Why Use a Pre-Modeling EDA Map?
Before fitting a population pharmacokinetic model, it helps to know what the analysis data actually contain: how concentrations are distributed, which times and doses are represented, how many observations each subject contributes, and how covariates vary across the sample. A structured review makes it less likely that an apparent pattern is really a coverage gap, a small subgroup, or a few densely sampled subjects.
This review is a map, not a model-selection procedure. A visible difference between groups does not establish a causal effect, and a sparse region in a plot does not by itself show that a model is wrong. The goal is to describe the data that will inform modeling and to formulate specific questions that later analysis can address. The dataset should already have passed the relevant construction and quality-control checks, including reconciliation of dose, time, concentration, and covariate records.
A Checklist for the Analysis Data
Begin by confirming the unit represented by each row. A concentration record is usually one sample for one subject at a recorded time; it is not a new independent subject. Keep a record-level view for sampling and concentration summaries, and a subject-level view for characteristics such as baseline covariates and number of records. For longitudinal covariates, also retain the time at which each value applies.
Count records with measured concentrations, records below the quantification limit, and missing or otherwise unusable values according to the analysis-data conventions. Review ranges and quantiles with units, and note whether unusual values occur in one subject, time region, dose group, or visit. Ask whether the pattern could reflect data coverage or recording conventions before proposing a biological explanation.
Describe the sampling-time range and the number of observations across the sampling window. Check which subjects contribute at early, middle, and late times, and whether visits or dosing occasions are represented consistently. A nominal schedule and the actual recorded times are not interchangeable descriptions.
Tabulate subjects and records by dose, regimen, route, formulation, or visit when these distinctions apply. Check whether dose groups have comparable time coverage and whether one group is represented by only a few subjects. Distinguish a subject's assigned dose from the number of concentration records available for that subject.
Summarize the number of subjects, records per subject, and subjects with sparse or unusually dense sampling. Check whether observations are concentrated in a small subset of subjects. Repeated samples may be informative, but they do not increase the number of independent subjects by the same amount.
For continuous covariates, inspect ranges, quantiles, missingness, and possible clustering. For categorical covariates, count subjects in every category, including unknown or missing categories as represented in the analysis data. Then check overlap: for example, whether the range of body weights is represented in more than one dose group.
The dimensions should be considered together. A concentration range may look broad overall because it combines different doses or sampling times. A covariate may have a wide overall range but little overlap between treatment groups. A late-time summary may depend on only a few subjects. Each of these is a reason to ask a more precise question, not a reason to conclude immediately that a covariate or dose has a particular effect.
Why Record-Level and Subject-Level Summaries Differ
A pooled record-level mean gives more weight to subjects with more records. This is a property of the arithmetic, not a defect in the calculation. It means that the pooled mean answers a different descriptive question from the mean of subject-specific means, where each subject receives equal weight.
Here \(N\) is the number of subjects, \(n_i\) is the number of records for subject \(i\), and \(\bar{x}_i\) is that subject's mean across the records being summarized. The formula follows by writing the sum of all observations as the sum of each subject's observations: \(\sum_i n_i\bar{x}_i\). Dividing by the total record count, \(\sum_i n_i\), gives the pooled record mean. By contrast, the equal-subject average is \(\frac{1}{N}\sum_i\bar{x}_i\). Neither summary alone describes the full longitudinal concentration-time pattern.
Worked Example: Unequal Numbers of Concentration Records
Suppose a hypothetical analysis subset contains three concentration records in mg/L: subject A contributes 2.0 and 4.0 mg/L, while subject B contributes 10.0 mg/L. Compare the pooled record mean with the mean of the two subject means.
Subject A's mean is \((2.0+4.0)/2=3.0\) mg/L; subject B's mean is \(10.0/1=10.0\) mg/L. The pooled record mean is
The equal-subject average is \((3.0+10.0)/2=6.5\) mg/L. The pooled value weights subject A twice as much as subject B because A contributes two records and B contributes one. These summaries differ because they weight the subjects differently; neither should be read as a typical concentration over the sampling window. The next question is whether the records were taken at comparable times and under comparable dosing conditions.
Worked Reviews Across the Five Dimensions
Worked Example: Mapping Time and Dose Coverage
Consider a hypothetical study with four subjects. All received the same assigned dose of 100 mg. Their post-dose concentration-sampling times, in hours, were: subject A, 0.5 and 2; subject B, 1 and 8; subject C, 0.5, 1, and 2; and subject D, 8 and 24.
There are four subjects and \(2+2+3+2=9\) concentration records. By subject, the record counts are 2, 2, 3, and 2. The observed time range is 0.5 to 24 hours. Records occur at early times (0.5, 1, and 2 hours), at 8 hours, and at 24 hours; however, only subject D contributes at 24 hours, and only subjects B and D contribute at 8 hours.
Dose has no between-subject variation in this example, so these data cannot describe a dose-group contrast. They can prompt questions about whether late-time information depends heavily on a small number of subjects and whether that is expected from the sampling design. They do not establish that the 24-hour concentration is representative of all subjects. The coverage summary is therefore a prompt for later modeling and study-design interpretation, not an estimate of a dose effect.
Worked Example: Reviewing Covariate Spread and Group Overlap
Suppose eight hypothetical subjects have baseline body weights, in kg, of 48, 52, 55, 58, 62, 66, 91, and 98. Six subjects received 100 mg and two received 200 mg. The 100-mg subjects had weights 48, 52, 55, 58, 62, and 66 kg; the 200-mg subjects had weights 91 and 98 kg.
The overall weight range is 48 to 98 kg. With the values ordered, the median is \((58+62)/2=60\) kg. The mean is \((48+52+55+58+62+66+91+98)/8=530/8=66.25\) kg. The mean is higher than the median because the two largest values pull it upward, so reporting only the mean would hide the concentration of six subjects between 48 and 66 kg and two subjects at 91 and 98 kg.
There is no weight overlap between the dose groups in this hypothetical dataset: the 100-mg weights are at most 66 kg, while the 200-mg weights are at least 91 kg. An apparent difference in concentration between dose groups, if seen, could not be separated descriptively from this covariate imbalance. The EDA map should record the limited overlap and raise a question about how much information the data contain to distinguish dose and weight patterns. It should not claim that either factor caused a concentration difference.
Turning Observations Into Modeling Questions
A useful EDA note has three parts: the observed feature, its scope, and a question that can be evaluated later. For example, “Only two subjects contribute late-time samples” is more informative than “late concentrations are sparse.” Adding “Does the planned model rely on late-time information from those subjects alone?” makes the implication explicit without answering it prematurely.
| Observed feature | Question to carry forward |
|---|---|
| Many records from a few subjects | Do pooled summaries mostly reflect those subjects, and are subject-level summaries also needed? |
| Uneven sampling times across dose groups | Could a group contrast reflect different time coverage rather than a dose-related pattern? |
| Few subjects in a covariate category | How much information is available to estimate a category-specific difference? |
| Limited covariate overlap across doses | Can dose and covariate patterns be distinguished with the observed data? |
| Concentrations or records concentrated in a narrow region | Which parts of the concentration-time profile are well represented, and which rely on sparse observations? |
This map complements, rather than replaces, focused displays and analyses. Later reviews can examine individual concentration-time profiles, concentration distributions, covariate relationships, or stratified profiles in detail. At this stage, the purpose is to establish what should be examined more closely and which comparisons may be poorly supported by the data.
Diagnostics, Pitfalls, and Limitations
Several warning signs indicate that an EDA summary may be misleading. Check whether a reported count is a number of records or a number of subjects; whether missing or below-quantification values are included in a concentration summary; whether nominal and actual times have been conflated; and whether one subject dominates a time region or group. Review units and analysis conventions before interpreting ranges. A surprising value should be investigated in context, not automatically deleted or treated as evidence of a biological exception.
The main alternative to a broad map is to start immediately with one focused display or a formal model. Focused displays can answer a specific question in greater detail, but may miss imbalances elsewhere in the dataset. A model can quantify effects under its assumptions, but it is not a substitute for checking data coverage and subject contribution first. The map is deliberately descriptive: it does not prove mechanisms, select a final model, resolve confounding, or replace formal diagnostics.
- Pitfall: Treating records as independent subjects. “There are 100 samples, so the study has 100 subjects” is wrong if those samples come from repeated measurements on fewer people. Report both the record count and the number of unique subjects.
- Pitfall: Reading an overall summary as a balanced comparison. A pooled concentration mean can be dominated by subjects with more samples or by a heavily represented time region. State what records were included and inspect subject and time coverage.
- Pitfall: Interpreting an imbalance as an effect. “The higher-dose group has higher concentrations, so dose caused the difference” does not follow from an exploratory comparison. Check time, covariate, and subject coverage, then frame the observation as a question for appropriate modeling.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A dataset contains 120 concentration records from 15 subjects. What are the record count and the subject count, and why should both be reported?
- Three subjects contribute 1, 2, and 5 records with subject means of 4, 6, and 8 mg/L, respectively. Calculate the pooled record mean.
- Only one subject contributes a concentration sample at the final scheduled time. Give one appropriate EDA observation and one question to carry forward.
- Two dose groups have sharply separated body-weight ranges. Can an exploratory concentration difference be attributed to dose? Explain.
Solutions. (1) There are 120 records and 15 subjects. Both are needed because repeated records from the same subject are not additional independent subjects, and the record count describes sampling volume while the subject count describes participant coverage. (2) The pooled mean is \((1\times4+2\times6+5\times8)/(1+2+5)=(4+12+40)/8=56/8=7.0\) mg/L. (3) State that the final-time observation comes from one subject; ask whether conclusions at that time depend on that subject alone. Do not claim the value represents the population. (4) No. The groups lack weight overlap, so a concentration contrast cannot be separated descriptively from the imbalance. Record the limitation and ask how it affects the information available to distinguish dose and weight patterns.