Mediation analysis and SAS CAUSALMED procedure

In a recent publication (Benza et al "Contemporary Risk Scores Predict Clinical Worsening in Pulmonary Arterial Hypertension - An Analysis of FREEDOM-EV"), we conducted an analysis called 'Mediation analysis'. In the statistical analysis section, the 'mediation analysis' was stated as the following: 

"To determine whether the change in Week 12 REVEAL Lite 2 risk score ‘mediated’ the treatment effect in delaying clinical worsening, we used SAS (v14.3) CAUSALMED procedure which operationalizes the work of Valeri and VanderWeele.

This analysis attempts to determine what fraction of the total treatment effect appears to be attributable to the treatment effect on the REVEAL Lite 2 score. The analysis was adjusted for baseline REVEAL Lite 2 score; we did the analysis both with and without assuming that there is a treatment and mediator (REVEAL Lite 2 score) interaction on the outcome model (clinical worsening). The definition ‘net clinical benefit’ has been previously proposed as the achievement of all three French non-invasive low risk factors without a clinical worsening event; we retrospectively used the present database to model the performance of this definition."

According to Wikipedia, the mediation model and mediation analysis are defined as the following: 

In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable (also a mediating variable, intermediary variable, or intervening variable). Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the mediator variable, which in turn influences the dependent variable. Thus, the mediator variable serves to clarify the nature of the relationship between the independent and dependent variables.

Mediation analyses are employed to understand a known relationship by exploring the underlying mechanism or process by which one variable influences another variable through a mediator variable. In particular, mediation analysis can contribute to better understanding the relationship between an independent variable and a dependent variable when these variables do not have an obvious direct connection.

A mediator variable can either account for all or some of the observed relationship between two variables. 

Full Mediation

Maximum evidence for mediation, also called full mediation, would occur if the inclusion of the mediation variable drops the relationship between the independent variable and dependent variable to zero. In other words, the effect of the independent variable on the dependent variable is all through the mediator variable. 

Partial mediation

Partial mediation maintains that the mediating variable accounts for some, but not all, of the relationship between the independent variable and dependent variable. Partial mediation implies that there is no only a significant relationship between the mediator and the dependent variable, but also some direct relationship between the independent and dependent variable - the line from independent variable to dependent variable is solid and c is not equal to zero. 

 

The mediation analysis has been used in the data analysis for observational data, clinical trial data, survey data, and epidemiology study data. 

In an article by Eyre et al "Effect of Covid-19 Vaccination on Transmission of Alpha and Delta Variants", the mediation analysis was used to assess whether the effect of the vaccination status of the index patient was explained by Ct values at diagnosis.  Ct values are cycle-threshold values (indicative of viral load21) in the index patient.

In an article by Reaven et al "Intensive Glucose Control in Patients with Type 2 Diabetes — 15-Year Follow-up", mediation analyses were performed:

In prespecified mediation analyses, Cox proportional-hazards models were used to examine the effects of the glycated hemoglobin level on the primary cardiovascular disease outcome and on the observed treatment effects. Specifically, the log-linear association of the cumulative glycated hemoglobin level (modeled as a time-varying covariate) with the primary cardiovascular disease outcome was assessed during the period of separation of the glycated hemoglobin curves and after convergence. Models examined the effect of treatment group (intensive therapy or standard therapy) on the primary outcome in an unadjusted analysis (model 1) or while accounting for baseline, most recent, or cumulative mean glycated hemoglobin level (models 2, 3, and 4, respectively).

A paper by Vo et al summarized "the conduct and reporting of mediation analysis in recently published randomized controlled trials: results from a methodological systematic review"

Mediation analysis can be performed using SAS procedure CAUSALMED. CAUSALMED procedure was developed for estimating causal mediation effects from observational data, but can definitely be used for estimating mediation effects from the randomized controlled clinical trial data. Please see the references below:

• SAS documentation about CAUSALMED procedure including the application examples
• Yung et al Causal Mediation Analysis with the CAUSALMED Procedure
• Yung Introducing the CAUSALMED procedure for causal mediation analysis - Youtube video 
• Youtube video: Modeling causal effect using SAS/Stat

Mediation analysis can be performed using other software. This is very well summarized in a paper by Valente et al "Causal Mediation Programs in R, Mplus, SAS, SPSS, and Stata".

Imputation of partial dates for adverse events, concomitant medications, and disease diagnosis

Many date variables are collected in the clinical trial database. The date variables include date of birth, date of disease diagnosis, date of medical history onset, start and stop date of adverse events, start / stop date of concomitant medications, ......

It is not uncommon that the partial dates may be collected where the partial dates mean that at least one of the components (day, month, or year) is missing. 

Partial date for date of birth is not because the subjects don't remember their birth date, is because the data security law prevents the sponsors from collecting the date of birth information in certain countries (especially in Germany). 

In statistical analyses, the partial dates need to be handled or imputed for the purpose of allocating the event (adverse events, concomitant medication) into the appropriate categories (treatment-emergent adverse events, prior medications, concomitant medications added during the study,...) or calculating the duration of the events (duration from the disease diagnosis to the study start).

For clarity, the algorithm and rules for imputing the partial dates need to be specified in the statistical analysis plan (SAP). There is no regulatory guidance about which algorithm and rules will be appropriate when imputing the partial dates. Different companies may have different rules when imputing partial dates. In general, the rules will be adequate as long as it is on the conservative side, for example, if an adverse event has a partial or missing start date and can't be determined if it occurs before the first dose of the study drug, the adverse event will be classified as 'treatment-emergent adverse event'. 

Partial date imputation is always a single imputation - the missing day or missing month will be replaced with a fixed day or month based on the imputation algorithm. The candidates for replacing the missing day could be: the first day of the month, the last day of the month, the day of the first dose of the study drug. The candidates for replacing the missing day and month could be Jun 30 of the year or July 1 of the year. 

Usually, if all day, month, and year are missing, the missing date will not be imputed. The adverse events with missing onset date will be classified as 'treatment-emergent AEs' and the concomitant medication will be classified as 'on treatment medications' (i.e., to be included in summaries of concomitant medications during the study). 

Below are a list of algorithm and rules for imputing the partial dates for adverse events and concomitant medications:

In an SAP for a Pfizer phase I study, if the day of the month is missing, the 1st day of the month is used. 

In a Novartis study SAP, the rather complicated algorithm was proposed for imputing the partial dates for adverse events and concomitant medications:

In a study by Johnson & Johnson, the appended SAP specified the rules for imputing the partial dates for adverse events, concomitant medications, and for disease diagnosis as the following: 

In a study by ChemoCentryx in NEJM, the appended SAP described the imputation rules for partial dates for adverse events and concomitant medications as the following: 

 

In the paper "Partial Dates; decisions and implications of handling partially missing dates" by Bowman, the following rules were stated for imputing the partial dates for adverse events and concomitant medications. 

Missing Adverse Event Start and Stop Dates date:

There are two options available. The partial start date may be set to the first of the month or to equal the study medication start date. As previously discussed, the first option would indicate the adverse event began prior to the study medication. However, the second option, setting the start date of AE1 to the study medication start date will suggest the adverse event had a short duration, as the adverse event end date is also defined as June 2006, but began during the treatment period of the study drug. Although the second option is not ideal, as AE1 may have had a longer duration, it is more conservative to associate the adverse event start with a date during study medication. Another solution to consider is not to impute a date at all but merely to assign a study phase to the start of the adverse event. In this example, a phase of "treatment" could be allocated to the start of teh adverse event, which would ensure it was classed most conservatively, without defining an actual date to the start of the adverse event. 

Concomitant Medications:

Subject has a partial concomitant medication start date of “--Apr2006” (see figure 1). As discussed above, missing start dates may be set to the first of the month, which is shown under option 1. However, this then pushes the concomitant medication to starting before the first dose of the Study Medication (15Apr2006) and would suggest that the Study Medication had no involvement with the concomitant medication being taken. Is this really the most conservative approach? If not is there an alternative? The missing concomitant medication start date could be set to equal the first dose of Study Medication, options 2. This option allows the concomitant medication to be classed as an on-treatment medication, and is therefore the most conservative.  

Restricted Mean Survival Time (RMST) for Handling the Non-Proportional Hazards Time to Event Data

Time to event analysis (or traditionally survival analysis) is one of the most common analyses in clinical trials. In general, the time to event analysis relies on the assumption of the proportional hazards. However, quietly frequently, we may find that the proportional hazards assumption is violated, especially in many immuno-oncology trials. When the proportional hazards assumption is violated, alternative approaches may be needed to analyze the data to achieve statistical power. As discussed in the previous post "Non-proportional Hazards: how to analyze the time-to-event data?", one of the alternative approaches is the restricted mean survival time (RMST) method. 

RMST is one of the Kaplan-Meier-based methods and is essentially calculating and comparing AUCs under Kaplan-Meier Curves for different treatment groups or different comparative groups. It has been said that RMST analysis has the following advantages:

• Model-free, robust, and easily interpretable treatment effect information
• Produces radically powerful patterns of difference as has been observed in some recent Oncology clinical trials
• Accepted approach by regulatory agencies and industry leaders

RMST has been mentioned in the latest FDA guidance for Industry (2020): Acute Myeloid Leukemia: Developing Drugs and Biological Products for Treatment as an alternative approach to analyzing the data when the non-proportionality hazards occur (e.g., plateauing effect). 

"Plateauing Effect

Trials designed to cure AML often result in survival contours characterized by an initial drop followed by a plateauing effect after some time point post randomization. This is an example of nonproportional hazards. While the log-rank test is somewhat robust to nonproportionality, it generally results in loss of power. Furthermore, nonproportionality can cause difficulty in describing the treatment effect. FDA is open to discussion about analyses based on other approaches, such as weighted Cox regression or other weighted methods, or summarizing the treatment effect using restricted mean survival time (RMST) or landmark survival analysis. Plans that use these alternative approaches should include:

• justification for what constitutes clinically meaningful difference,
• justification of design parameters, such as sample size and follow-up duration, based on this endpoint, and
• justification for the value of the threshold that will be used to calculate the RMST.

RMST analysis has also been used as a primary analysis approach or for sensitivity analysis in FDA reviews: 

In NDA of Baloxavir marboxil in treatment of acute, uncomplicated influenza, both applicants and the FDA reviewer analyzed the data using RMST. It stated:

Restricted mean survival time (RMST) up to Day 10 was estimated for each treatment group along with the difference between RMST in the two treatment groups. RMST is a measurement of the average survival from time 0 to a specified time point (e.g., 10 days) which is equivalent to the area under the Kaplan-Meier curve from the beginning of the study through that time point.

At an FDA CDRH Medical Devices Advisory Committee Circulatory System Panel meeting in 2019, the independent statistical consultant addressed the analysis issue when the proportional hazards assumption is violated:

The proposal they made was the restricted mean survival time. The restricted mean survival time is area under curve. Please note the word restricted. Mean survival time is over a period of time, according to the rules that have been laid out, so that you're not looking, like with proportional hazards, over all the follow-up that could have possibly happened or in binary where you're only looking at the patients that survive. The restricted mean would say we're going to look between, let's say, 0 and 5 years because we have sufficient information to make that kind of assessment.

The paper showed that the restricted mean has just as much power as proportional hazards when the assumptions are there for proportional hazards, and then has more power when the assumptions are violated.

There's also some advantages in terms for clinicians, in terms of explaining this to the patient. It's hard to talk about hazards or number needed to treat. But if you could say to a patient over a 60-month period the average survival time is 55 months with Device A versus 52 months with Device B, now they can look at what their life is going to look like in the next 60 months and make a decision.

Unfortunately, it was not me who noticed this. This was actually from a presentation by FDA. Several very smart statisticians had talked about the restricted mean and have made recommendations on using it for both proportional violations and for its interpretation.

In FDA Briefing Document for Oncologic Drugs Advisory Committee Meeting (December 17, 2019) to review Olaparib for the maintenance treatment of adult patients with deleterious or suspected deleterious germline BRCA mutated (gBRCAm) metastatic adenocarcinoma of the pancreas

FDA performed a test to evaluate whether the proportional hazard assumption was met. This test failed to detect evidence of non-proportionality; however, such a test may lack power to detect non-proportionality due to the small sample size. The Kaplan-Meier curves of PFS appear to show some degree of nonproportionality. The curves did not show separation until approximately 4 months, after approximately 53% of patients either had events or were censored. FDA performed additional sensitivity analyses by applying the restricted mean survival time (RMST) method using different truncation points (15 months and 18 months). The truncated time was selected (15 or 18 months) such that approximately 8-12% patients remained at risk. Based on the truncation times, the estimated RMST difference in PFS between arms ranged from 2.6 months (95% CI: 0.9, 4.3) to 3.1 months (95% CI: 1.0, 5.2). The range of the RMST differences again demonstrated great variation in the difference in PFS and the lower ends did not suggest that there was a clinically meaningful difference.

Thanks to the software, RMST analyses can be easily implemented in SAS or R. In the latest version (version 15.1 or above) of SAS/Stat, RMST is included in SAS Proc LIFETEST with RMST option and Proc RMSTREG. See a nice paper by 

With R, the package for RMST analysis is survRM2 that is developed by Hajime Uno from Dana-Farber Cancer Institute

For RMST analysis, it is important to select the cut-off value (tau) for the truncated time. The different selection of taus will give different results. The selection of tau can sometimes be arbitrary. In an FDA briefing document above, the FDA statistician chose the truncated time such that approximately 8-12% of patients remained at risk.

There are different ways to calculate the RMST:

• Non-parametric method
• Regression Analysis Method
• Pseudo-value Regression Method
• IPCW Regression - Inverse Probability of Censoring Weighting (IPCW) regression
• Conditional restricted mean survival time (CRMST)

According to the paper by Guo and Liang (2019) "Analyzing Restricted Mean Survival Time Using SAS/STAT®", non-parametric analysis can be implemented using Proc Lifetest; regression analysis, pseudo-value regression, and IPCW regression can be implemented using SAS Proc RMSTREG. 

FDA statisticians also proposed an approach 'conditional restricted mean survival time' or CRMST. This approach was described in the paper by Qiu et al (2019) "Estimation on conditional restricted mean survival time with counting process" and also in a presentation by Lawrence and Qiu (2020) Novel Survival Analysis When Hazards Are Nonproportional and/or There Are Multiple Types of Events. CRMST can allow the AUC under K-M curves to be calculated from an interval time (not necessarily to be started from the 0 time). They claim CRMST is better for event-driven studies where the time to the first event is the interest. They concluded the following: 

CRMST possesses all the desirable statistical properties of RMST. In particular, it does not rely on proportional hazard assumption. In addition, CRMST measures an average event-free time in the time range at issue and has straightforward interpretation. In case that two survival curves cross, CRMST can be estimated separately before and after crossing and the CRMST differences can be used to assess benefit versus harm.

Further Reading:

• Royston & Parmar (2013) Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome
• Huang & Kuan (2017) Comparison of the restricted mean survival time with the hazard ratio in superiority trials with a time-to-event end point
• McCaw, Yin, and Wei (2019) Using the Restricted Mean Survival Time Difference as an Alternative to the Hazard Ratio for Analyzing Clinical Cardiovascular Studies
• Rivano et al (2020) Restricted mean survival time as outcome measure in advanced urothelial bladder cancer: analysis of 4 clinical studies
  
• Lawrence et al (2016) Comparison of Hazard Ratio and Restricted Mean Survival Analysis for Cardiorenal Drug Trials
• Tian L, Zhao L, Wei LJ. Predicting the restricted mean event time with the subject's baseline covariates in survival analysis. Biostatistics 2014, 15, 222-233.

Intention-to-Treat Principle versus Treatment Policy Estimand: Different Names, but Same Meaning?

ICH E9 "Statistical Principles for Clinical Trials" was finalized in February 1998. The E9 guidelines established the Intention-to-Treat principle for the design and analysis of clinical trials. With the intention-to-treatment principle, we are required to include all study participants (full analysis set) in the analyses. Here are the definitions for 'full analysis set' and 'intention-to-treat principle' from ICH E9. 

In 90's, it took a while for the people to understand and accept the concept of the intention-to-treat principle. We also see that the intention-to-treat principle was misused, over-used, or undercut by the use of practical intention-to-treat and modified intention to treat. I had a presentation (in 2004) about the misuse/overuse of intention-to-treat and modified intention-to-treat. What I said then is still applicable today. 

The strict definition of intention-to-treat can be traced back to the book chapter by Fisher, LD et al. Intention to treat in clinical trials in Statistical Issues in Drug Research and Development. Edited by Peace KE (1990). The intention-to-treat was defined as:

Includes all randomized patients in the groups to which they were randomly assigned, regardless of their adherence with the entry criteria, regardless of the treatment they actually received, and regardless of subsequent withdrawal from treatment or deviation from the protocol

The intention-to-treat principle includes all randomized subjects in the analyses and ignores what happens to the subjects after the randomization (whether or not the subject discontinued the study drug, took prohibited or rescue therapies, crossed over the alternate treatment,...), which is obviously not the best option in estimating the treatment effect in some situations.  This leads to the development of Addendum to ICH E9 "ICH E9 (R1) Estimands and Sensitivity Analysis in Clinical Trials". ICH E9 (R1) explained the issues with the intention-to-treat principle and introduced the new concept of estimands (including treatment policy estimand) and intercurrent events. 

This addendum clarifies and extends ICH E9 in respect of the following topics. Firstly, ICH E9 introduced the Intention-To-Treat (ITT) principle in connection with the effect of a treatment policy in a randomised controlled trial, whereby subjects are followed, assessed and analysed irrespective of their compliance to the planned course of treatment, indicating that preservation of randomisation provides a secure foundation for statistical tests. Multiple consequences arising from the ITT principle can be distinguished. Firstly, that the trial analysis should include all subjects relevant for the research question. Secondly, that subjects should be included in the analysis as randomised. Taken directly from the definition of the ITT principle (see ICH E9 Glossary), a third consequence is that subjects should be followed-up and assessed regardless of adherence to the planned course of treatment and that those assessments should be used in the analysis. It remains undisputed that randomisation is a cornerstone of controlled clinical trials and that analysis should aim at exploiting the advantages of randomisation to the greatest extent possible. However, the question remains whether estimating an effect in accordance with the ITT principle always represents the treatment effect of greatest relevance to regulatory and clinical decision making. The framework outlined in this addendum gives a basis for describing different treatment effects and some points to consider for the design and analysis of trials to give estimates of these treatment effects that are reliable for decision making. Secondly, issues considered generally under data handling and “missing data” (see Glossary) are re-visited. Two important distinctions are made. 

With the intention-to-treat principle, subjects who discontinued the study drug prematurely should continue to be followed up and the data after dose discontinuation should continue to be collected. However, in practice for many studies, the data collection was stopped for subjects who discontinued the study drug, or the data collected after subjects' discontinuation of study drug were collected, but not used in the analyses. To some extent, the intention-to-treat principle was not fully followed. That is why the FDA has issued its guidance "Data Retention When Subjects Withdraw from FDA-RegulatedClinical Trials" to encourage the data collection after the subjects withdraw from the study. As discussed in the guidance:

The validity of a clinical study would also be compromised by the exclusion of data collected during the study. There is long-standing concern with the removal of data, particularly when removal is non-random, a situation called “informative censoring.” FDA has long advised “intent-to-treat” analyses (analyzing data related to all subjects the investigator intended to treat), and a variety of approaches for interpretation and imputation of missing data have been developed to maintain study validity. Complete removal of data, possibly in a non-random or informative way, raises great concerns about the validity of the study. 

The addendum to ICH E9 introduced the concept of estimands and intercurrent events. Those events that occurred after the randomization were previously ignored even though the analyses were under the intention-to-treat principle. With the addendum, Those events that occurred after the randomization would be called 'intercurrent events'. Here is the official definition of the intercurrent events:

Intercurrent Events:

Events occurring after treatment initiation that affect either the interpretation or the existence of the measurements associated with the clinical question of interest. It is necessary to address intercurrent events when describing the clinical question of interest in order to precisely define the treatment effect that is to be estimated.

Estimands can be classified based on the strategies of handling the intercurrent events. One way to handle the intercurrent events is the 'treatment policy' strategy - therefore, we have a treatment policy estimand. The treatment policy estimand under the addendum is almost identical to the intention-to-treatment principle under the original ICH E9. 

Treatment policy strategy

The occurrence of the intercurrent event is considered irrelevant in defining the treatment effect of interest: the value for the variable of interest is used regardless of whether or not the intercurrent event occurs. For example, when specifying how to address use of additional medication as an intercurrent event, the values of the variable of interest are used whether or not the patient takes additional medication.

If applied in relation to whether or not a patient continues treatment, and whether or not a patient experiences changes in other treatments (e.g. background or concomitant treatments), the intercurrent event is considered to be part of the treatments being compared. In that case, this reflects the comparison described in the ICH E9 Glossary (under ITT Principle) as the effect of a treatment policy.

The intention-to-treat and treatment policy estimand are two different names with the same meaning. If we have to differentiate them, we can say that the intention-to-treatment principle is more focused on which subjects should be included in the analyses while the treatment policy estimand is more focused on which data points should be included in the analyses. If a randomized subject has an intercurrent event (for example, discontinued the study treatment), the subject is still included in the intention-to-treatment population for analysis, but will the measures after the subject's discontinuation of the study treatment be included in the analyses? With the treatment policy estimand, these measures after the subject's discontinuation of the study treatment will need to be included in the analyses. 

Here is a thread discussing the difference between the Intention-to-treat principle and the treatment policy estimand in resident360.nejm.com. 

We have started to see that the ICH E9 addendum and the concept of estimands are gradually adopted, especially in EU countries. The adoption of the ICH E9 in the US is much slower than in EU countries. The concept of estimands and intercurrent events is still considered as the words invented by statisticians. It will take a while for non-statisticians to understand the concept and to accept these new terms. A presentation "Regulator’s experience with estimands" by Andreas Brandt from EMA summarized the challenges for the adoption and implementation of the ICH E9 Addendum. We will anticipate the difficulties ahead for non-statisticians and clinicians to accept the concept of estimand and intercurrent events. This is reflected in a paper by Min & Bain "Estimands in diabetes clinical trials"

During 2019 several type 2 diabetes trials results using the term estimand were published. This word will be unfamiliar to many clinicians (and to spellcheck) but given that regulatory bodies have endorsed its use, this word is likely to become a staple of medical jargon in the future.

ICH E9 Addendum described five different strategies for handling the intercurrent events: treatment policy strategy, hypothetical strategy, composite variable strategy, while on treatment strategy, and principle stratum strategy. However, in practice, the treatment policy estimand is used the vast majority of the studies where the estimand concept is mentioned. There are a few studies using the principle stratum strategy. The other three strategies (hypothetical strategy, composite variable strategy, while on treatment strategy) are rarely used in practice perhaps because they are relatively new, are uncertain with the regulatory acceptance, and because there is no available method to estimate the treatment difference for some estimands.  

If the vast majority of the estimand application is treatment policy strategy which is almost identical to the traditional intention-to-treat principle, we will question if it is worth revamping the entire ICH E9 to come up with an addendum for estimand and intercurrent event concept.  

Finkelstein-Schoenfeld Method, Win Ratio, and Hodges-Lehman Estimates - Statistical Methods Based on All Paired Comparisons

Finkelstein-Schoenfeld methods can be used in analyzing the data with a composite endpoint where different components for the composite endpoint have different levels of importance. Hodges-Lehmann estimate is used to estimate the magnitude of treatment difference in a non-parametric statistical test such as the Wilcoxon Rank Test. What is in common between these two methods? Well, both methods are based on the pairwise comparisons - the value/outcome from each subject in treatment group A is compared to each of all subjects in treatment group B - in other words, both methods are based on n (# of subjects in treatment group A) time m (# of subjects in treatment group B) comparisons. 

In clinical trials for serious conditions, but not deadly enough, a composite endpoint is often used as the primary efficacy endpoint. The composite endpoint usually consists of several categories (or components) with different degrees of importance because there will not be enough events for a single category for a feasible clinical trial. The examples of composite endpoints are: 

• a composite endpoint in heart failure may include death, hospitalization, and clinical status
• a composite endpoint in pulmonary arterial hypertension may include death, hospitalization, and disease progression; 
• a composite endpoint in cardiovascular outcome study may be the major adverse cardiovascular events (MACE) consisting of death; MI; stroke, hospitalization.

Usually, these different components are not weighted and treated as equally important and the statistical analyses are based on the time to first event (no matter if the first event is death, hospitalization, or others) - this approach of no weighting is the focal point being criticized. 

Finkelstein-Schoenfeld method is a non-parametric method aiming to bring the weighting into the analysis of the composite endpoints. Finkelstein-Schoenfeld's method was named after their paper in 1999 in Statistics in Medicine "Combining Mortality and Longitudinal Measures in Clinical Trials".  The method was a generalization of the Gehan‐Wilcoxon test based on pairwise comparison of patients on a primary outcome when possible but otherwise on a secondary outcome. The Finkelstein-Schoenfeld method was originally proposed for "analyzing the impact of treatment which combines a (possibly censored) event with a longitudinal measure of clinical effect", not explicitly for analyzing the composite endpoint. 

Based on the Finkelstein-Schoenfeld method, Pocock and colleagues suggested an estimate, the Win Ratio, which summarized the ratio of the number of patients who fared better versus worse on the experimental arm. The Win-Ratio method was proposed explicitly for analyzing the composite endpoint (Pocock et al 2012) "The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities".

With Finkelstein-Schoenfeld or Win-ratio method, pairwise comparisons are performed and the scores are calculated based on the comparison of the importance of the outcome. For example, for a study with composite endpoint including death and hospitalization, all patients had multiple pairwise comparisons performed, first with respect to time to death and to hospitalization, if the latter occurred. 

Below are some additional references discussing the Finkelstein-Schoenfeld or Win-Ratio method and their applications.  

• Finkelstein (2014) "Introduction: Challenges in Analyzing and Interpreting Multiple (Censored) Outcomes in Chronic Disease Trials"
• A novel test to compare two treatments based on endpoints involving both nonfatal and fatal events
• Exact Bootstrap and Permutation Distribution of Wins and Losses in a Hierarchical Trial∗
• Paul Brown's Ph.D. Dissertation (2017) Multiple Outcomes in Heart Failure Research: Composite Endpoints and Multivariate Modelling
• Sun et al (2012) Evaluating Treatment Efficacy by Multiple End Points in Phase II Acute Heart Failure Clinical Trials Analyzing Data Using a Global Method
• Svensson et al "A comprehensive review of the PARTNER trial"
• Graphing the Win Ratio and its components over time

There are several pivotal studies where the Finkelstein-Schoenfeld method is used to analyze the primary efficacy endpoint. The study protocol and statistical analysis plan posted online contain the detail descriptions about the application of the Finkelstein-Schoenfeld method. 

• EXCEL Trial ""Clinical Trial Evaluation of XIENCE versus Coronary Artery Bypass Surgery for Effectiveness of Left Main Revascularization" - Study Protocol;  Statistical Analysis Plan; 
• ATTR-ACT Trial "A Multicenter, International, Phase 3, Double-blind, Placebo-Controlled, Randomized Study to Evaluate the Efficacy, Safety, and Tolerability of Daily Oral Dosing of Tafamidis Meglumine 20 mg or 80 mg in Comparison to Placebo in Subjects Diagnosed with Transthyretin Cardiomyopathy (TTR-CM)" - Study Protocol; Statistical Analysis Plan
• THE PARTNER TRIAL: Placement of AoRTic TraNscathetER Valve Trial Edwards SAPIEN Transcatheter Heart Valve. -  Article (Makkar 2012);  Study Protocol from FDA; Study Protocol/SAP

In the protocol / statistical analysis plan for the Partner trial, there are the following descriptions for the Finkelstein-Schoenfeld method: 

In PARTNER Trial was the basis for FDA approval of Vyndaqel and Vyndamax and Finkelstein and Schoenfeld's method was mentioned in the product label. 

"The primary analysis used a hierarchical combination applying the method of Finkelstein-Schoenfeld (F-S) to all-cause mortality and frequency of cardiovascular-related hospitalizations, which was defined as the number of times a subject was hospitalized (i.e., admitted to a hospital) for cardiovascular-related morbidity. The method compared each patient to every other patient within each stratum in a pair-wise manner that proceeded in a hierarchical fashion using all-cause mortality followed by frequency of cardiovascular-related hospitalizations when patients could not be differentiated based on mortality."

Hodges-Lehmann estimate is used in totally different situations, but similar to the Finkelstein-Schoenfeld method, the estimate relies on the pairwise comparison. While the Finkelstein-Schoenfeld method is primarily used in the analysis of composite endpoint,  Hodges-Lehmann estimate is mainly used to obtain the treatment difference for a continuous variable with normality assumption violation and non-parametric method being used.

 

With the Hodges-Lehmann method, the treatment difference is calculated for each pair for total n x m pairs (where n and m are the # of subjects in each treatment group). The Hodges-Lehmann estimate is the median of differences from all pairs.  

• "Hodges-Lehmann estimator of location shift: Median of Differences versus Difference in Medians or Median Difference"
• Splitting p-value and estimate of the treatment difference
• Hodges-Lehmann Estimator

Hodges-Lehmann estimate has been used in many clinical trials that result in FDA approval of the products. For example, Hodges-Lehmann estimate was the method used in the SIROCCO trial in Asthma. The FDA statistical review document stated the primary analysis method of the study: 

"The primary analysis for the OCS percent reduction endpoint used the Wilcoxon rank-sum test approach. The primary analyses were performed in the FAS population. For each of the two Benralizumab dose regimen groups, the median difference in the OCS percent reduction between Benralizumab dose regimen and placebo was derived using asymptotic Hodges-Lehmann estimation, together with associated 95% CI and p-value. The same analyses were also performed for the EHS without multiplicity control."