Presenting Confounding and Standardization Graphically

1 Milo Schield, ([email protected]) has taught statistics and statistical literacy for over 20 years at Augsburg College in Minneapolis, MN. With a BS from Iowa State, an MS from the University of Illinois and a Ph.D. from Rice University he has pursued a variety of professional interests including Operations Research at a large property-casualty insurance company. Milo is the Director of the W. M. Keck Statistical Literacy Project at Augsburg College. See Schield (2004b) and www.StatLit.org for more details. Did you know that the US has a higher death rate than Mexico? It’s a fact. In 2003, the death rate was 80% higher in the US than in Mexico (8.4 per 100,000 versus 4.7). What does this statistic mean? Does Mexico have better health care than the US? That seems very unlikely. Yet it is difficult to claim that this unexpected relationship is due to chance, error or bias. The populations being studied are large; death is definite and usually counted accurately. You may be perplexed, confused or confounded when you learn that death rates are even lower in Ecuador and Saudi Arabia (4.3 and 2.7). An alternate explanation is confounding. Last (1995) defines confounding as “a situation in which the effects of two processes are not separated.” Confounding reflects the influence of a lurking variable. A lurking variable is often referred to as a confounder which Last defines as “a variable that can cause or prevent the outcome of interest ... and is associated with the factor under investigation.” In comparing these death rates, a lurking variable may be the difference in the age distributions. Mexico has a much younger population than the US. In 2003, people under 15 were 50% more prevalent in Mexico than in the US (32% compared to 21%). People 65 and older were more than twice as prevalent in the US as in Mexico (12% compared to 5%). It’s a fact that older people are much more likely to die than younger people. Unless we take age distribution into account, a comparison of these crude (unadjusted) death rates may be misleading. Mexico’s comparatively low death rate is most likely due to its youthful population, rather than to its health care system. So how can we untangle this confusion? How can we “take into account’ the influence of a lurking variable that confounds an association?