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conformeR: conformalized differential expression analysis of multi-condition single-cell data Justine Leclerc PhD candidate, Center of Experimental Rheumatology, University Hospital Zurich, University of Zurich Joint work with Christof Seiler EuroBioC 2025 – September 17th–19th, Barcelona 1 / 15
Motivation Goal: Detect differential expression in multi-condition single-cell datasets. Requirements: ✓Control the False Discovery Rate (FDR) ✓Gene-level p-values per cell type, aggregated over patients ✓Preferably use distribution-free methods conformeR combines conformal inference and counterfactual prediction for robust, valid p-values. 2 / 15
©Meet Mrs. and Mr. Smith We observe gene expression in cells from Mrs. and Mr. Smith: •Gene log-counts: YA,YBfor genes Aand B •Same cell-type, under two conditions: control (T= 0) and treatment (T= 1) Model: YA∼ N(0,1),YB=βTYA+ε, ε ∼ N(0,1) τ(YA)=(βT=1 −βT=0)·YA Research question: is gene Bdifferentially expressed under treatment? 3 / 15
Predicting the counterfactual Idea: Predict ˆ YBas if the cell were in the other condition. {Implementations available in conformeR: •Calling existing packages lemur (Ahlmann-Eltze, C., Huber, W., 2025), cfcausal (Lei, L. and Cand` es, E., 2021) •Built-in prediction model using conformal inference Prediction of the counterfactual assumes the unobserved condition can be predicted by the expression of other genes in the same sample, cell-type and condition. YB(T=t)∼YA(T=t) 4 / 15
Predicting the counterfactual Learn P(YB|YA,T) to make predictions. βT=0 =βT=1 = 1 τ(YA)=0 βT=0 = 1, βT=1 =−3 τ(YA) = −4·YA 5 / 15
Conformal testing: p-values ¬Test hypothesis H0:FYB|YA,T=0 =FYB|YA,T=1 ¬Conformal prediction intervals ˆ C∆,α over grid A ⊂ [0,1] for ∆ = (Yobs B−ˆ YB(0), T= 1 ˆ YB(1) −Yobs B,T= 0 ¬Test statistic and p-value C=X α∈A 1{0∈ˆ C∆,α},p=1 + C 1 + |A| 6 / 15
Prediction intervals for ∆ τ(YA)=4.04,p=1+5 1+99 = 0.06 τ(YA)=0,p=1+70 1+99 = 0.71 7 / 15
Interpretation of p-values conformeR p-values reflect signal presence. τ(YA)= 0 ⇒left-skewed τ(YA)=0⇒uniform 8 / 15
Cell-type level inference: Step 1 Step 1: Patient-wise transformation of p-values to Fdr •Convert p-values to local false discovery rates (lfdr) using qvalue::qvalue (Storey, Bass, Dabney, Robinson 2025). •Estimate marginal (frequentist) Fdr: Pi:pi<α lfdr(pi) PN i=1 1{pi≤α}−−−−→ N→∞ E[lfdr(p)|p≤α] = Fdr(α) 9 / 15
Conformal inference of the counterfactual cfcausal (Lei, L. and Cand` es, E., 2021) requires two conditions to be fulfilled: Assumptions 1. Stable Unit Treatment Value Assumption (SUTVA) 2. Strong ignorability (YB(1),YB(0)) ⊥T|YA ,Conditioning on post-treatment variable YA How big is the impact of the strong ignorability violation on the prediction? Future implementation with lemur bypasses the problem
Cell-type level inference: step 1 Transform cells p-values to local false discovery rates lfdr(p) = P(H0|p) π0=P(Hi= 0)
Conformal prediction intervals ¬Define ∆ = (Yobs B(1) −ˆ YB(0), T= 1 ˆ YB(1) −Yobs B(0), T= 0 ¬Prediction sets over grid A ⊂ [0,1] ˆ C∆,α = YB(1) −ˆ CYB(0),α(Yobs A),T= 1 ˆ CYB(1),α(Yobs A)−YB(0),T= 0
