Introduction

Hypothetical strategy: Several possibilities exist. Some examples include what would have happened if the ICE had not occurred and what would have happened under some alternative regimen, such as if rescue had not been taken. Here, the ICEs are a confounding factor.

Hypothetical strategies are used to address relevant questions when the desired experimental conditions cannot be ensured for all patients.

Most of the practical applications fall into a few categories:

1. Outcomes expected if patients did not have ICEs that constituted a break from the treatment or treatment regimen of interest – that is, if all patients had adhered to the treatment regimen

2. Outcomes expected if patients had followed a specific treatment regimen, typically involving a change in treatments, that either was not available in the trial or was not followed by some patients if available 如果患者遵循特定的治疗方案（通常涉及治疗方案的改变），则预期结局在试验中不可用或某些患者未遵循（如果有）

For example, a placebo-controlled clinical trial in Type 2 diabetes. It is not ethical to withhold res-cue treatment because that would prolong insufficient blood glucose control.

However, the use of rescue medication masks or enhances (i.e., confounds) the effects of the initial medication. If stakeholder questions relate to the initial medication, hypothetical strategies can be useful to estimate the treatment effect expected if patients (contrary to the fact) had not used rescue.

The hypothetical scenario assuming that all patients were adherent is sometimes criticized because it is counter to the fact that some patients were not adherent (Permutt, 2015a). However, the question of treatment effects if patients adhered is important (Mallinckrodt et al., 2014, 2017). A hypothetical strategy is needed because it is not ethical to ensure full adherence by design. We therefore abstract from the observed experiment to the question of interest via appropriate analytical methods.

Even when interest is primarily in estimands based on what happened as actually adhered to, secondary interest may be in effects if all patients had adhered (Mallinckrodt and Lipkovich, 2017; Mallinckrodt et al., 2017). For example, in oncology trials, the current standard treatment policy strategy for assessing the overall survival (OS) includes the effects of changing treatment following progression, which is ethically required. Adopting a hypothetical strategy focusing on the effect of the initial treatments on OS allows the benefit (or lack thereof) of the initial medication to be clearer. [comments:采用一种假想策略，重点关注初始治疗对OS的影响，可以使初始药物的益处（或缺乏益处）更加清晰]

Like composite or treatment policy strategies, hypothetical strategies can be limited to a portion of ICEs, for example, not all premature discontinuations of the initial randomized treatment occur for treatment-related reasons. It may be reasonable to consider what would happen if patients who discontinued for reasons not related to treatment had continued with treatment. Patients who discontinued for reasons related to treatment could be handled using a composite strategy, for example. Hypothetical strategies are especially relevant in long-term studies where attrition due to study fatigue and assessment burden may increase with time.

A scenario where the hypothetical strategy is likely not meaningful is when the ICE is death when assessing quality of life (QoL). Estimating hypothetical quality of life in patients who are dead can lead to irrelevant abstractions. For trials with few expected deaths or when death is not related to treatment or to the disease under investigation, the interpretation remains acceptable (Permutt, 2015a). A combination strategy could address interpretational issues around death by having most ICEs dealt with via a hypothetical strategy with death considered a bad outcome via a composite strategy.[comments: ICE为死亡时候,假想策略处理需谨慎,尤其终点是患者生活质量的时候(需考虑死亡患者的假想中的生活质量)]

Hypothetical strategies typically require unverifiable assumptions (无法核实的假设) and statistical modeling techniques to predict outcomes under the hypothetical conditions due to either missing or irrelevant data. Such unverifiable assumptions are not unique to hypothetical strategies and occur in any analysis with missing or irrelevant data (such as post-rescue outcomes when assessing effects of the initial medication).

Analyses for Hypothetical Strategy

Most of the practical applications of potential hypothetical scenarios fall into several categories:

1. Outcomes that would have been expected if patients had not experienced relevant intercurrent events [如果患者没有经历过相关的ICE，预期中会出现的结果]

or

2. what outcomes would have been if patients followed a specific treatment regimen, typically involving a change in treatments, that either was not available in the trial or was not followed by some patients if available [如果患者遵循特定的治疗方案，通常涉及治疗方法的改变，而该治疗方案在试验中没有; 或者即使有也没有被一些患者遵循(试验中有换药的那种设计,crossover)，那么结果会是怎样的. 这类估计目标的例子包括不考虑依从性和不启动救援药物的疗效之间的差异。这方面的一个具体例子是，如果病人在停用最初随机分配的研究药物后,服用了安慰剂，会发生什么情况。最近，出现了一系列被称为reference-based controlled imputation的方法，这些方法是pattern-mixture models的具体版本，旨在解决这些治疗的转换（见Mallinckrodt et al., 2019，和其中的参考文献）。这些方法可以追溯到Little and Yau (1996)].

For bullet point 1, methods valid under the assumption of MAR, such as ML, MI, and IPW, are analytic options when assessing outcomes expected if intercurrent events had not occurred.

For bullet point 2, methods that assume MNAR, especially reference-based imputation, are analytic options for scenarios involving changes in treatment, such as when a treatment regimen was not available or not followed in a trial.

The key assumption for MAR-based analyses is that the missing data arise from an MAR mechanism.

The key assumption of reference-based imputation is that the reference arm describes the desired trajectory of the experimental arm after the occurrence of the ICEs, typically modeling a change in treatment.

Sensitivity to departures from these assumptions can be tested using delta adjustment for MI-based approaches and mean delta adjustment for the likelihood-based approaches.