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American Journal of Epidemiology Vol. 154, No. 5 : 486-488
Copyright © 2001 by The Johns Hopkins University School of Hygiene and Public Health

LETTERS TO THE EDITOR

RE: "ASSESSING THE IMPACT OF CLASSICAL RISK FACTORS ON MYOCARDIAL INFARCTION BY RATE ADVANCEMENT PERIODS"

A. Pfahlberg and O. Gefeller

Department of Medical Informatics, Biometry, and Epidemiology University of Erlangen-Nuremberg Waldstr. 6 D-91054 Erlangen, Germany


   INTRODUCTION
TOP
 INTRODUCTION
REFERENCES
 INTRODUCTION 
 REFERENCES 
 
Liese et al. (1Go) report on interesting results concerning the impact of cardiovascular risk factors on myocardial infarction in terms of the associated rate advancement period for these factors. In addition to analyzing data from the Monitoring Trends and Determinants in Cardiovascular Diseases, Augsburg, Germany (MONICA Augsburg), cohort (2Go), they present a reanalysis of three other cohort studies (3GoGo–5Go) with respect to the rate advancement period associated with cigarette smoking.

The concept of the risk and rate advancement period as a novel approach to translate risk factor impact on disease occurrence into a time period was developed in a methodological paper 8 years ago (6Go). It took some time until the rate advancement period attracted the interest of practicing epidemiologists, but recently several studies (1Go, 2Go, 7Go, 8Go) used the concept to describe the effect of an exposure in terms of the time period by which exposed persons reach prematurely the same disease risk as unexposed persons reach later on.

We appreciate the interest by Liese et al. (1Go) in the rate advancement period approach and agree completely on most of their points, for example, that this rather neglected measure has an intuitive appeal conveying a useful message needed for risk communication. However, we would like to draw attention to a methodological aspect of rate advancement period estimation that has not been dealt with adequately in their and other rate advancement period analyses. Whereas the point estimation of the rate advancement period is very simple (6Go, 9Go), its interval estimation poses more complex problems because the structure of the rate advancement period parameter as a ratio of two continuous quantities needs special attention. For a similar problem in bioassays, Fieller introduced a classical solution (known as Fieller's theorem) more than 50 years ago (10Go). Using the notation of Liese et al. (1Go), the (1 - {alpha}) confidence interval based on Fieller's theorem (Fieller-CI) can be written as

(1)
where q is the (1 - {alpha}/2) quantile of the corresponding t distribution. In the case of a normally distributed vector b colone (b1, b2), this interval represents an exact confidence interval. If normality holds only asymptotically, as is the case for parameter estimates from generalized linear models, the nominal coverage level of this confidence interval will be attained asymptotically.

The Fieller-CI has already been mentioned in the paper introducing the rate advancement period (6Go, p. 232), but it has not been given explicitly. Instead, the simpler confidence interval based on the delta method (Delta-CI) has been presented there and has also been used in the analysis by Liese et al. (1Go). To demonstrate that a discussion about the appropriate confidence interval method is relevant, we computed the Fieller-CIs for the same rate advancement periods as used by Liese et al. (1Go). Comparison of the results from the two approaches in table 1 points to remarkable discrepancies. The asymmetric Fieller-CIs were not only always wider than the symmetric Delta-CIs but they also shifted to the right, meaning that the lower bound of the Fieller-CI is always higher than its counterpart of the Delta-CI.


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  		TABLE 1. Rate advancement periods associated with various cardiovascular risk factors for incident myocardial infarction (MONICA Augsburg* and GRIPS*) and incident coronary heart disease (FINMONICA* and PROCAM*), respectively: recalculation of interval estimates for the rate advancement period based on the information in tables 2 and 3 of A. D. Liese et al. (Am J Epidemiol 2000;152:884–8)

 
An extensive simulation study on the properties of different methods of interval estimation for the rate advancement period has shown that the Fieller-CI performed best among all seven competitors (including also resampling-based methods like variants of the Bootstrap and the Jackknife) (11Go). On average, the Delta-CI yielded acceptable results in terms of agreement between empirical coverage proportions and nominal confidence interval levels. However, in some cases, the Delta-CI failed dramatically. These situations can be characterized by the correlation structure of numerator and denominator terms that define the rate advancement period (here: b1 and b2, respectively) and by the magnitude of variation of the denominator terms (here: b2). If the coefficient of variation for b2 is high, the Delta-CI tends to be too narrow and ill positioned, leading to empirical coverage proportions of 0.75–0.85 instead of the nominal level of 0.95 even for large sample sizes. This underestimation is especially pronounced if b1 and b2 are uncorrelated (11Go).

The actual situations in the analyses by Liese et al. (1Go) resemble the scenarios where the Delta-CI is unreliable. The coefficients of variation for the age effect b2 amount up to 0.26, and the estimates b1 and b2 are nearly uncorrelated in all cases. Therefore, the Delta-CIs should not be trusted here. The Fieller-CIs shown in table 1 give a more valid impression of the high degree of imprecision in and the location of the rate advancement period estimates. The better performance of the Fieller-CI in these situations results from its flexibility in allowing an asymmetric structure of the intervals.


   REFERENCES
TOP
 INTRODUCTION
 REFERENCES
INTRODUCTION 
 REFERENCES 
 

  1. Liese AD, Hense HW, Brenner H, et al. Assessing the impact of classical risk factors on myocardial infarction by rate advancement periods. Am J Epidemiol 2000;152:884–8.[Abstract/Free Full Text]
  2. Keil U, Liese AD, Hense HW, et al. Classical risk factors and their impact on incident non-fatal and fatal myocardial infarction and all-cause mortality in southern Germany—results from the MONICA Augsburg cohort study 1984–1992. Eur Heart J 1998;19:1197–207.[Abstract/Free Full Text]
  3. Assmann G, Schulte H, von Eckardstein A. Hypertri-glyceridemia and elevated lipoprotein(a) are risk factors for major coronary events in middle-aged men. Am J Cardiol 1996;77:1179–84.[Web of Science][Medline]
  4. Cremer P, Nagel D, Mann H, et al. Ten-year follow-up results from the Goettingen Risk, Incidence, and Prevalence Study (GRIPS). I. Risk factors for myocardial infarction in a cohort of 5790 men. Atherosclerosis 1997;129:221–30.[Web of Science][Medline]
  5. Jousilahti P, Vartiainen E, Tuomilehto J, et al. Sex, age, cardiovascular risk factors, and coronary heart disease: a prospective follow-up study of 14,786 middle-aged men and women in Finland. Circulation 1999;99:1165–72.[Abstract/Free Full Text]
  6. Brenner H, Gefeller O, Greenland S. Risk and rate advancement periods as measures of exposure impact on the occurrence of chronic diseases. Epidemiology 1993;4:229–36.[Web of Science][Medline]
  7. Stevens J, Cai J, Juhaeri, et al. Consequences of the use of different measures of effect to determine the impact of age on the association between obesity and mortality. Am J Epidemiol 1999;150:399–407.[Abstract/Free Full Text]
  8. Stevens J. Impact of age on associations between weight and mortality. Nutr Rev 2000;58:129–37.[Web of Science][Medline]
  9. Pfahlberg A, Gefeller O, Brenner H. Computational realization of point and interval estimation for risk and rate advancement periods. (Letter). Epidemiology 1995;6:99–100.[Web of Science][Medline]
  10. Fieller EC. A fundamental formular in the statistics of biological assays and some applications. Q J Pharm Pharmacol 1944;17:117–23.
  11. Pfahlberg A. Statistische Aspekte des epidemiologischen Risikokonzepts der "Risk and Rate Advancement Period." (In German). Dortmund, Germany: Department of Statistics, University of Dortmund, 1999.
 

THREE AUTHORS REPLY

Angela D. Liese, Hermann Brenner and Hans-Werner Hense

Department of Epidemiology and Biostatistics Norman J. Arnold School of Public Health University of South Carolina Columbia, SC 29208
The German Centre for Research on Ageing at the University of Heidelberg 69115 Heidelberg, Germany
Institute of Epidemiology and Social Medicine University of Münster 48129 Münster, Germany


   INTRODUCTION 
TOP
 INTRODUCTION
 REFERENCES
 INTRODUCTION 
REFERENCES 
 
We appreciate the comments of Dr. Pfahlberg and Dr. Gefeller (1Go) on our recent article (2Go) and are grateful for their interesting expansion of confidence interval estimation for rate advancement periods as this issue clearly deserves attention. As illustrated by Pfahlberg and Gefeller, interval estimates obtained by different methods may differ considerably in some situations. Referring to their own unpublished work, Pfahlberg and Gefeller argue that it has been shown in an extensive simulation study that the confidence interval based on Fieller's theorem (Fieller-CI) (3Go) performs better than other estimators of the confidence interval for rate advancement periods, including the confidence interval based on the delta method (Delta-CI) used in our paper (2Go). In particular, Pfahlberg and Gefeller argue that the situations in our paper resemble the scenarios in their simulation study where the Delta-CI was unreliable, but they do not provide actual results of simulations reflecting the very situation encountered in our paper. On the basis of accessible evidence, the relevance of their point for our analysis is therefore somewhat difficult to evaluate. More importantly, it does not alter or invalidate any of the conclusions of our paper. We nevertheless hope that the important issue raised by Pfahlberg and Gefeller will stimulate more methodological work that would be helpful to enable more informed application and evaluation of different options of confidence interval estimation for rate advancement periods in the future.


   REFERENCES 
TOP
 INTRODUCTION
 REFERENCES
 INTRODUCTION 
 REFERENCES 
 

  1. Pfahlberg A, Gefeller O. Re: "Assessing the impact of classical risk factors on myocardial infarction by rate advancement periods." (Letter). Am J Epidemiol 2001;154:486–7.[Free Full Text]
  2. Liese AD, Hense HW, Brenner H, et al. Assessing the impact of classical risk factors on myocardial infarction by rate advancement periods. Am J Epidemiol 2000;152:884–8.
  3. Fieller EC. A fundamental formular in the statistics of biological assays and some applications. Q J Pharm Pharmacol 1944;17:117–23.

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A. Pfahlberg, O. Gefeller, A. D. Liese, H. Brenner, and H.-W. Hense
RE: "ASSESSING THE IMPACT OF CLASSICAL RISK FACTORS ON MYOCARDIAL INFARCTION BY RATE ADVANCEMENT PERIODS"
Am. J. Epidemiol., September 1, 2001; 154(5): 486 - 488.
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