Re. Prediagnostic Exposures and Cancer Survival

To the Editor:

Albers and colleagues highlighted the challenges of defining meaningful and useful estimands for effects of pre-cancer-diagnosis exposures on post-cancer-diagnosis outcomes.¹ We aim to contribute to this conversation by discussing (i) truncation and (ii) specification of causal estimands for cancer-relevant target populations.

First, we must contend with truncation: potential outcomes may be undefined under treatment levels that prevent cancer (or its diagnosis) if the outcome is defined relative to diagnosis (e.g., survival after diagnosis).² The causal estimands examined by Albers and colleagues handle truncation differently.¹ The target population for the survivor average causal effect (SACE) comprises individuals who would be diagnosed regardless of their exposure level. The controlled direct effect directly intervenes on diagnosis. Conditional separable effects consider distinct components of treatment that affect the outcome through separate pathways. The total effect example given by Albers et al. measures cancer mortality from the time of exposure, not diagnosis.

Second, it is crucial to specify causal estimands for cancer-relevant target populations here. Of the above estimands, only the SACE and conditional separable effect specify target populations of people diagnosed with cancer. Estimands (including controlled direct effects and total effects) can be defined among individuals diagnosed with cancer $(C=1)$, those who would be diagnosed with cancer under specified treatment(s) (e.g., $C^{X=1}=1$ or $C^{X=0}=1$), or combinations of these.^3,4

We could consider other estimands that avoid truncation and also target people diagnosed with cancer. Redefining $Y$ as survival time from exposure (or all-cause mortality some specified time after exposure), the total effect of a prediagnosis exposure among people diagnosed with cancer after the time of exposure assessment could be defined as $E[Y^{X=1}-Y^{X=0}\mid C=1]$ (Table). Here, outcomes under observed (factual) treatment are “post-diagnosis,” but outcomes under counterfactual treatment may occur before, and possibly preclude, diagnosis. Identification of such effects is theoretically possible but requires conditions that may only be plausible in particular scenarios.^5–7 Others have also defined the net treatment difference – a contrast of potential outcomes that allows the population in each part of the contrast to vary based on the exposure: $E\left[Y^{X=1}\mid C^{X=1}=1\right]-E\left[Y^{X=0}\mid C^{X=0}=1\right]$.^8,9

Table.

Selected Example Estimands Among People Diagnosed With Cancer or People Who Would be Diagnosed With Cancer Under Certain Levels of Treatment

Estimand	Description
	Y = Years of Survival Since Exposurea	Y = Years of Survival Since Cancer Diagnosisb
$E\left[Y^{X=1}-Y^{X=0}\mid C=1\right]$	Among people diagnosed with cancer after an exposure, what is the average difference in number of years of life lived since exposure assessment had they been exposed to $X=1$ versus $X=0$	Possibly ill-defined: $Y^{X=1}$ or $Y^{X=0}$ can be undefined for at least some individuals if $X$ affects $C$
$E\left[Y^{X=1}-Y^{X=0}\mid C=1,X=0\right]$ or $E\left[Y^{X=1}-Y^{X=0}\mid C_{X=0}=1,X=0\right]$	Among people who were exposed to $X=0$ and subsequently diagnosed with cancer, what is the average difference in number of years of life lived since exposure assessment had they been exposed to $X=1$ versus $X=0$	Possibly ill-defined: $Y^{X=1}$ can be undefined for at least some individuals if $X$ affects $C$
$E\left[Y^{X=1}-Y^{X=0}\mid C=1,X=1\right]$ or $E\left[Y^{X=1}-Y^{X=0}\mid C_{X=1}=1,X=1\right]$	Among people who were exposed to $X=1$ and subsequently diagnosed with cancer, what is the average difference in number of years of life lived since exposure assessment had they been exposed to $X=1$ versus $X=0$	Possibly ill-defined: $Y^{X=0}$ can be undefined for at least some individuals if $X$ affects $C$
$E\left[Y^{X=1}-Y^{X=0}\mid C_{X=0}=1\right]$	Among people who would be diagnosed with cancer under exposure $X=0$, what is the average difference in number of years of life lived since exposure assessment had they been exposed to $X=1$ versus $X=0$	Possibly ill-defined: $Y^{X=1}$ can be undefined for at least some individuals if $X$ affects $C$
$E\left[Y^{X=1}-Y^{X=0}\mid C_{X=1}=1,C_{X=0}=1\right]$	Survivor average causal effect (SACE): among people who would be diagnosed with cancer after either level of exposure, what is the average difference in number of years of life lived since exposure assessment had they been exposed to $X=1$ versus $X=0$	Survivor average causal effect (SACE): among people who would be diagnosed with cancer under either level of exposure, what is the average difference in number of years of life lived since diagnosis had they been exposed to $X=1$ versus $X=0$

$X$, prediagnosis exposure (binary); $C$, cancer diagnosis after exposure assessment (binary).

^aY could also be defined as the probability of survival a specified number of years after exposure.

^bY could also be defined as the probability of survival (or of cancer survival) a specified number of years after diagnosis.

In all cases, research questions and estimands should concur on and be explicit about the target population(s) of interest. The bias of a statistical procedure is then defined relative to a specified estimand. For prediagnosis exposures, some estimands with relevant target populations may be ill-defined because of truncation; others are well defined but may be challenging to identify. There may still be interest in the effects of these prediagnosis exposures or their use as proxies for the effects of exposures at other time points. Alternatively, prediagnosis exposures may be of interest as modifiers of postdiagnosis exposure effects, or, as Albers and colleagues suggest, for description and prediction.