Why an Event Can Seem to Follow a Biomarker
Suppose a biomarker is measured repeatedly, and people with lower values are more likely to experience hospitalization soon afterward. One possible explanation is that the biomarker itself contributes to event risk. Another is that a disease process already developing before hospitalization changes the biomarker and also makes hospitalization more likely. In the second case, the marker may predict the event without being its cause.
This second pattern is often called reverse causation. The phrase does not mean that a future recorded event literally changes a past measurement. Rather, the biological process that will culminate in the event is already under way and affects the biomarker before the event is recorded. The distinction matters because an association between a marker and a later event does not, by itself, establish which process generated the association.
The relevant time ordering is therefore more detailed than “biomarker first, event second.” A biomarker may be measured first, but the underlying illness may have begun before that measurement. A simplified causal picture is a preclinical process \(U(t)\) influencing both the marker and the event process. There may also be a separate pathway through which the marker itself affects event risk. Observational data can contain both pathways at once.
A Simple Formal Distinction
For a fixed follow-up horizon, let \(D=1\) indicate that an event occurs by that horizon and \(D=0\) otherwise. Let \(U\) represent a preclinical disease process that is present or more advanced during the horizon. A simple description is
Here \(\gamma\) describes how the preclinical process is associated with the biomarker, and \(g(U)\) describes how it is associated with event occurrence. This setup allows \(U\) to generate a biomarker–event association even when the biomarker has no causal effect on the event. To interpret \(\gamma\) as the only source of the association in this calculation, assume \(E(\varepsilon\mid U)=0\) and that \(\varepsilon\) is conditionally independent of \(D\) given \(U\). Equivalently for the covariance calculation, one can directly assume \(E(\varepsilon D\mid U)=0\). Mean zero without conditioning is not enough.
Under these assumptions, the covariance between the marker and the event indicator is
The factorization in the last line follows from conditional independence, and \(E(\varepsilon\mid U)=0\). Thus \(\operatorname{Cov}(Y,D)=\gamma\operatorname{Cov}(U,D)\). If more advanced \(U\) tends to raise event risk and lower the biomarker, then \(\gamma<0\) and \(\operatorname{Cov}(U,D)>0\), so the observed covariance is negative. This is an association generated by the preclinical process; it is not evidence that raising the biomarker would prevent the event.
This derivation is a deliberately simple illustration, not a general causal identification result. In real data, \(U\) may change over time, several processes may affect the marker and event, and the biomarker may also contribute to risk. The derivation shows why temporal precedence alone does not settle the causal direction.
Worked Example: A Shared Preclinical Process Creates an Association
Consider a hypothetical group in which \(U=1\) denotes an active preclinical disease process and \(U=0\) its absence. Suppose half the group has \(U=1\). The marker is \(Y=10-2U+\varepsilon\), in marker units, and the probability of an event by the horizon is 0.8 for \(U=1\) and 0.2 for \(U=0\). Assume \(E(\varepsilon\mid U)=0\) and that \(\varepsilon\) is conditionally independent of \(D\) given \(U\). There is no causal effect of \(Y\) in this data-generating description.
Among people with an event, the probability of \(U=1\) is
For people without an event, the corresponding probability is \(P(U=1\mid D=0)=0.2\). Since the residual has conditional mean zero, the event-group marker mean is \(10-2(0.8)=8.4\) units, while the non-event-group mean is \(10-2(0.2)=9.6\) units. The difference is \(8.4-9.6=-1.2\) units.
Thus the event group has a mean marker value 1.2 units lower, despite the model containing no marker-to-event effect. The shared preclinical process lowers the marker and raises event probability. This calculation does not prove that a particular observed association has this explanation; it demonstrates one coherent mechanism that can produce it.
What “Near an Event” Can Look Like
Repeated measurements can reveal a pattern that a single marker value hides. If the preclinical process intensifies as the event approaches, marker values may change more rapidly close to \(T_i\) than earlier in follow-up. Aligning measurements by time to event can make such a pattern visible. But this alignment describes a trajectory around observed events; it does not establish that the marker change causes the event or that the event itself reaches backward in time.
Worked Example: Interpreting an Event-Proximal Slope
In a hypothetical illustration, a patient has a marker measured three, two, and one month before hospitalization. The values are 8.0, 7.2, and 6.4 units, respectively. Assume for this arithmetic that the measurements are on the same scale and equally spaced in time.
From three months before hospitalization to one month before, the change is \(6.4-8.0=-1.6\) units over 2 months. The average slope is
The values therefore decline by an average of 0.8 marker units per month over this interval. Suppose a hypothetical comparison trajectory remains at 8.0 units over the same period. The contrast suggests a decline associated with the period preceding hospitalization. It is compatible with a preclinical process changing the marker, but it does not establish that the decline increased hospitalization risk. A causal marker effect, differences between the patient and comparison group, or other time-varying processes could also contribute.
Three measurements do not establish that the trajectory is linear, and a single patient's trajectory cannot establish a population pattern. The slope is a summary of these specified measurements, not a causal estimate.
Lagged Comparisons as a Diagnostic
A useful diagnostic is to compare associations at different distances from the event. For example, analysts may ask whether a marker measured more than a prespecified lag before an event remains associated with event occurrence. If an association is strongest very near the event and weakens when near-event observations are excluded, that pattern is consistent with a rapidly changing preclinical process. It is not proof: the lagged analysis changes which measurements and risk periods contribute, and it can also change the population being compared.
Worked Example: A Near-Event Association Weakens After a Lag
Suppose a hypothetical analysis compares event proportions in low- and high-marker groups during two periods. In the period close to an event, 24 of 100 low-marker observations and 12 of 100 high-marker observations are followed by an event. In a separate period more than 30 days from an event, the corresponding counts are 8 of 100 and 10 of 100. Treat these as illustrative proportions, not estimates from a real study.
For the near-event period, the proportions are \(24/100=0.24\) and \(12/100=0.12\), giving a risk ratio of \(0.24/0.12=2.00\). In that period, the observed event proportion is twice as high in the low-marker group. For the more distant period, the proportions are \(8/100=0.08\) and \(10/100=0.10\), giving a risk ratio of \(0.08/0.10=0.800\).
The contrast changes from 2.00 near the event to 0.800 in the distant period. This pattern motivates checking whether the marker is changing as the event approaches. It does not show that the marker protects against events in the distant period: the groups may differ in other ways, and the periods may represent different risk sets or follow-up conditions. A lag is a diagnostic choice, not a method that automatically removes confounding or identifies a causal effect.
Assumptions, Diagnostics, and Alternatives
Interpreting an event-proximal pattern requires attention to how the data were collected. Measurements must be ordered correctly in time, and their dates must be sufficiently accurate to distinguish a pre-event change from a measurement taken during or after the event. The event definition and the time origin should be stated. If visits become more frequent when patients become ill, the observed measurements may overrepresent the period of deterioration. If follow-up ends at the event, there are no post-event measurements to reveal what the marker would otherwise have done.
Useful checks include plotting individual trajectories against time to event, comparing event-proximal and earlier measurements, and showing how results change under more than one prespecified lag. Also inspect whether the apparent pattern is driven by a small number of individuals or by a change in who remains under observation. These checks can reveal fragility or a plausible preclinical trend; none can establish that the trend is causal on its own.
The main alternatives answer different questions. A baseline-marker analysis asks whether a measurement taken at the start of follow-up predicts later events; it is less directly exposed to a marker change immediately before the event, but baseline confounding and later changes remain possible. A time-updated association uses measurements as follow-up proceeds, but may be especially sensitive to an evolving preclinical process. A lagged analysis excludes or delays use of recent marker information, which can assess proximity but sacrifices information and changes the target comparison. A joint model can represent the longitudinal marker and event process together under specified assumptions; fitting one does not, by itself, identify reverse causation or guarantee a causal interpretation.
Reverse causation is especially difficult to distinguish from a marker effect when the preclinical process is not measured well, biomarker visits are sparse, or the process changes rapidly. Excluding observations near events may reduce one source of concern but cannot rule out a process that begins earlier. Conversely, finding a sharp pre-event change does not prove reverse causation: the marker could be part of a causal pathway, or both processes could have other causes. Causal conclusions require assumptions and evidence beyond temporal ordering and a changing association.
Check Your Understanding
Use the definitions and examples above to answer each question. Brief solutions follow the questions.
- In one sentence, explain why reverse causation near an event does not mean that a future event literally changes an earlier biomarker value.
- In the numerical example, what produced the 1.2-unit difference in mean marker values between event and non-event groups?
- A low marker is associated with events only in the 30 days before they occur. Name one interpretation consistent with this pattern and one reason it is not conclusive.
- Why is a lagged analysis a diagnostic rather than a guaranteed correction for reverse causation?
- Suppose a marker is measured at a clinic visit before hospitalization. What additional timing question should be asked before interpreting the marker as preceding the relevant disease process?
Solutions. (1) The preclinical process leading to the event may already be active and may change the marker before the event is recorded. (2) The latent process \(U\) lowered the marker and raised event probability; the example assumed no marker-to-event effect. (3) The pattern is consistent with a preclinical process changing the marker near the event; it is not conclusive because confounding, changing risk sets, or other time-varying processes can also produce it. (4) Excluding recent measurements changes the data and target comparison, and it does not remove unmeasured causes or processes that began earlier. (5) Ask whether the preclinical illness began before the clinic measurement, rather than checking only whether the recorded hospitalization occurred afterward.