Interaction terms in Multivariable Survival Analysis

Testing effect modification: does treatment benefit differ by biomarker?

ClinicoPath

2026-07-10

When to use this

A randomized trial rarely stops at “does the treatment work?” The next question is “who does it work for?” - does the treatment effect differ across a biomarker, a stage, or a histologic subtype? This is effect modification, and the standard way to test it in a Cox model is a Treatment × Biomarker interaction term: Surv(time, event) ~ Treatment * Biomarker.

multisurvival (Multivariable Survival Analysis) now supports building these interaction terms directly, without leaving jamovi.

Interaction is not the same as stratification. multisurvival already supports strata() for stratified Cox models: stratifying by a variable gives each stratum its own baseline hazard, but it forces the covariate effects to be identical across strata - it cannot tell you whether a treatment effect differs by subgroup. An interaction term does the opposite: it estimates a coefficient for the crossed term and directly tests whether the effect is modified. If your question is “does the biomarker predict who benefits from treatment?”, you need an interaction term, not (only) stratification.

Building an interaction term in the GUI

1. Assign variables to Explanatory Variables and/or Continuous Explanatory Variable as usual - these become the main effects in the Cox model.
2. Open the Interaction Terms section (collapsed by default). It lists every variable already chosen as a main effect as an available predictor.
3. Select two (or more) of those variables and use the transfer button to cross them into a term, exactly like jamovi’s regression/ANOVA Model Terms builders.

Because only variables already selected as main effects can be crossed, the builder enforces the marginality (hierarchy) principle by construction - you cannot add Treatment:Biomarker without both Treatment and Biomarker already present as main effects.

Convention: for a two-way term A × B, A (listed first) is the focal effect and B (listed second) is the moderator. The focal effect is the variable whose hazard ratio you want to see change across subgroups (e.g. Treatment); the moderator defines the subgroups (e.g. Biomarker status). To get the effect in the other direction, build B × A instead.

What you get

1. The standard outputs, extended. Interaction terms appear as additional rows in the main hazard-ratio table and in the forest plot, alongside the main effects - no separate step needed.

2. Interaction (Effect-Modification) Test. A dedicated table with one row per interaction term: hazard ratio, 95% CI, and the interaction p-value. A significant p indicates the focal effect genuinely differs across levels of the moderator (effect modification) - this is the formal test biomarker-by-treatment analyses report.

3. Within-Subgroup Hazard Ratios. For each two-way interaction whose moderator is categorical, multisurvival releveles the data to each moderator level in turn and refits the same full Cox model (all covariates and interactions, unchanged), then reports the focal variable’s hazard ratio within that subgroup. This gives the fully-adjusted “HR for Treatment in Biomarker-positive patients” / “HR for Treatment in Biomarker-negative patients” rows clinicians actually want to read, computed from one coherent model rather than separate subgroup-only fits.

Limitations

• Within-subgroup HRs need a categorical moderator. If the moderator is continuous, the interaction coefficient in the effect-modification test table is still reported, but per-subgroup HRs are not computed (there is no discrete “subgroup” to relevel to) - a note explains this in the output.
• Within-subgroup HRs are computed for two-way interactions only. Three-way and higher-order terms appear in the HR table and the effect-modification test, but are skipped for the subgroup breakdown.
• Disabled in competing-risks (Fine-Gray) mode. When Multiple Event Levels analysis is set to “Competing risks”, within-subgroup refits are disabled (weighted subdistribution refits are fragile); the output notes this and directs you to the interaction coefficient instead.
• Non-converged subgroups are flagged. If a subgroup refit fails to converge (typically small-sample separation), its row is marked with an asterisk and a footnote - treat that HR with extreme caution.

In R

The GUI builds exactly the Cox interaction model you would write directly with the survival package:

library(survival)

# A minimal simulated trial: does Treatment benefit differ by Biomarker status?
set.seed(1)
n <- 300
dat <- data.frame(
  Treatment = factor(sample(c("Control", "Drug"), n, replace = TRUE)),
  Biomarker = factor(sample(c("Negative", "Positive"), n, replace = TRUE))
)
lp <- with(dat, -0.1 * (Treatment == "Drug") +
                 -0.9 * (Treatment == "Drug" & Biomarker == "Positive"))
dat$time  <- rexp(n, rate = exp(lp) * 0.1)
dat$event <- rbinom(n, 1, 0.8)

# Treatment (focal) x Biomarker (moderator): the interaction test
fit <- coxph(Surv(time, event) ~ Treatment * Biomarker, data = dat)
summary(fit)

# Within-subgroup HR for Treatment, computed the same way multisurvival does:
# relevel Biomarker to each level and re-read the Treatment coefficient.
fit_neg <- coxph(Surv(time, event) ~ Treatment * relevel(Biomarker, ref = "Negative"), data = dat)
fit_pos <- coxph(Surv(time, event) ~ Treatment * relevel(Biomarker, ref = "Positive"), data = dat)

multisurvival’s Interaction (Effect-Modification) Test table reports the same HR/CI/p as the Treatment:BiomarkerPositive row of summary(fit) above, and its Within-Subgroup Hazard Ratios table reports the TreatmentDrug coefficient from each releveled refit.