Proteomics: from measured evidence to an estimand

Peptides, protein groups, detection, and abundance contrasts

Before reading: The Understanding an omics dataset page, means and logarithms; read Preprocessing and the quantity being estimated alongside this page.

1 Start with the feature, not the column heading

Proteomics measures proteins or evidence about proteins. In bottom-up mass spectrometry, proteins are digested into shorter amino-acid sequences called peptides. The instrument measures ions from those peptides, and a pipeline assigns identities and quantities. A protein table is therefore a derived summary, rather than a direct count of intact protein molecules.

A peptide sequence can occur in more than one protein. If the detected evidence cannot distinguish the candidates, the pipeline can report a protein group. A gene symbol used as its display label does not resolve that ambiguity. A proteoform is a particular molecular form, for example one affected by sequence processing or modification; a shared-peptide summary may not distinguish such forms. Affinity assays instead measure reagent binding, with their own specificity and calibration requirements. A change in binding signal needs a platform-specific interpretation.

Before analysis, reconstruct the chain from specimen to run to quantified feature. Record the platform, acquisition and processing versions, feature definition, mapping rules, measurement units, normalization, missing-value codes, and identification confidence. QFeatures keeps peptide and protein assay levels connected. Identification FDR addresses incorrect identifications among accepted identifications; differential-abundance FDR addresses false group-comparison discoveries. Controlling the first does not automatically control the second.

Which object does the comparison concern?

Independent people and specimensAliquots, runs, and peptide measurements retain their person and specimen IDs.
Measured evidencePeptide signals or reagent-binding measurements have platform-specific units.
Defined feature summaryMapping and aggregation produce a protein, protein group, or assay target.
Population contrastSpecify the scale, population, covariates, and observation process before inference.

More peptides can improve measurement of one specimen. They do not create more independently sampled people. Technical replicates are useful for studying assay error; their role differs from biological replication.

2 Aggregation makes an assumption about a shared signal

Suppose the idealized log2 intensity for peptide p in person i is

L_{ip}=a_p+Q_i+\epsilon_{ip}.

Here a_p is a peptide-specific response and Q_i a common protein-level component. Let A_i denote group and assume errors have mean zero within each group. If a_p is stable across groups, subtraction gives

E[L_{ip}\mid A_i=1]-E[L_{ip}\mid A_i=0]=E[Q_i\mid A_i=1]-E[Q_i\mid A_i=0].

The peptide’s baseline response cancels even if one peptide is systematically much brighter than another. Averaging a fixed set of peptides then estimates the shared contrast. It does not make raw intensities directly comparable or calibrate Q_i to concentration.

If specimens contribute different subsets of peptides, the average offset can change: the mean of a_p among observed peptides need not stay fixed. Missingness can therefore affect aggregation before a group test. Shared peptides, modifications, interference, or changing proteoform mixtures can also break the model. A discordant peptide warrants investigation; it does not identify a particular mechanism by itself.

Let \mathcal S_i be the peptides observed in specimen i. The naïve average of their log2 intensities is

\begin{aligned} \overline L_i^{\mathrm{obs}} &=Q_i+\overline a_{\mathcal S_i} +\overline\epsilon_{i,\mathcal S_i}. \end{aligned}

The bars denote averages over the retained peptides. Even with unchanged protein signal Q_i, this summary can change when the mean peptide response \overline a_{\mathcal S_i} changes.

The following noiseless synthetic example holds Q_i=12 in every specimen. Five peptides have fixed response offsets -2,-1,0,1,2, giving intensities 10 through 14. All five are observed in group 0. In group 1, progressively more of the lower-response peptides are unobserved. The missingness pattern is imposed for this illustration; the measured values that remain do not change. Follow each matrix column down to its average before reading the result.

Two vertically aligned panels. Above, five peptide rows and eight specimen columns show unchanged intensities 10 through 14. Group 0 has all five measurements; group 1 progressively lacks the lower-response peptides. Below, the corresponding observed-peptide averages are 12 for specimens S1 to S4, then 12.5, 13, 13.5, and 14 for S5 to S8. The complete-data average is 12 throughout, and the apparent group contrast is 1.25. — Figure 1: An imposed missingness pattern changes the peptide mix used in each average. Every specimen has protein signal 12, zero errors, and fixed peptide responses. Gray crosses mean unobserved, not zero. The naïve group contrast is +1.25 despite a true contrast of zero.

The apparent contrast comes entirely from changing which peptide offsets enter the average. For example, S8 contributes only peptide E, whose response is high in both groups. The group-1 summaries rise without a change in any retained peptide’s intensity. A protein-summary method needs a justified way to handle peptide responses and observation patterns; treating each specimen’s available-peptide average as the same quantity can fail.

A separate example: discordant peptide changes. For peptide contrasts 1, 1, and 0, the unweighted average is 2/3, while the concordant pair averages to 1. These log2 contrasts imply factors 2^{2/3}\approx1.59 and 2 for the defined geometric-mean summaries. The discrepancy shows the role of aggregation; it does not identify which summary is the true molecular change.

Selecting concordant peptides after looking at group effects can bias the downstream comparison. Prespecify mapping/aggregation or account for selection. Keep the original peptide evidence so a protein-level claim can be checked. ProteomeXchange’s reporting guidance distinguishes identification results, quantification outputs, and reconstruction files.

3 Missing signals do not have a single explanation

An entry can be missing because the analyte was not detected, a peptide was not selected or confidently identified, quality control removed a value, or a sample failed. Some mechanisms depend on abundance; others need a different model. Do not interpret every missing entry as zero concentration or every positive entry as a calibrated molecule count.

Consider a threshold mechanism: latent log2 intensity L is observed only if L>c. The observed-data mean is E[L\mid L>c], not E[L]. Detection depends directly on the outcome, so the MAR argument for a missing mean cannot be imported without further assumptions.

The figure uses L=\mu+U, with U\sim N(0,1). Detection is the event U>c-\mu. The standard-normal tail identity gives

E[L\mid L>c] =\mu+\frac{\varphi(c-\mu)}{1-\Phi(c-\mu)},

where \varphi and \Phi are the normal density and CDF. The added term is positive: only an upper tail is observed. At c=10, full group means 9 and 10 become detected means about 10.53 and 10.80. Their contrast falls from 1 to about 0.27 because selection differs between groups. This is what DetectedMean() calculates.

Knowing a threshold tells us that a non-detected value lies below it, but not where it lies. A parametric censored-data model can extrapolate under assumptions; the unseen distribution is not identified nonparametrically from the inequality alone.

Code

cutoff <- seq(6, 12, length.out = 150)
DetectedMean <- function(mu, cutoff) {
  a <- cutoff - mu
  mu + dnorm(a) / pnorm(a, lower.tail = FALSE)
}
observed_difference <- DetectedMean(10, cutoff) - DetectedMean(9, cutoff)
plot(cutoff, observed_difference, type = "l", lwd = 2, col = "#D55E00",
     xlab = "Detection threshold on latent log2 scale", ylab = "Group 1 minus group 0 mean",
     ylim = c(0, 1.15))
abline(h = 1, lty = 2, col = "#2F80C8")
legend("bottomleft", c("Detected-value contrast", "Full-population contrast"),
       col = c("#D55E00", "#2F80C8"), lty = c(1, 2), lwd = 2, bty = "n")

Two curves show the difference between detected group means changing with the detection threshold, while the full-population contrast stays at one. — Figure 2: A teaching censoring model with unit normal errors. Raising the threshold increasingly separates the mean of detected values from the full mean. This is a population calculation, not a universal proteomics detection model.

Filling every missing value with a low constant replaces an uncertain outcome by an assumed value. If detection fractions differ, the number of inserted constants also differs, changing the group contrast. Treating filled values as observed can understate uncertainty. Imputation needs an observation/outcome model and an uncertainty argument; a complete matrix alone supplies neither.

A detection-frequency target can be legitimate if explicitly defined, but it concerns the assay and detection rule as well as biology. Start with missingness by feature, group, run order, batch, and specimen quality; do not choose imputation by which method yields more discoveries.

4 Write the estimand on the available scale

For a prespecified, fully observed log2 feature summary Y, an unadjusted between-group contrast is E[Y\mid A=1]-E[Y\mid A=0]. An adjusted population-standardized contrast can instead be

\begin{aligned} \psi&=E_{Z\sim P_*}\{m_1(Z)-m_0(Z)\},\\ m_a(z)&=E[Y\mid A=a,Z=z]. \end{aligned}

Z contains the chosen covariates and P_* defines one covariate population used for both groups. Compare groups at the same z, then average using the same weights. For two equally weighted strata with conditional contrasts 1 and 0, the standardized contrast is 1/2, irrespective of their different frequencies in the observed groups. Both groups need outcome support at the target covariate values; otherwise modeling requires extrapolation. This remains associational unless additional causal assumptions justify more.

Outcome regression and, when needed, group/observation probabilities are nuisance functions. The From an influence function to an estimator page explains augmentation and remainder conditions; an assay-specific missingness mechanism must be identified first. Cross-fitting does not supply concentration calibration or a model for unseen outcomes.

Exponentiating a mean log2 contrast concerns geometric means of the defined positive measurement. Calling it a concentration ratio requires a calibration argument. Equal loading, reference samples, and internal standards address different sources of variation; record which quantity each normalization anchors. Global shifts can be absorbed by an assumed stable reference. Affinity-assay units likewise require their platform’s interpretation rather than an automatic absolute-abundance claim.

5 Before differential abundance analysis

Check sample IDs and technical replicates; inspect peptide counts/mapping ambiguity, quality measures, missingness patterns, and reference behavior. Check group–batch overlap and the estimability of the chosen contrast. Freeze the feature family, aggregation, scale, and inclusion rules before testing. Report pointwise uncertainty and the multiplicity procedure separately. The Differential expression and abundance page supplies a design/contrast framework; reuse it only after defending the proteomics measurement and variance assumptions.

6 Exercises

The checkpoint is this assay specialization’s completion target. Additional practice is optional. Try the checkpoint before opening its hint or solution.

Checkpoint · PROT-01 — Reconstruct a protein-level claim

Task type: Interpretation and diagnosis.

A protein group has three peptides, contrasts 1, 1, and 0 on the log2 scale, and 30% missing values concentrated in controls. There are 20 people per group, each run twice. State the independent replication count, calculate the unweighted peptide-average contrast, and identify what is still needed for a claim about absolute protein abundance.

Ready to continue when: you can separate biological replication, aggregation, observation, and calibration assumptions.

Transfer: Would adding ten technical runs per person identify the concentrations below a detection threshold?

Hint

Follow the specimen–peptide–protein chain; a technical run is not a new person.

Solution outline — open after trying

There are 40 independent people under independent sampling, not 80. The average peptide contrast is 2/3. Its protein interpretation needs an aggregation model and mapping evidence. Differential missingness can change the detected-value target; a full-data contrast needs an observation model or sensitivity analysis. Absolute abundance additionally needs calibration. Selecting the two increasing peptides after seeing the contrasts introduces selection.

Additional practice (optional)

Vary the peptide offsets in the missingness figure while holding every protein signal at 12. Which observed-peptide averages change? What happens if all peptide offsets are zero? Explain which two ingredients create the apparent group difference.
In the threshold example, calculate the detected fraction in each group at threshold 10 and describe a sensitivity analysis for the unseen values.
Audit a protein table: distinguish accession, protein group, gene symbol, peptide count, and quantitative unit.

7 Reading

QFeatures processing vignette: linked assay levels, processing, and aggregation.
ProteomeXchange submission guidance: identification and quantification records.

--- title: "Proteomics: from measured evidence to an estimand" subtitle: "Peptides, protein groups, detection, and abundance contrasts" guide-status: "Available" --- **Before reading:** The [Understanding an omics dataset](understanding-omics-data.qmd) page, means and logarithms; read [Preprocessing and the quantity being estimated](preprocessing-and-estimands.qmd) alongside this page. ## Start with the feature, not the column heading Proteomics measures proteins or evidence about proteins. In **bottom-up mass spectrometry**, proteins are digested into shorter amino-acid sequences called peptides. The instrument measures ions from those peptides, and a pipeline assigns identities and quantities. A protein table is therefore a derived summary, rather than a direct count of intact protein molecules. A peptide sequence can occur in more than one protein. If the detected evidence cannot distinguish the candidates, the pipeline can report a **protein group**. A gene symbol used as its display label does not resolve that ambiguity. A **proteoform** is a particular molecular form, for example one affected by sequence processing or modification; a shared-peptide summary may not distinguish such forms. Affinity assays instead measure reagent binding, with their own specificity and calibration requirements. A change in binding signal needs a platform-specific interpretation. Before analysis, reconstruct the chain from specimen to run to quantified feature. Record the platform, acquisition and processing versions, feature definition, mapping rules, measurement units, normalization, missing-value codes, and identification confidence. [QFeatures](https://bioconductor.org/packages/release/bioc/vignettes/QFeatures/inst/doc/Processing.html) keeps peptide and protein assay levels connected. Identification FDR addresses incorrect identifications among accepted identifications; differential-abundance FDR addresses false group-comparison discoveries. Controlling the first does not automatically control the second. ::: {.guide-flow} <div class="guide-flow-title">Which object does the comparison concern?</div> <ol> <li>Independent people and specimensAliquots, runs, and peptide measurements retain their person and specimen IDs.</li> <li>Measured evidencePeptide signals or reagent-binding measurements have platform-specific units.</li> <li>Defined feature summaryMapping and aggregation produce a protein, protein group, or assay target.</li> <li>Population contrastSpecify the scale, population, covariates, and observation process before inference.</li> </ol> ::: More peptides can improve measurement of one specimen. They do not create more independently sampled people. Technical replicates are useful for studying assay error; their role differs from biological replication. ## Aggregation makes an assumption about a shared signal Suppose the idealized log2 intensity for peptide $p$ in person $i$ is $$ L_{ip}=a_p+Q_i+\epsilon_{ip}. $$ Here $a_p$ is a peptide-specific response and $Q_i$ a common protein-level component. Let $A_i$ denote group and assume errors have mean zero within each group. If $a_p$ is stable across groups, subtraction gives $$ E[L_{ip}\mid A_i=1]-E[L_{ip}\mid A_i=0]=E[Q_i\mid A_i=1]-E[Q_i\mid A_i=0]. $$ The peptide's baseline response cancels even if one peptide is systematically much brighter than another. Averaging a fixed set of peptides then estimates the shared contrast. It does not make raw intensities directly comparable or calibrate $Q_i$ to concentration. If specimens contribute different subsets of peptides, the average offset can change: the mean of $a_p$ among observed peptides need not stay fixed. Missingness can therefore affect aggregation before a group test. Shared peptides, modifications, interference, or changing proteoform mixtures can also break the model. A discordant peptide warrants investigation; it does not identify a particular mechanism by itself. Let $\mathcal S_i$ be the peptides observed in specimen $i$. The naïve average of their log2 intensities is $$ \begin{aligned} \overline L_i^{\mathrm{obs}} &=Q_i+\overline a_{\mathcal S_i} +\overline\epsilon_{i,\mathcal S_i}. \end{aligned} $$ The bars denote averages over the retained peptides. Even with unchanged protein signal $Q_i$, this summary can change when the mean peptide response $\overline a_{\mathcal S_i}$ changes. The following **noiseless synthetic example** holds $Q_i=12$ in every specimen. Five peptides have fixed response offsets $-2,-1,0,1,2$, giving intensities 10 through 14. All five are observed in group 0. In group 1, progressively more of the lower-response peptides are unobserved. The missingness pattern is imposed for this illustration; the measured values that remain do not change. Follow each matrix column down to its average before reading the result. ```{r} #| label: fig-protein-peptides #| fig-width: 7 #| fig-height: 7 #| echo: false #| fig-cap: "An imposed missingness pattern changes the peptide mix used in each average. Every specimen has protein signal 12, zero errors, and fixed peptide responses. Gray crosses mean unobserved, not zero. The naïve group contrast is +1.25 despite a true contrast of zero." #| fig-alt: "Two vertically aligned panels. Above, five peptide rows and eight specimen columns show unchanged intensities 10 through 14. Group 0 has all five measurements; group 1 progressively lacks the lower-response peptides. Below, the corresponding observed-peptide averages are 12 for specimens S1 to S4, then 12.5, 13, 13.5, and 14 for S5 to S8. The complete-data average is 12 throughout, and the apparent group contrast is 1.25." specimen <- paste0("S", 1:8) group <- rep(0:1, each = 4) offset <- -2:2 protein_signal <- rep(12, length(specimen)) complete <- outer(offset, protein_signal, "+") dimnames(complete) <- list(LETTERS[1:5], specimen) observed <- complete for (j in 5:8) observed[seq_len(j - 4), j] <- NA_real_ available_mean <- colMeans(observed, na.rm = TRUE) number_used <- colSums(!is.na(observed)) group_means <- tapply(available_mean, group, mean) old_par <- par(no.readonly = TRUE) layout(matrix(1:2, ncol = 1), heights = c(1.5, 1)) group_colors <- c("#2F80C8", "#D55E00") cell_colors <- c("#EDF4F8", "#C5DDEB", "#8CB9D1", "#457E9E", "#164A68") # Matrix columns and summary points use the same horizontal positions. par(mar = c(0.5, 4.5, 3.6, 0.8), cex = 1.3, xpd = FALSE) plot.new() plot.window(xlim = c(0.5, 8.5), ylim = c(0, 6.35), xaxs = "i", yaxs = "i") mtext("A Which peptide measurements enter each average?", side = 3, line = 2.1, adj = 0, font = 2, cex = 0.95) mtext("Protein signal stays at 12 in all eight specimens", side = 3, line = 1.35, adj = 0, cex = 0.76) mtext("Numbers: observed log2 intensity Gray x: unobserved", side = 3, line = 0.6, adj = 0, cex = 0.76) for (g in 0:1) { xx <- c(0.55, 4.45) + 4 * g segments(xx[1], 5.72, xx[2], 5.72, col = group_colors[g + 1], lwd = 3) text(mean(xx), 6.08, paste("Group", g), font = 2, cex = 0.88) } for (p in 1:5) for (j in 1:8) { yy <- 6 - p missing <- is.na(observed[p, j]) rect(j - 0.47, yy - 0.44, j + 0.47, yy + 0.44, col = if (missing) "#E7E7E7" else cell_colors[p], border = NA) if (missing) { segments(j - 0.12, yy - 0.12, j + 0.12, yy + 0.12, col = "#666666", lwd = 1.4) segments(j - 0.12, yy + 0.12, j + 0.12, yy - 0.12, col = "#666666", lwd = 1.4) } else { text(j, yy, observed[p, j], cex = 0.87, col = if (p >= 4) "white" else "#182C38") } } axis(2, at = 5:1, labels = LETTERS[1:5], las = 1, tick = FALSE, cex.axis = 0.82) mtext("Peptide", side = 2, line = 2.4, cex = 0.85) text(0.38, 0.16, "Peptides used", adj = 1, xpd = NA, cex = 0.68, col = "#555555") text(1:8, 0.16, number_used, cex = 0.72, col = "#555555") segments(4.5, 0.55, 4.5, 5.45, col = "#888888", lty = 3) par(mar = c(3.1, 4.5, 2.8, 0.8), cex = 1.3) plot(1:8, available_mean, type = "n", xlim = c(0.5, 8.5), ylim = c(11.65, 14.65), xaxs = "i", yaxs = "i", axes = FALSE, xlab = "", ylab = "") mtext("B Changing the subset shifts the summary", side = 3, line = 1.4, adj = 0, font = 2, cex = 0.95) mtext(sprintf("Group means: %.2f vs %.2f | apparent contrast: +%.2f", group_means[1], group_means[2], diff(group_means)), side = 3, line = 0.1, adj = 0, cex = 0.76) abline(h = 12, lty = 2, col = "#777777") segments(4.5, 11.65, 4.5, 14.65, col = "#888888", lty = 3) points(1:8, available_mean, pch = 21, bg = group_colors[group + 1], col = group_colors[group + 1], cex = 1.15) text(5:8, available_mean[5:8] + 0.18, format(available_mean[5:8], trim = TRUE), cex = 0.76) text(0.7, 11.78, "Complete-data mean = 12 for every specimen", adj = 0, cex = 0.74, col = "#555555") axis(1, at = 1:8, labels = specimen, tick = FALSE, cex.axis = 0.8) axis(2, at = 12:14, las = 1, cex.axis = 0.82) mtext("Mean log2 intensity", side = 2, line = 2.8, cex = 0.85) mtext("Specimen (aligned with the matrix above)", side = 1, line = 1.6, cex = 0.8) par(old_par) ``` The apparent contrast comes entirely from changing which peptide offsets enter the average. For example, S8 contributes only peptide E, whose response is high in **both** groups. The group-1 summaries rise without a change in any retained peptide's intensity. A protein-summary method needs a justified way to handle peptide responses and observation patterns; treating each specimen's available-peptide average as the same quantity can fail. **A separate example: discordant peptide changes.** For peptide contrasts 1, 1, and 0, the unweighted average is $2/3$, while the concordant pair averages to 1. These log2 contrasts imply factors $2^{2/3}\approx1.59$ and 2 for the defined geometric-mean summaries. The discrepancy shows the role of aggregation; it does not identify which summary is the true molecular change. Selecting concordant peptides after looking at group effects can bias the downstream comparison. Prespecify mapping/aggregation or account for selection. Keep the original peptide evidence so a protein-level claim can be checked. [ProteomeXchange's reporting guidance](https://www.proteomexchange.org/docs/guidelines_px.pdf) distinguishes identification results, quantification outputs, and reconstruction files. ## Missing signals do not have a single explanation An entry can be missing because the analyte was not detected, a peptide was not selected or confidently identified, quality control removed a value, or a sample failed. Some mechanisms depend on abundance; others need a different model. Do not interpret every missing entry as zero concentration or every positive entry as a calibrated molecule count. Consider a threshold mechanism: latent log2 intensity $L$ is observed only if $L>c$. The observed-data mean is $E[L\mid L>c]$, not $E[L]$. Detection depends directly on the outcome, so the MAR argument for a missing mean cannot be imported without further assumptions. The figure uses $L=\mu+U$, with $U\sim N(0,1)$. Detection is the event $U>c-\mu$. The standard-normal tail identity gives $$ E[L\mid L>c] =\mu+\frac{\varphi(c-\mu)}{1-\Phi(c-\mu)}, $$ where $\varphi$ and $\Phi$ are the normal density and CDF. The added term is positive: only an upper tail is observed. At $c=10$, full group means 9 and 10 become detected means about 10.53 and 10.80. Their contrast falls from 1 to about 0.27 because selection differs between groups. This is what `DetectedMean()` calculates. Knowing a threshold tells us that a non-detected value lies below it, but not where it lies. A parametric censored-data model can extrapolate under assumptions; the unseen distribution is not identified nonparametrically from the inequality alone. ```{r} #| label: fig-protein-detection #| fig-height: 5 #| fig-cap: "A teaching censoring model with unit normal errors. Raising the threshold increasingly separates the mean of detected values from the full mean. This is a population calculation, not a universal proteomics detection model." #| fig-alt: "Two curves show the difference between detected group means changing with the detection threshold, while the full-population contrast stays at one." cutoff <- seq(6, 12, length.out = 150) DetectedMean <- function(mu, cutoff) { a <- cutoff - mu mu + dnorm(a) / pnorm(a, lower.tail = FALSE) } observed_difference <- DetectedMean(10, cutoff) - DetectedMean(9, cutoff) plot(cutoff, observed_difference, type = "l", lwd = 2, col = "#D55E00", xlab = "Detection threshold on latent log2 scale", ylab = "Group 1 minus group 0 mean", ylim = c(0, 1.15)) abline(h = 1, lty = 2, col = "#2F80C8") legend("bottomleft", c("Detected-value contrast", "Full-population contrast"), col = c("#D55E00", "#2F80C8"), lty = c(1, 2), lwd = 2, bty = "n") ``` Filling every missing value with a low constant replaces an uncertain outcome by an assumed value. If detection fractions differ, the number of inserted constants also differs, changing the group contrast. Treating filled values as observed can understate uncertainty. Imputation needs an observation/outcome model and an uncertainty argument; a complete matrix alone supplies neither. A detection-frequency target can be legitimate if explicitly defined, but it concerns the assay and detection rule as well as biology. Start with missingness by feature, group, run order, batch, and specimen quality; do not choose imputation by which method yields more discoveries. ## Write the estimand on the available scale For a prespecified, fully observed log2 feature summary $Y$, an unadjusted between-group contrast is $E[Y\mid A=1]-E[Y\mid A=0]$. An adjusted population-standardized contrast can instead be $$ \begin{aligned} \psi&=E_{Z\sim P_*}\{m_1(Z)-m_0(Z)\},\\ m_a(z)&=E[Y\mid A=a,Z=z]. \end{aligned} $$ $Z$ contains the chosen covariates and $P_*$ defines one covariate population used for both groups. Compare groups at the same $z$, then average using the same weights. For two equally weighted strata with conditional contrasts 1 and 0, the standardized contrast is $1/2$, irrespective of their different frequencies in the observed groups. Both groups need outcome support at the target covariate values; otherwise modeling requires extrapolation. This remains associational unless additional causal assumptions justify more. Outcome regression and, when needed, group/observation probabilities are nuisance functions. The [From an influence function to an estimator](../semiparametric-methods/influence-function-to-estimator.qmd) page explains augmentation and remainder conditions; an assay-specific missingness mechanism must be identified first. Cross-fitting does not supply concentration calibration or a model for unseen outcomes. Exponentiating a mean log2 contrast concerns geometric means of the defined positive measurement. Calling it a concentration ratio requires a calibration argument. Equal loading, reference samples, and internal standards address different sources of variation; record which quantity each normalization anchors. Global shifts can be absorbed by an assumed stable reference. Affinity-assay units likewise require their platform's interpretation rather than an automatic absolute-abundance claim. ## Before differential abundance analysis Check sample IDs and technical replicates; inspect peptide counts/mapping ambiguity, quality measures, missingness patterns, and reference behavior. Check group–batch overlap and the estimability of the chosen contrast. Freeze the feature family, aggregation, scale, and inclusion rules before testing. Report pointwise uncertainty and the multiplicity procedure separately. The [Differential expression and abundance](../analysis-problems/differential-expression-and-abundance.qmd) page supplies a design/contrast framework; reuse it only after defending the proteomics measurement and variance assumptions. ## Exercises The checkpoint is this assay specialization's completion target. Additional practice is optional. Try the checkpoint before opening its hint or solution. ::: {#checkpoint-prot-01 .checkpoint} ### Checkpoint · PROT-01 — Reconstruct a protein-level claim {.unnumbered} **Task type:** Interpretation and diagnosis. A protein group has three peptides, contrasts 1, 1, and 0 on the log2 scale, and 30% missing values concentrated in controls. There are 20 people per group, each run twice. State the independent replication count, calculate the unweighted peptide-average contrast, and identify what is still needed for a claim about absolute protein abundance. **Ready to continue when:** you can separate biological replication, aggregation, observation, and calibration assumptions. **Transfer:** Would adding ten technical runs per person identify the concentrations below a detection threshold? <details class="checkpoint-help"> <summary>Hint</summary> Follow the specimen–peptide–protein chain; a technical run is not a new person. </details> <details class="checkpoint-help"> <summary>Solution outline — open after trying</summary> There are 40 independent people under independent sampling, not 80. The average peptide contrast is 2/3. Its protein interpretation needs an aggregation model and mapping evidence. Differential missingness can change the detected-value target; a full-data contrast needs an observation model or sensitivity analysis. Absolute abundance additionally needs calibration. Selecting the two increasing peptides after seeing the contrasts introduces selection. </details> ::: ### Additional practice (optional) {.unnumbered} 1. Vary the peptide offsets in the missingness figure while holding every protein signal at 12. Which observed-peptide averages change? What happens if all peptide offsets are zero? Explain which two ingredients create the apparent group difference. 2. In the threshold example, calculate the detected fraction in each group at threshold 10 and describe a sensitivity analysis for the unseen values. 3. Audit a protein table: distinguish accession, protein group, gene symbol, peptide count, and quantitative unit. ## Reading - [QFeatures processing vignette](https://bioconductor.org/packages/release/bioc/vignettes/QFeatures/inst/doc/Processing.html): linked assay levels, processing, and aggregation. - [ProteomeXchange submission guidance](https://www.proteomexchange.org/docs/guidelines_px.pdf): identification and quantification records.