Summarizing Modality Availability Patterns

Why Summarize Availability Patterns?

A multi-omics cohort can have many different combinations of observed modalities. One subject may have RNA and protein measurements, another may have only RNA, and a third may have every planned modality. A list of modality-specific sample sizes gives useful marginal information, but it does not show which measurements occur together. Pattern-frequency tables make that joint structure explicit.

The aim here is descriptive: count the observed combinations, compare their frequencies, and identify combinations that are common, rare, or absent in the cohort being summarized. These counts help assess how much of the cohort has each modality and how many subjects have all modalities. They do not, by themselves, explain why a modality is unavailable or establish that the observed subjects represent a wider population.

A pattern uses a fixed modality order. For example, if the order is RNA, protein, metabolite, then \(101\) means RNA and metabolite are available, while protein is not. The order must be stated and used consistently; changing the order changes the interpretation of every string.

Before counting, define the cohort and the modalities being summarized, and make sure each subject has one correctly aligned indicator for each modality. Availability is a binary summary at the subject-by-modality level: it records whether that modality is available for the subject under the chosen definition. It does not describe how many features within a modality are measured or the reason any measurement is unavailable.

From Indicator Matrix to Pattern Frequencies

With \(K\) modalities, there are \(2^K\) mathematically possible binary patterns. A complete table lists every one of them, including those with frequency zero. Listing only patterns seen in the data can hide the fact that other combinations were considered and found to be absent.

Let \(n_r\) be the number of subjects whose pattern is \(r\), where \(r\) ranges over all \(2^K\) possible patterns. The patterns divide the cohort into mutually exclusive groups: every subject belongs to exactly one group. Consequently, the frequencies must sum to the cohort size.

The total number with modality \(j\) available is found by adding frequencies for patterns whose \(j\)th entry is 1. Dividing by \(n\) gives that modality’s availability proportion. The all-ones pattern gives the number and proportion of subjects with every listed modality available.

These are descriptive proportions for the defined cohort. They can be reported as counts, proportions, or percentages, but the denominator should be explicit. A modality’s availability proportion and the complete-case proportion answer different questions: the first concerns one modality at a time; the second concerns the simultaneous availability of all \(K\) modalities.

A Short Justification for the Checks

The frequency and marginal summaries are linked by the definition of a pattern. To see why, define \(I_i(r)=1\) when subject \(i\) has pattern \(r\), and \(I_i(r)=0\) otherwise. Since every subject has exactly one pattern, the indicators over all possible patterns sum to 1 for each subject. Summing over subjects gives the total-frequency identity.

For modality \(j\), a subject contributes to the availability count exactly when their pattern has \(r_j=1\). Thus adding the frequencies of precisely those patterns counts each subject with modality \(j\) once and every other subject zero times. This also gives a practical audit: calculate marginal counts both from the indicator matrix and from the pattern table, then verify they match.

Comparing Groups and Choosing a Summary

When the cohort contains predefined groups, such as collection sites, summarize each group with its own denominator before reporting an overall table. This makes the group-specific pattern distribution visible and prevents a pooled count from obscuring differences in the composition of the groups. The example below is descriptive; it does not identify what caused the difference.

Diagnostics, Alternatives, and Limitations

A pattern table is only as reliable as the subject alignment and availability definition behind it. Before interpreting the table, verify that subject identifiers refer to the same cohort across modalities, each subject appears once in the summary, and the order of modalities is documented. Then check the frequency total and independently reproduce each marginal count. If a pattern is not shown, determine whether it was deliberately omitted or has frequency zero; a complete table makes that distinction unambiguous.

A common mistake is to report only marginal sample sizes and assume they reveal the joint pattern. They do not: two cohorts can have identical counts for each modality but different combinations of modalities observed on the same subjects. Conversely, a long pattern table may be cumbersome when \(K\) is large, since the number of possible patterns grows as \(2^K\). In that setting, a concise report can show the most frequent patterns, the number of unobserved patterns, and key marginal and all-modality counts, while making clear what was omitted.

The main alternatives serve different purposes. Marginal availability counts are compact and useful when the question concerns each modality separately, but conceal co-occurrence. The complete-case count is compact when the question is specifically how many subjects have every modality, but discards information about partial combinations. Pattern frequencies retain that joint descriptive information, at the cost of a potentially large table. None of these summaries establishes why a modality is absent, whether availability is related to subject characteristics, or what an analysis should do with partially observed data. Those are separate questions.