CLINICAL TRIALS IN ACUTE MYOCARDIAL INFARCTION:

SHOULD WE ADJUST FOR

BASELINE CHARACTERISTICS?

Ewout W. Steyerberg, PhD 1, Patrick M.M. Bossuyt, PhD 2, Kerry L. Lee, PhD 3

1	Center for Clinical Decision Sciences, Department of Public Health, Erasmus University, Rotterdam, The Netherlands

2	Department of Clinical Epidemiology & Biostatistics, Academic Medical Center - University of Amsterdam, Amsterdam, The Netherlands

3	Department of Community and Family Medicine, Duke University Medical Center, Durham, NC, USA

Address for correspondence:

Ewout W. Steyerberg, PhD, Center for Clinical Decision Sciences, Ee2091, Department of Public Health, Erasmus University, PO Box 1738, 3000 DR Rotterdam, The Netherlands

Phone: 31 - 10 - 408 7053; Fax: 31 - 10 - 436 1760; e-mail: steyerberg@ckb.fgg.eur.nl

Date:	January 30, 1998 (9:18AM)

Word count text:	2169

Journal:	Circulation

Running head:	Baseline characteristics in acute MI trials

Part of this research was supported by a grant from the Netherlands Organization for Scientific Research (NWO, S96-156)

Acknowledgments: We would like to thank Amanda L. Stebbins, MPH, Duke Clinical Research Institute, Duke University, Durham NC, for discussions and practical support, and several colleagues from Erasmus University, Rotterdam, The Netherlands, for their helpful comments.

Abstract

Background: Clinical trials concerning acute myocardial infarction often evaluate short-term mortality. Several baseline characteristics are predictors of mortality, most notably age. Adjustment for one or more predictors in a multivariable analysis may be considered to correct the estimate of the treatment effect for any imbalance that -by chance- may have occurred between the randomized groups.

Methods and results: The effects of adjustment are illustrated with logistic regression analysis in the GUSTO-I trial. The primary end point was 30-day mortality, which occurred in 6.3% of 10,348 patients randomized to tissue plasminogen activator (tPA) and 7.3% of 20,162 patients randomized to streptokinase (SK) thrombolytic therapy. This is equivalent to an unadjusted odds ratio of 0.85. No significant imbalance occurred for any of 17 baseline characteristics considered, including well-known demographic, presenting, and history characteristics. Adjusted for age, the odds ratio was 0.83, which is a 18% increase in estimated effect on the logistic scale. When adjusted for 17 characteristics, the odds ratio was 0.82, an increase of 25%. Because of increased power, adjustment reduced the required sample size by 12 or 19% respectively.

Conclusions: Adjustment for predictive baseline characteristics, even when largely balanced, may lead to substantially different estimates of the treatment effect on mortality. Adjustment for important predictors, such as age, is recommended in clinical trials studying patients with acute myocardial infarction.

Condensed abstract

Randomized clinical trials in acute myocardial infarction often evaluate short-term mortality. The effects of adjustment for well-known predictors, such as age, are illustrated with the comparison between tissue plasminogen activator (tPA) and streptokinase (SK) thrombolytic treatment in 30,510 patients from the GUSTO-I trial. Adjusted analyses have several advantages and are therefore recommended in clinical trials studying patients with acute myocardial infarction.

Introduction

Randomized clinical trials provide the most reliable evidence of effectiveness of new treatments in acute myocardial infarction (MI). Trials have established the beneficial effect of several thrombolytics 1, such as streptokinase 2 3 and tissue plasminogen activator 4, and adjunctive medical therapy 5, such as beta-adrenergic-antagonists 6, and ACE inhibitors 7 8 9. On the other hand, some adjunctive therapies have been shown to be at best of limited value (nitrates, calcium-channel blockers, some anti-arrhytmetic drugs, magnesium) 5 8. Short-term mortality (within 28 to 42 days from randomization) is the main end point in most larger trials 4 8 9 10 11. Sometimes a composite measure is used, consisting of mortality plus severe left ventricular dysfunction 7, or reinfarction 12.

The statistical analysis of a randomized clinical trial is relatively straightforward, since comparability of treatment groups is guaranteed by randomization. Fortunately, most trialists currently adhere to the 'intention-to-treat' principle, which implies analysis of all randomized patients 13. A controversial topic is the role of baseline characteristics known or assumed to be predictive of the end point under study. Logistic regression analysis can be used to obtain an estimate of the treatment effect, adjusted for baseline characteristics. For example, 30-day mortality in the GUSTO-III trial was analyzed with adjustment for four pre-specified baseline characteristics 10. This approach contrasts with most other recently published larger trials (n>10,000), which report the unadjusted treatment effect as the main result 4 7 8 9 12. Balance of baseline characteristics between randomized groups is often statistically tested for, although testing is scientifically inappropriate in this setting 14 15 16. For example, in the GUSTO-I trial, the protocol specified that baseline characteristics would only be included in an adjusted analysis if tests for imbalance reached statistical significance (p<.05), which was not the case for any of seven pre-specified characteristics 4.

Most analysts probably do not realize that a different treatment effect will be estimated in a multivariable logistic regression analysis, even in the absence of any imbalance of predictive baseline characteristics 17 18. This phenomenon is caused by heterogeneity of the patient population, which is ignored in an unadjusted, or 'pooled', analysis. Adjusted analyses take this heterogeneity into account by stratification on baseline characteristics. Stratified estimates of the treatment effect are more extreme than unadjusted estimates in a fully balanced trial (relative risk away from unity, see Appendix A). Another less well known phenomenon is that the standard error of the stratified treatment effect will always be larger than the standard error of the pooled treatment effect 18. One might therefore expect that the power for detecting a treatment effect would decrease by performing adjusted analyses. This is not the case, since stratification causes the effect estimate of treatment to increase more than its standard error 18.

These features of adjustment will be illustrated with analyses of the comparison between tissue plasminogen activator (tPA) and streptokinase (SK) thrombolytic treatment in the GUSTO-I trial 4. We will argue that adjustment for a limited number of pre-specified baseline characteristics is the preferred mode of analysis for large-scale randomized clinical trials in acute MI.

Patients and Methods

Patients

The GUSTO-I trial enrolled patients with acute myocardial infarction from 1082 hospitals in 14 countries 4. Mortality within 30 days after randomization was the primary end point. We compared 30-day mortality between 10,348 patients randomized to tissue plasminogen activator (tPA) and 20,162 patients randomized to streptokinase (SK) in combination with subcutaneous or intravenous heparin. Average mortality was 7.0% (2,128 of 30,510 patients). Seventeen baseline characteristics were considered for their relation with 30-day mortality, based on previous analyses 19 20 21 22 23 24. Within the total data set, 16 geographical regions were distinguished: 8 in the United States 25, 6 in Europe, and 2 other (Australia+New Zealand, Canada) 4. These regions contained between 922 and 3,241 patients (mean 1,907), where between 64 and 222 deaths (mean 133) had occurred.

Methods

Logistic regression was applied to compare the effect of tPA and SK treatment on 30-day mortality (S-plus software, MathSoft, Inc., Seattle WA) 26. An indication of the prognostic strength of the baseline characteristics was provided by the univariable model 2, which was calculated as the difference in −2 log-likelihood between a univariable logistic regression model with and without the characteristic. We further calculated an R2 measure, which approximately indicated the percentage of variance explained 27. Differences between randomized groups were tested with the Mann-Whitney test (continuous variables) or Pearson chi-square test (discrete variables).

We considered three logistic regression models: one with treatment (tPA coded as 1, SK as 0) as the single covariable, a second with treatment and age (in years), and a third with treatment and 17 baseline characteristics (including age). The first model represented an unadjusted analysis, and the second and third model represented analyses adjusted for baseline characteristics. The difference between the unadjusted and the adjusted regression coefficient for the treatment variable was attributed to imbalance and stratification. We calculated the difference attributable to imbalance by multiplying the difference in mean value of the baseline characteristic(s) with the regression coefficient(s) in the adjusted analysis. For example, the tPA group was 0.17 years older than the SK group, and the regression coefficient for age in the adjusted analysis was 0.082. Imbalance hence was responsible for a difference of 0.17 0.082=0.014 in the logistic regression coefficient that represented the adjusted treatment effect. The remaining part of the difference between unadjusted and adjusted treatment effect was attributed to stratified estimation.

Results

The distribution of 17 baseline characteristics in the tPA and SK group is shown in Table 1. No significant imbalance had occurred for any of these characteristics. The strongest prognostic factor was age (R2=12%), followed by Killip class and hypotension.

In the tPA group, 30-day mortality was 6.3% (653 of 10,348 patients), in contrast to 7.3% (1,475 of 20,162 patients) in the patients randomized to SK. This corresponded to an Odds Ratio (OR) of 0.85 as estimate for the unadjusted treatment effect, or a logistic regression coefficient of -0.159 (Table 3). The standard error (SE) of this coefficient was 0.049. For comparison with Table 2 we note that the 2 of the treatment effect was 10.8 (p=0.001), and the R2 0.1%. The prognostic importance of treatment was small compared to patient characteristics such as age ( 2 1492).

The OR of the treatment effect was 0.83 (coefficient −0.188±0.050) when adjusted for age, and 0.82 (coefficient −0.198±0.053) when adjusted for 17 baseline characteristics (Table 2). The logistic regression coefficients treatment effect hence increased by 18 or 25%, respectively. Part of this difference could be attributed to imbalance. For example, patients in the tPA group were slightly older and age was a very strong predictor of short-term mortality. The slight difference in age accounted for a difference of 8.8% between unadjusted and age- adjusted treatment effect. The tPA group also had a slightly less favorable prognosis when all 17 characteristics were considered. This imbalance accounted for a difference of 4.3% in the treatment effect. Considerable differences in treatment effect (9% and 21%) were attributable to stratification on important predictors.

In the GUSTO-I trial, both imbalance and stratification led to more extreme estimates of the treatment effect. Note that the adjusted effect would have been less extreme than the unadjusted effect if a strong imbalance in the opposite direction had occurred.

Adjustment increased the standard errors by 3 and 8%, respectively. This increase was less than the increase in treatment effect due to stratification. This observation illustrates that the power of a study increases by adjustment for predictive baseline characteristics. The power of the unadjusted analysis with 30,510 patients could be achieved with 26,900 or 24,850 patients when adjusting for age or 17 characteristics, which equals a reduction in required sample size by 12 or 19%, respectively.

Discussion

In this era of evidence-based medicine, randomized clinical trials are essential instruments to quantify benefits and risks of treatment. The results reported in this study illustrate that adjustment for baseline characteristics has multiple effects on the estimation of the treatment effect in a clinical trial. First, it is well known that adjustment may correct for imbalance that occurred between the randomized groups. This imbalance is due to pure chance if a proper randomization procedure has been used 14 15 16. In the GUSTO-I trial, the imbalance was small and statistically non-significant, but it explained a difference of 4 to 9% in the adjusted estimate of the treatment effect of tPA versus SK on 30-day mortality. Second, adjustment leads to an estimate of the treatment effect that is stratified on the baseline characteristics. From the biostatistical literature it is known that such a stratified treatment effect is more extreme than the pooled effect in a heterogeneous population (see Appendix A) 17 18. Stratification accounted for a difference up to 21% between unadjusted and adjusted treatment effects in the GUSTO-I trial. This difference is specific to analyses of dichotomous end points, such as short- or long-term mortality, where logistic or Cox regression may be applied 28 29 30 31; it does not occur with linear regression analysis of continuous end points 17 18. Finally, adjustment leads to a higher statistical power in the analysis of differences between treatments.

Adjusted and unadjusted analyses of mortality result in identical estimates of the treatment effect in homogeneous populations, where no predictors exist. In heterogeneous populations, such as acute MI patients, the unadjusted treatment effect estimate may be interpreted as the pooled estimate for treating 'a patient' with an acute MI. Adjusting for age results in an estimate for 'a patient of a certain age'. Adjusting for all known predictive baseline characteristics results in an estimate for 'a patient with a certain risk profile'. Adjustment thus results in more individualized estimates of the treatment effect, in contrast to the pooled estimate.

It has been argued that the net benefit of treatment for the individual cardiologic patient depends on the estimated effect of treatment combined with his/her absolute risk 32 33 34. The latter can be obtained from multivariable risk equations, which need to be well-calibrated. The treatment effect can be derived from a randomized clinical trial, where adjusted analyses provide individualized estimates. An important assumption in this approach is that the relative risk reduction is constant for all patients, i.e. independent from their absolute risk. Treatment effects in specific subgroups might therefore be assessed, although multiple testing makes such analyses often exploratory in nature. Note that unadjusted analyses make an even stronger assumption, by implying that the trial enrolled a homogeneous patient population where a single treatment effect is applicable to all patients 16.

In practice, it may be difficult to select an appropriate set of baseline characteristics for adjustment 16. In the case of short-term mortality after acute MI, a large number of studies have analyzed risk factors 19 20 21 22 23 24. Important predictors include especially age, followed by presenting characteristics, such as Killip class, systolic blood pressure, heart rate and infarct location, and, to a lesser extent, history characteristics such as a previous infarction. Combinations of these six predictors provided most of the prognostic information in GUSTO−I 23. In the recently completed GUSTO−III trial, four of these characteristics (age, systolic blood pressure, heart rate, and infarct location) were pre-specified for adjustment of the effect of double-bolus reteplase versus accelerated alteplase (tPA) 10 35. The adjusted analysis was the primary statistical analysis, and the selection of these characteristics did not depend on statistical testing of the predictive effect nor imbalance of the characteristics 10. This set of baseline characteristics constitutes a small number of covariables in the regression analysis relative to the number of events. This limits any problems of statistical overfitting, which might especially occur in small trials 36 37 38 39.

Since adjusted analyses have advantages in making individualized treatment recommendations and also in statistical power, we can only speculate why adjusted analyses are not more common. Many may not be aware of the phenomena illustrated in this study. Also, multivariable methods are more complex, and may be distrusted 38. Especially, trials may cause concern when adjusted analyses show statistically significant results, while unadjusted analyses fail to do so 40. To prevent the evaluation of multiple models until significant results are found, the trial protocol should therefore pre-specify the adjusted analysis, i.e. the baseline characteristics to be included in the model and preferably also their coding 35.

The effects of new treatments for acute MI are expected to be small in comparison with currently available therapies, and randomized clinical trials will need to include very large numbers of patients to provide sufficient statistical power. Adjustment for well-established predictive baseline characteristics increases the power of these trials, such that beneficial effects of treatments on clinically relevant end points will more clearly be detected. Further, the large size of acute MI trials makes substantial differences in prognosis between treatment groups unlikely. The GUSTO-I example however illustrates that the effect of (statistically non-significant) imbalance is not neglectable. We therefore conclude that trials designed to test the effectiveness of treatments in the reduction or equivalence of short-term mortality in acute MI should be analyzed with adjustment for important, pre-specified baseline characteristics, regardless the amount of imbalance between treatment groups.

Appendix A: stratification

The effect of stratification is illustrated with a hypothetical randomized clinical trial with 398 patients, 200 allocated to treatment A and 198 to treatment B, with exact balance with regard to gender. The average mortality is 42% (169/398), but is lower in males than in females (27% versus 58%). The mortality odds ratio is 0.500 in the strata formed by gender, in contrast to 0.538 in the pooled table. Ignoring heterogeneity hence causes an underestimation of the treatment effect in a perfectly balanced trial.

Table A	Hypothetical example of stratification.

Pooled table: OR=0.54	Males: OR=0.50	Females: OR=0.50
Treatment	Dead	Survive	Total	Dead	Survive	Dead	Survive
A

B	70

99

(42%)	130

99	200

198	20

33

(27%)	80

66	50

66

(58%)	50

33

References