Lavaan
lavaan is an R package for latent variable analysis — confirmatory factor analysis (CFA), structural equation modeling (SEM), path analysis, mediation, and growth-curve models. It is the open-source counterpart to commercial tools like Mplus, AMOS, and LISREL.
When SEM earns its keep
Reach for lavaan only when at least one of these is true:
Latent constructs. The thing you care about is unobserved and measured by several noisy indicators (e.g., "tumor immunogenicity" indicated by TIL density, PD-L1, MHC-I, mutational load).
Mediation. You hypothesize a causal chain A → M → Y and want to decompose direct vs indirect effects.
Multiple correlated outcomes. Several endogenous variables that should be modeled jointly rather than one regression at a time.
Measurement invariance. You want to test whether a scale/score means the same thing across groups (e.g., across labs, across ethnicities, across tumor subtypes).
Growth / longitudinal trajectories. Repeated measures with random intercepts/slopes treated as latent factors.
If your question is "do features X₁…Xₚ predict outcome Y?" — that is regression, not SEM.
Sample-size reality check
SEM is hungry for data. Common rules of thumb:
≥ 10 cases per estimated parameter (≥ 20 is safer).
≥ 200 cases for any non-trivial model.
Categorical indicators (WLSMV estimator) need more, not less, than continuous ones.
Bootstrapped indirect effects for mediation typically want n ≥ 200.
A CFA with 8 indicators and 3 factors easily has 25+ parameters — that is a 250-case minimum, not a 60-case pilot.
Pathology study designs where lavaan is a good fit
1. Tumor microenvironment as a latent construct
"Immune-inflamed phenotype" is not directly measured. It is indicated by CD8⁺ density, CD4⁺ density, PD-L1 TPS, tertiary lymphoid structure count, and IFN-γ signature score.
Model. CFA with one latent factor Immune loaded by those five indicators, then a structural path on a continuous outcome (e.g., RFS_months ~ Immune + Stage + Age for uncensored data). Use WLSMV if any indicator is ordinal.
Why SEM helps. Each indicator alone is noisy and partially redundant. A regression with all five as covariates is collinear and hard to interpret. The latent variable averages signal and discards measurement error.
Caveat on survival outcomes. lavaan does not natively handle right-censored time-to-event data. For survival endpoints, either (a) extract the latent factor scores and feed them into a Cox model in survival, or (b) use a two-stage approach with lavaan.survreg / regsem extensions. Don't treat censored survival time as a continuous outcome inside sem().
2. Mediation: biomarker → microenvironment → outcome
Does MMR-deficient status improve survival because it produces a hotter immune microenvironment?
Model. Use a continuous mediation outcome (e.g., a continuous prognostic score, biomarker level, or recurrence indicator). For survival as the final outcome, the cleanest path is the two-stage approach: estimate Immune factor scores in lavaan, then fit a Cox model with MMRd and the predicted scores in survival, and bootstrap the indirect effect at the wrapper level (boot::boot or the mediation package with a Cox model).
Why SEM helps. Standard Cox regression tells you MMRd is prognostic but not why. Mediation decomposes how much of the effect runs through immunity vs other pathways (e.g., neoantigen-independent mechanisms). Use bootstrap CIs for indirect.
3. Inter-observer agreement as measurement invariance
Do three pathologists scoring stromal TILs measure the same underlying construct, or do they each have a different idiosyncratic version of it?
Model. Multi-group CFA with each pathologist as a group, testing configural → metric → scalar invariance.
Why SEM helps. κ tells you agreement on a scale; invariance testing tells you where the disagreement lives — different loadings (they weight features differently), different intercepts (one is systematically high), or different residuals (one is noisier).
4. Growth curves of biomarker change
Ki-67 measured at biopsy, mid-treatment, and resection. Does the trajectory (intercept and slope) predict pathologic complete response, after adjusting for baseline?
Model. Latent growth curve with intercept and slope factors, regressing pCR on slope.
Why SEM helps. Models the trajectory as a person-level latent variable. Cleaner than per-patient OLS slopes, handles missing time points under MAR, and lets you test whether intercept-slope correlation is non-zero.
5. Composite scoring — reflective vs formative
A "histologic aggressiveness" score built from grade, mitoses/mm², LVI, perineural invasion, and necrosis. Are these genuinely indicators of one construct, or several?
Model. If you believe the underlying construct causes the indicators (e.g., aggressiveness manifests as higher grade, more mitoses, more LVI), use exploratory followed by confirmatory factor analysis to test one-factor vs two-factor (proliferation vs invasion) structures — this is a reflective measurement model.
Caveat — formative composites. If indicators instead constitute the score (each adds independent information rather than reflecting a shared latent cause), CFA is the wrong tool. Reach for PLS-SEM (cSEM, seminr) or MIMIC models. This distinction matters: dropping a redundant reflective indicator barely moves the latent factor; dropping a formative indicator changes the construct's meaning.
Why SEM helps. Validates whether a clinical composite is internally coherent — and forces you to make the reflective/formative assumption explicit before it gets used as a single risk score.
Minimal lavaan example
Reporting checklist
Model specification (path diagram or equations)
Estimator (
ML,MLR,WLSMV) and rationaleSample size and missing-data handling (FIML vs listwise)
Fit indices: χ², CFI ≥ 0.95, TLI ≥ 0.95, RMSEA ≤ 0.06, SRMR ≤ 0.08
Standardized loadings and path coefficients with CIs
For mediation: bootstrap CI for indirect effect
Modification indices: report only if used, and justify any post-hoc changes
When not to use lavaan
Single binary outcome with predictors → logistic regression / penalized regression / ML classifier. Worked example: Lasocki et al. (AJNR 2018, n=69, 21 codeleted) and Yan et al. (Lab Invest 2022, n=555, ResNet-34) — both predict 1p/19q co-deletion from MRI. lavaan/WLSMV can handle the binary/ordinal indicators in these data; the binding constraint for Lasocki is sample size, and for both papers there is a deeper definitional-circularity problem (covered two sections below) that no estimator fixes.
Time-to-event with one outcome → Cox model. (See Kaplan Meier and competing-risk regression.)
n < 100 with many indicators → underpowered; consider a simpler composite score or partial least squares (
plspm,cSEM).Pure prediction without theoretical structure → SEM is a confirmatory tool, not a feature-selection method.
Adjacent tools that often fit better — or complement lavaan
When the question doesn't involve latent constructs or causal pathways, these are usually the better fit. Some (poLCA, glmnet) also pair naturally with lavaan in mixed workflows:
Discover imaging/molecular subtypes from categorical indicators — and the cleanest non-circular test of imaging→molecular claims (form classes from imaging alone, then ask post-hoc whether they align with molecular labels)
Latent class analysis (closest in spirit to CFA, but for categorical class membership)
poLCA
Multivariable prediction with small n and many candidate features
Penalized logistic regression (LASSO / elastic net)
glmnet
Calibration of a prediction model (not just discrimination/AUC)
Calibration curves, Brier score, calibration-in-the-large
rms, CalibrationCurves
Clinical utility of a prediction model at varying thresholds
Decision curve analysis (net benefit)
dcurves, rmda
Inter-observer agreement on ordinal ratings
Weighted κ, intraclass correlation (ICC)
irr, psych
Time-to-event with multiple competing causes
Fine–Gray subdistribution hazards
cmprsk, tidycmprsk
Survival modeling with covariates
Cox PH, with calibration and DCA on top
survival, rms
Rule of thumb: if the outcome is a single observed variable and the question is purely "how well do features predict it?" — start with this table. Reach for lavaan only if you also care about a latent construct, a mediating mechanism, or measurement structure.
A deeper problem the statistics can't fix: definitional circularity
The lavaan-vs-logistic-regression debate above is a tool choice. Underneath it sits a more dangerous failure mode that no estimator rescues — when the target itself has been redefined to include the very thing you are using to predict it.
The two glioma/MRI papers cited above are textbook examples.
The circular chain.
What the studies actually demonstrate is MRI predicts oligodendroglial histology → which by 2016 definition is 1p/19q co-deletion. The molecular feature is no longer independent of the histological entity; it constitutes it.
Why each paper is vulnerable.
Lasocki et al. explicitly note that "1p/19q testing was generally performed on the basis of an oligodendroglial component on standard histologic assessment." The cohort was pre-selected to look oligodendroglial; radiologists were then asked whether the imaging looked oligodendroglial. Agreement was inevitable.
Yan et al. trained a ResNet-34 on cases where 1p/19q FISH was performed because the tumors looked oligodendroglial. The CNN learned a category boundary that decades of neuroradiology had already encoded into the imaging phenotype. The near-perfect AUCs (0.999 train, 0.983 test) are consistent with a tautology, not a discovery.
Why no statistical fix saves you. Logistic regression, LASSO, deep learning, lavaan, latent class analysis — all of them inherit the circularity from the labels. Calibration plots, DCA, and bootstrap CIs are necessary but powerless here: a perfectly calibrated tautology is still a tautology.
The escape hatch: biological-substrate test. A finding earns "imaging → biology" status only when there is a mechanistic basis independent of the morphological category that drove enrollment. T2-FLAIR mismatch passes — microcystic tumor architecture plausibly drives differential free-water signal. Calcification → "looks oligodendroglial" doesn't.
What a non-circular study would require.
Unselected glioma cohort across grades and histologies, not enriched for oligodendroglial appearance.
Imaging assessment blinded before any histology.
Molecular testing on all cases, not only those suspected oligodendroglial.
Prospective design to remove retrospective enrichment.
The defensible claim. "MRI features can serve as a surrogate for histological subtype, and since subtype is now molecularly defined, imaging may reduce the need for formal molecular testing in resource-limited settings." That is clinically useful but much more modest than "imaging predicts molecular biology."
Generalizable pitfall. Watch for this trap any time a classifier's training labels were retrospectively redefined to include features correlated with the predictors. Candidates beyond gliomas: MMR/MSI imaging surrogates after MMR became part of Lynch-spectrum classification, IDH-mutant prediction in cohorts pre-selected by morphology, NTRK-fusion morphology claims in tumors selected by suspicion. The methodological reflex: ask "what defined the cohort, and is the target downstream of that definition?"
Methods that can formally test the circularity claim
lavaan and adjacent latent-variable methods (poLCA for LCA, psych for polychoric correlations) handle categorical and ordinal data through polychoric/tetrachoric correlations and the WLSMV estimator. Depending on which question you ask, one of these methods is the direct statistical test of the circularity argument above; another sidesteps it.
A worked typology against the variables in the two glioma papers:
1p/19q status
Binary
Outcome
T2-FLAIR mismatch
Ordinal
<33%, 33–50%, >50%
Calcification
Binary
Present / absent
Cortical involvement
Ordinal
<33%, 33–50%, >50%
IDH mutation
Binary
Present / absent
WHO grade
Ordinal
II vs III
Enhancement pattern
Nominal
None / blurry / nodular / ring
Age, KPS
Continuous
Paper 2 only
1. Measurement question — "Do these MRI features reflect a single underlying tumor phenotype?"
Polychoric/tetrachoric correlation matrix feeding a CFA with WLSMV. This separates the imaging construct from the molecular label — conceptually important given the circularity concern.
2. Structural question — "Do imaging features predict molecular status through histological phenotype?" (the direct circularity test)
This is the model that formally tests the tautology: if the path from imaging features to 1p/19q co-deletion drops to non-significance after conditioning on histological phenotype, that is statistical evidence the imaging→molecular signal is fully mediated by histology — i.e., the circularity is real.
3. Reliability question — "Is T2-FLAIR mismatch measured consistently?" (CFA as a complement to weighted κ)
Paper 1 reports weighted κ for two radiologists. A latent-true-score model can do something κ cannot: it separates measurement error from true disagreement by treating raters as noisy indicators of a latent true score. Identification matters here — a single-factor model with only 2 indicators is just-identified at best (zero degrees of freedom, no testable fit), so you must either constrain loadings/residuals to be equal across raters (the τ-equivalent assumption) or — better — use ≥ 3 raters so the model is over-identified and fit can actually be assessed.
With ≥ 3 raters this becomes the more general congeneric reliability model and is closer to ICC under classical test theory. κ remains the right answer when raters are exchangeable and the goal is a single agreement scalar; CFA earns its keep when you want to partition rater bias from rater noise.
4. Latent-class question — "Do these tumors form discrete imaging subtypes?" (the non-circular test, with caveats)
This is arguably the most scientifically appropriate question post-WHO 2016: form classes from imaging alone, then ask post-hoc whether they align with molecular status.
Important caveat. LCA only escapes the labeling circularity (molecular labels aren't used to form classes). It does not escape the cohort-selection circularity: if the cohort itself was enriched for oligodendroglial-appearing cases (Lasocki explicitly states this), the latent classes will recover that enrichment, not a generalizable imaging-biology relationship. To be a true non-circular test, LCA needs an unselected cohort sampled across grades and histologies — the same prospective design listed earlier as a non-circularity requirement.
If imaging classes recover molecular structure without molecular labels being used in class formation, that is the strongest possible evidence of a real imaging-biology relationship. If they don't, the circularity is confirmed.
Which method fits which paper
Method
Lasocki AJNR 2018 (n=69)
Yan Lab Invest 2022 (n=555)
Scientific value
Polychoric CFA
Marginal — n too small
Yes
Tests measurement structure
Path analysis / SEM with mediation
No — n too small
Yes
Direct test of circularity
Two-rater reliability CFA
Best fit — improves on κ
N/A (single reader for many features)
Separates measurement error from disagreement
Latent class analysis
Borderline
Best fit — non-circular
Recovers imaging structure without using molecular labels
The reframe
The shift this enables is from "does imaging predict molecular status?" (circular by construction post-2016) to "does imaging independently recover molecular structure?" (non-circular and falsifiable on an appropriately sampled cohort). Latent-variable methods — lavaan path analysis (the formal mediation-by-histology test) and poLCA (the imaging-only class-discovery test) — are well-suited to answer this once the cohort design supports it. On retrospectively pre-selected cohorts they cannot rescue the result; on unselected prospective cohorts they can give it real teeth.
Related resources
Rosseel Y. lavaan: An R Package for Structural Equation Modeling. J Stat Softw 2012; 48(2).
Kline RB. Principles and Practice of Structural Equation Modeling, 4th ed.
lavaanwebsite: lavaan.ugent.be
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