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## Title

Effect of enalapril on survival in patients with reduced left ventricular ejection fraction and congestive heart failure

## Introduction

We demonstrate the application of our software using the data from a randomized controlled trial of the effect of an Angiotensin-converting-enzyme inhibitor (ACE inhibitor) called enalapril on survival in patients with reduced left ventricular ejection fraction and congestive heart failure (CHF).

Patients were randomized to either placebo (n=1284) or enalapril (n=1285).

The study showed that enalapril sigificantly reduced mortality and hospitalizations for heart failure. In the original paper the trial investigators (NEJM 1991) reported an overall treatment effect of 16% reduction in relative risk of mortality (95% CI: 5% - 26%, p-value = .0036). They also examined the consistency of this overall treatment effect in subgroups which were defined a priori in the study protocol.

The subgroups were defined according to the following 5 characteristics measured at baseline:k

1. sodium level, by tertiles
2. whether or not patients used vasodilators other than ACE inhibitors
3. ejection fraction, by tertiles
4. the cause of CHF (ischemia or other/unknown)
5. functional status as per New York Heart Association (NYHA) classes (I - IV)

The subgroups were defined using one characteristic at a time. We call this "univariate subgroup analyses." The univariate subroups are not mutually exclusive and hence, the subgroup effects will becorrelated.

## Analysis Plan

Here we conduct analyses using multivariate subgroups, i.e. subgroups defined using multiple baseline characteristics. If we used the original 5 charateristics, we will end up with 144 subgroups (144 = 3 x 2 x 3 x 2 x 4). This makes the analyses a bit unwieldy, even though our software can easily handle this complexity.

For the purposes of demonstrating the software, we considered multivariate subgroups defined by only 3 characteristics:

1. sodium level, by tertiles
2. whether or not patients used vasodilators other than ACE inhibitors
3. ejection fraction, by tertiles

This resulted in 18 mutually excusive subgroups. The point estimate and standard error of these 18 subgroups form the input to our software.

## Reference

Solvd Investigators and others, Effect of enalapril on survival in patients with reduced left ventricular ejection fraction and congestive heart failure. N Engl j Med. 1991 ;325:293–302.