Missing-Data Mechanisms in Genetic Association

Why Missingness Matters in Genetic Association

A genetic association analysis relates a phenotype to genotype, often while adjusting for covariates. In practice, a phenotype may not be recorded for every participant, some covariate values may be absent, and a genotype may fail quality control or produce no call. The crucial question is not just how many values are missing. It is what determines which values are missing.

If the chance of a missing phenotype, covariate, or genotype is related to the value itself, the observed participants or calls may not represent the data the association model is meant to describe. If missingness is related only to information already observed, some likelihood-based approaches can still be valid under additional conditions. The labels MCAR, MAR, and MNAR make these distinctions precise.

These definitions concern a specified set of data and missingness indicators. A mechanism can be MCAR for one variable and MAR or MNAR for another. For example, a phenotype could be missing more often at one observed study site, while genotype calls could fail more often for a particular true genotype. The first pattern might be MAR with site observed; the second is MNAR with respect to the unobserved genotype.

Reading Missingness Patterns

Suppose a study records a binary disease phenotype \(Y\), genotype \(G\), and age \(C\). If age is missing more often at one observed site, missingness is not MCAR with respect to the study data: it is associated with an observed variable. If site and the other observed information explain the missingness, and missingness does not further depend on the unrecorded age after conditioning on that information, the age missingness is MAR. If participants with unusually high unrecorded ages are more likely to omit age even among participants with the same observed information, that is MNAR.

The same reasoning applies to the phenotype. If disease status is unrecorded more often among people with an observed clinical characteristic, that can be MAR if the observed information accounts for the missingness. If the probability of recording disease status depends on the unrecorded disease status itself, even after conditioning on observed variables, the mechanism is MNAR. For genotype calls, a failure rate that varies with observed batch may be MAR if batch is observed and adequately accounts for the pattern. A failure rate that depends on the true, unobserved genotype is MNAR.

A dataset can contain several missingness patterns at once. Some participants may have phenotype but not age, others may have genotype but not phenotype, and still others may have all three. MCAR, MAR, and MNAR must be understood relative to the variables and patterns under consideration; an overall percentage missing does not identify a mechanism.

What the Assumptions Support

Under MCAR, selection into the observed subset is independent of the complete data. Subject to the study’s sampling design and the analysis model, complete cases therefore do not differ systematically from the target data because of this additional missingness. This is a strong assumption; different missingness rates across observed groups are evidence against it.

MAR is less restrictive because it allows missingness to depend on observed variables. It can support likelihood-based inference when the full-data model is correctly specified, the missingness mechanism is MAR, and the parameters governing the data and the missingness mechanism are distinct. There must also be adequate information in the observed data to estimate the quantities of interest; in particular, relevant observed-data patterns cannot have zero probability in the target setting. MAR does not mean that every complete-case analysis is unbiased. A method must account appropriately for the observed variables related to missingness.

Under MNAR, the missingness probability depends on values that are themselves unobserved, even after conditioning on recorded information. The observed data generally do not identify that dependence without additional assumptions or information. Standard likelihood analysis that simply ignores missingness is therefore not justified by the MAR argument. The mechanism may require explicit modeling or sensitivity analysis.

For an association odds ratio, selection can be seen directly. Let \(R=1\) mean that both binary \(Y\) and genotype group \(G\) are observed, and define \(q_{gy}=P(R=1\mid G=g,Y=y)\). The odds of \(Y=1\) rather than \(Y=0\) among retained participants in genotype group \(g\) equal the full-data odds multiplied by \(q_{g1}/q_{g0}\). Consequently, the observed odds ratio comparing \(G=1\) with \(G=0\) is the full-data odds ratio multiplied by a factor involving the selection probabilities.

This expression assumes that the same binary outcome and genotype groups define both odds ratios, and that retention requires both values to be observed. It shows why a missingness rate alone cannot determine bias: the relevant issue is how retention varies jointly across outcome and genotype groups. If retention is MCAR, all \(q_{gy}\) are equal and the multiplier is 1. More generally, the multiplier can also equal 1 under particular selection patterns, but that does not make the mechanism MCAR or guarantee validity for other estimands.

Genotype Calls and Phenotype Observation

Genotype missingness deserves particular care because “missing genotype” can arise at different stages. A call may fail because of an observed batch or technical condition, or because the underlying genotype affects how likely a call is to succeed. If batch is observed and accounts for the failure pattern, MAR may be plausible relative to the recorded variables. If heterozygotes, for example, are more likely to be uncalled even after conditioning on observed technical information, the mechanism is MNAR with respect to true genotype. Whether a particular analysis is robust then depends on how that call process relates to the association being estimated.

Phenotype and covariate missingness also need not share a mechanism. A clinical phenotype could be missing because of observed clinic attendance, while a covariate is missing because of a participant’s unobserved value. Calling the entire dataset “MAR” without specifying which variables and observed information are involved can hide this distinction.

A Practical Assessment

Missingness patterns are useful for checking implications of an assumption, not for proving the mechanism. Researchers can summarize missingness by observed phenotype, genotype calls, covariates, site, and technical batch. Large differences across these groups can rule out MCAR relative to those recorded variables, but similar rates do not establish MCAR. In particular, MAR and MNAR generally cannot be distinguished from observed data alone: the values that would reveal dependence on the missing data are not observed.

A defensible assessment names the variable that is missing, the observed information considered, and the assumption used by the analysis. For example: “Age is missing more often at Site B; we assume that, conditional on site and the other recorded covariates, age missingness does not depend on the unobserved age.” That is a MAR assumption, not a finding established by the rate comparison.

Common Mistake

Wrong reasoning: “Only 2% of genotypes are missing, so missingness cannot bias the association.” A small missing fraction can still be concentrated in a genotype–phenotype group and alter the observed association. The percentage alone contains no information about how missingness is distributed.

Correction: Examine missingness patterns against observed variables, state the assumptions about unobserved values, and connect those assumptions to the analysis used. Diagnostics can challenge MCAR, but they cannot prove MAR or rule out MNAR. A complete-case result is not automatically justified just because most participants have complete data.