Can econometrics rescue epidemiology?

EI.SEVIER

EDITORIAL

Can Econometrics Rescue Epidemiology? Has the science of epidemiology reached its limits? According to a recent report in Science, epidemiology is losing credibility and causing unjustified fears because it is trying to find subtle links between disease, diet, lifestyle, and environmental factors (1). Reports by the popular press about epidernlolilgical studies are accused of contributing to unnecessary alarms and public misunderstanding (2). Econometric methods may be helpful to epidemiologists in rheir search for subtle links. Some of the problems in epidemic&@al studies may be detected by econometric approaches. In this issue of the AnnaEs of Epidemiology, Namvar Zohor)ri and David Savitz discuss the econometric conceprs oiendogeneity and unobserved heterogeneity (E&C UH) (3). A related paper by Zohoori shows how breastfeeding may be used by some women to delay their return to fertility and how their actions can hide the exact biological relation between breast-feeding and the return of menses (4). The key point is that a simple regression analysis may mislead if ir does not recognize chat one of its independent variables may be correlated with the error term because of intervening human action. The auci~~s explain how to use “instrumental” variables to tix these problems. Their explanation is nothing new. As explained below, an instrumental variable is essentially a substitute variable rhat is constructed to be free of the correlation with the error term that mars the original independent variable. Economists have been using instrumental variables for dec.ades to analyze everything from monetary policy to minimum wage laws (5-6). However, applications in ep&micrlogy have been rare, and they usually appear in journals of eccjnometrics and health economics. An excellent illustration is a recent paper by Shmueli (7) that has considered how an unobserved variable-here health status when an inditridual stopped smoking-may mask the relationship hctween health status and the decision to stop smoking. J0ne.s (X), in a reply to Shmueli, used instrumental \:ariahles and ;in expanded data set ro show how the decision to srcip smoking may be influenced by either a desire to preserve current ~~xKI health or the physical limitation imposed hy bad h&h.

Karl Popper has had an important inAucncc (in the philosophy of science with his injunction that scientific hypotheses are useful only if they are falsitiablc with empirical evidence (9, 10). Zohoori and Savitz (3) hypothesize the existence ofE&UH. They show how instrumental variables can give different results from a simple regression if the hypothesized problem is present. They use the Hausman test to determine whether the simple and instrumental variable models are different enough to show the presence of the suspected problem. If rhe problem is presenr, rhe search for why the models differ can then he startell. Economists themselves are not completely en&us&tic, about instrumental variable estimators. A key step in developing the estimator is to regress variable s (the variable suspected of being correlated with the error term) on a set of exogenous variables supposed to be highly correlated with x but uncorrelated with the error term cjt the original regression. The predicted values (i) of this “reduce&form” regression are then used as the “instrument~~l” variable in the original regression. Finding an appropriate XP of exogenous variables is sometimes problematic. Assuring th.at t-he rcduced-form regression is not itself subject rcr ali that can go wrong in fitting a regression is still anothei- prttblem. Despite these technical difficulties, it I\ -not surprising that economerric tools are becoming useitul IO epidetniologists. Hayek says that the distinguishing feat~ure of et:onrs&prt>ductiol~ are fixed. Because theory restricts the v&.:e\ OI ~OII~Ccr>efhd cienrs, economic models can be fir more ~Xs111;tc bdiscover the exact \.aIues ofother cvefficienrs (e.g., rhc price elasticitv of dental ser\rices) about which only ;i range ~-aube specified. ln fact, sc~me economists question if it is :ruly “sclcntific” to include in a statistic;\1 model anv varishlths (ti.g~$ KICC or

250

AEP Vol. 7, No. 4 May 1997: 249-250

Mennemeyer EDITORIAL

sex) for which theory cannot make a prediction about the sign or magnitude of the regression coefficients ( 12). Epidemiology is much more of an exploratory enterprise than economics, so theory cannot give it as much guidance. Epidemiology uses statistics to find clues about the causes of an illness. Clues that make biological or medical sense are helpful; any other clues may be a wasteful distraction-or the start of a paradigm shift. Thinking that econometrics can rescue epidemiology from all of its problems in detecting subtle risk factors with imperfect data would be foolish. Consider the problems of the instrumental variable estimator. When a regressor’s observations are correlated with the corresponding observations of the error term, simple regression will produce an inefficient coefficient; that is, larger sample sizes do not increase the chance of estimating the true value of the coefficient. In practice, this usually means that the slope of the simple regression line is found to be too steep or too flat, but the slope might be estimated as positive when in fact it is negative (or the reverse). Estimation by use of an instrumental variable produces a consistent regression coefficient. It thus may rescue the researcher from finding a slope that is in the wrong direction from the truth. This rescue, however, comes at a price. The slope coefficient produced by the estimator has a wider variance than the coefficient of the simple model and is thus less likely to be judged “statistically significant” when using the common 95% confidence interval as a criterion (5-6). Practicing epidemiologists have to weigh the danger of missing the existence of an effect against the danger of concluding that a beneficial effect is a dangerous one. This concern speaks to the purpose of an epidemiological study and the opportunity costs of following up on its findings. If the purpose of a study is to encourage the public to do or to avoid doing something, then finding the true direction of a slope is very important even if this may delay warning the public. If the purpose is to get biological and medical scientists to give attention to a previously unsuspected relationship, then finding the hint of a slope may be more important than being sure of its statistical significance. This assumes that mobilizing the public in the wrong direction is more wasteful than distracting scarce scientific talent on a fruitless search. Econometric tools can at least alert epidemiologists to where the problems may lie in their data. Zohoori’s paper illustrates both the potential benefit and

the risks of postulating E&UH and of using an instrumental variable model to fix the problem. He finds that a simple statistical model yields a medically plausible dose-response relationship between breast-feeding and the return of menses. His more elaborate instrumental variable model does not find the dose-response relationship, but it does discover another plausible result, namely, a tendency (“diminishing returns”) for marginal increases in breast-feeding to produce marginal decreases in delaying the return to menses. Neither statistical model may be entirely correct, but the instrumental variable model, by adjusting for hypothesized human behavior, is giving clues about the strength and duration of the biological mechanism.

S.T. Mennemeyer, PhD Department of Health Care Organization and Policy University of Alabama at Birmingham Birmingham, AL

REFERENCES 1. Taubes G. Epidemiology Faces Its Limits. Science 1995;269:16+169. 2. Angel1 M. Science on Trial: The Clash of Medical Evidence and the Law in the Breast Implant Case. New York: W.W. Norton; 1996. 3. Zohoori N, Savitz D. Econometric approaches to epidemiologic data: Relating endogeneity and unobserved heterogeneity to confounding. Ann Epidemiol. 1997;7:251-267. 4. Zohoori N. Does endogeneity matter? A comparison of empirical analy ses with and without control for endogeneity. Ann Epidemiol. 1997;7:258-266. 5. Kennedy P. A Guide to Econometrics. 3rd ed. Cambridge MA: MIT Press; 1992. 6. Judge CC, Griffiths WE, Hill RC, Lutkepohl H, and Lee T-C. The Theory and Practice of Econometrics. 2nd ed. New York: John Wiley and Sons; 1985. 7. Shmueli A. Smoking cessation and health: A comment. J Health Economics 1996;15:751-754. 8. Jones AM. Smoking cessation and health: A response. J Health Economics 1996;15:755-759. 9. Popper K. The Logic of Scientific Discovery. New York: Harper &a Row; 1959. 10. Caldwell BJ. Clarifying Popper. J Economic Literature 1991;29(1): l-33. 11. Hayek F. The pretense of knowledge. American Economic Review 1989;79(6):3-7. 12. Neuberg LG. Conceptual Anomalies in Economics and Statistics: Lessons from the Social Experiments. Cambridge, UK: Cambridge University Press; 1989.