Two Causes of Missing Records, One Mechanism Question
An intended measurement may be absent because a record was lost during a transfer, because a participant did not provide an answer, or because both events occurred. These are different operational histories. They do not, by themselves, tell us whether the missingness is MCAR, MAR, or MNAR. That classification concerns how the probability of missingness relates to the values in the data, not whether the cause seems administrative or personal.
The distinction matters in practice. An archive outage might remove records without regard to their values, but a system upgrade affecting particular clinics could remove records associated with a particular patient group. A participant may decline for reasons unrelated to the unanswered value, or may be less likely to answer precisely because of that value. The cause is useful evidence to investigate; it is not the classification.
Here, “administrative record loss” means that an intended record or measurement was not available through a data-collection, storage, linkage, or transfer process. “Participant nonresponse” means that an intended measurement was not supplied by the participant. Neither should be confused with structural absence: in structural absence, the measurement was not defined or intended for that unit.
For a single \(Y\) and fully observed \(X\), these distinctions can be expressed as follows. MCAR requires \(P(R=1\mid Y,X)=P(R=1)\). A MAR process may satisfy \(P(R=1\mid Y,X)=P(R=1\mid X)\): response can vary with \(X\), provided that this observed information accounts for the dependence and the probability does not further depend on missing \(Y\). If it still depends on \(Y\) after conditioning on the observed data, it is MNAR. With several variables missing in different combinations, the MAR condition is applied pattern by pattern using the variables observed in each pattern.
What Information Does the Classification Require?
A useful assessment begins by specifying what the intended data were and which units belonged in the target data set. For an administrative loss, a sampling frame, archive inventory, or linkage roster may show that an intended record is absent even when no row for that unit appears in the analysis file. For participant nonresponse, contact records or item-level response indicators may identify which people or questions were not answered. Without a clear denominator and a defined set of intended measurements, even a missingness rate can be misleading.
Next, identify information that was available for the missing and observed cases alike. Examples include sampling-frame variables, site, enrollment date, contact mode, batch or system version, and information recorded before the loss or nonresponse. These data can help assess whether the event varies across observed characteristics. Process logs can show whether failures followed a known technical event; contact histories can distinguish, for example, noncontact from refusal. Such details can make one mechanism more plausible than another, but they do not automatically reveal the missing values.
Finally, ask what could have made the missing measurement itself more or less likely to be unavailable. This question is especially important for MNAR. If the missing value is income, for example, information that people with higher income were less likely to report it would matter even after accounting for observed age and education. External validation data, a follow-up study, or a defensible account of the collection process may inform this question. A reason code such as “refused” identifies an event, not necessarily the relationship between refusal and the unreported value.
Worked Example: Records Lost in a Random Archive Failure
Suppose a hypothetical archive contains records for 100 sampled patients. A documented storage failure deletes 20 records, and a recovery audit establishes that the affected record identifiers were selected by a random hardware process unrelated to any patient or record characteristic. The remaining 80 records are available. What mechanism is plausible for a target measurement \(Y\)?
The observed record availability is \(80/100=0.800\), so 80% of the intended records are available and 20% are lost. The percentage alone does not classify the mechanism. The relevant information is the specified random failure process: under the stated assumption, each record's loss indicator is independent of \(Y\) and of the other data values \(X\).
Thus, for this hypothetical process, \(P(R=1\mid Y,X)=P(R=1)=0.800\), and MCAR is a defensible classification. The assumption is supported here by the audit of random record identifiers and the absence of value-related selection in the described failure process. If the failure instead affected a particular site or data-system version, the conclusion would need to be reconsidered using that information. The phrase “archive failure” alone would not justify MCAR.
Worked Example: Administrative Loss Concentrated in One System Batch
In a hypothetical data set, 60 records came from system batch A and 60 from batch B. Administrative logs show that 18 of the 60 batch A records and 3 of the 60 batch B records lack a planned laboratory result. Batch is retained for all 120 records, including those with the result missing.
The missing-result rates are \(18/60=0.300\) in batch A and \(3/60=0.0500\) in batch B, a difference of \(0.300-0.0500=0.250\), or 25 percentage points. This is evidence that availability varies by an observed variable, so MCAR across these batches is not a plausible description if the rates reflect the process rather than chance variation.
A MAR description is plausible if, within each batch, record loss does not additionally depend on the missing laboratory result or on other unobserved values. In that case, the observed batch indicator accounts for the differing loss probabilities: \(P(R=1\mid Y,\text{batch})=P(R=1\mid\text{batch})\). The logs establish the batch pattern, but do not establish the within-batch independence assumption. If batch A processed a patient group with different laboratory values and loss within A also depended on those values, the process could be MNAR relative to the available observed data. The correct conclusion is conditional: batch supports a MAR explanation only if the within-batch assumption is credible.
Worked Example: Participant Nonresponse Related to the Unreported Value
Consider a hypothetical survey of 100 people about annual income. For this illustration, suppose the complete-data values are known to the investigator: 50 people have income below $50,000 and 50 have income of $50,000 or more. Among the lower-income group, 40 answer; among the higher-income group, 20 answer. Assume this response pattern is generated by income itself, even after any observed variables are held fixed.
The response rates are \(40/50=0.800\) and \(20/50=0.400\). Overall, \(40+20=60\) people answer, so the overall response rate is \(60/100=0.600\). The different rates show how response can vary with the target value in this stipulated example. Since income is missing for nonrespondents, the income-based pattern would not ordinarily be directly visible from the survey responses alone.
By assumption, knowing the observed data does not remove the dependence of response on income. In notation, \(P(R=1\mid Y,X)\) still varies with \(Y\) after conditioning on \(X\), so this is MNAR. This conclusion follows from the stated data-generating assumption, not merely from the response-rate contrast. In an actual survey, where the missing incomes are unknown, the same contrast cannot usually be calculated from the respondent data alone; external follow-up or substantive evidence would be needed to support such a conclusion.
A Short Justification: Why the Cause Does Not Set the Label
The mechanism labels are defined by conditional relationships. For a single target variable, if loss is independent of all complete-data values, then conditioning on observed \(X\) cannot introduce dependence on missing \(Y\). In symbols, MCAR implies \(P(R=1\mid Y,X)=P(R=1)\), which is also a function of observed information alone. Thus MCAR is a special case of MAR.
The implication does not run in reverse: MAR permits response probabilities to vary with observed \(X\). Nor does the label change based on whether a person or a computer initiated the event. A participant might respond at random with respect to all data values, yielding MCAR; an administrative system might preferentially lose records for a group identified by observed site, yielding a MAR explanation if the dependence is fully accounted for by site. Either process could instead be MNAR if availability also depends on values that are missing.
Comparison, Diagnostics, and Limits
| Question | Administrative record loss | Participant nonresponse |
|---|---|---|
| What operational evidence is useful? | Archive inventories, system logs, transfer records, batch and linkage information | Contact attempts, response dates, item completion, and documented response reasons |
| What can support a MAR explanation? | Loss explained by observed process or frame variables, with no further dependence on missing values assumed | Nonresponse explained by observed respondent or frame characteristics, with no further dependence on unanswered values assumed |
| What raises an MNAR concern? | Loss related to the unrecorded measurement or an unobserved characteristic associated with it | Willingness or ability to answer related to the unanswered value after accounting for observed information |
| What does the cause establish by itself? | That an intended record was not recovered through the data process | That the participant did not provide an intended answer |
Practical diagnostics should follow the data path. Confirm the number of eligible units, compare the frame with the analysis file, inspect reason and process codes, and summarize missingness across observed characteristics. If the records lost in a system event also lack the variables that would explain the event, those variables cannot simply be treated as observed predictors. Check whether timestamps or site labels are actually available for the missing units, and whether the same variables were measured consistently across batches.
Patterns in observed data have limited interpretations. A clear difference in missingness across observed groups is evidence against MCAR, but does not by itself distinguish MAR from MNAR. Similar observed rates do not prove MCAR: missingness may depend on an unobserved value without producing a visible difference in the observed summaries. Likewise, nonresponse reasons and administrative logs can support a process account without proving that no dependence on missing values remains.
The main alternatives are not competing explanations of the same kind. Administrative-versus-participant is a distinction about the operational source of missingness; MCAR, MAR, and MNAR are distinctions about its statistical relationship to the data. Record both: document how the value became unavailable, then assess the mechanism using the variables and process evidence that are genuinely observed. When evidence cannot separate MAR from MNAR, state the uncertainty rather than treating a convenient assumption as a finding.
Common Mistakes
- “It was a technical failure, so it is MCAR.” A system event can affect particular batches or groups. Establish whether the event was unrelated to data values, or whether observed variables account for its selectivity.
- “Participants refused, so it is MNAR.” Refusal is an operational reason. It does not establish that the unanswered value itself influenced response after observed information is considered.
- “Response rates differ by site, so missingness is MNAR.” A site difference can be consistent with MAR if site is observed and accounts for the dependence. It is not, by itself, evidence of residual dependence on missing values.
- “The reason code says ‘random loss,’ so it is MCAR.” Treat such a code as a claim to examine against logs, frame information, and the actual process, not as a statistical demonstration.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A transfer error removes records from one observed clinic but does not appear to depend on values within clinic. What mechanism may be plausible, and what assumption is still needed?
- A participant nonresponse rate is higher among people with lower observed education. Does this alone establish MNAR? Explain.
- Why does an administrative reason code of “record not found” not establish MCAR?
- What additional information would help investigate whether income nonresponse is MNAR?
Solutions. (1) MAR may be plausible if clinic is observed for the affected and unaffected units and, conditional on clinic, loss does not depend on the missing value or other missing data. The clinic-specific pattern alone does not verify that assumption. (2) No. The difference is evidence against MCAR if reliable, but it can be consistent with MAR if observed education accounts for response differences; MNAR would require residual dependence on missing values. (3) The code describes the operational event, not whether loss depends on complete-data values. Clinic, batch, patient characteristics, or the target measurement could still relate to loss. (4) Useful evidence could include a follow-up that obtains income for some initial nonrespondents, an external income measure linked with appropriate safeguards, or strong process information about response conditional on observed characteristics. Such evidence can inform the assessment, though the reason for nonresponse alone is insufficient.