03-causal-inference-bias: 1
Proximal indirect comparison
Zehao Su1, Helene Rytgaard1, Henrik Ravn2, Frank Eriksson1
1University of Copenhagen; 2Novo Nordisk
Background
We consider the problem of indirect comparison, where a treatment arm of interest is absent by design in one randomized controlled trial (RCT) but available in the other. That is, we are interested in the contrast of treatments that are not compared in head-to-head RCTs. e.g., the comparison of a new treatment and an existing treatment, when both treatments have only been studied in placebo-controlled RCTs.
Identifiability of the target RCT population average treatment effect often relies on conditional transportability assumptions. However, it is a common concern whether all relevant effect modifiers are measured and controlled for. If the treatments of interest come from RCTs which are conducted with a considerable time gap apart, there may be a drift in unmeasured social determinants of health or changes in the standard of care or that could affect the treatment effects. When there are unobserved shifted effect modifiers, transportability cannot be established by controlling for observed baseline variables.
Methods and results
Recently a family of methods called proximal causal inference has shown how appropriately selected proxies, or negative controls, may rectify confounding bias. We borrow these ideas and propose a novel method that uses proxies to tackle bias arising from shifted unobserved effect modifiers. We give a new proximal identification result based on two proxies, an adjustment proxy in both RCTs and an additional reweighting proxy in the source RCT. We propose an estimator that is doubly-robust against misspecifications of the so-called bridge functions and asymptotically normal under mild consistency of estimators for the bridge functions.
We use two placebo-controlled weight management trials conducted 5-6 years apart as a context to illustrate selection of proxies and apply our method to compare the weight loss effect of the active treatments from these trials.
Conclusion
Proximal indirect comparison may allow for treatment effect estimation via transportability in the presence of unobserved effect modifiers. The proximal indirect comparison estimator can be bias-free even when transportability of the conditional average treatment effect fails to hold conditioning on the observed data.
03-causal-inference-bias: 2
Selection bias of cause-specific hazard ratios: the impact of competing events
Mari Brathovde1,2, Morten Valberg1,2, Hein Putter3, Richard A.J. Post4
1Oslo University Hospital, Norway; 2University of Oslo, Norway; 3Leiden University Medical Center, The Netherlands; 4Erasmus Medical Center, The Netherlands
Background: Competing risks generalize standard survival analysis of a single, often composite outcome when interest lies in the different causes of the event. In the presence of heterogeneity, the complex causal interpretation of the hazard ratio for all-cause mortality is well-known and has been formalized. Yet the current recommendation in epidemiology is to use cause-specific hazard ratios when aiming to understand etiology in a competing risk setting.
Methods: In this work, we formalize how observed cause-specific hazard ratios evolve and deviate from the (conditional) causal effect of interest in the presence of heterogeneity of the hazard rate of unexposed individuals (frailty) and heterogeneity in effect (individual modification). Importantly, we do so without imposing assumptions on the baseline hazard rate or the distributions of the latent effect modifiers and frailty factors. We show that the presence of a competing event can amplify the selection bias of the all-cause mortality setting, as it introduces selection on the frailties and effect modifiers associated with both the event of interest and the competing event.
Results: We provide illustrative examples using frailties from the family of power variance function (PVF) distributions, along with categorical effect modifiers (harmful, beneficial, or neutral). The PVF family of frailties yields convenient analytical expressions for the observed cause-specific hazard ratios, enabling a clear separation of the selection bias introduced by different events. This approach allows for a straightforward evaluation of the impact of treatment effects and event prevalence on the bias using simple monotonicity principles. The numerical examples include settings with crossover of the cause-specific hazard rates between exposed and non-exposed individuals, which would not occur without competing events.
Conclusion: We show that the size and sign of the bias in the cause-specific hazard ratios depend on the prevalence of, and the treatment’s effect on, the competing event. Consequently, the cause-specific hazard ratio suffers from both selection bias inherent to all-cause mortality hazard ratios and dependence on the competing event, complicating its causal interpretation and limiting its suitability for addressing etiological questions without relying on untestable assumptions. This work highlights the importance of employing more appropriate estimands in a competing risk setting, such as marginal cumulative incidences.
03-causal-inference-bias: 3
qbaconfound: A flexible Monte Carlo probabilistic bias analysis to unmeasured confounding
Emily Kawabata, Chin Yang Shapland, Tom Palmer, David Carslake, Kate Tilling, Rachael Hughes
University of Bristol
Background: Unmeasured confounding is a persistent concern in observational studies. We can quantitatively assess the impact of unmeasured confounding using a probabilistic bias analysis (PBA). A PBA specifies the relationship between the unmeasured confounder(s), U, and study data via its bias parameters. External information about U is incorporated via prior distribution(s) placed on these bias parameters. A Bayesian PBA combines the prior distribution(s) with the data’s likelihood function whilst a Monte Carlo PBA samples the bias parameters directly from its prior distributions. Software implementations of PBAs to unmeasured confounding are scarce and mainly limited to unadjusted analyses of a binary exposure and outcome. One exception is R package unmconf (Hebdon et al 2024, BMC Med. Res. Methodol., https://doi.org/10.1186/s12874-024-02322-2) which implements a Bayesian PBA, applicable when the analysis is a generalised linear model (GLM). However, for a study with Ρ measured confounders and a single U, unmconf requires information on 3+Ρ to 6+2Ρ bias parameters, which is burdensome when validation data are unavailable.
Aim: We propose a flexible Monte Carlo PBA where the number of bias parameters is independent of the number of measured confounders. It is applicable to a GLM or survival proportional hazards model, with binary, continuous, or categorical exposure and measured confounders, allows for nonlinear and interaction terms (of exposure and measured confounders), and one or more binary or continuous unmeasured confounders.
Methods: Via simulations, we evaluate our PBA for different analyses (e.g., varying the regression model, exposure type, and with or without interactions), and different levels of dependency between the measured and unmeasured confounders. Also, we compare our Monte Carlo approach to a fully Bayesian implementation when fitting a linear or logistic regression. We repeat the simulation study for prior distributions with different levels of informativeness.
Results: Ignoring U resulted in substantially biased estimates with substantial confidence interval undercoverage (e.g., 56%). Our Monte Carlo PBA (with informative priors) results in point estimates with minimal or no bias and interval estimates with close to nominal coverage. For binary U, levels of bias are marginally higher when U is strongly correlated with the measured confounders. The performances of the Monte Carlo and Bayesian implementations are comparable except the Monte Carlo version is slightly quicker.
Conclusion: Our Monte Carlo PBA is applicable to a variety of regression-based analyses, with minimal burden to the user. It will be implemented as a Stata command and R package, qbaconfound.
03-causal-inference-bias: 4
Selection bias due to omitting interactions from inverse probability weighting
Liping Wen, Kate Tilling, Rosie Cornish, Rachael Hughes, Apostolos Gkatzionis
University of Bristol, United Kingdom
Background
The estimated causal effect of an exposure on an outcome might be biased if the analysis sample is subject to selection, e.g. due to non-random participation or dropout. Inverse probability weighting (IPW) is often used to adjust for selection bias, typically using a simple logit weighting model without interactions. However, the size of selection bias depends on the interaction between exposure and outcome in their effect on selection. This implies that it may be important to include interaction terms in the IPW model.
Methods
We compare IPW methods using a simulation study, where the estimand of interest is the causal effect of exposure on outcome. The selection mechanisms are simulated using a logit/log-additive/probit model with and without interaction terms, with either exposure, causes of exposure, or causes of outcome influencing selection. We analysed each simulated dataset by: full data analysis, complete case analysis (CCA), and four IPW methods which differ only in the weighting model used. These weighting models are either a logit or log-additive model, and either include or exclude the interaction between variables causing the selection. In a real-data application, we use data from the Understanding Society study to investigate the effect of unemployment on sleep duration, using IPW to adjust for dropout. Exposure, mediator and 6 confounders, as well as all possible two-way interactions, are included in the weighting model. Then the least absolute selection and shrinkage operator (LASSO) is used for variable selection to avoid overfitting.
Results
The simulation study shows that IPW including an interaction term gives less biased estimates than IPW without this term in all scenarios studied. Importantly, IPW using a logit model with no interaction terms often gives estimates very close to CCA. IPW including 89 interaction terms suggests that unemployment reduces sleep duration by around 23 (9, 38) minutes, compared to 27 (14, 40) minutes for IPW without interactions, and 31 (19, 43) minutes for the CCA.
Conclusion
We strongly recommend that researchers include interaction terms in weighting models to adjust for selection bias. Also, an agreement between CCA and IPW without interactions arises mathematically and so does not indicate that results are robust to selection bias.
03-causal-inference-bias: 5
External reproduction of a proxy-based causal model estimating average survival effects of sequential vs concurrent chemo-radiotherapy in stage III NSCLC
Charlie Cunniffe1, Wouter van Amsterdam2, Matthew Sperrin1, Rajesh Ranganath3, Fiona Blackhall1,4, Gareth Price1
1The University of Manchester, United Kingdom; 2University Medical Center Utrecht, Netherlands; 3New York University, USA; 4The Christie NHS Foundation Trust, United Kingdom
Background/Introduction
Randomised controlled trials (RCTs) offer the most reliable evidence for treatment decisions. However, in cancer care, frail, elderly, and disadvantaged patients are often underrepresented, causing uncertainty about optimal treatment strategies, such as whether sequential or concurrent chemo-radiotherapy yields better outcomes. Observational causal inference may supplement RCT evidence; however, confounding factors that are not directly observed remain a challenge. Using available proxy measurements to infer these variables offers a potential solution. In the cancer setting, the patient's overall fitness is an important unobserved confounder for treatment and outcome, for which proxies like “performance score” are widely available within patient records. This study reproduces a recently introduced proxy-based causal inference method to assess transportability over populations with different data structures and treatment guidelines.
Methods
This study employs proxy-based individual treatment effect modelling in cancer (PROTECT) to estimate the individual treatment effect of concurrent vs sequential chemo-radiotherapy on overall survival in 1117 routinely treated patients with stage III Non-Small Cell Lung Cancer (NSCLC) seen between 2013 and 2023. A local model was developed by adapting the PROTECT directed acyclic graph to include our selected proxies of patient fitness – performance, comorbidity, and frailty scores. While the causal effect is generally not identifiable in the presence of unobserved confounding, PROTECT assumes that the proxies are conditionally independent given the unobserved confounder and incorporates domain knowledge via functional constraints on a Bayesian latent factor model. Individual treatment effect estimates for each patient are averaged to get the population's average treatment effect (ATE) estimate, reported as a hazard ratio. We compared the ATE to standard multivariable Cox regression, the ATE from the PROTECT development study and the results of a meta-analysis of RCTs.
Results
The ATE on survival in our population is 0.92 [0.73, 1.15] in favour of concurrent chemo-radiotherapy. The standard multivariable analysis gives 0.60 [0.48,0.75]. The PROTECT development publication reports 1.01 [0.68,1.53]. The RCT meta-analysis reports a stronger effect size (0.84 [0.74,0.95]) than the causal analysis but has a younger (19% > 70 vs 43%) and fitter (50% ECOG 0 vs 27%) population than our study.
Conclusion
Our results show causal analysis yields more credible ATEs than standard methods. RCT inclusion criteria explain differences from meta-analysis ATEs. Repeated analysis in two separate populations yielded comparable results, implying a robust estimation of the ATE. PROTECT is a promising new method that can be applied more broadly in cancer and other settings.
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