Why Treatment Choice Can Distort a Drug Comparison
In an observational pharmacogenomic study, patients do not necessarily receive drugs at random. Clinicians may choose a treatment because a patient is more severely ill, has responded poorly to another drug, or carries a genotype believed to affect drug response. Those same features can also predict the outcome. As a result, a comparison of observed outcomes between treatment groups can reflect who was prescribed each treatment, as well as any effect of the treatments themselves.
This problem is called confounding by indication when the clinical reason for prescribing a treatment is also related to the outcome. Pharmacogenomics adds a possible prescribing pathway: a genotype may influence which drug or dose a patient receives. The goal is not to assume that every observational comparison is biased, but to specify how treatment was chosen, define the comparison of interest, and assess whether the data support a credible adjusted comparison.
Specify the Comparison Before Adjusting
Let \(A\) denote an initiated treatment, \(Y\) a defined clinical outcome over a specified follow-up period, \(G\) genotype, and \(L\) measured characteristics assessed before treatment begins. \(L\) may include disease severity, prior treatment, comorbidities, age, and clinical measurements used in prescribing. A useful target is often a contrast between outcomes under two treatment strategies, such as initiating drug A versus initiating an active comparator drug B, in a defined eligible population.
For a binary outcome, write \(Y^a\) for the outcome that would be observed if a person followed treatment strategy \(a\). A population average causal risk difference is \(E[Y^A-Y^B]\), where \(Y^A\) and \(Y^B\) here denote outcomes under the named strategies. For a pharmacogenomic question, the target might instead be a contrast within genotype group \(g\), or a comparison of treatment effects across genotype groups. These targets are different: estimating an effect within \(G=g\) does not by itself establish that the effect differs by genotype.
Before analyzing, define the population, treatment strategies, outcome, and follow-up. Specify whether treatment means initiation of a drug, a particular dose strategy, or another well-defined intervention. Do not compare vague categories such as “ever treated” with “never treated” if patients must remain alive and under observation long enough to enter the treated group; that timing can create additional selection bias.
Standardization Across Severity Groups
A direct way to see the problem is to compare outcomes within levels of disease severity, then average those conditional risks over one common severity distribution. If \(L\) is a set of measured baseline confounders, the standardized risk under treatment \(a\) is calculated from the observed conditional risks as
The same distribution \(P(L=l)\) is used for each treatment. If the required causal assumptions hold, this standardization estimates the risk that would occur if everyone in the target population received strategy \(a\). It does not merely describe the people who happened to receive \(a\).
Worked Example: Severity Reverses the Crude Comparison
Suppose a hypothetical cohort contains 200 patients: 100 with severe disease and 100 with mild disease. Clinicians tend to prescribe drug A to patients with severe disease. The table gives the number with an adverse outcome in each treatment-by-severity group.
| Severity | Drug A: outcome / total | Drug B: outcome / total |
|---|---|---|
| Severe | 32 / 80 | 10 / 20 |
| Mild | 2 / 20 | 8 / 80 |
The crude risk for A is \(34/100=0.34\), while the crude risk for B is \(18/100=0.18\). The unadjusted risk difference is \(0.34-0.18=0.16\), or 16 percentage points more adverse outcomes among A recipients.
Within severe disease, the risks are \(32/80=0.40\) for A and \(10/20=0.50\) for B. Within mild disease, they are \(2/20=0.10\) for A and \(8/80=0.10\) for B. Standardizing to the cohort’s 50% severe and 50% mild distribution gives
The standardized risk difference is \(0.25-0.30=-0.05\): five percentage points fewer adverse outcomes under A in this standardized comparison. The crude comparison is misleading because 80% of A recipients are severely ill, compared with 20% of B recipients. This example illustrates adjustment for severity; by itself, it does not prove that A causes a lower risk.
Genotype-Related Prescribing and Selection
A genotype can influence treatment assignment directly, for example when clinicians use a test result to choose a drug. Genotype can also be associated with ancestry, disease characteristics, or other factors that influence treatment and outcome. Thus, comparisons of recipients of different drugs may require adjustment for the clinical reasons for treatment and, where appropriate, genotype and relevant population structure.
There is a second, distinct concern: restricting an analysis to people who received a particular treatment can create an association between genotype and severity even when they were unrelated before treatment selection. In causal-diagram terms, treatment can be a collider on the path \(G\rightarrow A\leftarrow L\rightarrow Y\). Conditioning on a collider, such as analyzing only \(A=1\), can open a noncausal path between \(G\) and \(Y\). This is selection bias, not ordinary confounding that is automatically fixed by adjusting for treatment.
Worked Example: Conditioning on Treatment Creates a Genotype Association
Consider a hypothetical population in which genotype \(G\) and severity \(U\) are independent, each with prevalence 0.50. Suppose neither genotype nor treatment has any effect on the outcome; only severity matters. The outcome risk is 0.40 for severe patients and 0.10 for mild patients. However, prescribing probabilities differ: \(P(A=1\mid G=1,U=1)=0.90\), \(P(A=1\mid G=1,U=0)=0.60\), \(P(A=1\mid G=0,U=1)=0.60\), and \(P(A=1\mid G=0,U=0)=0.10\).
Among treated patients with \(G=1\), the probability of severe disease is
Among treated patients with \(G=0\), it is
Consequently, the outcome risks among treated patients are \(0.60(0.40)+0.40(0.10)=0.28\) for \(G=1\) and \(0.857(0.40)+0.143(0.10)\approx0.357\) for \(G=0\). The treated-only comparison makes \(G=1\) appear protective, despite the stipulated absence of a genotype effect. The difference arises because severity distributions became unequal after restricting to treatment. In a real analysis, measuring and appropriately handling severity may help, but selecting only treated patients still requires a clear target and careful justification.
Design and Adjustment Strategies
Good design reduces reliance on statistical adjustment. An active-comparator, new-user design can compare patients beginning alternative treatments for a similar indication, rather than comparing treated patients with a heterogeneous group of nonusers. Define eligibility and baseline covariates before initiation, align follow-up at a common time zero, and record the clinical information and genotype knowledge available to the prescriber at that time. This makes the treatment groups more comparable and helps avoid mixing treatment effects with differences in disease history or follow-up.
When treatment is not randomized, regression standardization and propensity-score methods can adjust for measured baseline covariates. The propensity score is the probability of receiving a specified treatment conditional on observed baseline covariates, \(e(L)=P(A=1\mid L)\). Matching, stratification, or weighting can use this score to improve measured covariate balance. None makes unmeasured confounding disappear. The relevant assumptions for a causal interpretation are:
- Consistency: the observed outcome under the received treatment agrees with the potential outcome under that treatment strategy. Treatment strategies must be sufficiently well defined.
- Conditional exchangeability: given the measured baseline covariates \(L\), treatment assignment is independent of the relevant potential outcomes. This rules out remaining unmeasured confounding conditional on \(L\).
- Positivity: each treatment being compared has a nonzero probability for every covariate pattern included in the target population. If, for example, all patients with a particular genotype and severe disease receive A, the data cannot directly support a comparison with B in that subgroup.
- Correct measurement and analysis: treatment, outcome, and important confounders are measured well enough, and the adjustment model or weighting procedure is adequately specified.
Standardization and propensity methods are alternative ways of using observed covariates, not guarantees of causal validity. Overlap should be checked: extremely low or high estimated treatment probabilities can produce unstable weights and indicate that some patients have no credible comparator. Restricting the target population to a region of overlap may be more defensible than extrapolating, but it changes the population to which the result applies.
Worked Example: Inverse-Probability Weighting Balances Measured Severity
In a second hypothetical cohort, 100 patients have severe disease and 100 have mild disease. Among severe patients, 75 receive A and 25 receive B; among mild patients, 25 receive A and 75 receive B. The outcome counts are 30 of 75 and 10 of 25 for severe patients on A and B, respectively, and 3 of 25 and 9 of 75 for mild patients on A and B. Assume the treatment probabilities are correctly estimated from severity: \(e(\text{severe})=0.75\) and \(e(\text{mild})=0.25\).
For the average treatment effect, use weight \(1/e(L)\) for A recipients and \(1/[1-e(L)]\) for B recipients. Among A recipients, the severe patients receive weight \(1/0.75=1.333\), and the mild patients receive weight \(1/0.25=4\). Each severity group then contributes total weight \(75(1.333)\approx100\) and \(25(4)=100\). The weighted A risk is
Among B recipients, severe patients receive weight \(1/(1-0.75)=4\), and mild patients receive weight \(1/(1-0.25)=1.333\). The weighted B risk is
The crude risks were \(33/100=0.33\) for A and \(19/100=0.19\) for B, because the treatment groups had different severity distributions. Weighting balances the measured severity distribution and yields equal weighted risks in this example. The result is still conditional on the assumptions above; weighting cannot correct for severity measured poorly or for other unmeasured prescribing factors.
Deriving the Standardized Risk
The identifying argument for standardization is short but depends on substantive assumptions. Let \(Y^a\) be the potential binary outcome under treatment \(a\). Under consistency, among people who actually received \(a\), the observed outcome equals \(Y^a\). Under conditional exchangeability, the distribution of \(Y^a\) among people with covariates \(L=l\) is the same as it would be if treatment were assigned within that covariate group. Therefore,
Averaging over the target population’s covariate distribution gives
This is the standardization formula. Positivity is needed so the conditional outcome risk for treatment \(a\) can be informed by observed patients at each covariate pattern being averaged. The derivation explains both the value and the limit of adjustment: it replaces the treatment group’s covariate mix with a common target mix, but it cannot establish exchangeability from the data alone.
Common Mistakes and Practical Interpretation
- “The more severe group did worse, so the drug caused harm.” Severity can raise outcome risk and make treatment more likely. Compare like covariate profiles and state the assumptions behind the adjusted estimate.
- “Genotype is fixed at birth, so it cannot be involved in bias.” A genotype may influence prescribing; conditioning on the resulting treatment group can create selection associations with severity or other causes of outcome.
- “Including every available variable is safest.” Adjusting for variables affected by treatment, or for colliders, can introduce bias or change the estimand. Prioritize well-measured causes of treatment and outcome that precede treatment.
- “A propensity score removes confounding.” It balances measured covariates only when the score is adequate and overlap is sufficient. It does not balance an unrecorded clinical indication by magic.
- “An adjusted association proves a pharmacogenomic mechanism.” An observational treatment contrast can remain confounded, and an association is not itself evidence that genotype biologically changes drug response.
Check Your Understanding
Answer each question using the distinction between treatment selection, outcome risk, and the assumptions needed for adjustment.
- Why can greater disease severity make an untreated comparison of two drugs misleading?
- In the genotype-selection example, why did the genotype groups have different severity distributions after restricting to treated patients, despite being independent initially?
- What does standardization change about the covariate distribution used to compare treatment risks?
- What does the positivity assumption require for a treatment comparison within a genotype and severity subgroup?
- Why does a propensity score based on recorded covariates not guarantee removal of confounding by indication?