Why Baseline Respiratory Support Matters
A treatment can have different effects in patients with different levels of illness at enrollment. In RECOVERY, baseline respiratory support offered a clinically important way to describe illness severity when participants were randomized to dexamethasone or usual care. The central interpretive task is not simply to ask whether dexamethasone “worked” overall. It is to distinguish the evidence in patients receiving invasive mechanical ventilation, those receiving oxygen without invasive ventilation, and those receiving neither.
The distinction matters because a subgroup estimate answers a narrower question than an overall trial result. A comparison within one subgroup estimates the treatment contrast among patients in that category. Evidence that treatment effect varies by subgroup requires a comparison of treatment effects across categories. Those are related questions, but they are not the same test.
The relevant outcome was death within 28 days of randomization. The published comparison used time-to-event analyses and reported rate ratios. A rate ratio below 1 favors dexamethasone for mortality; a value above 1 points toward a higher mortality rate with dexamethasone. A rate ratio is not necessarily the same as the ratio of the two groups’ crude 28-day mortality proportions: the former uses the timing of deaths in the analysis, whereas the latter compares only the proportions dead by day 28.
RECOVERY’s Results by Support at Randomization
The reported subgroup results show a pattern across increasing levels of respiratory support. In patients receiving invasive mechanical ventilation, the published mortality rate ratio was 0.64 (95% CI 0.51 to 0.81; p=0.0003). In patients receiving oxygen without invasive ventilation, it was 0.82 (95% CI 0.72 to 0.94; p=0.0021). In patients receiving neither oxygen nor invasive ventilation, it was 1.19 (95% CI 0.92 to 1.55; p=0.14). The trial reported evidence that the treatment effect varied with the level of respiratory support (p<0.001 for trend).
| Support at randomization | Dexamethasone deaths / participants | Usual-care deaths / participants | Published mortality rate ratio (95% CI) | Within-group p-value |
|---|---|---|---|---|
| Invasive mechanical ventilation | 95 / 324 (29.3%) | 283 / 683 (41.4%) | 0.64 (0.51 to 0.81) | 0.0003 |
| Oxygen, without invasive ventilation | 298 / 1,279 (23.3%) | 682 / 2,604 (26.2%) | 0.82 (0.72 to 0.94) | 0.0021 |
| Neither oxygen nor invasive ventilation | 89 / 501 (17.8%) | 145 / 1,034 (14.0%) | 1.19 (0.92 to 1.55) | 0.14 |
For the first two groups, the confidence intervals lie below 1, and the reported p-values indicate evidence against a null rate ratio of 1 within those groups. The estimates support lower mortality rates with dexamethasone among participants receiving invasive ventilation or oxygen at randomization. The results are strongest in the ventilated group by the reported relative effect, though the size and precision of subgroup estimates should not be judged solely by comparing their p-values.
For participants receiving no respiratory support, the estimated rate ratio is above 1, but its confidence interval includes 1 and is compatible with effects ranging from a lower mortality rate to a substantially higher one. The result does not establish that dexamethasone increased mortality in this group. It is an imprecise estimate that does not provide clear evidence of benefit or harm on its own.
The crude 28-day risks make the direction of the observed differences more concrete. For those receiving neither form of support, the difference in observed mortality proportions is \(89/501-145/1034=0.03741\), or 3.741 percentage points higher with dexamethasone. That descriptive difference is not the published rate ratio, and it does not override the uncertainty shown by the subgroup confidence interval. In the oxygen group, the crude difference is about 2.891 percentage points lower with dexamethasone; in the invasive-ventilation group it is about 12.11 percentage points lower. These are comparisons of observed proportions, not substitutes for the trial’s time-to-event estimates.
Subgroup Evidence and Treatment-Effect Variation
A common error is to reason that treatment effects differ because one subgroup has a statistically significant result and another does not. That is not a valid test of a difference. A small p-value in one group and a larger p-value in another can arise even when the underlying effects are similar, because precision and sample size differ. To assess whether treatment effect varies, compare the subgroup effects directly using an interaction analysis or an appropriate trend test.
In broad terms, an interaction analysis asks whether treatment effect, expressed on a chosen scale, changes across baseline-support categories. For example, a model may include treatment, support group, and treatment-by-support terms. Evidence for interaction is evidence against equal treatment effects on that model’s chosen scale. It does not by itself identify a biological mechanism, nor does it establish that every pair of subgroups differs.
A simplified derivation clarifies the distinction. Suppose two independent subgroups have estimated rate ratios \(\widehat{RR}_1\) and \(\widehat{RR}_2\), with standard errors \(SE_1\) and \(SE_2\) for their log rate ratios. Under the null hypothesis of equal rate ratios, the log-scale contrast is zero. Independence gives the contrast standard error \(\sqrt{SE_1^2+SE_2^2}\), so a Wald statistic is the observed contrast divided by this standard error. The test concerns the difference between subgroup effects; it is not a comparison of whether each separate p-value crosses a threshold.
The simple calculation assumes independent subgroup estimates and approximate normality of the log estimates. A trial’s prespecified model may use a different but suitable interaction procedure, especially for multiple ordered categories. For RECOVERY, the reported p<0.001 for trend supports variation in effect across respiratory-support levels. It is distinct from the within-subgroup p-values in the table.
Worked Example: Reading a Hypothetical Oxygen-Group Risk Difference
Suppose a hypothetical randomized trial reports 46 deaths among 200 participants assigned to a treatment and 60 deaths among 200 assigned to control in an oxygen-only subgroup. Assume participants were randomized within the subgroup, follow-up for 28-day death is complete, and the groups were analyzed according to randomized assignment.
The observed risks are \(46/200=0.23\), or 23%, in the treatment group and \(60/200=0.30\), or 30%, in the control group. The risk difference, treatment minus control, is \(0.23-0.30=-0.07\), equal to 7 percentage points fewer deaths in the treatment group over 28 days in this hypothetical sample.
The crude risk ratio is \(0.23/0.30=0.767\). In this example, the observed treatment-group risk is about 0.77 times the control-group risk. The calculation is a descriptive comparison of proportions. It would not automatically equal a time-to-event rate ratio if participants’ death times or censoring patterns were incorporated into a different analysis.
These observed differences alone do not establish a treatment effect. An uncertainty interval and the trial’s analysis are needed for inferential conclusions. The hypothetical result illustrates how to state the direction, scale, and time period without claiming that a 7-percentage-point difference is certain to recur.
Worked Example: Why “Significant Here, Not There” Is Not an Interaction Test
Consider two hypothetical support groups with estimated mortality rate ratios of 0.70 in one group and 1.20 in another. Suppose the standard errors of the log rate ratios are 0.10 and 0.15, respectively. Treat the estimates as independent and use a two-sided Wald test for equality of rate ratios.
The log-scale contrast is \(\log(0.70)-\log(1.20)=\log(0.70/1.20)=\log(0.5833)=-0.5390\). Its standard error is \(\sqrt{0.10^2+0.15^2}=\sqrt{0.0325}=0.1803\).
Therefore, \(Z=-0.5390/0.1803=-2.99\). The two-sided normal p-value is approximately 0.0028. Under the stated assumptions, this is evidence that the two hypothetical rate ratios differ on the log scale. It is the direct contrast that answers the interaction question—not the fact that one subgroup’s separate test might be significant while the other’s is not.
This calculation is illustrative, not a recalculation of RECOVERY’s reported interaction test. Actual analyses should use the trial’s specified model, account for the design and outcome data, and state the effect scale on which interaction is assessed.
Interpreting the No-Support Finding Carefully
The no-support subgroup requires particular care. Its point estimate is above 1, and its crude mortality proportion is higher in the dexamethasone arm than in usual care. But the uncertainty interval for the published rate ratio includes 1, with p=0.14. Thus, the result does not provide strong evidence of a difference from no effect within this subgroup. It is also not proof that the treatment has no effect: the interval permits clinically relevant benefit as well as harm.
The no-support finding should be interpreted together with the pattern across support levels and the reported trend test, while keeping the different statistical questions separate. The evidence supports benefit among patients already receiving oxygen or invasive ventilation. It does not warrant a claim that dexamethasone benefits every hospitalized patient, regardless of respiratory status. Nor does the imprecise estimate among patients receiving neither type of support establish that treatment causes harm there.
Worked Example: Translating a Hypothetical No-Support Estimate
Suppose a hypothetical no-support subgroup has a published mortality rate ratio of 1.15 with a 95% confidence interval from 0.85 to 1.56 and p=0.36. Assume the rate-ratio analysis is appropriate for the trial’s follow-up and the subgroup was defined before treatment.
The point estimate is 15% above 1, so the estimated mortality rate is higher in the treatment group on this scale. However, the interval contains 1. Values below 1 and above 1 remain compatible with the data under the analysis. The p-value is not evidence that the null is true; it indicates that these data are not unusual enough, under the null and model, to reject it at conventional significance levels.
A careful conclusion is: “This hypothetical subgroup result is inconclusive about benefit or harm; its point estimate is above 1, but the interval is wide and includes no difference.” It would be incorrect to conclude either that harm was demonstrated or that the treatment has no effect.
Assumptions, Diagnostics, and Limitations
Interpretation depends on the trial’s randomized comparison and the quality of subgroup classification. Randomization supports a causal comparison of assignment within the trial, provided the analysis respects assignment and follow-up is handled appropriately. Respiratory support must be classified at baseline; defining groups using support received after randomization could condition on a variable affected by treatment and complicate causal interpretation. The reported effect is an effect of assignment to dexamethasone versus usual care in the relevant trial context, not necessarily the effect of receiving every dose as assigned.
When reading a subgroup table, check that the categories are mutually exclusive, their participant totals reconcile with the randomized groups, and the outcome, time window, and effect measure are clear. Check whether the interaction or trend test is reported and whether subgroup analyses were prespecified. Many subgroup comparisons create opportunities for chance patterns, so isolated estimates deserve restraint. Also ask whether confidence intervals are sufficiently precise for the clinical distinction being discussed.
The principal alternative to subgroup interpretation is to report only the overall treatment effect. That is more concise and may be more precise, but it can conceal clinically meaningful variation by baseline severity. Conversely, emphasizing subgroup estimates without the overall result or the interaction evidence invites overinterpretation. The appropriate approach is to report the overall comparison, clinically motivated subgroup estimates, uncertainty intervals, and the formal evidence for effect variation—without treating every subgroup as an independent trial.
A further limitation is that interaction depends on scale. Treatment effects can appear more or less heterogeneous when expressed as risk differences rather than rate ratios. A rate ratio below 1 does not imply the same absolute number of deaths prevented in groups with different baseline risks. Therefore, relative and absolute effects answer complementary questions, and their units must be explicit.
Confirm that respiratory support is the baseline category and that the endpoint is 28-day mortality.
For a rate ratio, compare with 1; for a risk difference, identify which arm is subtracted from which and state percentage points.
Use the confidence interval and p-value to describe evidence for that subgroup contrast, not to declare the null true or false with certainty.
Use a direct interaction or trend test rather than comparing subgroup p-values informally.
Describe the randomized population, treatment contrast, follow-up, effect scale, and the uncertainty around subgroup conclusions.
Check Your Understanding
Answer each question, then compare with the solutions below.
- In RECOVERY, what did the no-respiratory-support subgroup estimate show, and what conclusion does its confidence interval permit?
- Why is it invalid to conclude that treatment effects differ merely because one subgroup has p<0.05 and another has p>0.05?
- A hypothetical subgroup has 36 deaths among 180 treated participants and 45 among 180 controls. Calculate the risk difference in percentage points, treatment minus control.
- What does a reported interaction p-value address that a subgroup-specific p-value does not?
Solutions. (1) The published rate ratio was 1.19 (95% CI 0.92 to 1.55; p=0.14). The point estimate is above 1, but the interval includes 1 and permits both lower and higher mortality rates; the result does not establish benefit or harm. (2) Separate p-values depend on each estimate’s uncertainty. A direct interaction test evaluates whether the estimates differ from one another. (3) The treated risk is \(36/180=0.20\), or 20%; the control risk is \(45/180=0.25\), or 25%. The risk difference is \(0.20-0.25=-0.05\), or 5 percentage points fewer deaths in the treated group in this hypothetical sample. (4) An interaction p-value tests evidence that the treatment effect varies across subgroups on the analysis scale; a subgroup-specific p-value tests the treatment contrast within one subgroup.