We define dynamic treatment regimes and associated potential outcomes for data described by marked point processes (MPPs). These definitions motivate MPP analogues of the commonly used consistency, exchangeability, and positivity conditions that are sufficient for identifying effects in MPP data structures. The conditions are formulated based on martingale theory, which allows us to derive explicit identifying assumptions for data described by stochastic processes. The definitions and conditions align with well-established discrete-time results in important special cases. Thus, this work bridges the large literatures on survival (event history) analysis with counting processes in continuous time and causal inference with variables in discrete-time. After formulating a set of identification conditions, we derive and characterize marginal g-formulas. The g-formulas are generally different from those studied in related works, though they coincide in important special cases. We relate our findings to previous work on causal inference with (counting) processes, the classical survival literature, and the discrete-time causal inference literature.

We derive augmented inverse probability weighted estimators for occupation probabilities of multistate models under two levels of coarsening; right-censoring and baseline exposure. The key exchangeability assumption for identification is coarsening at random, while allowing for time-varying confounders, but not requiring Markov properties. Using existing techniques from causal inference and missing data literature, the derived estimators have highly desirable robustness and efficiency properties. These properties are demonstrated through both theoretical results, and a simulation study.

We consider continuous-time survival or more general event-history settings, where the aim is to infer the causal effect of a time-dependent treatment process. This is formalised as the effect on the outcome event of a (possibly hypothetical) intervention on the intensity of the treatment process, i.e. a stochastic intervention. To establish whether valid inference about the interventional situation can be drawn from typical observational, i.e. non-experimental, data we propose graphical rules indicating whether the observed information is sufficient to identify the desired causal effect by suitable re-weighting. In analogy to the well-known causal directed acyclic graphs, the corresponding dynamic graphs combine causal semantics with local independence models for multivariate counting processes. Importantly, we highlight that causal inference from censored data requires structural assumptions on the censoring process beyond the usual independent censoring assumption, which can be represented and verified graphically. Our results establish general non-parametric identifiability and do not rely on particular survival models. We illustrate our proposal with a data example on HPV-testing for cervical cancer screening, where the desired effect is estimated by re-weighted cumulative incidence curves.

BACKGROUND Non-ST-segment elevation acute coronary syndrome (NSTE-ACS) is a frequent cause of hospital admission in older people, but clinical trials targeting this population are scarce. OBJECTIVES The After Eighty Study assessed the effect of an invasive vs a conservative treatment strategy in a very old population with NSTE-ACS. METHODS Between 2010 and 2014, the investigators randomized 457 patients with NSTE-ACS aged center dot 80 years (mean age 85 years) to an invasive strategy involving early coronary angiography with immediate evaluation for revasculari-zation and optimal medical therapy or to a conservative strategy (ie, optimal medical therapy). The primary endpoint was a composite of myocardial infarction, need for urgent revascularization, stroke, and death. The long-term outcomes are presented. RESULTS After a median follow up of 5.3 years, the invasive strategy was superior to the conservative strategy in the reduction of the primary endpoint (incidence rate ratio: 0.76; 95% CI: 0.63-0.93; P = 0.0057). The invasive strategy demonstrated a significant gain in event-free survival of 276 days (95% CI: 151-400 days; P = 0.0001) at 5 years and 337 days (95% CI: 123-550 days; P = 0.0001) at 10 years. These results were consistent across subgroups of patients with respect to major cardiovascular prognostic factors. CONCLUSIONS In patients aged center dot 80 years with NSTE-ACS, the invasive strategy was superior to the conservative strategy in the reduction of composite events and demonstrated a significant gain in event-free survival. (The After Eighty Study: a randomized controlled trial; NCT01255540) (J Am Coll Cardiol 2023;82:2021-2030) (c) 2023 The Authors. Published by Elsevier on behalf of the American College of Cardiology Foundation. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Patients with end-stage kidney disease can expect to wait for several years before they receive a transplant, all the while their health deteriorates. How would the survival change if we managed to reduce these waiting times? To provide an answer, we present a continuous-time marginal structural model (MSM) of hypothetical scenarios in which the time until treatment is changed. In these scenarios, the treatment process is defined on a hypothetical time scale where time passes at a different rate compared to the time actually observed. Changing the time of the treatment process corresponds to changing the joint probability distribution, thereby making it possible to identify and estimate hypothetical parameters from observational data using previously developed methodology. We demonstrate this treatment-accelerated MSM using observational data from a Norwegian cohort of elderly patients with kidney failure. This model can potentially be useful to health authorities looking to assess the impacts of reducing the waiting times for organ transplantation in a given patient population.

Background. Kidney transplantation (KT) is considered the best treatment for end-stage kidney disease (ESKD). In the increasing elderly ESKD population, KT should be reserved for carefully selected candidates who are expected to experience favorable outcomes. We aimed to prospectively evaluate pretransplant recipient factors that may predict patient survival and can eventually guide therapeutic decisions in elderly with ESKD. Methods. Recipient factors were evaluated in KT candidates aged ≥65 y. Comorbidity was assessed at waitlisting according to the Liu comorbidity index (LCI). Health-related quality of life outcomes were measured using the Kidney Disease Quality of Life Short Form, version 1.3. The Cox proportional hazard regression was used to evaluate predictors of patient survival. Results. We included 192 recipients, with a mean age of 72.1 (4.1) y, who were transplanted with kidneys from deceased brain-dead donors. During a median observation period of 4.6 (3.2–6.3) y, 66 recipients died. Elevated LCI consistently predicted poor patient survival. In recipients with LCI ≥4, dialysis >2 y comprised a 2.5-fold increase in mortality risk compared with recipients on dialysis ≤2 y. Self-reported pretransplant physical function was also proven to be a significant positive predictor of survival. Conclusion. The implementation of LCI and a physical function score during the evaluation of older kidney transplant candidates may improve the selection and thereby optimize posttransplant outcomes.

ObjectivesHead trauma may cause dislodgement of otoconia and development of benign paroxysmal positional vertigo (BPPV). The risk of developing BPPV is expected to be highest shortly after the trauma, then decrease and approach the risk seen in the general population. The aim of this study was to estimate the risk‐time curve of BPPV development after head trauma.Study DesignProspective observational study.MethodsPatients with minimal, mild, or moderate head trauma treated at the Department of Neurosurgery or the Department of Orthopedic Emergency at Oslo University Hospital, were interviewed and examined for BPPV using the Dix‐Hallpike and supine roll maneuvers. BPPV was diagnosed according to the International diagnostic criteria of the Bárány Society. Telephone interviews were conducted at 2, 6, and 12 weeks after the first examination.ResultsOut of 117 patients, 21% developed traumatic BPPV within 3 months after the trauma. The corresponding numbers were 12% with minimal trauma, 24% with mild, and 40% with moderate trauma. The difference in prevalence between the groups was significant (P = .018). During the first 4 weeks after the trauma, it was observed 20, 3, 0, and 1 BPPV onsets, respectively. No BPPV cases were seen for the remainder of the 3‐month follow‐up.ConclusionThe risk of developing BPPV after minimal‐to‐moderate head trauma is considerable and related to trauma severity. Most cases occur within few days after the trauma, but any BPPV occurring within the first 2 weeks after head trauma are likely due to the traumatic event.Level of Evidence3 Laryngoscope, 132:443–448, 2022

Summary We present a method for estimating several prognosis parameters for cancer survivors. The method utilizes the fact that these parameters solve differential equations driven by cumulative hazards. By expressing the parameters as solutions to differential equations, we develop generic estimators that are easy to implement with standard statistical software. We explicitly describe the estimators for prognosis parameters that are often employed in practice, but also for parameters that, to our knowledge, have not been used to evaluate prognosis. We then apply these parameters to assess the prognosis of five common cancers in Norway.

According to the revised World Health Organization (WHO) Classification of Tumors of the Central Nervous System (CNS) of 2016, oligodendrogliomas are now defined primarily by a specific molecular signature (presence of IDH mutation and 1p19q codeletion). The purpose of our study was to assess the value of dynamic susceptibility contrast MR imaging (DSC-MRI) and diffusion-weighted imaging (DWI) to characterize oligodendrogliomas and to distinguish them from astrocytomas. Seventy-one adult patients with untreated WHO grade II and grade III diffuse infiltrating gliomas and known 1p/19q codeletion status were retrospectively identified and analyzed using relative cerebral blood volume (rCBV) and apparent diffusion coefficient (ADC) maps based on whole-tumor volume histograms. The Mann-Whitney U test and logistic regression were used to assess the ability of rCBV and ADC to differentiate between oligodendrogliomas and astrocytomas both independently, but also related to the WHO grade. Prediction performance was evaluated in leave-one-out cross-validation (LOOCV). Oligodendrogliomas showed significantly higher microvascularity (higher rCBVMean ≥ 0.80, p = 0.013) and higher vascular heterogeneity (lower rCBVPeak ≤ 0.044, p = 0.015) than astrocytomas. Diffuse gliomas with higher cellular density (lower ADCMean ≤ 1094 × 10−6 mm2/s, p = 0.009) were more likely to be oligodendrogliomas than astrocytomas. Histogram analysis of rCBV and ADC was able to differentiate between diffuse astrocytomas (WHO grade II) and anaplastic astrocytomas (WHO grade III). Histogram-derived rCBV and ADC parameter may be used as biomarkers for identification of oligodendrogliomas and may help characterize diffuse gliomas based upon their genetic characteristics.

The conventional nonparametric tests in survival analysis, such as the log-rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. Finally, we use our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomised controlled trial.

Methods to assess sufficient cause interactions are well developed for binary outcomes. We extend these methods to handle time-to-event outcomes, which occur frequently in medicine and epidemiology. Based on theory for marginal structural models in continuous time, we show how to assess sufficient cause interaction nonparametrically, allowing for censoring and competing risks. We apply the method to study interaction between intensive blood pressure therapy and statin treatment on all-cause mortality.

Marginal structural models (MSMs) allow for causal analysis of longitudinal data. The standard MSM is based on discrete time models, but the continuous-time MSM is a conceptually appealing alternative for survival analysis. In applied analyses, it is often assumed that the theoretical treatment weights are known, but these weights are usually unknown and must be estimated from the data. Here we provide a sufficient condition for continuous-time MSM to be consistent even when the weights are estimated, and we show how additive hazard models can be used to estimate such weights. Our results suggest that continuous-time weights perform better than IPTW when the underlying process is continuous. Furthermore, we may wish to transform effect estimates of hazards to other scales that are easier to interpret causally. We show that a general transformation strategy can be used on weighted cumulative hazard estimates to obtain a range of other parameters in survival analysis, and explain how this strategy can be applied on data using our R packages ahw and transform.hazards.

OBJECTIVE:We conducted a randomized, controlled, noninferiority trial to investigate if intravenous, multimodal, patient-controlled analgesia (IV-PCA) could be noninferior to multimodal thoracic epidural analgesia (TEA) in patients undergoing open liver surgery.SUMMARY BACKGROUND DATA:The increasing use of minimally invasive techniques and fast track protocols have questioned the position of epidural analgesia as the optimal method of pain management after abdominal surgery.METHODS:Patients operated with open liver resection between February 2012 and February 2016 were randomly assigned to receive either IV-PCA enhanced with ketorolac/diclofenac (IV-PCA, n = 66) or TEA (n = 77) within an enhanced recovery after surgery protocol. Noninferiority would be declared if the mean pain score on the numeric rating scale (NRS) for postoperative days (PODs) 0 to 5 in the IV-PCA group was no worse than the mean pain score in the TEA group by a margin of <1 point on an 11-point scale (0-10).RESULTS:The primary endpoint, mean NRS pain score was 1.7 in the IV-PCA group and 1.6 in the TEA group, establishing noninferiority. Pain scores were lower in the TEA group on PODs 0 and 1, but higher or equal on PODs 2 and 5. Postoperative hospital stay was significantly shorter for patients in the IV-PCA group (74 vs 104 h, P < 0.001). The total opioid consumption during the first 3 days was significantly lower in the IV-PCA group.CONCLUSIONS:IV-PCA was noninferior to TEA for the treatment of postoperative pain in patients undergoing open liver resection.

We discuss causal mediation analyses for survival data and propose a new approach based on the additive hazards model. The emphasis is on a dynamic point of view, that is, understanding how the direct and indirect effects develop over time. Hence, importantly, we allow for a time varying mediator. To define direct and indirect effects in such a longitudinal survival setting we take an interventional approach (Didelez, 2018) where treatment is separated into one aspect affecting the mediator and a different aspect affecting survival. In general, this leads to a version of the nonparametric g-formula (Robins, 1986). In the present paper, we demonstrate that combining the g-formula with the additive hazards model and a sequential linear model for the mediator process results in simple and interpretable expressions for direct and indirect effects in terms of relative survival as well as cumulative hazards. Our results generalize and formalize the method of dynamic path analysis (Fosen, Ferkingstad, Borgan, & Aalen, 2006; Strohmaier et al., 2015). An application to data from a clinical trial on blood pressure medication is given.

When comparing time varying treatments in a non-randomized setting, one must often correct for time-dependent confounders that influence treatment choice over time and that are themselves influenced by treatment. We present a new two-step procedure, based on additive hazard regression and linear increments models, for handling such confounding when estimating average treatment effects on the treated. The approach can also be used for mediation analysis. The method is applied to data from the Swiss HIV Cohort Study, estimating the effect of antiretroviral treatment on time to acquired immune deficiency syndrome or death. Compared with other methods for estimating the average treatment effects on the treated the method proposed is easy to implement by using available software packages in R.

The concept of causality is naturally related to processes developing over time. Central ideas of causal inference like time-dependent confounding (feedback) and mediation should be viewed as dynamic concepts. We shall study these concepts in the context of simple dynamic systems. Time-dependent confounding and its implications are illustrated in a Markov model. We emphasize the distinction between average treatment effect, ATE, and treatment effect of the treated, ATT. These effects could be quite different, and we discuss the relationship between them. Mediation is studied in a stochastic differential equation model. A type of natural direct and indirect effects is considered for this model. Mediation analysis of discrete measurements from such processes may give misleading results, and one needs to consider the underlying continuous process. The dynamic and time-continuous view of causality and mediation is an essential feature, and more attention should be payed to the time aspect in causal inference.

In marginal structural models (MSMs), time is traditionally treated as a discrete parameter. In survival analysis on the other hand, we study processes that develop in continuous time. Therefore, Røysland (2011. A martingale approach to continuous-time marginal structural models. Bernoulli 17, 895-915) developed the continuous-time MSMs, along with continuous-time weights. The continuous-time weights are conceptually similar to the inverse probability weights that are used in discrete time MSMs. Here, we demonstrate that continuous-time MSMs may be used in practice. First, we briefly describe the causal model assumptions using counting process notation, and we suggest how causal effect estimates can be derived by calculating continuous-time weights. Then, we describe how additive hazard models can be used to find such effect estimates. Finally, we apply this strategy to compare medium to long-term differences between the two prostate cancer treatments radical prostatectomy and radiation therapy, using data from the Norwegian Cancer Registry. In contrast to the results of a naive analysis, we find that the marginal cumulative incidence of treatment failure is similar between the strategies, accounting for the competing risk of other death.

When comparing time varying treatments in a non-randomized setting, one must often correct for time-dependent confounders that influence treatment choice over time and that are themselves influenced by treatment. We present a new two-step procedure, based on additive hazard regression and linear increments models, for handling such confounding when estimating average treatment effects on the treated. The approach can also be used for mediation analysis. The method is applied to data from the Swiss HIV Cohort Study, estimating the effect of antiretroviral treatment on time to acquired immune deficiency syndrome or death. Compared with other methods for estimating the average treatment effects on the treated the method proposed is easy to implement by using available software packages in R.

Time to event outcomes are often evaluated on the hazard scale, but interpreting hazards may be difficult. Recently, there has been concern in the causal inference literature that hazards actually have a built in selection-effect that prevents simple causal interpretations. This is even a problem in randomized controlled trials, where hazard ratios have become a standard measure of treatment effects. Modeling on the hazard scale is nevertheless convenient, e.g. to adjust for covariates. Using hazards for intermediate calculations may therefore be desirable. Here, we provide a generic method for transforming hazard estimates consistently to other scales at which these built in selection effects are avoided. The method is based on differential equations, and generalize a well known relation between the Nelson-Aalen and Kaplan-Meier estimators. Using the martingale central limit theorem we also find that covariances can be estimated consistently for a large class of estimators, thus allowing for rapid calculations of confidence intervals. Hence, given cumulative hazard estimates based on e.g. Aalen's additive hazard model, we can obtain many other parameters without much more effort. We present several examples and associated estimators. Coverage and convergence speed is explored using simulations, suggesting that reliable estimates can be obtained in real-life scenarios.

Counter-intuitive associations appear frequently in epidemiology, and these results are often debated. In particular, several scenarios are characterized by a general risk factor that appears protective in particular subpopulations, for example, individuals suffering from a specific disease. However, the associations are not necessarily representing causal effects. Selection bias due to conditioning on a collider may often be involved, and causal graphs are widely used to highlight such biases. These graphs, however, are qualitative, and they do not provide information on the real life relevance of a spurious association. Quantitative estimates of such associations can be obtained from simple statistical models. In this study, we present several paradoxical associations that occur in epidemiology, and we explore these associations in a causal, frailty framework. By using frailty models, we are able to put numbers on spurious effects that often are neglected in epidemiology. We discuss several counter-intuitive findings that have been reported in real life analyses, and we present calculations that may expand the understanding of these associations. In particular, we derive novel expressions to explain the magnitude of bias in index-event studies.