Why Classify the Interim View?
An interim review can use information at different levels of detail. A summary across all randomized participants may show overall outcome behavior, while separate summaries by arm can show an observed difference between two groups. Whether the groups are labelled only with arbitrary codes or with their actual treatment identities determines whether that difference can be attributed to a particular treatment. Participant-level records add still another kind of detail: they preserve each person's outcome and potentially other recorded characteristics.
These distinctions matter because the form of information constrains what a reviewer can learn. A pooled average does not usually reveal a treatment contrast. A coded arm comparison can reveal the size and sign of a contrast between the coded groups, but not which group received which treatment. An identified comparison can attach that contrast to the actual treatment groups. Individual-level data can support more detailed examination, but their granularity alone does not reveal treatment identity or make an observed difference conclusive.
Two Questions Behind the Four Labels
The four labels are useful, but they do not all describe the same feature. Pooled, treatment-coded, and treatment-identified primarily describe how group membership is represented in a summary. Individual-level describes the granularity of the records. Consequently, individual-level data can also be treatment-coded or treatment-identified, or can omit group membership. For a precise description, state both the level of detail and whether treatment identity is available.
Suppose a two-arm randomized trial compares treatments \(A\) and \(B\) on a quantitative endpoint \(Y\). Let \(n_A\) and \(n_B\) denote the numbers with observed interim outcomes in the two groups, and let \(\bar{x}_A\) and \(\bar{x}_B\) denote their observed sample means. If the endpoint is measured in points, for example, the difference \(\bar{x}_A-\bar{x}_B\) is also measured in points. A positive difference means the observed mean is higher in group \(A\); whether that is favorable depends on what higher endpoint values mean.
Assume for the examples that randomized assignment is the basis for group membership, that the same endpoint and measurement units are used in both groups, and that the reported summaries include the stated participants. These conditions make the numerical comparisons interpretable as descriptions of the observed interim data. They do not by themselves establish that an interim difference is a reliable estimate of a treatment effect: chance variation, incomplete outcomes, or changes in who contributes data can affect it. In particular, do not infer a causal effect merely from a difference in observed means.
What a Pooled Summary Can and Cannot Show
For a quantitative endpoint, a pooled mean combines observations from both groups without reporting separate group means. If every observed participant contributes one outcome, the overall mean is the sample-size-weighted average of the two group means:
This formula can summarize the overall observed outcome level. By itself, however, it does not determine either group mean or their difference. Different pairs of arm means can produce the same pooled mean. When group sizes are equal, for example, raising one group mean by a given amount and lowering the other by the same amount leaves the pooled mean unchanged. Thus a pooled average cannot disclose whether one group is doing better than the other.
Worked Example: A Pooled Mean Hides the Contrast
Suppose a hypothetical interim summary contains 20 observed outcomes from each of two randomized groups. The group means are not reported, but the pooled mean is 10.4 points. What can a reviewer conclude about the comparison between groups?
The reported pooled mean is compatible with many group-specific results. For example, group means of 10.4 and 10.4 give
But group means of 11.8 and 9.0 give the same pooled summary:
In the first case, the observed group difference is 0 points; in the second, the first group's mean is 2.8 points higher. Both match the reported pooled mean. Therefore, this pooled view permits a statement about the overall observed mean, but it does not identify the interim comparative outcome.
Coded and Identified Group Summaries
An arm-specific summary preserves more comparative information than a pooled summary. In a treatment-coded view, the groups might be labelled “Code A” and “Code B.” The labels distinguish groups, so the reviewer can calculate and describe their observed contrast. If the code-to-treatment mapping is unavailable to that reviewer, the reviewer cannot say which actual treatment corresponds to either label.
In a treatment-identified view, the group summaries are linked to actual treatment identities, such as the investigational treatment and the control treatment. The direction of the observed contrast can then be described in those terms, subject to knowing how the endpoint is oriented. Identification does not remove uncertainty or establish that the observed contrast is a true treatment effect.
Worked Example: An Arm-Specific Contrast With Unknown Identity
In a hypothetical review, “Code A” has 24 observed outcomes with a mean of 12.1 points, and “Code B” has 26 outcomes with a mean of 10.7 points. Calculate the coded contrast and state what the reviewer can and cannot learn.
Taking Code A minus Code B gives
The coded information shows that the observed mean for Code A is 1.4 points higher than the observed mean for Code B. It also shows the two arm means and their sample sizes. If the mapping from codes to treatments is not available, the reviewer cannot determine whether the investigational treatment or the control group has the higher observed mean. Even if higher scores are known to be better, that mapping is still needed to say which treatment's group had the higher mean.
Worked Example: Identified Groups and Endpoint Direction
Suppose a hypothetical trial compares an investigational treatment with control on a symptom-burden score, where lower scores indicate fewer symptoms. At an interim review, 30 participants in the investigational group have a mean of 7.2 points and 28 participants in the control group have a mean of 8.0 points. Describe the observed comparison.
Define the contrast as investigational treatment minus control:
The identified interim summaries show an observed mean symptom-burden score 0.8 points lower in the investigational group than in the control group. Because lower scores indicate fewer symptoms, the direction of this observed comparison favors the investigational group. This is a description of the interim data, not proof of benefit: the sample means can vary by chance, and the assumptions needed for any stronger inference have not been established by this calculation.
What Individual-Level Information Adds
An individual-level view contains one record per participant, rather than only a summary such as a mean. Depending on its fields and access controls, each record might contain an outcome, a participant identifier, a randomization code, or other variables. Individual-level records can preserve information about the distribution of outcomes, missing observations, and differences among participant subgroups. But a record-level file without treatment assignment does not by itself support an arm comparison; a file with coded assignment supports a coded comparison; and a file with identified assignment makes the treatment mapping available.
This distinction prevents a frequent category error: granularity and treatment identity are separate properties. A line listing with coded group labels is individual-level and treatment-coded. A table of identified group means is treatment-identified but aggregated. Describing only one of these properties can leave the actual information available unclear.
Worked Example: Classifying a Participant-Level Extract
A hypothetical interim extract has eight rows, one for each participant with an observed endpoint. Each row contains the participant's outcome in points and a group label, “Code A” or “Code B”; the code mapping is held separately and is not available to the reviewer. How should this view be classified, and what can be learned?
It is individual-level because each participant's outcome is retained in a separate row. It is also treatment-coded because the rows identify two groups by arbitrary labels without revealing the actual treatments.
The reviewer can calculate coded group summaries from the rows and inspect the observed participant outcomes within each coded group. The reviewer cannot attach either group's outcomes to the investigational treatment or control. Furthermore, the eight rows represent only participants with observed endpoints; without information about participants whose endpoints are missing, the extract alone cannot establish whether the observed outcomes represent everyone randomized.
A Short Justification: Why Pooling Loses the Contrast
The information loss in pooling can be shown directly. Let \(N=n_A+n_B\), and define the group difference \(\Delta=\bar{x}_A-\bar{x}_B\). Solving the weighted-mean equation together with this definition gives
For fixed group sizes and fixed pooled mean, every possible value of \(\Delta\) yields a corresponding pair of group means through these equations. The pooled mean therefore does not determine the group contrast. Group-specific information is needed to identify it. Even when a coded contrast is available, treatment identity is needed to interpret its direction as investigational treatment versus control.
Classification Checks and Common Pitfalls
When classifying an interim view, identify what the reviewer can actually access, not merely what exists somewhere in the trial's data system. A treatment mapping stored separately does not make an otherwise coded view treatment-identified for a reviewer who cannot access that mapping. Conversely, if the reviewer can link the code to actual treatment identity, the view is identified for that reviewer.
- Calling any group comparison pooled. If separate group summaries are reported, the view is arm-specific, even if no participant-level records are shown.
- Treating codes as treatment identities. “Code A” is not inherently the investigational treatment. Without the mapping, the contrast can be described only in coded-group terms.
- Assuming individual-level means unblinded. Participant-level detail describes granularity; treatment identity depends on whether assignment labels or their mapping are available.
- Calling an observed difference a treatment effect without qualification. A numerical difference is descriptive. Its interpretation as an effect requires appropriate design, measurement, and inferential assumptions.
- Ignoring endpoint direction. A higher mean is not automatically better. State what higher or lower values mean before describing which direction favors a treatment.
A practical diagnostic is to ask whether the view contains separate group summaries or labels, whether those labels are mapped to actual treatments for this reviewer, and whether each participant remains separately represented. If the answers are unclear, the information description is incomplete. Also check that both groups use the same endpoint definition, units, and interim cutoff; incompatible summaries should not be treated as a meaningful direct comparison.
Comparing the Views and Their Limits
| View | What it preserves | What it cannot establish by itself |
|---|---|---|
| Pooled summary | Overall aggregate outcome information | The arm-specific means or their contrast |
| Treatment-coded summary | Separate group outcomes and a coded contrast | Which actual treatment corresponds to each code |
| Treatment-identified summary | Separate outcomes linked to actual treatment identities | That an observed contrast is conclusive evidence of a treatment effect |
| Individual-level records | Participant-level outcome detail, with whatever group fields are included | Any group comparison if assignment is absent; treatment identity if labels remain unmapped |
These views are not competing statistical procedures. They are different representations of interim information. More detailed or identified information can answer additional descriptive questions, but it also carries limitations: summaries may conceal variation, coded labels prevent treatment-specific interpretation, and participant-level files may include incomplete or selectively observed outcomes. The appropriate description is the most precise one supported by the actual fields and access—not an assumption that one category automatically implies another.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A report gives one overall mean across both randomized groups, with no group-specific results. What information category is this, and can the treatment contrast be recovered from the mean alone?
- A table gives separate means for “Code R” and “Code S,” but the reviewer cannot access the code mapping. What can the reviewer say about a difference of 0.6 points?
- A file has a separate row for each participant and includes the actual treatment assignment. Which information properties should be named?
- Why can two equal-sized groups have different mean contrasts while producing the same pooled mean?
- An identified comparison shows a lower mean on an endpoint where higher values indicate improvement. Which group has the favorable observed mean, and what qualification is needed?
Solutions. (1) It is a pooled summary. The treatment contrast cannot be recovered from the overall mean alone because different arm means can yield the same weighted average. (2) It is treatment-coded and arm-specific; the reviewer can say which coded group has the higher or lower mean by 0.6 points, but cannot attribute the difference to an actual treatment. (3) It is individual-level and treatment-identified, because it retains participant rows and links assignment to actual treatment identity. (4) With equal group sizes, the pooled mean is the average of the two group means; increasing one mean and decreasing the other by the same amount leaves that average unchanged while changing the contrast. (5) The group with the higher mean has the favorable observed mean. This remains a description of the interim data, not by itself proof that the treatment caused an improvement.