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There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly robust estimator and/or to misuse more complex established doubly robust estimators. A simple alternative, canonical link generalized linear models (GLM) fit via inverse probability of treatment (propensity score) weighted maximum likelihood estimation followed by standardization (the g-formula) for the average causal effect, is a doubly robust estimation method. Our aim is for the reader not just to be able to use this method, which we refer to as IPTW GLM, for doubly robust estimation, but to fully understand why it has the doubly robust property. For this reason, we define clearly, and in multiple ways, all concepts needed to understand the method and why it is doubly robust. In addition, we want to make very clear that the mere combination of propensity score weighting and an adjusted outcome model does not generally result in a doubly robust estimator. Finally, we hope to dispel the misconception that one can adjust for residual confounding remaining after propensity score weighting by adjusting in the outcome model for what remains ‘unbalanced’ even when using doubly robust estimators. We provide R code for our simulations and real open-source data examples that can be followed step-by-step to use and hopefully understand the IPTW GLM method. We also compare to a much better-known but still simple doubly robust estimator.

Background Syringomyelia (SM) and myxomatous mitral valve disease (MMVD) are highly prevalent in Cavalier King Charles spaniels (CKCS). Cardiac status in CKCS with and without SM is currently unknown. Objectives To investigate the association between SM and MMVD severity in CKCS and CKCS with SM with and without clinical signs of SM. Animals Fifty-five CKCS: 40 with SM (22 symptomatic and 18 asymptomatic) and 15 without SM. Methods A combined retrospective and prospective study. MRI and echocardiography were used to diagnose SM and MMVD, respectively. The association between SM and MMVD severity (left ventricle internal diameter in diastole normalized to bodyweight [LVIDDN] and left atrium to aortic ratio [LA/Ao]) were tested using multivariable linear regression analysis adjusting for sex and age. Results Overall, no significant difference in LVIDDN and LA/Ao was found between CKCS with or without SM. However, CKCS with symptomatic SM had significantly smaller LVIDDN (1.45 [1.30-1.50]) (median [IQR]) and LA/Ao (1.20 [1.10-1.28]) compared to CKCS with asymptomatic SM (1.60 [1.50-1.90] and 1.40 [1.20-1.75]) as well as CKCS without SM (0.24 [0.03-0.45] and 0.30 [0.05-0.56]) (all P values <.03). Conclusions and Clinical Importance An association between MMVD and SM was not confirmed in this cohort of CKCS, indicating that MMVD and SM do not co-segregate. However, CKCS with symptomatic SM had smaller left ventricle and atrial size compared to CKCS with asymptomatic SM and CKCS without SM., BACKGROUND: Syringomyelia (SM) and myxomatous mitral valve disease (MMVD) are highly prevalent in Cavalier King Charles spaniels (CKCS). Cardiac status in CKCS with and without SM is currently unknown.OBJECTIVES: To investigate the association between SM and MMVD severity in CKCS and CKCS with SM with and without clinical signs of SM.ANIMALS: Fifty-five CKCS: 40 with SM (22 symptomatic and 18 asymptomatic) and 15 without SM.METHODS: A combined retrospective and prospective study. MRI and echocardiography were used to diagnose SM and MMVD, respectively. The association between SM and MMVD severity (left ventricle internal diameter in diastole normalized to bodyweight [LVIDDN] and left atrium to aortic ratio [LA/Ao]) were tested using multivariable linear regression analysis adjusting for sex and age.RESULTS: Overall, no significant difference in LVIDDN and LA/Ao was found between CKCS with or without SM. However, CKCS with symptomatic SM had significantly smaller LVIDDN (1.45 [1.30-1.50]) (median [IQR]) and LA/Ao (1.20 [1.10-1.28]) compared to CKCS with asymptomatic SM (1.60 [1.50-1.90] and 1.40 [1.20-1.75]) as well as CKCS without SM (0.24 [0.03-0.45] and 0.30 [0.05-0.56]) (all P values <.03).CONCLUSIONS AND CLINICAL IMPORTANCE: An association between MMVD and SM was not confirmed in this cohort of CKCS, indicating that MMVD and SM do not co-segregate. However, CKCS with symptomatic SM had smaller left ventricle and atrial size compared to CKCS with asymptomatic SM and CKCS without SM.

Inference for the conditional association between an exposure and a time-to-event endpoint, given covariates, is routinely based on partial likelihood estimators for hazard ratios indexing Cox proportional hazards models. This approach is flexible and makes testing straightforward, but is nonetheless not entirely satisfactory. First, there is no good understanding of what it infers when the model is misspecified. Second, it is common to employ variable selection procedures when deciding which model to use. However, the bias and uncertainty that imperfect variable selection adds to the analysis is rarely acknowledged, rendering standard inferences biased and overly optimistic. To remedy this, we propose a nonparametric estimand which reduces to the main exposure effect parameter in a (partially linear) Cox model when that model is correct, but continues to capture the (conditional) association of interest in a well understood way, even when this model is misspecified in an arbitrary manner. We achieve an assumption-lean inference for this estimand based on its influence function under the nonparametric model. This has the further advantage that it makes the proposed approach amenable to the use of data-adaptive procedures (e.g., variable selection, machine learning), which we find to work well in simulation studies and a data analysis. for this article are available online.

In some clinical studies patient survival beyond a specific point in time, , say, may be of special interest as it may for instance indicate patient cure. To analyze the -year risk for such patients may be accomplished using logistic regression with appropriate weights (IPWCC) that may further be augmented (AIPWCC) to improve efficiency. In this paper, we derive the most efficient estimator for this problem, which is different from the AIPWCC based on the full data efficient influence function. We first give the result for a survival endpoint and then generalize to the competing risk setting. The proposed estimators superior behavior is illustrated using simulations as well as applying it to some real data concerning the survival of blood and marrow transplanted patients., In some clinical studies patient survival beyond a specific point in time, t(0), say, maybe of special interest as it may for instance indicate patient cure. To analyze the t(0)-year risk for such patients may be accomplished using logistic regression with appropriate weights (IPWCC) that may further be augmented (AIPWCC) to improve efficiency. In this paper, we derive the most efficient estimator for this problem, which is different from the AIPWCC based on the full data efficient influence function. We first give the result for a survival endpoint and then generalize to the competing risk setting. The proposed estimators superior behavior is illustrated using simulations as well as applying it to some real data concerning the survival of blood and marrow transplanted patients.

Discussion on "A formal causal interpretation of the case-crossover design" by Zach Shahn, Miguel A. Hernan, and James M. Robins

Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause specific or subdistribution hazards, are fundamentally hard to interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a clear causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause specific hazard functions. We describe the asymptotic properties of these estimators, and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we re-analyze the prostate cancer trial from Stensrud et al. (2020)., Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause-specific or subdistribution hazards, are fundamentally hard to interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a clear causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause-specific hazard functions. We describe the asymptotic properties of these estimators and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we reanalyze the prostate cancer trial from Stensrud et al. (2020)

There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly robust estimator and/or to misuse more complex established doubly robust estimators. A simple alternative, canonical link generalized linear models (GLM) fit via inverse probability of treatment (propensity score) weighted maximum likelihood estimation followed by standardization (the -formula) for the average causal effect, is a doubly robust estimation method. Our aim is for the reader not just to be able to use this method, which we refer to as IPTW GLM, for doubly robust estimation, but to fully understand why it has the doubly robust property. For this reason, we define clearly, and in multiple ways, all concepts needed to understand the method and why it is doubly robust. In addition, we want to make very clear that the mere combination of propensity score weighting and an adjusted outcome model does not generally result in a doubly robust estimator. Finally, we hope to dispel the misconception that one can adjust for residual confounding remaining after propensity score weighting by adjusting in the outcome model for what remains ‘unbalanced’ even when using doubly robust estimators. We provide R code for our simulations and real open-source data examples that can be followed step-by-step to use and hopefully understand the IPTW GLM method. We also compare to a much better-known but still simple doubly robust estimator., There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly robust estimator and/or to misuse more complex established doubly robust estimators. A simple alternative, canonical link generalized linear models (GLM) fit via inverse probability of treatment (propensity score) weighted maximum likelihood estimation followed by standardization (the (Formula presented.) -formula) for the average causal effect, is a doubly robust estimation method. Our aim is for the reader not just to be able to use this method, which we refer to as IPTW GLM, for doubly robust estimation, but to fully understand why it has the doubly robust property. For this reason, we define clearly, and in multiple ways, all concepts needed to understand the method and why it is doubly robust. In addition, we want to make very clear that the mere combination of propensity score weighting and an adjusted outcome model does not generally result in a doubly robust estimator. Finally, we hope to dispel the misconception that one can adjust for residual confounding remaining after propensity score weighting by adjusting in the outcome model for what remains ‘unbalanced’ even when using doubly robust estimators. We provide R code for our simulations and real open-source data examples that can be followed step-by-step to use and hopefully understand the IPTW GLM method. We also compare to a much better-known but still simple doubly robust estimator.

We use semi-parametric efficiency theory to derive a class of estimators for the state occupation probabilities of the continuous-time irreversible illness-death model. We consider both the setting with and without additional baseline information available, where we impose no specific functional form on the intensity functions of the model. We show that any estimator in the class is asymptotically linear under suitable assumptions about the estimators of the intensity functions. In particular, the assumptions are weak enough to allow the use of data-adaptive methods, which is important for making the identifying assumption of coarsening at random plausible in realistic settings. We suggest a flexible method for estimating the transition intensity functions of the illness-death model based on penalized Poisson regression. We apply this method to estimate the nuisance parameters of an illness-death model in a simulation study and a real-world application., We use semi-parametric efficiency theory to derive a class of estimators for the state occupation probabilities of the continuous-time irreversible illness-death model. We consider both the setting with and without additional baseline information available, where we impose no specific functional form on the intensity functions of the model. We show that any estimator in the class is asymptotically linear under suitable assumptions about the estimators of the intensity functions. In particular, the assumptions are weak enough to allow the use of data-adaptive methods, which is important for making the identifying assumption of coarsening at random plausible in realistic settings. We suggest a flexible method for estimating the transition intensity functions of the illness-death model based on penalized Poisson regression. We apply this method to estimate the nuisance parameters of an illness-death model in a simulation study and a real-world application.