics in Medicine, 2020Co-Authors: Peter C Austin, Aurelien Latouche, Jason P FineAbstract:In survival analysis, time-varying Covariates are Covariates whose value can change during follow-up. Outcomes in medical research are frequently subject to competing risks (events precluding the occurrence of the primary outcome). We review the types of time-varying Covariates and highlight the effect of their inclusion in the subdistribution hazard model. External time-dependent Covariates are external to the subject, can effect the failure process, but are not otherwise involved in the failure mechanism. Internal time-varying Covariates are measured on the subject, can effect the failure process directly, and may also be impacted by the failure mechanism. In the absence of competing risks, a consequence of including internal time-dependent Covariates in the Cox model is that one cannot estimate the survival function or the effect of Covariates on the survival function. In the presence of competing risks, the inclusion of internal time-varying Covariates in a subdistribution hazard model results in the loss of the ability to estimate the cumulative incidence function (CIF) or the effect of Covariates on the CIF. Furthermore, the definition of the risk set for the subdistribution hazard function can make defining internal time-varying Covariates difficult or impossible. We conducted a review of the use of time-varying Covariates in subdistribution hazard models in articles published in the medical literature in 2015 and in the first 5 months of 2019. Seven percent of articles published included a time-varying Covariate. Several inappropriately described a time-varying Covariate as having an association with the risk of the outcome.
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A review of the use of time‐varying Covariates in the Fine‐Gray subdistribution hazard competing risk regression model
Statistics in Medicine, 2019Co-Authors: Peter Austin, Aurelien Latouche, Jason FineAbstract:In survival analysis, time-varying Covariates are Covariates whose value can change during follow-up. Outcomes in medical research are frequently subject to competing risks (events precluding the occurrence of the primary outcome). We review the types of time-varying Covariates and highlight the effect of their inclusion in the subdistribution hazard model. External time-dependent Covariates are external to the subject, can effect the failure process, but are not otherwise involved in the failure mechanism. Internal time-varying Covariates are measured on the subject, can effect the failure process directly, and may also be impacted by the failure mechanism. In the absence of competing risks, a consequence of including internal time-dependent Covariates in the Cox model is that one cannot estimate the survival function or the effect of Covariates on the survival function. In the presence of competing risks, the inclusion of internal time-varying Covariates in a subdistribution hazard model results in the loss of the ability to estimate the cumulative incidence function (CIF) or the effect of Covariates on the CIF. Furthermore, the definition of the risk set for the subdistribution hazard function can make defining internal time-varying covari-ates difficult or impossible. We conducted a review of the use of time-varying Covariates in subdistribution hazard models in articles published in the medical literature in 2015 and in the first 5 months of 2019. Seven percent of articles published included a time-varying Covariate. Several inappropriately described a time-varying Covariate as having an association with the risk of the outcome.
Jason Fine - One of the best experts on this subject based on the ideXlab platform.
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A review of the use of time‐varying Covariates in the Fine‐Gray subdistribution hazard competing risk regression model
Statistics in Medicine, 2019Co-Authors: Peter Austin, Aurelien Latouche, Jason FineAbstract:In survival analysis, time-varying Covariates are Covariates whose value can change during follow-up. Outcomes in medical research are frequently subject to competing risks (events precluding the occurrence of the primary outcome). We review the types of time-varying Covariates and highlight the effect of their inclusion in the subdistribution hazard model. External time-dependent Covariates are external to the subject, can effect the failure process, but are not otherwise involved in the failure mechanism. Internal time-varying Covariates are measured on the subject, can effect the failure process directly, and may also be impacted by the failure mechanism. In the absence of competing risks, a consequence of including internal time-dependent Covariates in the Cox model is that one cannot estimate the survival function or the effect of Covariates on the survival function. In the presence of competing risks, the inclusion of internal time-varying Covariates in a subdistribution hazard model results in the loss of the ability to estimate the cumulative incidence function (CIF) or the effect of Covariates on the CIF. Furthermore, the definition of the risk set for the subdistribution hazard function can make defining internal time-varying covari-ates difficult or impossible. We conducted a review of the use of time-varying Covariates in subdistribution hazard models in articles published in the medical literature in 2015 and in the first 5 months of 2019. Seven percent of articles published included a time-varying Covariate. Several inappropriately described a time-varying Covariate as having an association with the risk of the outcome.
Jason P Fine - One of the best experts on this subject based on the ideXlab platform.
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a review of the use of time varying Covariates in the fine gray subdistribution hazard competing risk regression model
Statistics in Medicine, 2020Co-Authors: Peter C Austin, Aurelien Latouche, Jason P FineAbstract:In survival analysis, time-varying Covariates are Covariates whose value can change during follow-up. Outcomes in medical research are frequently subject to competing risks (events precluding the occurrence of the primary outcome). We review the types of time-varying Covariates and highlight the effect of their inclusion in the subdistribution hazard model. External time-dependent Covariates are external to the subject, can effect the failure process, but are not otherwise involved in the failure mechanism. Internal time-varying Covariates are measured on the subject, can effect the failure process directly, and may also be impacted by the failure mechanism. In the absence of competing risks, a consequence of including internal time-dependent Covariates in the Cox model is that one cannot estimate the survival function or the effect of Covariates on the survival function. In the presence of competing risks, the inclusion of internal time-varying Covariates in a subdistribution hazard model results in the loss of the ability to estimate the cumulative incidence function (CIF) or the effect of Covariates on the CIF. Furthermore, the definition of the risk set for the subdistribution hazard function can make defining internal time-varying Covariates difficult or impossible. We conducted a review of the use of time-varying Covariates in subdistribution hazard models in articles published in the medical literature in 2015 and in the first 5 months of 2019. Seven percent of articles published included a time-varying Covariate. Several inappropriately described a time-varying Covariate as having an association with the risk of the outcome.
Robert L. Ohsfeldt - One of the best experts on this subject based on the ideXlab platform.
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squeezing the balloon propensity scores and unmeasured Covariate balance
Health Services Research, 2013Co-Authors: John M. Brooks, Robert L. OhsfeldtAbstract:The strength of randomized controlled trials (RCTs) is the assumption that randomized treatment assignment yields a balanced distribution of Covariates thought to be related to outcome between the treatment and control groups (Rubin 2001). Published studies of RCT results traditionally report a table displaying the balance in measured Covariates (e.g., patient age, gender, baseline clinical conditions, etc.) between the treatment and control groups. Demonstrated balance of measured Covariates across treatment groups is intended to lend credence that such balance extends to unmeasured Covariates (Berk 2004). In the context of observational (nonrandomized) data, researchers have espoused designing treatment effect studies that mimic the measured Covariate balancing properties of RCTs (Rosenbaum and Rubin 1983a,b; Rubin 1997, 2001, 2007; Joffe and Rosenbaum 1999; Shah et al. 2005). The use of a propensity score (PS)—the probability a patient received treatment given the patient's measured Covariate values—has become a mainstay in efforts to find measured Covariate balance in observational data studies to estimate treatment effects. It has been said that PS-based methods “can be used to design observational studies in a way analogous to the way randomized experiments are designed” (Rubin 2001) with a design attempting to “assemble groups of treated and control units such that within each group the distributions of Covariates is balanced” (Rubin 2001). While methodologists are quick to qualify that achieving balance in measured Covariates between groups of treated and untreated patients does not “guarantee” balance in unmeasured Covariates across groups, measured Covariate balance often creates an “expectation” of unmeasured Covariate balance as in RCTs (Ward and Johnson 2008). Indeed, a review of the PS literature noted that “many of the articles in our review” imply that “propensity scores might also balance the unknown confounders between exposure groups” (Shah et al. 2005). Several PS-based algorithms have been suggested to create patient samples that are balanced in measured Covariates between treated and untreated patients. These algorithms range from stratification (D'Agostino 1998) and matching based on propensity scores (Hall, Summers, and Oberchain 2003; Frolich 2007; Stuart 2010) to using patient-specific propensity scores to weight observations (Rosenbaum 1987; Robins, Hernan, and Brunback 2000). Treatment effect inferences are then made by contrasting average outcomes between treated and untreated patients with similar propensity scores (and correspondingly similar distributions of measured Covariates). These algorithms yield unbiased treatment effect estimates only if after balancing measured Covariates, unmeasured Covariates are “ignorable” or that the remaining unmeasured Covariates that affected treatment choice are independent of outcome (Rosenbaum and Rubin 1983a,b; Joffe and Rosenbaum 1999). Unmeasured Covariates affecting treatment choice are ignorable if either (1) they have no relationship (either directly or indirectly) with outcome, or (2) they are balanced between treatment and control groups after balancing measured Covariates. Neither of these conditions can be verified directly with data available to researchers. The condition that the unmeasured Covariates affecting treatment choice have no relationship with outcome is identical to the assumption required to yield unbiased estimates in standard multivariate regression-based treatment effect estimators—treatment is orthogonal to the error term in the outcome relationship after adjusting for the measured Covariates included in the regression model (Angrist and Pischke 2009). Stated differently, this condition assumes that none of the unmeasured Covariates affecting treatment choice confound the relationship between treatment and outcome. This orthogonal assumption requires theory-based persuasion by researchers for acceptance. Therefore, the conceptual advantage of PS-based methods relative to standard regression appears to hinge on the assumption that balancing measured Covariates between treated and nontreated patients leads to unmeasured Covariate balance between treated and nontreated patients. If this assumption holds, unbiased treatment effect estimates can be obtained without relying on theory to support the orthogonal assumption. However, PS-based analyses of treatment effects using observational data largely ignore what seems to be a fundamental question—why did patients with the same or similar propensity scores receive different treatments? Intuitively, it would seem that unmeasured factors not accounted for in the PS model must be different between two patients with similar propensity scores for them to receive different treatments. Let patient utility associated with treatment U(T) and no treatment U(NT) be represented in terms of measured (XM) and unmeasured Covariates (XU): (1) (2) The measured and unmeasured Covariates in equations (1) and (2) represent any factors affecting the utility of treatment versus no treatment for the patient. These Covariates could represent factors related to patient preferences over the outcome changes induced by treatment choice (e.g., an actor may value facial changes from cosmetic surgery more than a construction worker) or factors affecting the relative effectiveness of treatment (e.g., a child with an ear infection and a high fever will expect more benefit from an antibiotic than a child with an ear infection and a low fever). A patient will choose treatment if the net utility gain from treatment—NG(T)—is positive: (3) Based on equation (3), patient treatment choices depend on their respective values of XM and XU. If (α2 − β2) > 0 treated patients will tend to have higher average values of XU than untreated patients, but with XM also varying across patients it may be possible to find treated patients with low values of XU and untreated patients with high values of XU. If, however, two patients A and B are matched to have identical values of the measured Covariate——and patient A chooses treatment and patient B does not, it must be that: (4) where for patient i NG(T)i equals the net gain of treatment and equals i's value of XU. With a fixed value of XM, for equation (4) to hold it must be that . If (α2 − β2) > 0 treated patients with matched XM values must have higher values of XU than untreated patients. Therefore, across a set of treated and nontreated patients matched on XM, we would expect greater average differences in XU than the average differences in XU between the population of treated and nontreated patients not matched by XM. In this study, we demonstrate the Covariate balancing properties of PS-based algorithms through the lens of a simple treatment choice simulation model in which Covariates affecting treatment choice are both measured and unmeasured. Prior simulation-based research showed that imbalance in unmeasured Covariates related to treatment assignment remains after using PS-based algorithms (Austin, Grootendorst, and Anderson 2007). Others have described the extent in which treatment effect estimates from propensity score-based approaches are sensitive to imbalance in unobserved Covariates (Rosenbaum and Rubin 1983a,b; Lin, Psaty et al. 1998). However, it has not been shown how PS-based algorithms affect the balance of unmeasured Covariates between treated and untreated patients. In our simulations, we find properties that are problematic for researchers hoping to make treatment effect inferences relying only on the expectation that balancing measured Covariate implies balanced unmeasured Covariates. To yield treated and untreated patients with similar propensity scores, we find that PS algorithms require imbalance in the portion of the variation of the unmeasured Covariates that affect treatment choice that is unrelated to the measured Covariates. In addition, as compared with the full unweighted sample, PS algorithms exacerbate the imbalance in the portion of the unmeasured Covariates unrelated to the measured Covariates between treated and untreated patients. This result is directly counter to the assumption often relied on in applications of propensity score methods that balancing measured Covariates implies balance in the unmeasured Covariates that affected treatment choice (Shah et al. 2005).
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Squeezing the Balloon: Propensity Scores and Unmeasured Covariate Balance
Health services research, 2012Co-Authors: John M. Brooks, Robert L. OhsfeldtAbstract:To assess the Covariate balancing properties of propensity score-based algorithms in which Covariates affecting treatment choice are both measured and unmeasured. A simulation model of treatment choice and outcome. Simulation. Eight simulation scenarios varied with the values placed on measured and unmeasured Covariates and the strength of the relationships between the measured and unmeasured Covariates. The balance of both measured and unmeasured Covariates was compared across patients either grouped or reweighted by propensity scores methods. Propensity score algorithms require unmeasured Covariate variation that is unrelated to measured Covariates, and they exacerbate the imbalance in this variation between treated and untreated patients relative to the full unweighted sample. The balance of measured Covariates between treated and untreated patients has opposite implications for unmeasured Covariates in randomized and observational studies. Measured Covariate balance between treated and untreated patients in randomized studies reinforces the notion that all Covariates are balanced. In contrast, forced balance of measured Covariates using propensity score methods in observational studies exacerbates the imbalance in the independent portion of the variation in the unmeasured Covariates, which can be likened to squeezing a balloon. If the unmeasured Covariates affecting treatment choice are confounders, propensity score methods can exacerbate the bias in treatment effect estimates. © Health Research and Educational Trust.
