IHC Heterogeneity: How Much Does a Biopsy Tell You About the Tumour?

The Question

A pathologist scores Ki-67 on a core biopsy and the report carries that number forward as though it described the tumour. It describes the core. If the marker is heterogeneously expressed, a second core from the same tumour would have given a different answer, and the difference between those two numbers is not measurement error — it is the tumour.

ihcheterogeneity quantifies that gap. Give it a reference measurement (whole section, or a hot-spot score) and two or more regional measurements from the same cases, and it reports how well the regions reproduce the reference, whether they do so with a systematic offset, and how much of the total variance is sampling rather than real between-case difference.

This matters clinically wherever a threshold is applied to a single sample: Ki-67 cut-offs in neuroendocrine tumours and breast cancer, PD-L1 scoring, HER2 quantification. A marker with high within-tumour variability crossing a threshold on one core is not the same finding as one that sits comfortably on one side of it.

Data Layout

One row per case. One column for the reference measurement, one column per region.

set.seed(11)
n <- 40
ihc <- data.frame(CaseID = sprintf("C%02d", 1:n))
ihc$Whole <- round(pmin(100, pmax(0, rnorm(n, 45, 18))), 1)   # whole-section Ki-67 %

jitter_from <- function(mu, sd) round(pmin(100, pmax(0, mu + rnorm(n, 0, sd))), 1)
ihc$Biopsy1 <- jitter_from(ihc$Whole, 8)    # a well-sampled region
ihc$Biopsy2 <- jitter_from(ihc$Whole, 11)
ihc$Biopsy3 <- jitter_from(ihc$Whole, 14)   # a poorly representative one

head(ihc)

wholesection is optional. Without it the analysis compares the regions against each other, which answers “do two cores agree?” rather than “does a core represent the tumour?” — a weaker question, but the only one available when no whole-section score exists.

A Complete Run

res <- ihcheterogeneity(
  data         = ihc,
  wholesection = "Whole",
  biopsy1      = "Biopsy1",
  biopsy2      = "Biopsy2",
  biopsy3      = "Biopsy3",
  # biopsy4 and `biopsies` take a fourth region and any number beyond that
  analysis_type            = "comprehensive",  # reproducibility | bias | variability | comprehensive
  sampling_strategy        = "random",         # random | systematic | stratified | unknown
  cv_threshold             = 20,               # CV% above this is flagged as unacceptable
  correlation_threshold    = 0.7,              # minimum acceptable region-reference correlation
  variance_components      = TRUE,
  power_analysis           = TRUE,
  generate_recommendations = TRUE,
  show_variability_plots   = TRUE
)

Reproducibility

                             metric     value ci_lower ci_upper  interpretation
 Mean Regional-Reference Correlation     0.760       NA       NA  Good representativeness
       ICC(2,1) - absolute agreement     0.663    0.527    0.783  Moderate reliability
 ICC(3,1) - consistency (bias-blind)     0.658    0.521    0.779  Ignores systematic offset
     Mean Inter-Regional Correlation     0.554       NA       NA  Variable sampling

Both ICCs are reported deliberately. ICC(3,1) asks whether the regions rank cases the same way; ICC(2,1) asks whether they give the same number. A large gap between them means a systematic offset — one region reads consistently high or low — which ranking-based agreement hides. Here they are nearly identical (0.658 vs 0.663), so there is no meaningful offset; the disagreement is scatter, not bias.

Note that mean inter-regional correlation (0.554) is well below the region-reference correlation (0.760). Two cores agree with each other less than either agrees with the whole section, which is what you would expect when each core samples a different part of a heterogeneous tumour.

Sampling Bias

                   comparison mean_diff p_value effect_size clinical_impact
        Region 1 vs Reference     0.288   0.813      0.0369   Minimal (<5%)
        Region 2 vs Reference     0.110   0.949      0.0101   Minimal (<5%)
        Region 3 vs Reference     1.400   0.555      0.0923   Minimal (<5%)
 Mean of Regions vs Reference     0.599   0.547      0.0942   Minimal (<5%)

clinical_impact is the column to read, not p_value. A non-significant p-value on 40 cases does not establish that the bias is small; the effect size and the stated impact band do.

Variance Components

                       component variance percentage                  contribution
           Between-Case Variance    196.65       65.8             Major contributor
 Within-Case Variance (Sampling)    102.19       34.2     High sampling variability
                 Method Variance      0.00        0.0 Negligible method differences
                  Total Variance    298.84      100.0

This is the number to quote in a validation report. 34.2% of the total variance is within-case — that is the proportion of the spread in your dataset that comes from where you sampled, not from which patient you sampled. A cut-off applied to a single core inherits all of it.

Power

              scenario effect_size power required_n                     recommendation
  Small Effect (r=0.1)        0.10 0.094        783    Substantial sample increase
 Medium Effect (r=0.3)        0.30 0.469         85    Substantial sample increase
  Large Effect (r=0.5)        0.50 0.916         30       Adequate power achieved
  Observed Effect Size        0.91 1.000          7  Post-hoc (observed) power

The last row is labelled as post-hoc for a reason: power computed from the observed effect is a restatement of the p-value, not evidence that the study was adequately powered. Use the first three rows for planning.

Spatial Compartments

When regions are labelled by anatomical compartment — invasive front versus tumour centre, say — spatial_id names that column and the two compartment options compare them:

res_spatial <- ihcheterogeneity(
  data                = ihc_with_regions,
  wholesection        = "Whole",
  biopsy1             = "Region_A",
  biopsy2             = "Region_B",
  spatial_id          = "Compartment",
  compareCompartments = TRUE,
  compartmentTests    = TRUE
)

A significant compartment difference is a different finding from general heterogeneity: it says the marker varies systematically by location, so where the biopsy is taken from is a protocol decision, not a matter of chance.

Reading the Result

analysis_type narrows the output when you only need part of it: reproducibility for correlations and ICCs, bias for the systematic-offset tests, variability for CV and variance components, comprehensive (the default) for all of them.
cv_threshold (default 20) and correlation_threshold (default 0.8) set the bars against which results are labelled acceptable. They are conventions, not standards — if your assay has a published reproducibility requirement, use that number instead.
sampling_strategy documents how the regions were chosen. It does not change the arithmetic, but it belongs in the record: results from systematically placed cores do not generalise to randomly placed ones.
showSummary adds a plain-language summary and showGlossary a statistics glossary, both useful when the output is going to a tumour board rather than a statistician.

Limitations

The analysis describes the cases you measured. It cannot tell you that two cores are sufficient in general — only that, in this cohort, two cores left 34% of the variance unexplained. Extending that to a clinical protocol needs a prospectively defined validation study with the threshold and the decision it drives specified in advance.

ClinicoPath Development Team

2026-08-15