
==== Front
JCO Clin Cancer Inform
JCO Clin Cancer Inform
cci
CCI
JCO Clinical Cancer Informatics
2473-4276
Wolters Kluwer Health

38913964
CCI.23.00262
10.1200/CCI.23.00262
Statistics in Oncology
Clarifying Causal Effects of Interest and Underlying Assumptions in Randomized and Nonrandomized Clinical Trials in Oncology Using Directed Acyclic Graphs and Single-World Intervention Graphs
https://orcid.org/0000-0001-6817-5235
Tanaka Shiro PhD 1
Muramatsu Yuriko MMedSc 1
https://orcid.org/0000-0001-9614-8103
Inoue Kosuke PhD 2 3
1 Department of Clinical Biostatistics, Graduate School of Medicine, Kyoto University, Kyoto, Japan
2 Department of Social Epidemiology, Graduate School of Medicine, School of Public Health, Kyoto University, Kyoto, Japan
3 Hakubi Center, Kyoto University, Kyoto, Japan
Shiro Tanaka, PhD; e-mail: tanaka.shiro.8n@kyoto-u.ac.jp.
2024
24 6 2024
24 6 2024
8 1 e230026213 12 2023
10 3 2024
15 4 2024
© 2024 by American Society of Clinical Oncology
2024
American Society of Clinical Oncology
https://creativecommons.org/licenses/by-nc-nd/4.0/ Creative Commons Attribution Non-Commercial No Derivatives 4.0 License: https://creativecommons.org/licenses/by-nc-nd/4.0/

Recent clinical trials in oncology have used increasingly complex methodologies, such as causal inference methods for intercurrent events, external control, and covariate adjustment, posing challenges in clarifying the estimand and underlying assumptions. This article proposes expressing causal structures using graphical tools—directed acyclic graphs (DAGs) and single-world intervention graphs (SWIGs)—in the planning phase of a clinical trial. It presents five rules for selecting a sufficient set of adjustment variables on the basis of a diagram representing the clinical trial, along with three case studies of randomized and single-arm trials and a brief tutorial on DAG and SWIG. Through the case studies, DAGs appear effective in clarifying assumptions for identifying causal effects, although SWIGs should complement DAGs due to their limitations in the presence of intercurrent events in oncology research.

OPEN-ACCESSTRUE
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pmcINTRODUCTION

One of the key principles of clinical trials is to establish the statistical analysis plan in advance, specifying the causal estimand (ie, the causal effect of interest) and the underlying assumptions for statistical inference. Recent clinical trials in oncology have used increasingly complex methodologies, posing challenges in adhering to such fundamental principles.1

As motivating examples, we will consider three case studies.2-4 The first study, a randomized phase III trial of letrozole for early breast cancer, encountered a situation where one quarter of the patients in the tamoxifen group switched to letrozole after its approval.2 To address selective crossover, the trial conducted four secondary analyses of overall survival (OS) and reported inconsistent conclusions arising from different estimands, such as intention-to-treat analysis and per-protocol analysis.2,5,6 The second study faced challenges related to salvage intervention.2 Although this randomized phase II trial on neuroblastoma did not reveal any significant difference in OS between the TOPO and TOPO/CTX groups, the latter exhibited a higher remission rate, with three times as many patients undergoing off-protocol autologous stem-cell transplantation (ASCT). In response to these challenges, advanced causal inference approaches, such as marginal structural models, to estimate causal effects under hypothetical interventions on intercurrent events were used.3,6 Another type of complexity arises in external controlled trials. In the phase II trial of chimeric antigen receptor-T (CAR-T) cell therapy using ciltacabtagene autoleucel for relapsed or refractory multiple myeloma, a comparison with an external control obtained from another trial of idecabtagene vicleucel prompted criticism not only on the observational nature of analysis but also on the initial OS results as being premature, leading to an updated analysis on the basis of long-term follow-up data.4,7 In these situations, covariates must be appropriately selected to minimize bias, although regulatory and health technology assessment agencies emphasize prespecifying covariates in the protocol.8-11

Recent epidemiological studies have increasingly used graphical tools for causal inference.12 Directed acyclic graphs (DAGs) are valuable in visualizing relationships among variables and representing the underlying assumptions intuitively (see Lipsky and Greenland13 for commentary). For example, informative censoring is a serious issue in clinical trials of advanced diseases,14 but DAGs can examine the potential of selection bias.15 In the context of external controlled trials, DAGs can help to identify confounders in the planning phase of the study.16 The use of external controls is seen not only in single-arm trials but also in randomized controlled trials (RCT) in molecularly targeted subpopulations.17 Single-world intervention graphs (SWIGs) are transformations of DAGs that introduce hypothetical interventions and nodes representing potential outcomes into the causal diagram through node-splitting.18,19 When using advanced causal modeling,20 SWIGs allow us to address assumptions related to time-dependent confounding and to make the estimand explicit.21,22

The aim of this research therefore was to streamline the understanding of typical causal structures in both randomized and nonrandomized clinical trials in oncology, presenting concise guidelines for the effective use of DAGs and SWIGs in these settings. The guidelines are particularly helpful for covariate selection, and its application is illustrated through the case studies.

METHODS

Concepts of DAG and SWIG

In a DAG, any actual variables representing a phenomenon or a measurement in the causal structure are symbolized by a node. Given a single DAG and a specific set of hypothetical interventions, SWIGs represent not only actual variables but also potential outcomes through node-splitting (Data Supplement, Appendix S1).18 When two nodes in a DAG or SWIG, A and B, are directly linked with a causal relationship from A to B, they are connected by an arrow, representing A→B. An important assumption shared by both DAGs and SWIGs is the necessity to identify all phenomena and measurements involved in the causal structure. To assess the variables requiring data collection to minimize bias, it is imperative to construct either of these graphs during the planning phase. In such instances, comprehensive knowledge of the research field and the research design characteristics forms the primary basis for the graph. See also Glossary in Table 1 for definitions of other technical terms.

TABLE 1. Five Rules for Selecting a Sufficient Set of Adjustment Variables on the Basis of DAG and SWIG in Clinical Trials

Rules	
 1. The primary focus should be on the total effect as the most relevant measure of treatment efficacy, rather than on a path-specific effect. While other estimands, effects of treatment and hypothetical interventions on intercurrent events, for instance, can be considered, it is recommended to provide a clear definition using SWIGs if such estimands differ from the total effect	
 2. Caution is advised when adjusting for mediators, as this may introduce bias in the estimation of the total effect. In randomized and nonrandomized clinical trial, it is recommended to incorporate prognostic factors other than mediators in covariate adjustment	
 3. Adjustment for at least one node on every backdoor path is imperative for effective covariate adjustment, given the potential for confounding when some backdoor paths are unblocked	
 4. Paths containing one or more colliders are considered blocked. Additional adjustment at colliders might unblock the path, thereby introducing bias due to confounding or selection	
 5. It is essential to note that even if bias attributed to confounding is minimal, additional adjusting for an instrumental variable might paradoxically amplify the degree of bias	
Glossary		
 Prognostic factor	A node that has an outgoing arrow into outcome (eg, Prognostic factor→Outcome)	
 Mediator	A node on a directed path from exposure to outcome (eg, Treatment→Mediator→Outcome)	
 Collider	A node on an undirected path between exposure and outcome at which the arrows intersect (eg, Treatment→Collider←Outcome)	
 Instrumental variable	A node that is not associated with any unmeasured confounders and has an outgoing arrow to exposure but does not have an outgoing arrow to outcome other than the outgoing arrow to exposure (eg, Instrumental variable→Treatment→Outcome)	
 Backdoor path	An undirected path that traces the arrow backward from exposure to outcome	
 Block	A path that carries a causal effect is designated as open, while a path devoid of such an effect is termed blocked. If there is no collider on a path, the path is blocked by conditioning, an operation that fixes the value of a node on the path	
Abbreviations: DAG, directed acyclic graph; SWIG, single-world intervention graph.

Covariate Selection for Adjustment on the Basis of DAG

A concern in a clinical trial is bias, such as confounding and informative censoring, and there must be a variable that is causing it. By representing the causal structure among variables in terms of DAGs, we can not only determine whether a node causes bias but also identify nodes that should be adjusted to eliminate the bias.

Suppose a non-RCT where the main focus lies in evaluating the total effect of an exposure on an outcome. Given a DAG that correctly reflects the trial, a challenge arises when an alternative undirected path, other than the legitimate directed paths, might also contribute to the apparent association between the exposure and the outcome. In this context, if nodes on the path that cause bias can be identified, it is possible to collect data to minimize bias due to confounding. Among the undirected paths, particular attention should be given to the paths that trace the arrow backward from the focal exposure to the outcome. This is referred to as the backdoor path (Glossary in Table 1). Identifying and addressing all backdoor paths is crucial as nodes on the backdoor paths constitute a sufficient set of covariates to be adjusted.23

Once the causal structure of a clinical trial is graphically expressed, a sufficient set of covariates to be adjusted can be selected according to the five rules in Table 1. A tutorial on DAGs and SWIGs is provided in the Data Supplement (Appendix S1). Refer to Greenland et al (1999), VanderWeele (2019), and Richardson and Robins (2013) for excellent introductions to DAGs and SWIGs.16,18,24

Clarifying Causal Effects of Interest Using SWIG

Causal effects are formally defined by introducing potential outcomes under interventions (eg, experimental and control treatments), but DAGs do not allow the inclusion of nodes representing potential outcomes. SWIGs provide a visual representation of causal effects to make the estimand of the trial explicit. In other words, the key distinction between two types of graphs, DAGs and SWIGs, lies in the former's exclusive focus on phenomena and measurements in the real world, whereas the latter incorporates potential outcomes as well. Indeed, given a single DAG and hypothetical interventions or, more technically, a specific set of contrasts of potential outcomes, it becomes feasible to construct SWIGs on the basis of these inputs.18 The terminology and usage of DAGs are therefore also applicable to SWIGs.

As discussed in the next section, intercurrent events such as censoring, progression of disease, and salvage intervention can occur during a clinical trial in oncology and can affect the interpretation of trial results. SWIGs are particularly useful to clarify how intercurrent events are handled in statistical analysis, typically when advanced causal modeling is applied,20 and to effectively communicate estimands of the trial.21

APPLICATIONS OF DAG AND SWIG TO CLINICAL TRIALS

Total Effect and Path-Specific Effects

Although the fact that two nodes are connected by arrows or directed paths indicates the existence of causal effects, this is solely qualitative. To establish quantitative definitions of causal effects, potential outcome models are typically used.

A potential outcome is a counterfactual variable, as illustrated in the numerical example below and in Figure 1. Suppose that the standard treatment of a patient in the advanced stage leads to a progression of the disease 4 months after the start of the treatment. Then, the patient dies 11 months after the progression. On the other hand, if the same patient is given the experimental treatment, the time to progression is 8 months, and post-progression survival (PPS) is also 11 months. Figure 1A depicts this scenario, illustrating the presence of treatment effect on time to progression by the path Treatment→Progression→Death. Furthermore, there is no direct arrow from treatment to death, which corresponds to the fact that the 4-month expansion in OS is mediated only by the delay in progression. In other words, Progression is the mediator of the treatment effect (Glossary in Table 1).

FIG 1. Effects on time to progression and post-progression survival represented by DAGs. (A) Time to progression under the standard and experimental treatments is 4 and 8 months, respectively. PPS is 11 months regardless of the treatment. (B) Time to progression under the standard and experimental treatments is 4 and 8 months, respectively. PPS is 11 months under the standard treatment and 7 months under the experimental treatment. DAGs, directed acyclic graphs; PPS, post-progression survival.

Alternatively, suppose that PPS under the experimental treatment is 7 months and other values remain the same (Fig 1B). The progression of the disease could be delayed by 4 months by substituting the experimental treatment with the standard treatment, which is the effect corresponding to the path Treatment→Progression→Death. This effect is called a path-specific effect. On the other hand, OS is 15 months under either of the treatments. The quantity that reflects the effects of all paths is called the total effect. In Figure 1B, the total effect is zero, and the difference of 4 months between the total effect and the path-specific effect corresponds to the direct path Treatment→Death not through Progression.

In clinical trials of advanced disease, the ongoing debate about selecting PFS or OS as the primary end point is multifaceted.14,25,26 The first point of contention is whether PFS can be considered a clinical end point on its own. If PFS itself is not the primary focus, the key question is whether PFS serves as a surrogate end point for OS, which is an uncontroversially acceptable clinical end point. If the total effect approximately equals the indirect effect through progression as indicated in Figure 1A, then PFS could be regarded as a surrogate end point for OS. However, if it is not plausible that the direct effect of treatment unmediated through delayed progression is zero, prioritizing OS as the primary end point becomes reasonable, as the effect on PFS reflects solely the path Treatment→Progression→Death. Therefore, the primary focus should be on the total effect on OS, rather than on a path-specific effect, and any adjustment for PFS is not necessary for this estimand (Rules 1 and 2 in Table 1).

Indeed, the assumption in Figure 1A that the PPS remains equal between the standard treatment and the experimental treatment is unrealistic. In most advanced settings, such as metastatic breast cancer, PPS significantly contributes to OS.25 Furthermore, the treatment regimen post-progression typically differs.1 Consequently, the correlation between the effect on PFS and the effect on OS at the trial level is limited.26 Therefore, studies on treatment for advanced disease should determine the estimand in accordance with the DAG, as depicted in Figure 1B.

Causal Effects of Intention-To-Treat Analysis in RCTs

When estimating a population-level causal effect on a time-to-event outcome in an RCT, survival analysis on the basis of the intention-to-treat (ITT) principles is generally used. There are two important issues. First, it is notable that some methods for survival analysis assume noninformative censoring, which introduces bias when censoring depends on covariates or the outcome. Second, for RCTs in contexts where there is controversy over whether to handle crossover of treatment or use of salvage intervention as censoring, the estimand should be clarified. In the ITT analysis, patients with such intercurrent events are neither censored nor excluded from the analysis population, and therefore, the effect of treatment on delaying death irrespective of whether a patient experiences an intercurrent event is estimated.22

Figure 2A illustrates the typical ITT analysis in RCTs in oncology. There is no arrow from Prognostic factors to Censoring or from Censoring to OS in this DAG, implying that statistical analysis is based on the presumption of censoring at random within a treatment arm. Unfortunately, censoring is not at random in practice,14 and it is reasonable to add arrows from some prognostic factors to Censoring in the DAG, anticipating causes of censoring. Addressing bias by clarifying specific causes of censoring can help formulate strategies to enhance the follow-up rate within the protocol.27

FIG 2. Intention-to-treat analysis of a randomized controlled trial under censoring. (A) Observed variables represented by a DAG and (B) an estimand of hypothetical interventions on treatment and censoring represented by two SWIGs created from the DAG. aPatients who experienced intercurrent events are not censored. There is no arrow from prognostic factors to OS because censoring is assumed to be at random within a treatment arm. DAG, directed acyclic graph; OS, overall survival; SWIGs, single-world intervention graphs.

It is noteworthy that survival analysis is not conditional on the node Censoring on the DAG, which corresponds to adjustment for the variable representing censoring as a covariate. In other words, the estimand of the ITT analysis is the causal effect under the hypothetical scenario where censoring is assumed to be absent, rather than the causal effect among patients who were not censored. However, how the fact that censoring is accounted for by survival analysis influences the interpretation of estimand cannot be illustrated through a DAG.

Splitting the nodes representing treatment and censoring in the DAG, SWIGs serve as an extension, allowing for the representation of hypothetical interventions (Rule 1 in Table 1; see also the Data Supplement, Appendix S1). Within this framework, we designate the standard treatment as t = 0 and the experimental treatment as t = 1. The main focus is to comprehend OS in scenarios where all individuals are thoroughly tracked and administered either the standard treatment (t = 0 and c = 0) or the experimental treatment (t = 1 and c = 0). Consequently, each SWIG in Figure 2B comprises six nodes: two split nodes Treatment, two split nodes Censoring, Prognostic factors, and OS. The ITT estimand is usually defined by the hazard ratio of two potential survival times, OS (t = 0, c = 0) and OS (t = 1, c = 0). Notably, with the split nodes for treatment and censoring, two SWIGs emerge with different potential OS values, depending on the values of c = 0 and t, and the arrow from Censoring to OS is meaningless, although up to four potential outcomes may arise if c = 0 is not supposed.

Identification of Confounders in Cohort Studies and External Controlled Trials

A DAG in Figure 3A illustrates a cohort study in an ideal situation. In this DAG, there are only two arrows pointing to OS. One is from Measured prognostic factors and the other is from Treatment. If all the prognostic factors for the outcome are measured, as shown in this DAG, adjusting for the prognostic factors can block the backdoor path Treatment←Measured prognostic factors→OS (Fig 3B; see also Glossary in Table 1). Furthermore, if the assumption of noninformative censoring is met, conventional survival analysis allows one to account for the presence of censored patients.

FIG 3. Causal structures of (A) a valid cohort study, (B) a valid cohort study with adjustment for measured prognostic factors, (C) the external controlled trial of CAR-T cell therapy represented by DAGs, (D) the external controlled trial of CAR-T cell therapy with adjustment for five prognostic factors, (E) the external controlled trial of CAR-T cell therapy under informative censoring, and (F) the external controlled trial of CAR-T cell therapy under informative censoring with adjustment for five prognostic factors. Parentheses mean adjustment for the node. aRefractory status, cytogenic profile, R-ISS stage, and total plasmacytoma. CAR-T, chimeric antigen receptor-T; DAGs, directed acyclic graphs; OS, overall survival; TTP, time to progression.

Consider again the second study7 that compared outcomes of ciltacabtagene autoleucel in CARTITUDE-1 with those of idecabtagene vicleucel in KarMMa in relapsed or refractory multiple myeloma. They used the matching-adjusted indirect comparison (MAIC) method for the indirect comparison of CARTITUDE-1 and KarMMa. In this study, they identified prognostic factors of multiple myeloma and ranked them in order of clinical importance and adjusted for these prognostic factors using the MAIC method when estimating the causal effect. First, they listed more than 50 potential prognostic factors according to the published literature and clinical expert consensus. Second, five clinical experts on multiple myeloma reviewed the list and selected 15 clinically important factors. Finally, the five most important factors (refractory status, cytogenic profile, revised International Staging System stage, total plasmacytoma, and time to progress on the last regimen) were identified and the highest ranked four factors were selected as covariates for adjustment because time to progress on the last regimen was not measured.

The DAG in Figure 3C represents the assumption behind the analysis of OS in this study. This diagram implies that the five most important factors identified by the expert panel are assumed to be the only prognostic factors for OS. This DAG has an arrow from Inclusion in the trial or external control to Censoring, reflecting the fact that the follow-up rates were different between CARTITUDE-1 and KarMMa. It is worth noting whether Inclusion in the trial or external control is an instrumental variable or not (Glossary in Table 1). According to Figure 3C, this node satisfies one of the conditions of instrumental variable since there is no arrow pointing to OS. However, it does not satisfy another condition because of the presence of prognostic factors that serve as confounders between Inclusion in the trial or external control and OS.

Here, we use the concept of backdoor criteria to investigate a set of variables sufficient to adjust for confounding in Figures 3C and 3E. There is an unblocked backdoor path from Treatment to OS through Inclusion in the trial or external control and four prognostic factors and time to progression (TTP) on last regimen. Adjustment for the prognostic factors, represented by parentheses in Figure 3D, blocks the backdoor path Treatment←Inclusion in the trial or external control→ 4 prognostic factors and TTP on last regimen→OS, eliminating bias due to confounding. Figure 3E shows a different causal structure, assuming that censoring is outcome-dependent. There is an additional unblocked backdoor path from Treatment to OS through Inclusion in the trial or external control and Censoring in Figure 3E. This DAG suggests that adjustment for the prognostic factors may not be sufficient for controlling bias due to differential follow-up rates because, as shown in Figure 3F, it fails to block the backdoor path that passes through Censoring, although this analysis blocks the other backdoor path. Both the backdoor paths pass through Inclusion in the trial or external control, so it would be ideal to block this node, but it is not possible because a patient included in one trial receives corresponding treatment deterministically.

Causal Effects of Hypothetical Interventions on Chemotherapy and Off-Protocol ASCT

As discussed earlier, the primary interest usually lies in the total effect. However, intercurrent events between the commencement of treatment and the outcome can distort the findings, complicating the interpretation of the total effect. Intercurrent events would include lost to follow-up, alterations in treatment regimen after disease progression, salvage interventions like stem-cell transplantation, and noncompliance or discontinuation of treatment due to toxicity.

In the randomized phase II trial on neuroblastoma, differential occurrences of remission and off-protocol ASCT complicated the interpretation of ITT analysis of OS.3 Consequently, London et al3 sought to estimate the causal effect of chemotherapy using a hypothetical strategy,21,22 assuming that patients selected ASCT under an optimal rule on the basis of remission status.

The interpretation and assumptions behind the hypothetical strategy could be clarified using SWIGs. As depicted in the SWIG in Figure 4A, intercurrent events such as Response and ASCT lie between Treatment and OS. Treatment and ASCT are split nodes with t and a indexing hypothetical interventions to these nodes, suggesting that the differential proportions of ASCT were considered by assuming that the decision of ASCT is governed by a rule expressed by the index a (ie, a = 0 if ASCT is not allowed and a = 0.3 if 30% of patients undergo ASCT). Furthermore, Figure 4A supports an understanding of the assumptions behind this analysis. In this structure, there is no backdoor path from Treatment to OS(t,a), but concerning ASCT, there are four backdoor paths: ASCT←Treatment→OS, ASCT←Treatment→Response→OS, ASCT←Response→OS, and ASCT←Response←Treatment→OS. This observation implies that, according to Rule 3 in Table 1, adjusting for Treatment and Response is sufficient for the identification of the causal effects of the hypothetical interventions if the causal structure of Figure 4A is correct.

FIG 4. Estimands of hypothetical interventions on treatment and intercurrent events represented by SWIGs. (A) The RCT of neuroblastoma and (B) the RCT of early breast cancer. aChemotherapy use, age, local treatment, nodal status, estrogen receptor/progesterone receptor status, and tumor grade. ASCT, autologous stem-cell transplantation; OS, overall survival; RCT, randomized controlled trial; SWIGs, single-world intervention graphs.

Causal Effects of Hypothetical Interventions on Treatment and Selective Crossover

Let us redirect our focus to the case study of selective crossover in early breast cancer. The analysis published in 2011 used the inverse probability weighting (IPW) method grounded in a hypothetical strategy that assumes complete preventability of crossover.6 The estimand of the IPW analysis is illustrated through the SWIG depicted in Figure 4B. Through this SWIG, it becomes evident that this analysis is based on the presumption that the backdoor path Crossover←Time-varying confounders→OS can be blocked by the IPW method that accounts for chemotherapy use, age, local treatment, nodal status, estrogen receptor/progesterone receptor status, tumor grade, and time-varying performance status, in addition to the usual justification of analysis on the basis of random treatment assignment.

Covariates Selection for As-Treated Analysis in RCTs

In RCTs, some patients may not receive the treatment regimen to which they were assigned, raising the question of how to treat them in the statistical analysis. For example, in a noninferiority trial, as-treated analysis in addition to ITT analysis is usually performed to compare the groups actually treated by the treatment regimens. Figure 5A shows a DAG that represents as-treated analysis in an RCT. Which node in the DAG should be blocked when estimating the effect of treatment actually received?

FIG 5. Causal structures of (A) as-treated analysis of an RCT and (B) intention-to-treat analysis of stratified RCT represented by DAGs. DAGs, directed acyclic graphs; OS, overall survival; RCT, randomized controlled trial.

According to Rules 1-3, Measured and unmeasured prognostic factors should be blocked because they are on the backdoor path. However, since only measured variables among the prognostic factors can be adjusted for in statistical analysis, bias may not be completely eliminated. Furthermore, Randomization is an instrumental variable (Glossary in Table 1) that does not have an arrow pointing directly to the outcome. Therefore, Randomization should not be adjusted in accordance with Rule 5.

Covariates Selection for ITT Analysis in Stratified RCTs

The case study of early breast cancer used stratified randomization with institute and chemotherapy use as the strata.2 The primary motivation behind using stratified randomization is to avoid imbalance by chance of covariates, particularly in small trials. The primary analysis was done using the stratified log-rank test adjusted for chemotherapy use.

A general causal structure of a stratified RCT with OS as the outcome is depicted in Figure 5B. Typically, the strata used for randomization are generally chosen from prognostic factors related to OS. The node Other prognostic factors represents all the remaining prognostic factors, both measured and unmeasured, not all of which can be statistically adjusted. The lack of arrows between Treatment and Other prognostic factors indicates that the randomization algorithm relies solely on the strata. Note that Treatment←Strata for randomization→Outcome forms a backdoor path outgoing from Treatment. According to Rule 3 in Table 1, it could lead to confusion as it contradicts the usual claim that ITT analysis is valid with or without adjustment because the backdoor path is unconditionally open.

This discrepancy is clarified by the notion of faithfulness.28 Although that path correctly reflects the randomization algorithm, this manipulation does not create an association between the treatment and the strata. In accordance with Rule 2 in Table 1, however, it is preferable to include the strata into covariate adjustment to improve the accuracy of the treatment effect estimation and increase the statistical power. Note that our investigation of the DAG leads us to recommendations consistent with the regulatory guidelines.8,10

DISCUSSION

This article showed that typical causal structures that arise in clinical trials can be expressed by DAGs and SWIGs, proposing five rules to determine which paths in the graph need to be blocked. A case study of CAR-T cell therapy4 demonstrates that significant sources of bias in a single-arm trial, compared with an external control, are differences in patient characteristics and follow-up status. Experiences in RCTs of breast cancer and neuroblastoma reveal that, even when OS is analyzed according to the ITT principle, intercurrent events often complicate the interpretation of results.3,6 Through these case studies, DAGs appear effective in clarifying assumptions for identifying causal effects, although SWIGs should complement DAGs due to their limitations in the presence of intercurrent events in oncology research.

We commence our presentation by distinguishing between total and path-specific effects using a DAG that includes three nodes: treatment, progression, and death. This causal structure is notable despite its simplicity because PFS cannot serve as a surrogate end point for OS in advanced diseases,26,29-31 making the choice of OS and PFS critical. When investigating whether a treatment prolongs life, estimating the total effect of the treatment on OS is necessary, representing the estimand of ITT analysis, also known as the treatment policy estimand.21

Unfortunately, ITT analysis does not always provide a correct answer to the clinical question. With the development of effective salvage treatments, interpreting the results of ITT analysis on OS becomes increasingly challenging.1 Consequently, there is a tendency to rely on short-term end points such as PFS and pathological complete response. However, if these end points do not comprehensively reflect the treatment's efficacy, alternative directions must be explored.22 Two techniques would be useful for making inferences about estimands other than those in ITT analysis. The first is advanced causal inference approaches such as g-methods and mediation analysis. These methods can estimate the causal effects of hypothetical interventions on intercurrent events, and it is vital to demonstrate whether the requisite assumptions are met. The other techniques are DAGs and SWIGs. As demonstrated in the phase III trial of anastrozole,6 constructing a DAG with unmeasured nodes and determining whether the backdoor path can be blocked by the variables included in the IPW analysis would assist clinicians and regulatory reviewers in examining the validity of the analysis.

External controlled trials for regulatory approval are anticipated to increase as most accelerated approvals are based on single-arm trials,32 and an external control may be obtained from real-world data that become acceptable for regulatory settings. External controlled trials require particular attention to disparities in study design, such as eligibility criteria, geographic region, and follow-up methods, as evident in the case of CAR-T cell therapy. DAGs and SWIGs are valuable tools not only against the confounding problem but also for identifying selection bias associated with differential follow-up.15,33 If the follow-up methods of the external control systematically vary from those of the trial, the application of statistical techniques such as IPW methods or artificial censoring becomes necessary. Conducting external comparisons without a prespecified statistical analysis plan raises concerns about arbitrariness introduced by covariate selection. Mandating DAGs and SWIGs during the planning phase would ensure the integrity of the analysis and facilitate communication with reviewers.

Implementing the development of DAGs and SWIGs in practice entails more than merely an analysis plan prepared by biostatisticians. It requires the successful extraction of clinical knowledge and study design features, which may involve unconventional practices, such as identifying prognostic factors on the basis of the review of medical experts and gathering data to support the DAG through pilot studies. This comprehensive process appears vital for enhancing the scientific quality of causal inference in future clinical trials in oncology.

In conclusion, the typical causal structures that emerge in randomized and nonrandomized clinical trials in oncology can be effectively represented through DAGs and SWIGs even during the planning phase. This approach not only aids in clarifying the estimands and assumptions but also serves as a means to communicate adherence to the guidelines set forth by regulatory and health technology assessment agencies and the predetermined nature of the analysis plan.

ACKNOWLEDGMENT

The authors thank K Fujii (Kyoto University) for secretarial assistance.

SUPPORT

AUTHOR CONTRIBUTIONS

Conception and design: Shiro Tanaka

Manuscript writing: All authors

Final approval of manuscript: All authors

Accountable for all aspects of the work: All authors

AUTHORS' DISCLOSURES OF POTENTIAL CONFLICTS OF INTEREST

The following represents disclosure information provided by authors of this manuscript. All relationships are considered compensated unless otherwise noted. Relationships are self-held unless noted. I = Immediate Family Member, Inst = My Institution. Relationships may not relate to the subject matter of this manuscript. For more information about ASCO's conflict of interest policy, please refer to www.asco.org/rwc or ascopubs.org/cci/author-center.

Open Payments is a public database containing information reported by companies about payments made to US-licensed physicians (Open Payments).

Supported in part by the Project Promoting Clinical Trials for Development of New Drugs (21lk0201702t0001) from the Japan Agency for Medical Research and Development (AMED).

Shiro Tanaka

Honoraria: Research Institute of Healthcare Data Science

Consulting or Advisory Role: Lilly, Welby, Daiichi Sankyo Company, Limited, Janssen

Research Funding: Novo Nordisk

No other potential conflicts of interest were reported.
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REFERENCES

1. Freidlin B , Korn EL : Assessing causal relationships between treatments and clinical outcomes: Always read the fine print. Bone Marrow Transplant 47 :626-632, 2012 21625225
2. Breast International Group BIG 1-98 Collaborative Group, Thürlimann B , Keshaviah A , et al : A comparison of letrozole and tamoxifen in postmenopausal women with early breast cancer. N Engl J Med 353 :2747-2757, 2005 16382061
3. London WB , Frantz CN , Campbell LA , et al : Phase II randomized comparison of topotecan plus cyclophosphamide versus topotecan alone in children with recurrent or refractory neuroblastoma: A Children’s Oncology Group study. J Clin Oncol 28 :3808-3815, 2010 20660830
4. Martin T , Usmani SZ , Schecter JM , et al : Matching-adjusted indirect comparison of efficacy outcomes for ciltacabtagene autoleucel in CARTITUDE-1 versus idecabtagene vicleucel in KarMMa for the treatment of patients with relapsed or refractory multiple myeloma. Curr Med Res Opin 37 :1779-1788, 2021 34256668
5. BIG 1-98 Collaborative Group, Mouridsen H , Giobbie-Hurder A , et al : Letrozole therapy alone or in sequence with tamoxifen in women with breast cancer. N Engl J Med 361 :766-776, 2009 19692688
6. Colleoni M , Giobbie-Hurder A , Regan MM , et al : Analyses adjusting for selective crossover show improved overall survival with adjuvant letrozole compared with tamoxifen in the BIG 1-98 study. J Clin Oncol 29 :1117-1124, 2011 21321298
7. Martin T , Usmani SZ , Schecter JM , et al : Updated results from a matching-adjusted indirect comparison of efficacy outcomes for ciltacabtagene autoleucel in CARTITUDE-1 versus idecabtagene vicleucel in KarMMa for the treatment of patients with relapsed or refractory multiple myeloma. Curr Med Res Opin 39 :81-89, 2023 36271807
8. European Medicines Agency: Guideline on Adjustment for Baseline Covariates in Clinical Trials. 2015. https://www.ema.europa.eu/en/documents/scientific-guideline/guideline-adjustment-baseline-covariates-clinical-trials_en.pdf
9. Phillippo DM , Ades AE , Dias S , et al : NICE DSU Technical Support Document 18: Methods for Population-Adjusted Indirect Comparisons in Submissions to NICE. 2016. https://research-information.bris.ac.uk/ws/portalfiles/portal/94868463/Population_adjustment_TSD_FINAL.pdf
10. US Food and Drug Administration: Guidance for industry. Adjusting for covariates in randomized clinical trials for drugs and biological products. 2023. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/adjusting-covariates-randomized-clinical-trials-drugs-and-biological-products
11. US Food and Drug Administration: Guidance for industry. Considerations for the design and conduct of externally controlled trials for drug and biological products. 2023. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/considerations-design-and-conduct-externally-controlled-trials-drug-and-biological-products
12. Tennant PWG , Murray EJ , Arnold KF , et al : Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: Review and recommendations. Int J Epidemiol 50 :620-632, 2021 33330936
13. Lipsky AM , Greenland S : Causal directed acyclic graphs. JAMA 327 :1083-1084, 2022 35226050
14. Templeton AJ , Amir E , Tannock IF : Informative censoring-a neglected cause of bias in oncology trials. Nat Rev Clin Oncol 17 :327-328, 2020 32273582
15. Hernán MA , Hernández-Díaz S , Robins JM : A structural approach to selection bias. Epidemiology 15 :615-625, 2004 15308962
16. Greenland S , Pearl J , Robins JM : Causal diagrams for epidemiologic research. Epidemiology 10 :37-48, 1999 9888278
17. Freidlin B , Korn EL : Augmenting randomized clinical trial data with historical control data: Precision medicine applications. J Natl Cancer Inst 115 :14-20, 2023 36161487
18. Richardson TS , Robins JM : Single world intervention graphs (SWIGs): A unification of the counterfactual and graphical approaches to causality. Cent Stat Soc Sci Univ Washingt Ser Work Pap 128 :1-146, 2013
19. Ocampo A , Bather JR : Single-world intervention graphs for defining, identifying, and communicating estimands in clinical trials. Stat Med 42 :3892-3902, 2023 37340887
20. Korn EL , Freidlin B : Causal inference for definitive clinical end points in a randomized clinical trial with intervening nonrandomized treatments. J Clin Oncol 28 :3800-3802, 2010 20660828
21. International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use: E9(R1) draft guideline: Estimands and sensitivity analysis in clinical trials. 2017. https://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Efficacy/E9/E9-R1EWG_Step2_Guideline_2017_0616.pdf
22. Degtyarev E , Zhang Y , Sen K , et al : Estimands and the patient journey: Addressing the right question in oncology clinical trials. JCO Precis Oncol 10.1200/PO.18.00381
23. Pearl J : Causal diagrams for empirical research. Biometrika 82 :669-710, 1995
24. VanderWeele TJ : Principles of confounder selection. Eur J Epidemiol 34 :211-219, 2019 30840181
25. Saad ED , Katz A , Buyse M : Overall survival and post-progression survival in advanced breast cancer: A review of recent randomized clinical trials. J Clin Oncol 28 :1958-1962, 2010 20194852
26. Burzykowski T , Buyse M , Piccart-Gebhart MJ , et al : Evaluation of tumor response, disease control, progression-free survival, and time to progression as potential surrogate end points in metastatic breast cancer. J Clin Oncol 26 :1987-1992, 2008 18421050
27. Little RJ , D'Agostino R , Cohen ML , et al : The prevention and treatment of missing data in clinical trials. N Engl J Med 367 :1355-1360, 2012 23034025
28. Greenland S , Mansournia MA : Limitations of individual causal models, causal graphs, and ignorability assumptions, as illustrated by random confounding and design unfaithfulness. Eur J Epidemiol 30 :1101-1110, 2015 25687168
29. Buyse M , Burzykowski T , Carroll K , et al : Progression-free survival is a surrogate for survival in advanced colorectal cancer. J Clin Oncol 25 :5218-5224, 2007 18024867
30. Paoletti X , Oba K , Bang YJ , et al : Progression-free survival as a surrogate for overall survival in advanced/recurrent gastric cancer trials: A meta-analysis. J Natl Cancer Inst 105 :1667-1670, 2013 24108811
31. Mushti SL , Mulkey F , Sridhara R : Evaluation of overall response rate and progression-free survival as potential surrogate endpoints for overall survival in immunotherapy trials. Clin Cancer Res 24 :2268-2275, 2018 29326281
32. Kim C , Prasad V : Strength of validation for surrogate end points used in the US Food and Drug Administration's approval of oncology drugs. Mayo Clinic Proc 91 :713-725, 2016
33. Kenah E : A potential outcomes approach to selection bias. Epidemiology 34 :865-872, 2023 37708480
