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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.

In this paper, we respond to comments on our paper, "Instrumental variable estimation of the causal hazard ratio."

Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated using a Cox model is subject to unmeasured confounding bias. To address this, we propose a novel approach for the identification and estimation of the causal hazard ratio in the presence of unmeasured confounding factors. Our approach is based on a binary instrumental variable, and an additional no-interaction assumption in a first stage regression of the treatment on the IV and unmeasured confounders. We propose, to the best of our knowledge, the first consistent estimator of the (population) causal hazard ratio within an instrumental variable framework. A version of our estimator admits a closed-form representation. We derive the asymptotic distribution of our estimator, and provide a consistent estimator for its asymptotic variance. Our approach is illustrated via simulation studies and a data application. This article is protected by copyright. All rights reserved.

Dette speciale omhandler kausal inferens med observationelt longitudinelt overlevelsesdata. Mere specifikt, estimation af effekten som en behandling har på overlevelse, når behandlingen varierer over tid og er påvirket af tidsafhængig confounding. Vi definerer først kausale effekter ud fra potentielle udfald, og viser i diskret-tids tilfældet hvordan fordelingen af potentielle udfald kan relateres til observationelt data gennem g-formlen. Vi forklarer hvorfor hazard-ratioer ikke kan fortolkes kausalt, og viser hvordan parameteren i en Cox proportional hazards model i stedet kan fortolkes kausalt som en log-overlevelses ratio, hvis man antager Markov-egenskaben for hazardfunktionen, og at overlevelsesstatus ikke påvirker fremtidig eksponering. Vi fortsætter med et nærmere kig på Markov-antagelsen, og viser at den i tilfælde at uobserveret skrøbelighed medfører at den underliggende fordeling ikke er tro mod sin kausale graf, med den konsekvens at Markov-antagelsen må anses som fundamentalt uplausibel fra et modelleringssynspunkt. Til sidst redefineres kausale effekter med udgangspunkt i målskift, hvilket giver et naturligt udgangspunkt for at definere kausale effekter i kontinuert tid. Det vises herefter hvordan disse effekter kan estimeres ved hjælp af en kontinuert-tids udgave af de klassiske inverse sandsynlighedsvægte, herunder et særligt nemt specialtilfælde med effekten af altid at behandle mod aldrig at behandle. Metoderne illustreres på virkelige data fra patienter der lider af kræft i spiserøret., This thesis concerns causal inference for observational longitudinal survival data. In particular, estimation of the effect a treatment has on survival, when the treatment varies over time and is subject to time-varying confounding. First, we define causal effects in terms of potential outcomes, and for the discrete-time case show how the distribution of potential outcomes can be related to observational data through the g-formula. We explain why hazard ratios cannot be interpreted causally, and show how the parameter in a Cox proportional hazards model might instead be interpreted causally as a log-survival ratio, assuming the Markov property for the hazard, and that survival status does not affect future exposure. We continue with a deeper look at the Markov assumption, and show that in the presence of unobserved frailty, it implies that the underlying distribution is not faithful to its causal graph, suggesting that the Markov assumption is fundamentally implausible from a modeling perspective. Finally, a change-of-measure framework is used to redefine causal effects, giving a definition that extends quite naturally to the continuous-time case. It is then shown how these effects can be estimated using a continuous-time version of the classic inverse probability weights, with a particularly easy special case being the effect of always treating compared to never treating. The methods are illustrated on real data from patients suffering from esophageal cancer.

BACKGROUND AND OBJECTIVE: Exposures of gallstones and treatments thereof in relation to development of cancer have not been explored before in long-term follow-up studies. Our objective was to determine whether symptomatic gallstones, cholecystectomy, or sphincterotomy were associated with development of upper gastrointestinal cancers.METHODS: This is a nationwide cohort study of persons born in Denmark 1930-1984 included from age 30 years with long-term follow-up (1977-2014). Exposures were hospital admissions with gallstones, cholecystectomy, and sphincterotomy. Time-varying covariates were included in analyses to allow the impact of exposures to change with time. Follow-up periods were 2-5 and > 5 years. Hazard ratios (HR) with 95% confidence intervals (CI) were reported.RESULTS: A total of 4,465,962 persons were followed. We found positive associations between sphincterotomy and biliary (>5 years HR 4.34, CI [2.17-8.70]), gallbladder (2-5 years HR 20.7, CI [8.55-50.1]), and pancreatic cancer (2-5 years HR 3.68, CI [2.09-6.49]). Cholecystectomy was positively associated with duodenal (2-5 years HR 2.94, CI [1.31-6.58]) and small bowel cancer (2-5 years HR 2.75, CI [1.56-4.87]). Inverse associations were seen for cholecystectomy and biliary (>5 years HR 0.60, CI [0.41-0.87]), pancreatic (>5 years HR 0.45 CI [0.35-0.57]), esophageal (>5 years HR 0.57, CI [0.43-0.74]), and gastric cancer (>5 years HR 0.68, CI [0.55-0.86]) and for gallstones and pancreatic cancer (>5 years HR 0.66, CI [0.47-0.93]). Gallstones were positively associated with gallbladder (>5 years HR 3.51, CI [2.02-6.10]) and small bowel cancer (2-5 years HR 3.21, CI [1.60-6.45]).CONCLUSIONS: A positive association between sphincterotomy and biliary cancer was identified. Cholecystectomy seems to be inversely associated with biliary, pancreatic, esophageal, and gastric cancer. Associations should be explored in similar large cohorts.

This article surveys results concerning the interpretation of the Cox hazard ratio in connection to causality in a randomized study with a time-To-event response. The Cox model is assumed to be correctly specified, and we investigate whether the typical end product of such an analysis, the estimated hazard ratio, has a causal interpretation as a hazard ratio. It has been pointed out that this is not possible due to selection. We provide more insight into the interpretation of hazard ratios and differences, investigating what can be learned about a treatment effect from the hazard ratio approaching unity after a certain period of time. The conclusion is that the Cox hazard ratio is not causally interpretable as a hazard ratio unless there is no treatment effect or an untestable and unrealistic assumption holds. We give a hazard ratio that has a causal interpretation and study its relationship to the Cox hazard ratio.

BACKGROUND: Folate prevents neural tube defects and may play a role in some neurodevelopmental disorders.OBJECTIVE(S): To investigate whether higher intakes of periconceptional or midpregnancy folate as recommended were associated with a reduced risk of offspring cerebral palsy (CP).METHODS: We included participants from the Nordic collaboration cohort consisting of mother-child dyads in the Danish National Birth Cohort and the Norwegian Mother, Father and Child Cohort Study (MOBAND-CP). A total of 190 989 live-born children surviving the first year of life were included. Missing covariate data were multiply imputed. Our exposures were defined as any or no folic acid supplementation in gestational weeks (GWs) -4 to 8 (periconceptional), GWs 9 to 12, and -4 to 12, and supplemental, dietary, and total folate during midpregnancy (GWs 22 to 25). CP overall and the unilateral and bilateral spastic subtypes, as well as CP with low or moderate/high gross motor function impairment were our outcomes of interest.RESULTS: Periconceptional folic acid supplementation was not associated with CP (adjusted odds ratio (aOR) 1.02; 95% confidence intervals (CI) 0.82, 1.28). However, supplementation in GWs 9 to 12 was associated with a reduced risk of CP (aOR 0.74; 0.57, 0.96), and inverse associations were indicated for both the unilateral (aOR 0.68; 0.46, 1.02) and bilateral (aOR 0.70; 0.49, 1.02) spastic subtypes, although not statistically significant. Supplemental or dietary folate in midpregnancy alone were not associated with CP. Strong inverse associations were observed with low gross motor function impairment (aOR 0.49; 0.29, 0.83), while for unilateral CP the aOR was 0.63 (0.34, 1.22) for intakes of ≥ 500 compared to ≤ 199 dietary folate equivalents/day during midpregnancy.CONCLUSIONS: Our findings suggested that folate intakes in GWs 9 to 12 and midpregnancy were associated with a lower risk of CP, while no association was observed for periconc