Introduction"

In hce: Design and Analysis of Hierarchical Composite Endpoints

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hce package intro

Background

The purpose of the package is simulate and analyze hierarchical composite endpoints (HCEs). Win odds is the main analysis method, but other win statistics (win ratio, net benefit) are implemented as well in case of no censoring. The power and sample size calculation are based on Brunner-Munzel theorem [@brunner2000nonparametric] with the default value being based on the Noether's formula [@noether1987sample]. For the review of the ideas of designing HCEs in clinical trials see @gasparyan2022design, also @gasparyanhierarchical and @khce1. The Basic Data Structure conforming to the Analysis Data Model [@CDISC] principles for hierarchical composite endpoints is described in @gasp2024bds. For visualization of the HCE the maraca plot [@karpefors2023maraca] can be used.

Setup

Load the package hce and check the version

library(hce)
packageVersion("hce")

devtools::load_all()

For citing the package run citation("hce") [@hce].

Contents

List the functions and the datasets in the package

ls("package:hce")

In brief, the package contains the following:

1. Datasets: use data(package = "hce") for the list of all datasets included in the package.

2. Simulated datasets - HCE1 - HCE4 that contain two treatment groups and analysis values AVAL of an hierarchical composite endpoint.

3. The datasets COVID19, COVID19b of COVID-19 ordinal scale outcomes [@beigel2020remdesivir].

4. The datasets ADET (event-time), ADLB (laboratory), ADSL (subject-level baseline characteristics) datasets, correspondingly, for kidney events and their timing, kidney related laboratory measurements of eGFR (estimated glomerular filtration rate), and, based on this, derived kidney hierarchical composite endpoint dataset KHCE for the same patients [@khce2].

5. Functions to create hce objects - hce(), as_hce(), simHCE() (see @gasp2024bds).

6. Win odds (win ratio with ties) calculation generic functions for hierarchical composite endpoints - calcWO(), summaryWO() (see @gasparyan2021adjusted, @gasparyan2021power).
7. Win statistics (win odds, win ratio, net benefit, Goodman Kruskal's gamma) and their confidence intervals calculation function - calcWINS(). Back-calculation of number of wins, losses, and ties given the win odds and win ratio using the function propWINS().
8. Adjusted win odds calculation for a single, numeric covariate using the function regWO().
9. Stratified win odds with a possible adjustment after stratification with a single, numeric covariate using the function stratWO().
10. Power, sample size, and minimum detectable win odds calculation functions - powerWO(), sizeWO(), minWO() (see @gasparyan2021power, @gasparyan2022comments). Win ratio sample size calculation formula sizeWR() [@yu2022sample]. By default uses the Noether's formula [@noether1987sample].
11. Print and plot methods for hce_results objects, generated by functions powerWO(), sizeWO(), minWO().

hce objects

hce() function

The main objects in the package are called hce objects which are data frames with a specific structure, matching the design of hierarchical composite endpoints (HCE), which are complex endpoints combining into a composite events of different clinical importance using a hierarchy for prioritizing in the analysis the clinically most important event of a patient. These endpoints are implemented in clinical trials in different therapeutic areas. See for example, @gasparyan2022design for an implementation in COVID-19 setting and some practical considerations for constructing hierarchical composite endpoints, for the Chronic Kidney Disease (CKD) setting see [@khce1; @khce2].

HCE are ordinal endpoints that can be thought of as having 'greater', 'less' or 'equal' defined for them but without having the definition by how much greater or less. In this sense the ordinal outcomes can be represented as numeric vectors as long as numeric operations (e.g. sum or division) are not performed on them.

hce objects can be constructed using the helper function hce() which has three arguments

args("hce")

We see that the required arguments are GROUP, which specifies clinically the most important event of a patient to be included in the analysis and TRTP which specifies the (planned) treatment group of a patient (exactly two treatment groups should be present). Note that

• hce structure assumes that only one event per patient is present for the analysis, meaning that the resulting hce object created by the hce() function is a patient-level dataset. The function hce() does not do a selection of the clinically most important event of the patient but requires it to be already done when calling it.

• argument TRTP should have exactly two levels.

Consider the following example of ordinal outcomes 'I', 'II', and 'III':

set.seed(2022)
n <- 100
dat <- hce(GROUP = rep(x = c("I", "II", "III"), each = 100), 
           TRTP = sample(x = c("Active", "Control"), size = n*3, replace = TRUE))
class(dat)

This dataset has the appropriate structure of hce objects, but its class inherits from an object of class data.frame. Meaning that all functions available for data frame can be applied to hce objects, for example the function head()

head(dat)

We see that the dataset has a very specific structure. The column GROUPN shows how the function hce() generated the order of given events (it uses usual alphabetic order for the unique values in GROUP column to determine the clinical importance of events)

unique(dat[, c("GROUP", "GROUPN")])

In the class hce the higher values for the ordering mean clinically less important event. For example, death which is the most important event always should get the lowest ordinal value. If there is a need to specify the order of outcomes, then the argument ORD can be used

set.seed(2022)
n <- 100
dat <- hce(GROUP = rep(x = c("I", "II", "III"), each = 100), 
           TRTP = sample(x = c("A", "P"), size = n*3, replace = TRUE), ORD = c("III", "II", "I"))
unique(dat[, c("GROUP", "GROUPN")])

This means that the clinically most important event is 'III' instead of 'I'. The argument AVAL0 is meant to help in the cases where we want to introduce sub-ordering within each GROUP category. For example, if two events in the group 'I' can be compared based on other parameters, then AVAL0 argument can be specified to take that into account.

Below we use the built-in data frame HCE1 to construct an hce object. Before specifying the order of events it is a good idea to check what are the unique events included in the GROUP column

data(HCE1)
unique(HCE1$GROUP)

Therefore, we can construct the following hce object

HCE <- hce(GROUP = HCE1$GROUP, TRTP = HCE1$TRTP, AVAL0 = HCE1$AVAL0, 
           ORD = c("TTE1", "TTE2", "TTE3", "TTE4", "C"))
class(HCE)
head(HCE)

Create an hce object from a data frame

Consider the dataset HCE1 which is part of the package hce

data(HCE1, package = "hce")
class(HCE1)
head(HCE1)

This dataset has the appropriate structure of hce objects, but its class is data.frame. A generic way of coercing data structures to an hce object is to use the function as_hce() which, for given data structure, will perform checks (using internal validator function) and create an hce object from it (using an internal constructor function), if possible or will throw an error explaining the issue.

dat1 <- as_hce(HCE2)
str(dat1)

Simulate hce objects using simHCE()

To simulate values from a hierarchical composite endpoint we use the function simHCE(), which has the following arguments

args("simHCE")

• The vector arguments TTE_A and TTE_P show the event rates per year for time-to-event outcomes in the active and control groups, respectively. The function assumes Weibull survival function with the same shape parameter for simulating all time-to-event outcomes in both treatment groups (by default shape = 1 hence assumes exponential survival function). These two vectors should have the same length and their length shows the number of time-to-event outcomes, which can be arbitrary.

• By default, the event rates are presented per 100 patient-years (pat = 100), which can be changed using the argument pat. The function simulates event times in days, hence yeardays = 360 argument can be used to change the number of days in a year (for example, 365 or 365.25 can be used).

• The function simulates events during a fixed-follow-up time only, hence argument fixedfy can be used to change the length of the follow-up (in years).

• The function simulates the continuous outcome from a normal (default) or log-normal (if logC = TRUE) distribution with given means and standard deviations for two treatment groups.

Rates_A <- c(1.72, 1.74, 0.58, 1.5, 1) 
Rates_P <- c(2.47, 2.24, 2.9, 4, 6) 
dat3 <- simHCE(n = 2500, n0 = 1500, TTE_A = Rates_A, 
               TTE_P = Rates_P, 
               CM_A = -3, CM_P = -6, 
               CSD_A = 16, CSD_P = 15, 
               fixedfy = 3, seed = 2023)

class(dat3)
head(dat3)

Generics for hce objects

As we see, it creates an object of type hce which inherits from the built-in class data.frame. We can check all implemented methods for this new class as follows:

methods(class = "hce")

The function calcWO() calculates the win odds and its confidence interval, while summaryWO() provides more detailed calculation of win odds, providing also the number of wins, losses, and ties by GROUP categories.

HCE <- hce(GROUP = HCE3$GROUP, TRTP = HCE3$TRTP,
           ORD = c("TTE1", "TTE2", "TTE3", "TTE4", "C"))
calcWO(HCE)
summaryWO(HCE)

References

hce documentation built on May 29, 2024, 5:52 a.m.