Analytical Overview

• Many sponsors are still using minimum-power responder analysis
• Time to event is a limited outcome
  • Time to first event ignores recurring events
  • Time to first of several events ignores severity of events
  • Time to recovery ignores unrecovery and is bothered by death

Analytical Overview, continued

• Power gained by using a high-resolution outcome scale
  • For ordinal outcome power as # levels
• Further gain by using multiple scales
• Further gain by using longitudinal data
• Need to take death + other clinical events formally into account
• Power & making the most of N importance in rare diseases
• A fundamental principle of statistics: maximize information extraction from raw data

RCT Outcome Overview

• Function & symptoms important to the patient must be included
• Results of analyzing an outcome that is masked by another are impossible to interpret
  • Example: functional status in survivors
• Serious clinical events should be part of any outcome
• Fundamental outcome unit: current state

RCT Outcome Overview, continued

• On a given day, how bad is the worst thing that happened to the patient?
• Fundamental analytical tool: longitudinal state transition models
• Y = ordinal scale for a time period, including clinical event overrides

Analytical Options

WIN and DOOR

• WIN ratio/odds and DOOR (desirability of outcome rankings) are longitudinal extensions of the Wilcoxon two-sample test
• Gain power by breaking ties in time-to-event outcomes
• Provide only within-study estimand; no clinical-scale readouts
  • Pr(randomly chosen pt on B has better outcome than pt on A)
  • How much better?
  • What is the outcome of pts on Tx B?

WIN and DOOR, continued

• The relative ordering estimand is influenced by narrowness of study inclusion criteria
• Similar to reporting -statistic without reporting difference in means
• Very difficult to deal with missing component data + covariate adj.
• Results depend on the distribution of censoring times
• Assumes Tx affects all outcome categories equally

Ordinal Longitudinal Models (OLM)

• Extension of Wilcoxon test and Cox model to allow covariate adjustment + repeated measures
• Most flexible form uses a Markov process for an ordinal state transition model
• Demonstrated to handle within-pt serial correlation almost perfectly in multiple RCTs
• Better modeling of intra-pt correlation effective sample size
• Elegantly handles missing components + absorbing states precluding pt scale assessment
  • Death and need for rescue therapy accounted for

OLM, continued

• Underlying statistical parameter is a transition odds ratio for Tx
• Huge variety of clinical readouts clinical significance
  • Pr(transitioning to state at time given in state at )
  • Pr(being at severity y or worse as a function of time, Tx)
  • Mean time in any set of states
  • Treatment difference in expected time in specified states (like time to recovery or time to loss of function)
• Generalizes Wilcoxon test, Cox model, recurrent event analysis, and longitudinal analysis

Popular OLM Readout

Efficiency Gain: # Visits

Another OLM Example: ORBITA-2

FA Simader et al (2024): Symptoms as a predictor of the placebo-controlled efficacy of PCI in stable coronary artery disease. JACC 84: 13-24.

• Daily angina frequencies
• Y = ordinal scale
  • Angina frequencies magnified by # units of anti-anginal meds required to control angina
  • Clinical event overrides at top of scale
  • Graphic design by Matthew Shun-Shin, Imperial College London

OLM, continued

• OLM works for Tx that improves pt condition as well as for Tx for slowing progression
• Detailed case study with complete R code at hbiostat.org/rmsc/markov
• FDA CDER OB project underway to reanalyze an ALS trial using OLM

First-Order Discrete Time Markov Proportional Odds Model

• Current state depends only on covariates, previous state
• Let measurement times be , and the measurement for a patient at time be denoted
• Transparent, verifiable assumptions

Markov OLM, continued

• Simple sums of multiplied transition probabilities to uncondition on previous states state occupancy probabilities (SOPs)
• SOPs are ITT quantities with standard causal interpretation
• Example: death is the only outcome
• Transition odds ratio hazard ratio
• SOP = cumulative incidence of mortality

SOPs, continued

• General example: SOP at 6 months
  • Probability that functional ability is worse than or patient is dead
  • Prob. that function is better than and pt is alive
• Sum of SOPs over regularly-spaced times is mean time in state
  • Mean # days alive and well
  • Gain (difference) in mean # days alive and well due to treatment
• Mean time in state is simple even with time treatment interaction present

Unified Approach

• Standard longitudinal continuous
• Longitudinal continuous or ordinal interrupted by clinical events
• Easily handles multiple absorbing states
• Serial correlation: condition on previous outcome
• Random intercepts (compound symmetry correlation): condition on average of all previous outcomes

Examples of Longitudinal Ordinal Outcomes

• 0=alive 1=dead
  • censored at 3w: 000
  • death at 2w: 01
• 0=at home 1=hospitalized 2=MI 3=dead
  • hospitalized at 3w, rehosp at 7w, MI at 8w & stays in hosp, f/u ends at 10w: 0010001211

Examples, continued

• 0-6 QOL excellent--poor, 7=MI 8=stroke 9=dead
  • QOL varies, not assessed in 3w but pt event free, stroke at 8w, death 9w: 12[0-6]334589
  • MI status unknown at 7w: 12[0-6]334[5,7]89
• Can make first 200 levels be a continuous response variable and the remaining values represent clinical event overrides

Extension of OLM: Partial Proportional Odds Markov Model

• Allows effect of Tx to vary over outcome categories
• Example: Tx may affect mortality differently than how it affects function/Sx
• Bayesian prior can specify limits on the amount of borrowing of Tx effects across outcomes
• Example Bayesian posterior prob.: probability that Tx affects death by effect on function
• See fharrell.com/post/yborrow

Composite Outcome Scales

• Choice of scales is very important
• Gold standard is pt utility for current status
• OLM approximates the gold standard
• Several ways to combine multiple scales

Analyzing Multiple Scales That Can't Be Combined Into an Ordinal Scale

• Multiple functional / symptom / QOL scales at a given time
• Not recommended: combining separate -values
• Time-trade-off to arrive at overall utility, but difficult
• Ordinal regression to relate all scales to an ultimate outcome or pt global scale
• Projects all scales into a single global scale for OLM

How to Analyze Multiple Scales, continued

• Take one outcome scale as an anchor, calibrate all scales to it
  • Compute optimum weighted average of scales
  • Treat as ordinal
  • Add clinical event overrides
• Put all scales on the same Likert scale
  • Ask pt which scale is most important to them
  • Use that scale for that patient, as ordinal

A Completely Different Approach (Bayesian)

• Bayesian multivariate model using all scales
  • Copula or correlated random effects to model scale dependencies
• For outcome measures compute the Bayesian posterior probability that the treatment benefits pts on at least of these
• Probability treatment has any effect on some of the outcomes and a major effect on one particular outcome

More Information

• Composite outcomes: fharrell.com/talk/cos (also includes the "time savings" approach)
• Composite outcome details: hbiostat.org/doc/comp
• General principles for constructing clinical endpoints: hbiostat.org/endpoint
• OLM: hbiostat.org/proj/covid19
• Ordinal regression: hbiostat.org/ordinal