Dataset 1: ASPC1 cells treated across 20 compound-dose combinations in two experiments.

Dataset 1 is represented by a table with 29,503 rows (individual ASPC1 pancreatic cancer cells) and multiple columns representing cell-specific features, including:

• mean cell velocity
• well identifier, indexed as
• plate identifier, indexed as
• wells on plates (generated as part of experiment A) and (generated as part of experiment B) were each treated with the same sets of 13 treatments; in total, there were 20 distinct treatments, indexed by , with only three treatments common to both plate groups
• each treatment represents a combination of a chemical compound and its administered concentration, applied across 4 wells per plate (referred to as technical replicates)

We observed between 10 and 275 cells per well (mean = 87 cells). Cell velocities ranged from 0.04 to 4 µm/min (mean velocity = 0.76 µm/min). Velocities on plates were systematically lower compared to those on , attributable to slight differences in imaging configurations used for the two plate groups. This batch effect is corrected by our model, as described in the following sections, which was developed and benchmarked based on Dataset 1 and applied based on Dataset 2.

Dataset 2: Large-scale screen of ASPC1 cells treated across 80 compound-dose combinations.

Dataset 2 is represented by a table with 84,122 rows (individual ASPC1 cells) and multiple columns representing cell-specific features, including:

• mean cell velocity
• well identifier, indexed as
• plate identifier, indexed as
• each treatment represents a combination of a chemical compound and its administered concentration, applied across 3–4 wells per plate (referred to as technical replicates)

We observed between 3 and 303 cells per well (mean = 76 cells). Cell velocities ranged from 0.04 to 3.25 µm/min (mean velocity = 0.65 µm/min). Mean velocities per plate varied from 0.55 to 0.85 µm/min.

Model structure.

The observed migration velocity for cell i was modeled using a gamma likelihood. The gamma distribution was chosen for the likelihood due to its flexibility in modeling positive, right-skewed data:

(1)

where w[i] is the index of well of cell i, and and are the shape and rate parameters of that well. The mean () of the gamma distribution is the ratio of to , which allows reparameterization of the likelihood in terms of and as:

(2)

This parameterization expresses the gamma likelihood in terms of mean () and shape () rather than the canonical shape-rate form, facilitating direct interpretation of treatment effects on the natural velocity scale. By modeling all cells within a well through shared parameters and , information is pooled across cells to produce stable well-level estimates even when individual wells contain varying numbers of tracked cells.

Well-level model: Accounting for technical replicates and batch effects: Each well w belongs to a plate (biological replicate) and is treated by a treatment . Multiple wells per plate may receive the same treatment (technical replicates, indexed as pt[w]). The log-transformed means of wells receiving the same treatment are modeled hierarchically, by treating the corresponding coefficients () as random samples drawn from normal distributions:

(3)

where is mean effect of treatment t on plate p; and captures the variability between technical replicates. However, we know that cell migration assays are affected by plate-specific batch effects that can systematically bias the migration velocity across all wells on the plates. To correct for plate-specific batch effects, we include an offset term , defined as the mean migration velocity (on log-scale) of a control treatment (e.g., dimethyl sulfoxide (DMSO)) on plate p, effectively normalizing batch effects across plates:

(4)

where the treatment effect captures deviations from this baseline for treatment t on plate p; and captures the variability between technical replicates. This structure pools information across technical replicates, producing more stable estimates than analyzing each well independently while still allowing for well-to-well variation.

Plate-level model: Accounting for biological replicates: Wells treated with the same treatment (t) will have similar cell migration velocities (similar coefficients) after accounting for batch effects. Hence, the model treats as random samples drawn from normal distributions:

(5)

where is the overall (across plates) effects of treatment t on cell migration; and is the standard deviation between biological replicates. The hierarchical structure enables sharing of information across plates while preserving treatment-specific estimates.

Treatment-level model: partial pooling across treatments: High-throughput cell migration screens enable researchers to characterize treatment effects of hundreds or even thousands of compounds simultaneously. In such high-dimensional scenarios, the peril of false positive effects increases due to multiple testing. cellmig implements a hierarchical layer that treats the overall treatment effects () as draws from an overarching population of effects:

(6)

where is the standard deviation between estimates. This hierarchical structure enables partial pooling (shrinkage) of information across treatments [19]. Parameters with high uncertainty (e.g., due to low cell counts or high variability) are pulled more strongly toward the population mean (zero effect), while well-estimated parameters remain data-driven.

This shrinkage mechanism inherently regularizes the model against false positives in large-scale screening. By stabilizing estimates for weak signals, it improves the reliability of ranking treatments by their effects (). Thereby, the model automatically controls the amount of pooling that is applied to the treatment-specific parameters, ensuring that prioritization decisions are driven by robust evidence rather than noise.

Gamma distribution shape parameter modeling: We observed a linear relationship between the means and variances of the gamma-distributed velocities across wells on a log–log scale (S2A Fig), as expected from the analytic mean () and variance () of the Gamma distribution. Across wells, the variances were on average approximately five-fold smaller than the means (S2A Fig), indicating stable measurements and controlled experimental conditions with a small coefficient of variation (CV):

(7)

Notably, the Gamma shape parameter satisfies , i.e., it is the inverse squared coefficient of variation. The empirical distribution of the inverse squared CV in Dataset 1 was approximately normal on a logarithmic scale (S2B Fig). Hence, we assumed that values are also approximately normally distributed, and treated them as random samples drawn from a normal distribution with mean and standard deviation :

(8)

Quantifying treatment effects.

For treatments i and j, the contrast represents the log-fold change in migration velocity. If 0 and the 95% Highest Density Intervals (HDIs) of lie mostly or completely below 0 (0 = null effect), we have strong evidence of reduced cell velocity in i relative to j. On the other hand, if and the 95% HDI of lie mostly or completely above 0, we have strong evidence of increased cell velocity in i compared to j. Distributions with the 95% HDIs more or less centered around 0 indicate that there is no evidence for a clear change in the cell velocity. Note that unclear evidence is not equivalent to no change, because for a treatment group with 0 we may also have a wide 95% HDI, including possibilities for positive or negative change. cellmig outputs mean and 95% HDI of , including the probability of differential effect on migration ():

(9)

Here, indicates strong evidence for a difference in cell migration velocity between the treatments, while suggests negligible evidence.

For easier interpretation, cellmig exponentiates the log-fold-changes described by , , and , yielding fold-changes , , and , respectively. Throughout the Results, we present effects on the natural scale (fold-change), where the null effect equals 1 (no change).

Model priors.

Our Bayesian framework requires prior distributions for location parameters (, ) and scale parameters (, , , ). We adopted a dual strategy: literature-informed priors for location parameters to ensure biological plausibility across cell types, and regularizing priors for scale parameters to handle variance components where literature is scarce. We validated these choices through prior predictive checks and prior sensitivity analysis, confirming that the priors generate realistic data without unduly constraining posterior inferences (see Validation via prior predictive checks and Validation via prior sensitivity analysis below). The following subsections detail the justification for each prior choice.

Location parameters: and : Location parameters define the baseline velocity and Gamma distribution shape. To ensure cellmig accommodates diverse cell types—from slow epithelial cells to fast immune cells—we elicited priors using three data sources: the World Cell Race study [20], high-throughput neutrophil data [9], and our experimental datasets.

The parameter represents the baseline migration velocity (log-scale) of control treatments (e.g., DMSO) on plate p. The World Cell Race study [20] reported mean velocities for 54 cell types ranging from 0.1 to 0.9 µm/min (log-scale means: -2.3 to -0.1), with maximum individual velocities up to 5.2 µm/min (log-scale: 1.65). Combining these sources with our empirical data from Dataset 1 (range of mean well velocities 0.3–1.63 µm/min; log-scale means: -1.2 – + 0.3), we assigned:

(10)

This prior places 99% of density between -3 and 2 on the log-scale (0.05 to 7.4 µm/min), accommodating both slow and fast migration.

We validated this prior choice against control-treated neutrophil data [9]. Neutrophils have velocities an order of magnitude higher than tumor cells. While neutrophil velocities fall in the right tail of our prior, they remain within high-density regions (S2C Fig), confirming the prior accommodates faster cell types without being overly diffuse.

The parameter defines the population mean of , where controls the skewness of the velocity distribution. To assign a prior on we examined the means and standard deviations of 54 cell types reported in [20], observing that standard deviations were typically an order of magnitude smaller than means. From Fig 1D of that study, we extracted approximate means and standard deviations for ten cell types and computed , yielding values around 3.3 on the log-scale. These values exceeded our empirical observations from Dataset 1 (mean = 1.55, standard deviation (SD) = 0.4) and Dataset 2 (mean = 1.52, SD = 0.45), likely reflecting lower measurement variability in the low-throughput World Cell Race study compared to our standardized high-throughput assay. Second, we computed well-specific values for high-throughput control-treated neutrophils [9], which yielded values centered around 0 on the log-scale with SD = 0.4, i.e., somewhat lower than our empirical observations from Datasets 1 and 2. To ensure the model accommodates the variability inherent to both low-throughput assays and large-scale high-throughput screens, we centered the prior at 1.5 with an inflated standard deviation (SD = 1.0):

(11)

This choice encompasses estimates from the World Cell Race study, neutrophil data, and our empirical datasets (S2B Fig):

Scale parameters: , , , : For variance components, we employed regularizing Half-Normal priors [19]. Comprehensive literature on variance components across high-throughput platforms is lacking; thus, regularizing priors constrain parameters to plausible ranges while allowing data to dominate inference. This approach also facilitates efficient sampling in Stan.

The hyperparameter controls shrinkage of treatment effects toward zero (Equation 6): small values pull treatment effects toward zero (appropriate when most compounds have negligible effects), while larger values allow more treatment-specific variation. To justify our prior choice for , we considered the expected magnitude of treatment effects in typical screens. If we assume and ignore the technical and biological variability in Equations 4 and 5, then from Equation 4 it follows that , i.e., the mean cell velocity increases by a factor of over the baseline cell migration velocity of the plate. However, if , then the mean cell velocity would increase by a staggering factor of over the baseline migration. Using the control treatments in our experiments, we observed =-0.53 (95% HDI=[-0.46, -0.60]) for the compound CK666 at 40 µM, and =0.55 (95% HDI=[0.48, 0.62]) for fluvastatin at 10 µM, which are associated with severe reduction and increase in the cell migration velocity relative to DMSO (control treatment), respectively. Hence, for most treatments we expected , which implied that we need a prior distribution that assigns high density to values around 0, and low density to values larger than 1 and smaller than −1. In fact, even if CK666 or fluvastatin were chosen as the the control treatment, barely crosses the magnitude 1. Hence, for most treatments in a typical screen we expected , as the majority of compounds are expected to have negligible effects on migration. This sparsity assumption constrains the plausible range for . Since values are drawn from a Normal distribution with standard deviation , most values (approximately 95%) will fall within roughly two standard deviations of zero (). To ensure most treatment effects remain within our observed range of , we need around 0.5 (since ). To allow for occasional strong effects up to for potent compounds, we need up to 1.0 (since ). Therefore, should be approximately 0.5–1.0 to balance the expectation that most compounds have negligible effects while remaining flexible enough to detect genuinely strong effects. We therefore assigned a regularizing half-normal prior:

(12)

This prior places 95% of density below approximately 2, with median around 0.67, concentrating density in the 0.5–1.0 range that matches our empirical observations while allowing larger values for screens with more heterogeneous treatment effects. This ensures shrinkage is strong enough to control false positives without being so restrictive that it masks genuine large effects (e.g., from newly synthesized compounds with stronger effects).

We applied similar regularizing priors to the remaining scale parameters, capturing technical, biological, and Gamma shape variability. These capture technical (well-to-well), biological (plate-to-plate), and Gamma shape variability, respectively. The magnitude of our observed treatment effects constrains these variance components: since we reliably detected effects as small as (e.g., CK666, fluvastatin) with narrow uncertainty intervals, and must be substantially smaller than typical effect sizes. Empirical estimates from our datasets ranged from 0.1 to 0.45 on the log-scale, consistent with this constraint and falling well within the prior’s high-density region (95% below 2).

(13)

Validation via prior predictive checks: To confirm these priors generate biologically plausible data, we performed prior predictive checks (S3 Fig). We compared our default configuration (all scale parameter SD = 1) against wider priors (SD = 3). While posterior estimates remained stable under both configurations, the wider priors generated implausible velocities: over 5% of simulated velocities exceeded 100 µm/min, compared to only 1% under the default priors. Consequently, we retained the default priors (SD = 1) to ensure realistic data generation.

Validation via prior sensitivity analysis: To assess whether our prior choices influence posterior inferences, we compared the default cellmig model (all scale parameter SD = 1: =1, =1, =1) against a model with wider priors (all scale parameter SD = 3: =3, =3, =3). Both models were fit to Dataset 1 using identical MCMC settings (4 chains, 2,000 iterations, 1,000 warm-up). Posterior estimates for all parameters were nearly identical between the two configurations (S4A Fig): overall treatment effects (), plate-specific effects (), plate intercepts (), and variance components (, , ) showed differences in posterior means of less than 0.01 on the log-scale. All parameters achieved convergence (Rhat ≈ 1.00) in both models. This demonstrates that the priors are appropriately regularizing—they constrain parameters to plausible ranges without influencing posterior estimates, allowing the data to dominate inference. Consequently, we retained the default priors (SD = 1) for all analyses, as they provide adequate regularization while generating biologically plausible data (see prior predictive checks above).

Experiment planning by simulation.

Our Bayesian model (M) is generative and can simulate cell velocities using the same error model (Equation 1). In this framework, the values of and are drawn from their priors, which are themselves informed by parameters in subsequent layers of the model. This simulation process is critical for optimizing experimental design, particularly in determining the optimal number of (i) cells, (ii) technical replicates, and (iii) biological replicates. These factors directly affect the uncertainty in estimating treatment effects () and their differences (). The model can operate in two modes: fully generative, where all free parameters are sampled from their priors, or partially generative, where certain parameters are fixed by the user (e.g., to align with estimates from prior experiments).

Both modes support experimental design but serve distinct purposes. The fully generative mode (function gen_full()) draws all parameters from priors, serving as a prior predictive check to validate model generalizability across diverse biological contexts (S3 Fig). The partially generative mode (function gen_partial()) allows users to fix specific parameters (e.g., effect sizes, variance components) based on prior data while sampling others from priors. This reflects standard practice in power analysis, where researchers specify anticipated effect sizes to estimate sample size requirements. This flexibility allows users to tailor simulations to their available knowledge: incorporating specific estimates from pilot studies when planning similar experiments, or using broader assumptions when designing novel studies where less prior information is available. We note that the power analysis results presented in the Results section reflect the specific noise structure of our imaging assay. For experimental setups with different variability profiles (e.g., different microscopy systems or cell lines), users should estimate variance components from a small pilot study and use the gen_partial() function to generate power curves tailored to their specific context.

Visualization and prioritization of treatment effects.

To facilitate decision-making across varying screen sizes, the cellmig function get_pairs() automatically generates appropriate visualizations based on the number of treatments. For modestly sized experiments (treatments < 100), the function produces heatmaps comparing and across all pairwise conditions, enabling comprehensive inspection of treatment relationships (Fig 5). For large-scale screens involving hundreds or thousands of conditions, where heatmaps become impractical, get_pairs() generates Bayesian volcano plots combining effect size () and support () (S5 Fig). Similar to the use of posterior means and b-values in metabolomic screening [21], cellmig utilizes to represent biological magnitude and to extract maximum information from the posterior distribution regarding evidence strength. By balancing effect size against variability, this framework aligns with established high-throughput screening practices for prioritizing promising candidates for validation [22,23], particularly in large-scale settings where traditional visualization becomes impractical.

Cell line and cultures.

ASPC1 cells (American Type Culture Collection (ATCC) Catalog number (Cat#) CRL-1682, Research Resource Identifier (RRID):CVCL_0152, sex: female) were cultured under humidified atmosphere at 37 °C and 5% CO₂ in Dulbecco’s Modified Eagle’s Medium (DMEM) high glucose, pyruvate (Gibco, Cat # 41966052) supplemented with 10% Fetal bovine serum (FBS) (VWR/Biowest, Cat #S1600-500), 1% non-essential amino acids (ThermoFisher, Cat #11140035), 50 U/ml penicillin and 50 μ g/ml streptomycin (ThermoFisher, Cat #10378016). Identity was authenticated by Short Tandem Repeats (STR) analysis. Testing to exclude mycoplasma contamination was performed regularly.

Chemicals.

The following commercially available compounds were used at concentrations as indicated: fluvastatin (abcam, Cat# ab120651, Chemical Abstracts Service Number (CAS No) 93957-55-2), pravastatin (Sigma-Aldrich, Cat# 524403, CAS No 81131-70-6), pitavastatin (Sigma Aldrich, Cat# SML2473, CAS No 147526-32-7), benproperine (Hycultech, Cat# HY114657A, CAS No 19428-14-9), haloperidol (Sigma Aldrich, Cat# H1512, CAS No 52-86-8), CK666 (Sigma Aldrich, Cat# SML0006, CAS No 442633-00-3), CK869 (Sigma Aldrich, Cat# C9124, CAS No 388592-44-7). All compounds were dissolved in DMSO (AppliChem, Cat# A3672, CAS No 67-68-5). The final concentration of DMSO for all compounds and vehicle control was at maximum 0.1% and serially diluted down in lower concentrations, except for pravastatin, where it was 1%, indicated by “DMSO high” (included as additional experimental vehicle control).

For the application screen, to assess structure activity relationships 15 derivatives of the “parent” compound pimozide were synthesized (S6 Fig and S1 Table) and used at the indicated concentrations. All compounds were dissolved in DMSO (AppliChem, Cat# A3672, CAS No 67-68-5). The final concentration of DMSO for all compounds and vehicle control was at maximum 0.1% and serially diluted down in lower concentrations.

Assessment of in vitro viability.

ASPC1 cells were seeded in triplicate per condition on 96-well plates ( to cells/well, depending on the time point). Compounds were added to ASPC1 cells at indicated concentrations. For the setup experiments A and B cell viability was assessed using the PrestoBlue cell viability assay (Invitrogen, Cat #A13262) per manufacturer’s instructions after 0, 24, 48 and 72 hours (S7 Fig). For the application data set, viability was assessed at 0 and 48 hours, at the start and endpoint of the live-cell imaging experiment (S8 and S9 Figs). Absorbance at 570 and 600 nm was measured with a Tecan Spark 10M plate reader (Tecan Trading AG, RRID:SCR_021897).

Live-cell imaging.

96-well plates were coated with Collagen I (Sigma Aldrich, Cat #C8919, CAS No 9007-34-5) for 1 hour at 37 °C and 5% CO₂ to promote cell attachment and migration behavior. Following incubation, the wells were washed once with Phosphate Buffered Saline (PBS). Cells were seeded at 2,000 cells per well in DMEM and allowed to adhere overnight under standard culture condition (37 °C and 5% CO₂). On the following day, cells were treated with either DMSO vehicle control or the indicated compounds and incubated for 48 hours prior to imaging. For each plate, four technical replicates per condition were imaged.

Time-lapse brightfield imaging was performed using a cell imaging multimode reader (Cytation 5, Agilent Technologies, RRID:SCR_019732). Each plate was imaged with the objective for 4 hours at 37 °C and 5% CO₂ with a fixed number of kinetic reads/looping times as indicated. Individual images were aligned and stitched into .mp4 files using Gen5 software (RRID:SCR_017317). Quality-control procedures were performed prior to downstream analysis. Videos were excluded if the automated alignment by Gen5 software failed, if substantial stage drift or focus instability was observed, or if non-cellular debris was incorrectly identified as migrating cells. Only wells passing all quality-control criteria were included in subsequent migration analyses.

Computational segmentation and tracking.

The tracking workflow was established as previously described [9]. The generated movies, exported as .mp4 files, underwent automated segmentation using the cellular segmentation tool Cellpose [24]. To adapt to the domain-specific characteristics of the ASPC1 cell line, a pretrained Cellpose model was fine-tuned using representative samples. Subsequent single-cell tracking was carried out using a classical tracking algorithm based on the Earth Mover’s Distance [25]. The tracking data contained unique tracking labels for each cell within the segmented images of the time-lapse sequence. Only cells in at least 10 consecutive frames were analyzed.

For each well, approximately 50–200 cells were measured in this way. Distances in micrometers were obtained from pixel displacements using the pixel size (0.348 µm/pixel) and combined with the acquisition interval of one frame every 4 minutes to calculate migration velocity in µm/min.

To ensure the reliability of velocity measurements, we quantified detection and linking errors using an Acyclic Oriented Graphs Matching (AOGM)-inspired framework [26]. We manually curated a representative subset of nine movies (20 frames each) and compared automated outputs against corrected annotations. This analysis identified 153 false-positive detections (fp), 174 false-negative detections (fn), 1 object-splitting operation (sc), 88 edge-deletion operations (de), and 220 edge-addition operations (ae) (S2 Table). Here, fp and fn represent spurious and missed cell detections, respectively; de and ae correspond to redundant/incorrect and missing temporal links, respectively; and sc indicates instances where detected objects required separation. The mean relative error across all error types was below 3.69% (S2 Table). Representative visual examples of segmentation masks and track overlays from the curated movies are provided in S10 Fig.

We further performed a sensitivity analysis to evaluate the impact of tracking artifacts on downstream velocity estimates. Comparing automated tracks (354 tracks, mean velocity = 0.441 µm/min) against manually corrected tracks (360 tracks; mean velocity = 0.438 µm/min); difference due to recovery of false-negative detections revealed a negligible difference in mean velocity (difference = 0.003, 95% confidence interval [-0.028, 0.034]; Welch Two Sample t-test, p = 0.85). This indicates that the observed level of tracking artifacts does not substantially affect migration readouts.

Comparison with frequentist methods (H-test).

To mimic common workflows assuming minimal variability and negligible batch effects, we pooled cells by treatment for the H-test, inflating sample sizes but ignoring experimental hierarchy–an issue avoided by cellmig. This revealed systematic discrepancies between H-test outputs (p-values, z-scores) and cellmig’s probabilistic metrics (, ) (Fig 6A–6B).

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Fig 6. Benchmarking cellmig against the H-test and a simplified Bayesian model.

(A) cellmig probability of differential effect () vs. H-test adjusted p-values () for 171 treatment pairs. Labeled points show diverging results. Dashed lines: =0.99 and adjusted p = 0.01. (B) cellmig fold-change () vs. H-test z-scores. Black/red: intra-/inter-experiment pairs. on log₁₀ scale. (C) cellmig vs. simplified model overall treatment effects () with 95% HDIs. Triangles/circles: treatments from Experiment A/B. Dashed line: identity. (D) cellmig vs. simplified model pairwise effects (). Red dots above diagonal: inter-experiment pairs with inflated effects due to unmodeled batch effects in simplified model.

https://doi.org/10.1371/journal.pcbi.1014472.g006

We note that the probability of differential effect () and frequentist p-values are fundamentally different quantities with different interpretations. Our benchmark is not intended to equate these metrics, but rather to compare the decision-making frameworks that researchers use in practice. In large-scale screens (with >100 treatments), experimental biologists must prioritize a subset of compounds for experimental validation. The current standard practice is to use frequentist methods with a p-value threshold (e.g., p < 0.05) to declare effects “significant.” Our Bayesian approach provides an alternative decision-making framework based on . Here, we evaluate how each approach would guide experimental decisions–specifically, which treatments each method would prioritize for follow-up–and demonstrate that -based decisions are more reliable in the presence of hierarchical structure and batch effects.

Discordant calls between H-test and cellmig: Two cross-experiment pairs (e.g., benproperine (10 µM) vs. CK666 (40 µM) showed non-significant adjusted p-values (p > 0.01) in H-test despite strong evidence from cellmig ( 0.99) (Fig 6A, bottom-right). All involved batch effects between experiments A/B, where systematic velocity differences masked true treatment effects (Fig 4). Because the H-test pools cells across plates, it conflates biological treatment effects with plate-specific batch offsets. cellmig’s hierarchical structure separates these variance components, allowing detection of effects consistent across biological replicates despite batch shifts.

Meanwhile, seventeen pairs (e.g., haloperidol (5 µM) vs. DMSO (high); pravastatin (10 µM) vs. DMSO (high)) showed significant adjusted p-values ( 0.01) but low values ( 0.99). While some of the significant differences based on the H-test arose from unmodeled batch effects (e.g., cross-experiment pairs), others involved treatment groups from the same experiment. These discrepancies stemmed from two factors: (1) Pooling cells amplified apparent statistical power (green crosses vs. black dots in S14 Fig), rendering small effect sizes significant–a known challenge in large migration datasets [16]; (2) Applying the H-test to individual plates revealed fluctuating p-values (e.g., on log10-scale 0.8-4.7 for CK666 (10 µM) vs. haloperidol (10 µM); 0.6-7.5 for fluvastatin (2.5 µM) vs. pitavastatin (5 µM)), reflecting non-negligible biological variability which is ignored by the H-test (S15 Fig). These inconsistent results, where some plates show significant p-values while others do not, highlight a key problem of the H-test, namely the interpretation of fluctuating p-values on individual plates.

In contrast, cellmig explicitly models biological variability, resulting in wider posterior distributions for overall treatment effects (). For example: haloperidol (5 µM) vs. DMSO (high) had overlapping 95% HDIs: =0.83, 95% HDI [0.75, 0.92] vs. =0.95, 95% HDI [0.87, 1.03]. Hence, the resulting =0.88, 95% HDI [0.77, 1.01] included 1 (the null effect) with =0.94. We obtained similar results for pravastatin (10 µM) vs. DMSO (high).

Result robustness and interpretability: cellmig reports effect sizes () with uncertainties and evidence probabilities (), while H-test relies on point estimates (z-scores, p-values). The z-score’s sensitivity to sample size amplifies trivial differences in large datasets (Fig 6B) and yields inconsistent interpretations across experiments with varying sample sizes. This fundamentally limits biological insight, as identical effect magnitudes may show divergent statistical significance. cellmig avoids this pitfall: its effect sizes remain stable across sample sizes, with the availability of more data improving precision rather than inflating significance.

Comparison with simplified Bayesian model.

To explicitly validate the necessity of modeling the full nested experimental structure and batch effects, we compared cellmig’s hierarchical model against a simplified Bayesian counterpart that ignored both the nested experimental design (cells within wells within plates) and plate-specific batch effects. While both models yielded similar posterior means for overall treatment effects (), the uncertainty estimates diverged substantially (Fig 6C). The simplified model produced artificially narrow 95% HDIs due to pseudoreplication (pooling all cells receiving the same treatment) and the inability to account for plate-to-plate variability. Furthermore, we observed systematic shifts in treatment effects corresponding to experiments A and B, reflecting unmodeled batch effects (most triangles/circles in Fig 6C shifted above/below the diagonal).

The underestimation of uncertainty propagated to pairwise comparisons (Fig 6D), generating spurious differences between treatment groups. The simplified model identified 30 additional treatment pairs with high probability ( 0.99) of differential effect compared to cellmig’s hierarchical model, the majority of which (27) occurred between treatments from the same experiment (S16 Fig). For example, the simplified model detected a significant difference between pravastatin doses (5 µM vs. 2.5 µM: = 0.95, 95% HDI = [0.93, 0.98], = 1), despite the hierarchical model finding low evidence for differential effects ( = 0.97, 95% HDI = [0.86, 1.07], = 0.44). Additionally, unmodeled batch effects created systematic discrepancies in effect magnitude between the two models, visible as red dots above the diagonal in Fig 6D (inter-experiment comparisons). This highlights the importance of plate-specific intercepts () to correct for systematic batch effects, thereby separating technical bias from biological signal.

Leave-One-Out Cross-Validation (LOO-CV) assessed the predictive performance of both models by estimating their ability to generalize to unseen data [33]. We compared the Expected Log Pointwise Predictive Density (ELPD), where higher values indicate better predictive accuracy, and the LOO Information Criterion (LOOIC = ELPD), where lower values are preferred. The hierarchical model achieved an ELPD_LOO of -6113.9 (standard error (SE) = 146.7), compared to -6972.5 (SE = 145.9) for the simplified model. This corresponds to an ELPD difference of 858.6 (SE = 45.9) in favor of the hierarchical model, and a lower LOOIC (12227.9, SE = 293.4 vs. 13945.0, SE = 291.9). Although the hierarchical model required more effective parameters (p_loo = 504.8 vs. 40.2) to account for the nested structure, the substantial gain in predictive accuracy indicates the added complexity is warranted. These results demonstrate that accounting for data hierarchy and batch structure is critical to avoid false positives and ensure reliable uncertainty quantification in high-throughput migration assays.

Biological replicates dominate uncertainty reduction.

First we investigated the impact of experimental configuration (N_cells, N_tech, N_bio) on W (Fig 7A). While increasing any of these three sample size dimension reduced W, the most substantial reduction occurred with increasing biological replicates (N_bio).

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Fig 7. Power analysis.

(A) Mean widths (W) of 95% Highest Density Intervals (HDIs) for effect sizes (, fold changes) for different experimental configurations. Dots are mean W of 1,000 bootstraps. Error bars are 95% HDIs of bootstrapped W. Panels correspond to technical replicates (N_tech). Colors represent cells per well (N_cells), and x-axes show biological replicates (N_bio). (B) True positive rates (TPR, %) for effect sizes (). Lines connect TPR values (color-coded by ) across N_bio. Grid columns = N_tech, rows = N_cells. Dots are mean TPR values of 1,000 bootstraps, error bars are 95% HDIs of bootstrapped TPR values. Horizontal dashed lines indicate 80% TPR. Simulations used values of and inferred from Dataset 1. Users should adjust these parameters to reflect the noise structure of their own experimental setups.

https://doi.org/10.1371/journal.pcbi.1014472.g007

Specifically, setting N_bio to 3, 6, 9, and 12, was associated with consistently smaller W (Fig 7A) from W = 0.35 to W = 0.12, i.e., increasing N_bio to 6, 9, and 12 reduced W by factors of about 1.45, 1.8, and 2.1, respectively, relative to N_bio = 3 (S17A Fig). Increasing N_tech shifted W to smaller values (panels in Fig 7A), however, we saw diminishing returns: W was reduced by a factor of 1.25 for N_tech = 12 vs. N_tech = 3 (S17B Fig). Cell counts per well had negligible impact, with N_cells = 50 and 100 reducing W by less than 1.1-fold versus N_cells = 25 (S17C Fig).

In summary, experimental designs should therefore prioritize biological replicates for minimizing uncertainty in . Technical replicates showed limited impact in these simulations, consistent with our assumption of low technical variability based on empirical data. We note that cellmig enables power analysis under diverse experimental conditions (e.g., high variability regimes), where technical replicates may have greater influence on W. Consequently, while biological replicates dominated uncertainty reduction in our specific dataset, the relative importance of technical vs. biological replication may shift in assays with higher technical noise. cellmig allows users to explore these trade-offs by adjusting variance parameters to match their specific experimental conditions.

Controlling the number of true positives.

A narrow uncertainty interval is only valuable if it actually contains the true effect size. We quantified whether an uncertainty interval contains the true effect size (here synthetic fold-changes ), but not the null effect (=1). If it does, we call this a true positive. Otherwise, if the uncertainty interval contains the null effect, we call this a false negative. From 300 simulations performed with the same experimental configuration we computed the TPR (Fig 7B).

Large effects (e.g., migration enhancing =2, 1.5 and 1.4; or migration reducing = 0.5, 0.6 and 0.7) achieved high TPR ≥90% across all designs. Smaller effects (e.g., = 0.8 or = 1.3 and 1.2) required at least 6 biological replicates for TPR ≥80%. For the smallest effects in our simulation ( or 1.1), maximum number of biological replication (N_bio = 12) combined with at least 6 technical replicates yielded TPR close to 80%. This demonstrates that detecting subtle treatment effects ( close to 1) requires substantial biological replication.

Uncertainty interval calibration.

A critical requirement for uncertainty-aware methods is that reported intervals must be statistically calibrated, containing the true effect at the expected rate (e.g., 95% for a 95% HDI). We reused the simulated data with the same true effect sizes to assess whether cellmig’s 95% HDIs contained the true simulated effect. The observed coverage was 95.1% across all simulations and experimental configurations (varying N_cells, N_tech, N_bio). This confirms cellmig produces well-calibrated uncertainty estimates.