The Tumor Growth tab provides two statistical modeling approaches selectable from the Statistical Model dropdown:

• Linear Mixed-Effects Model (LME4) — fits a mixed-effects model to repeated tumor volume measurements. Accounts for inter-animal variability and unequal observation times. Recommended for most longitudinal datasets.
• Area Under Curve (AUC) — summarises each animal’s total tumor burden as the trapezoidal AUC of its growth curve. Non-parametric and robust to missing timepoints, but discards trajectory shape information.

Both modes compute Tumor Growth Inhibition (TGI) for each treatment group relative to the reference. TGI = (1 − V_treated / V_control) × 100 at the final timepoint.

Model

A linear mixed-effects model is fitted to transformed tumor volumes:

log(Volume) ~ Treatment × Day + (1 | ID)

The Treatment × Day interaction captures whether treatment groups differ in their growth trajectories over time, not just at a single endpoint.

Transformation

Log (default) stabilises variance and linearises exponential growth. Square root suits moderate heteroscedasticity. Use ‘None’ only for already-linear data.

Random Effects

‘Intercept only’ allows each animal to have its own baseline volume. ‘Intercept + Slope’ additionally allows individual growth rates — more flexible but may fail to converge with small groups.

Cage Effect

When a cage ID is mapped in Data Upload, cage can be included as a covariate to account for housing-level clustering. ‘Include if not collinear’ adds it automatically when it is statistically separable from treatment.

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ANOVA Tab

Type III ANOVA F-test for Treatment, Day, and the Treatment × Day interaction. A significant interaction (p < 0.05) indicates that treatment groups differ in their growth trajectories — the primary analysis target.

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Comparisons Tab

Pairwise group comparisons at the mean observation day using estimated marginal means (EMMs):

• vs Reference (Dunnett) — each treatment vs the reference group only. Dunnett correction controls the familywise error rate for this one-vs-many structure and is less conservative than Bonferroni.
• All Comparisons (Tukey HSD) — every pairwise combination. Use when all inter-group differences are of scientific interest.

Comparisons are marginalised at the mean study day. For trajectory differences across time, see the Treatment Effects tab.

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Treatment Effects Tab

Estimated marginal means (EMMs) of transformed volume per treatment group. EMMs are shown at the mean observation day and at five quantile days (min, Q1, median, Q3, max), capturing the Treatment × Day interaction that a single mean-day estimate would miss.

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Growth Rates Tab

Per-animal exponential growth rates estimated by log-linear regression of each animal’s volume trajectory independently. Reported as growth rate (log-scale slope), fold change, and % change per day with 95 % CIs and R². These are descriptive; for group-level inference use the ANOVA and Comparisons tabs.

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Diagnostics Tab

Q–Q plot of residuals and residuals vs fitted values. Systematic curvature suggests the transformation choice should be revisited. Funnel-shaped spread indicates heteroscedasticity.

Trapezoidal AUC of tumor volume over time is computed per animal. AUC (mm³·day) captures total tumor burden integrated over the study, not just the final timepoint.

Individual AUC

Per-animal AUC values with group summaries (mean, SD, SEM).

AUC Summary

Group comparisons via Welch t-tests with Benjamini–Hochberg correction.

LOCF (last observation carried forward) can extrapolate AUC to a common endpoint for animals censored early, so all animals contribute to the same time window. Set Extrapolation Points to 0 to use only observed data.

Method

Fits the same model formula as LME4 using full Bayesian inference via brms / Stan. Instead of point estimates and p-values, every parameter has a posterior distribution : a probability distribution over plausible values given the data and priors.

log(Volume) ~ Treatment × Day + (1 | ID)

Results are summarised as posterior medians with 95 % highest posterior density (HPD) credible intervals . A 95 % CrI has a direct probability interpretation: there is a 95 % posterior probability that the true parameter lies within the interval — unlike a frequentist confidence interval.

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Prior Strength

Priors express what you believe about parameter values before seeing the data. They regularise estimates and prevent the model from chasing noise in small samples. All presets use Normal priors on fixed effects and Exponential priors on variance components; only the widths differ.

Skeptical

Default. N(0, 0.25) on fixed effects; Exponential(2) on SDs. Encodes the reasonable belief that treatment effects are small — effects > ±0.5 log-units per day are considered very unlikely a priori. Recommended for exploratory preclinical studies where large effects have not been previously established.

Weakly informative

N(0, 1) on fixed effects; Exponential(1) on SDs. Broader than Skeptical — appropriate when prior work suggests the treatment category can produce moderate-to-large effects.

Informative

N(0, 0.5) on fixed effects; Exponential(2) on SDs. Between Skeptical and Weakly informative. Useful when effect sizes in the 0.1–0.5 log-unit range are plausible based on prior data.

Diffuse

N(0, 2.5) on fixed effects; Exponential(0.5) on SDs. Near-flat priors; use with caution on small datasets as estimates can be driven entirely by noisy data.

Manual

Specify the prior family and parameters for each model class independently. Fixed effects (b): Normal or Student-t. Intercept: same. Random-effect SD and residual sigma: Exponential or half-Normal.

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Result Tabs

• Summary — posterior median and 95 % CrI for every model parameter.
• Treatment Effects — group-level estimated marginal means (posterior) at the mean study day.
• Comparisons — posterior contrasts of each group vs the reference.
• Posterior Check — overlay of observed data density vs 50 draws from the posterior predictive distribution. Systematic mismatch indicates model mis-specification.
• MCMC Diagnostics — Rhat and effective sample size (ESS) per parameter. Rhat > 1.01 indicates non-convergence; increase iterations or inspect trace plots.
• Growth Rates — per-animal log-linear regression rates (same as LME4, not MCMC-based).

When a Necrotic Flag column is mapped in Data Upload, a handling selector appears in the sidebar. Necrotic tumors have a non-viable core that inflates caliper-based volume estimates without contributing to proliferating tissue.

Exclude (recommended)

Removes flagged observations from the model input. Conservative and publication-defensible. The Necrosis tab reports how many observations were flagged and which groups were affected, regardless of handling mode.

Covariate

Adds a 0/1 .necrotic_flag fixed effect to the LMM formula. Estimates the average volume bias attributable to necrosis. Useful when necrosis is approximately evenly distributed across groups and you want to retain all timepoints.

No adjustment

All observations are used as-is (current default when no necrotic column is mapped). The Necrosis summary table is still shown for documentation purposes.

Reference Group

The vehicle/control group used as comparator. Auto-detected from common names (Vehicle, Control, DMSO, PBS, Saline) or defaults to the first group alphabetically.

Post-hoc Comparisons

Dunnett (vs reference, default) or Tukey HSD (all pairs). Applies to the Comparisons tab in LME4 mode.

Extrapolation Points

Number of recent timepoints used to fit a slope for animals that died before study end, then extrapolate their volume to the final day. Set to 0 to use observed data only.

Time Column

Numeric study day, or calculated from a date column mapped in Data Upload (days elapsed from first observation).

The Survival tab fits Kaplan–Meier (KM) survival curves and a Cox proportional hazards model to time-to-endpoint data. In mouse tumor experiments the 'endpoint' is typically the day a tumor exceeds the IACUC volume limit, not true animal death.

Three outputs are produced:

• Kaplan–Meier curves with log-rank test p-values.
• Cox proportional hazards model reporting hazard ratios (HR) per group relative to the reference.
• Risk table showing animals at risk, events, and KM estimates at each event time.

The KM estimator computes a non-parametric step-function survival probability S(t) = P(T > t) from event times. Each downward step corresponds to one or more events on that day.

Log-rank test

Tests whether the survival curves of two or more groups are statistically equivalent. The omnibus p-value tests all groups simultaneously; pairwise p-values are computed by restricting each comparison to the relevant two groups (df = 1).

Median survival

Day by which 50 % of animals reached the endpoint. 'Not reached' if fewer than half had events before study end.

Censoring

Animals that never reach the endpoint contribute their last observation day as a censored time. This correctly uses partial information rather than excluding them.

When all animals in a group are censored (zero events), a log-rank test is not meaningful. The model falls back to pairwise comparisons using only groups with at least one event.

The Cox model estimates the hazard ratio (HR) for each treatment group relative to the reference:

h(t) = h₀(t) × exp(β₁ × Treatment)

HR < 1

Lower hazard than reference — animals reach the endpoint more slowly (better outcome).

HR = 1

Identical hazard to reference.

HR > 1

Higher hazard than reference — animals reach the endpoint faster (worse outcome).

Firth's bias-reduced estimation is applied automatically when any group has zero events. Standard Cox partial likelihood produces infinite coefficient estimates in this case; Firth's penalisation regularises them.

The proportional hazards assumption requires that the HR is constant over time. Crossing KM curves indicate a time-varying HR, which violates this assumption — interpret Cox results with caution in that case.

Mapped censor column

When an Event/Censor column is mapped in Data Upload (0 = censored, 1 = event), it is used directly.

Auto-detection

When no censor column is mapped, animals that disappear before the final study day are automatically treated as events; animals present at the final day are censored.

Volume threshold

Optionally generate an event indicator by flagging animals whose tumor volume exceeds a specified threshold at any timepoint.

Natural death

If checked (recommended), animals that die before reaching the volume threshold are counted as events. If unchecked, only volume threshold crossings are events and natural deaths are censored.

The Toxicity tab provides two complementary analysis modes selectable from the Statistical Model dropdown:

• Body Weight Analysis — models longitudinal weight trajectories using a linear mixed-effects model, and derives AUC-based and time-to-event (KM) toxicity summaries.
• Efficacy-Toxicity Analysis — integrates body weight toxicity with tumor efficacy data to assess the overall therapeutic window. Requires a tumor volume column.

Body weight is used as the toxicity surrogate throughout. When 'Subtract estimated tumor weight' is enabled, the gross weight is corrected by subtracting Volume(mm³) × density(g/cm³) / 1000, giving a net host weight.

Mixed-Effects Model

Fits a linear mixed-effects model to all repeated weight measurements:

Weight ~ Treatment × Day + [covariates] + (Day | Mouse)

Random slopes allow each mouse's weight trend to deviate from the group average. Fixed effects test whether trajectories differ by treatment group over time.

REML

Restricted Maximum Likelihood — preferred for final parameter estimates (default).

ML

Maximum Likelihood — use when comparing models with different fixed-effect structures.

Covariates (optional):

• Tumor Volume — controls for tumor-driven weight changes independent of drug toxicity.
• Sex — adjusts for sex-specific baseline weight differences.
• Initial Mass — adjusts for pre-treatment weight variation across animals.

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Body Weight AUC

For each mouse, body weight is expressed as % change from baseline at each timepoint, then a trapezoidal AUC is computed over the study. A negative AUC indicates sustained weight loss; a positive AUC indicates net weight gain.

• Individual AUC values are shown as a jitter plot with a configurable centre mark (mean or median) and error bars (SEM, SD, or 95% CI).
• Units are % · days : e.g. a value of −100 means an average 5% weight loss sustained over 20 days.
• Pairwise group comparisons use t-tests with Benjamini-Hochberg correction.

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Nadir Analysis

The nadir (minimum weight) is identified per mouse. Reported metrics include nadir day, nadir weight, % loss at nadir, and days to recovery.

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Weight Loss KM Curve

Treats each mouse as an event-time observation where the event is crossing the weight-loss threshold (default 20%). Mice that never reach the threshold are censored at their last observation. A Kaplan-Meier curve is fitted per group; group differences are tested with the log-rank test.

Weight Loss Threshold: The % body weight loss that constitutes a toxicity event. The default (20%) is a common IACUC endpoint; adjust to match study-specific welfare criteria.

Efficacy Metrics

Three metrics quantify anti-tumor efficacy per mouse relative to the control group:

Final TGI (%)

Tumor Growth Inhibition at the final timepoint: TGI = (1 − V_treated / V̅_control) × 100 . Values > 0 indicate tumor suppression; > 100 indicates tumor regression.

Tumor AUC

Trapezoidal AUC of tumor volume over time, normalised to the control AUC: (1 − AUC_treated / AUC_control) × 100 . Captures the full trajectory rather than a single endpoint.

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Therapeutic Window Metric (TWM)

A summary ratio combining efficacy and toxicity per group:

TWM = TGI(%) / Mean Body Weight Loss(%)

Higher TWM indicates a more favourable balance. The denominator is the group mean of per-mouse maximum weight loss (not the single worst-case mouse). A noise floor prevents division by near-zero weight changes. Displayed as a ranked bar chart.

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Safety-Efficacy Scatter

A per-mouse bivariate plot where each point represents one animal. X-axis shows the chosen efficacy metric; Y-axis shows maximum % body weight loss. Points in the top-right quadrant (high efficacy, high toxicity) represent the least favourable profile.

• Group ellipses — 68% confidence ellipses (1 SD) per treatment group.
• Group centroids — mean efficacy and mean max weight loss per group, shown as large diamonds.

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Total Benefit Score

An integrated scalar combining efficacy and toxicity AUCs over time:

B = AUC(efficacy) − λ × AUC(toxicity)

A positive score indicates net benefit; negative indicates net harm. The trade-off parameter λ (lambda) controls how strongly toxicity is penalised:

• λ = 1.0 (default) — equal weight on efficacy and toxicity.
• λ > 1 — penalise toxicity more heavily; use for fragile populations or curative intent.
• λ < 1 — tolerate more toxicity; use when efficacy improvement is the primary goal.

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Weight-Corrected TGI

Recalculates TGI using only mice that stayed within the safety weight-loss threshold throughout the study. Mice exceeding the threshold are excluded from the corrected calculation.

This prevents a drug that arrested tumor growth due to severe toxicity from appearing falsely effective. Comparing the standard and corrected TGI reveals the extent of this confound.

Safety threshold: Mirrors the Weight Loss Threshold in Body Weight Analysis. Mice whose maximum weight loss exceeds this value are excluded from the corrected TGI.

Reference Group

The vehicle/control group used as the denominator for TGI and AUC ratios. Auto-detected from common names (DMSO, Vehicle, Control, PBS, Saline) or defaults to the first group alphabetically.

Subtract Tumor Weight

Removes the estimated tumor mass (Volume × density / 1000) from gross body weight before all calculations, so that body weight reflects host tissue rather than tumor burden.

Tumor Density

Used only when tumor weight adjustment is enabled. Default 1.0 g/cm³ (water density). Typical soft-tissue tumor density is 0.9–1.1 g/cm³.

Baseline Day

The study day used to compute % change from baseline. Defaults to the earliest available day.

The Dose-Response tab models how tumor volume (or TGI) varies across dose levels. Three complementary analyses are performed simultaneously:

• Linear regression — tests whether there is a significant linear trend in tumor volume with increasing dose.
• One-way ANOVA — tests whether any dose group differs from the others, followed by Tukey HSD post-hoc comparisons if significant.
• Non-linear dose-response model (4PL) — fits a four-parameter log-logistic (Hill) model to quantify ED50 and curve steepness.

Tumor Growth Analysis must be run before using this tab — dose-response uses volume data preprocessed there. A Dose column must also be mapped in Data Upload.

Fits Volume ~ Dose by ordinary least squares. The slope quantifies the change in mean tumor volume per unit increase in dose.

Slope

Change in volume per dose unit. A negative slope indicates dose-dependent tumor suppression.

R²

Proportion of variance in volume explained by dose. Low R² with a significant slope can occur when individual variability is high relative to group differences.

p-value

Significance of the slope. A non-significant p-value does not exclude a non-linear relationship — inspect the 4PL model output and plots as well.

Treats dose as a categorical factor and tests whether group means differ. A significant F-test (p < 0.05) triggers Tukey HSD post-hoc comparisons to identify which specific dose pairs differ.

F-statistic

Ratio of between-group to within-group variance. Larger values indicate greater separation between dose groups relative to within-group noise.

Tukey HSD

Family-wise error rate corrected pairwise differences. Values in 'p adj' below 0.05 indicate a significant difference at the 5 % level after correction for all comparisons.

ANOVA assumes equal variances across groups (homoscedasticity). When this is violated, interpret alongside the linear regression, which is more robust to mild heteroscedasticity.

A four-parameter log-logistic (4PL / Hill) model is fitted via the drc package:

Volume = c + (d − c) / (1 + (Dose / ED50)^b)

b

Hill coefficient: steepness of the dose-response curve. Larger absolute values indicate a sharper transition.

c

Lower asymptote (response at saturating inhibitory dose).

d

Upper asymptote (response in the absence of drug).

ED50

Dose producing 50 % of the maximal effect. The primary pharmacodynamic summary statistic.

The Drug Synergy tab assesses whether a drug combination produces greater tumor suppression than predicted from the individual drugs acting independently. Two reference models are evaluated simultaneously:

• Bliss Independence — treats the two drugs as probabilistically independent. The expected combined TGI is the sum of individual TGIs, capped at 100 %.
• Loewe Additivity — treats the drugs as dose-equivalent. The Combination Index (CI) measures how the observed combination effect compares to the expected additive effect.

Four treatment groups must be assigned in the sidebar: Control, Drug A only, Drug B only, and the Combination (A + B). Analysis can be run at a single timepoint or tracked over the full study duration.

Tumor Growth Analysis must be run first — Drug Synergy uses preprocessed volume data from that tab.

Under Bliss independence, drugs act on independent targets and their joint fractional effect (FE) is:

Expected TGI = min(FE_A + FE_B, 1.0) × 100

where FE = TGI / 100 for each single agent. The cap at 1.0 prevents the expected value from exceeding the biological ceiling.

Bliss Difference

TGI_combo − Expected TGI. Positive = synergy; negative = antagonism; near zero = independence.

Loewe additivity assumes that drugs acting on the same pathway are dose-equivalent and interchangeable. The Combination Index (CI) is:

CI = min(FE_A + FE_B, 1.0) / FE_combo

Interpretation thresholds:

• CI < 0.85 — synergistic: the combination outperforms the additive expectation.
• 0.85 ≤ CI ≤ 1.15 — additive: the combination matches the expected additive effect.
• CI > 1.15 — antagonistic: the combination underperforms the additive expectation.

Loewe Difference

TGI_combo − Loewe Expected TGI. Positive = synergy; negative = antagonism.

When 'Analyze over time' is enabled in the sidebar, Bliss and Loewe scores are computed at every measured timepoint and plotted as a synergy trend. This reveals whether synergy emerges, fades, or reverses over the course of treatment.

Per-timepoint p-values (Combination vs Drug A and vs Drug B, two-sample t-test) are included in the Synergy Metrics table. These are unadjusted for multiple testing across timepoints — interpret overall patterns rather than individual p-values at isolated days.