Els Goetghebeur

Introduction: As patient-reported outcomes (PROs) are increasingly used in the evaluation of medical treatments, it is important that PROs are carefully analyzed and interpreted. This may be challenging due to substantial missing values. The missingness in PROs is often closely related to patients’ disease status. In that case, using observed information about intercurrent events (ICEs) such as disease progression and death will improve the handling of missing PRO data. Therefore, the aim of this study was to develop imputation models for repeated PRO measurements that leverage information about ICEs. Methods: We assumed a setting in which missing PRO measurements are missing at random given observed measurements, as well as the occurrence and timing of ICEs, and potentially other (baseline or time-varying) covariates. We then showed how these missingness assumptions can be translated into concrete imputation models that also account for a longitudinal data structure. The resulting models were applied to impute anonymized PRO data from a single-arm clinical trial in patients with advanced lung cancer. Results: In our trial example, accounting for death and other ICEs in the imputation of missing data led to lower estimated mean health-related quality of life (while alive) compared to an available case analysis and a naive linear mixed model imputation. Conclusion: Information about the timing and occurrence of ICEs contribute to a more plausible handling of missing PRO data. To account for ICE information when handling missing PROs, the missing data model should be separated from the analysis model.

Recently, it has become common for applied works to combine commonly used survival analysis modeling methods, such as the multivariable Cox model and propensity score weighting, with the intention of forming a doubly robust estimator of an exposure effect hazard ratio that is unbiased in large samples when either the Cox model or the propensity score model is correctly specified. This combination does not, in general, produce a doubly robust estimator, even after regression standardization, when there is truly a causal effect. We demonstrate via simulation this lack of double robustness for the semiparametric Cox model, the Weibull proportional hazards model, and a simple proportional hazards flexible parametric model, with both the latter models fit via maximum likelihood. We provide a novel proof that the combination of propensity score weighting and a proportional hazards survival model, fit either via full or partial likelihood, is consistent under the null of no causal effect of the exposure on the outcome under particular censoring mechanisms if either the propensity score or the outcome model is correctly specified and contains all confounders. Given our results suggesting that double robustness only exists under the null, we outline 2 simple alternative estimators that are doubly robust for the survival difference at a given time point (in the above sense), provided the censoring mechanism can be correctly modeled, and one doubly robust method of estimation for the full survival curve. We provide R code to use these estimators for estimation and inference in the supporting information.

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.

Long-term register data offer unique opportunities to explore causal effects of treatments on time-to-event outcomes, in well-characterized populations with minimum loss of follow-up. However, the structure of the data may pose methodological challenges. Motivated by the Swedish Renal Registry and estimation of survival differences for renal replacement therapies, we focus on the particular case when an important confounder is not recorded in the early period of the register, so that the entry date to the register deterministically predicts confounder missingness. In addition, an evolving composition of the treatment arms populations, and suspected improved survival outcomes in later periods lead to informative administrative censoring, unless the entry date is appropriately accounted for. We investigate different consequences of these issues on causal effect estimation following multiple imputation of the missing covariate data. We analyse the performance of different combinations of imputation models and estimation methods for the population average survival. We further evaluate the sensitivity of our results to the nature of censoring and misspecification of fitted models. We find that an imputation model including the cumulative baseline hazard, event indicator, covariates and interactions between the cumulative baseline hazard and covariates, followed by regression standardization, leads to the best estimation results overall, in simulations. Standardization has two advantages over inverse probability of treatment weighting here: it can directly account for the informative censoring by including the entry date as a covariate in the outcome model, and allows for straightforward variance computation using readily available software.

When drawing causal inference from observed data, failure time outcomes present additional challenges of censoring often combined with other missing data patterns. In this article, we follow incident cases of end‐stage renal disease to examine the effect on all‐cause mortality of starting treatment with transplant, so‐called pre‐emptive kidney transplantation, vs starting with dialysis possibly followed by delayed transplantation. The question is relatively simple: which start‐off treatment is expected to bring the best survival for a target population? To address it, we emulate a target trial drawing on the long term Swedish Renal Registry, where a growing common set of baseline covariates was measured nationwide. Several lessons are learned which pertain to long term disease registers more generally. With characteristics of cases and versions of treatment evolving over time, informative censoring is already introduced in unadjusted Kaplan‐Meier curves. This leads to misrepresented survival chances in observed treatment groups. The resulting biased treatment association may be aggravated upon implementing IPW for treatment. Aware of additional challenges, we further recall how similar studies to date have selected patients into treatment groups based on events occurring post treatment initiation. Our study reveals the dramatic impact of resulting immortal time bias combined with other typical features of long‐term incident disease registers, including missing covariates during the early phases of the register. We discuss feasible ways of accommodating these features when targeting relevant estimands, and demonstrate how more than one causal question can be answered relying on the no unmeasured baseline confounders assumption.

Background: Polygenic risk scores (PRS) could potentially improve breast cancer screening recommendations. Before a PRS can be considered for implementation, it needs rigorous evaluation, using performance measures that can inform about its future clinical value. Objectives: To evaluate the prognostic performance of a regression model with a previously developed, prevalence-based PRS and age as predictors for breast cancer incidence in women from the Estonian biobank (EstBB) cohort; to compare it to the performance of a model including age only. Methods: We analyzed data on 30,312 women from the EstBB cohort. They entered the cohort between 2002 and 2011, were between 20 and 89 years, without a history of breast cancer, and with full 5-year follow-up by 2015. We examined PRS and other potential risk factors as possible predictors in Cox regression models for breast cancer incidence. With 10-fold cross-validation we estimated 3- and 5-year breast cancer incidence predicted by age alone and by PRS plus age, fitting models on 90% of the data. Calibration, discrimination, and reclassification were calculated on the left-out folds to express prognostic performance. Results: A total of 101 (3.33‰) and 185 (6.1‰) incident breast cancers were observed within 3 and 5 years, respectively. For women in a defined screening age of 50–62 years, the ratio of observed vs PRS-age modelled 3-year incidence was 0.86 for women in the 75–85% PRS-group, 1.34 for the 85–95% PRS-group, and 1.41 for the top 5% PRS-group. For 5-year incidence, this was respectively 0.94, 1.15, and 1.08. Yet the number of breast cancer events was relatively low in each PRS-subgroup. For all women, the model’s AUC was 0.720 (95% CI: 0.675–0.765) for 3-year and 0.704 (95% CI: 0.670–0.737) for 5-year follow-up, respectively, just 0.022 and 0.023 higher than for the model with age alone. Using a 1% risk prediction threshold, the 3-year NRI for the PRS-age model was 0.09, and 0.05 for 5 years. Conclusion: The model including PRS had modest incremental performance over one based on age only. A larger, independent study is needed to assess whether and how the PRS can meaningfully contribute to age, for developing more efficient screening strategies.

Numerous tutorials and research papers focus on methods in either survival analysis or causal inference, leaving common complications in medical studies unaddressed. In practice one must handle problems jointly, without the luxury of ignoring essential features of the data structure. In this paper, we follow incident cases of end-stage renal disease and examine the effect on all-cause mortality of starting treatment with transplant, so-called pre-emptive kidney transplantation, versus dialysis. The question is relatively simple: which treatment start is expected to bring the best survival for a target population? To address the question, we emulate a target trial drawing on the Swedish Renal Registry to estimate a causal effect on survival curves. Aware of important challenges, we see how previous studies have selected patients into treatment groups based on events occurring post treatment initiation. Our study reveals the dramatic impact of resulting immortal time bias and other typical features of long term incident disease registries, including: missing or mismeasured covariates during (the early) phases of the register, varying risk profile of patients entering treatment groups over calendar time and changes in risk as care improves over the years. With characteristics of cases and versions of treatment evolving over time, informative censoring is introduced in unadjusted Kaplan-Meier curves and also their IPW version is no longer valid. Here we discuss feasible ways of handling these features and answer different research questions relying on the no unmeasured baseline confounders assumption.