Research NoteLRST

What is the Longitudinal Rank-Sum Test?

A visual guide to one global question from many repeated outcomes.

The problem

Clinical trials rarely give us one clean number.

They give us a grid of measurements: several clinically important outcomes, measured repeatedly over time.

Month 6
Month 12
Month 18
Month 24
Cognition
small
modest
small
modest
Daily function
small
small
modest
modest
The wrong question

“Which single box is significant?”

The treatment effect may be spread across the whole pattern rather than concentrated in one dramatic measurement.

LRST asks instead

“Across the outcomes and visits taken together, does treatment tend to do better overall?”

MANY MEASUREMENTS  →  ONE GLOBAL QUESTION
How LRST thinks

Forget the formula for a moment.

Think in terms of who tends to rank better.

T1
T2
P1
P2
→
Repeat across outcomes × visits
Cog · M6
Cog · M12
Cog · M18
Func · M6
Func · M12
Func · M18
LRST combines the pattern into one global statistic.
GLOBAL TREATMENT SIGNAL
The intuition

LRST is looking for a repeated overall advantage — not one dramatic box.

That makes the method natural when the scientific question is about overall treatment benefit across multiple repeatedly measured outcomes.

Use LRST when your question is...

“Is there an overall treatment advantage across important outcomes and visits?”

This is the sweet spot for LRST: several outcomes, repeated visits, different scales, and a desire for one robust global test rather than many scattered p-values.

Multiple outcomesRepeated visitsDifferent scalesRobust global test
Use a more targeted model when...

“Exactly how much does this specific endpoint change at this specific time?”

If the real goal is a precise mean difference, an individual trajectory, a treatment-by-time interaction, or prediction, then a more targeted longitudinal model is usually the better fit.

Specific mean differenceTreatment × time slopeIndividual trajectoriesPrediction
The LRST program

The core idea has grown into a broader family of methods.

The same research program includes extensions for increasingly complex longitudinal settings.

Core LRSTMulti-armPower & sample sizeMissing dataCovariate adjustmentObservational
Using the LRST R package

Install → shape the data → run LRST → interpret the global result

This workflow follows the current package README and exported R functions.

1

Install from GitHub

devtools::install_github("djghosh1123/LRST")
library(LRST)

No wrapper is needed: the documented package API works directly with the LRST functions.

2

Shape the data as arrays

For the two-arm test, provide one placebo array and one treatment array.

n patientsK outcomesT time points
3

Run the two-arm LRST

fit <- lrst.2arm(X_c, Y_c)
fit$p.value

The returned object includes the test statistic, standard error, p-value, visit-level score vector, covariance estimate, and relative treatment-effect estimates.

Interpretation: the p-value is evidence about the global treatment comparison across the multivariate longitudinal profile. It does not replace endpoint-specific scientific interpretation.
Estimated power

Use the same two arrays

estimated_Power(0.05, X_c, Y_c)

The package estimates power at the chosen significance level using the observed placebo and treatment arrays.

Multi-arm LRST

Placebo + a list of treatment arrays

Y <- list(X_dose_1, X_dose_2)
lrst.MultiArm(X_c, Y)

The documented multi-arm function returns the p-value, selected arm index v, and final test statistic T.

Package workflow based on the current djghosh1123/LRST GitHub README and exported function documentation.

View LRST on GitHub Related publications Back to Research Notes