(2)- Department of Medicine. Diabetes Section. San Juan de Dios Hospital. Faculty of Medicine. University of Chile. Santiago, Chile.
Abstract: ORINTA is a small software
program that runs under Microsoft Windows and can be used to learn risk ratio
(RR) and odds ratio (OR) in an elementary course of epidemiology. Students can
explore in an interactive way (or guided by the teacher) several situations in
the common contingency table of epidemiological prospective research. They can
experiment by themselves 1) The exposure OR in cases versus controls equals the
disease OR for exposed versus unexposed 2) How OR approximates the RR in prospective
studies when the disease is rare 3) The asymmetry of the confidence intervals
for OR and RR and 4) The effect of the sample size on the p-value of the chi-square
statistic and on confidence intervals.
Keywords: odds ratio; risk ratio; educational software;
epidemiology
The use of statistics in epidemiology is essential due to the quantitative nature of this discipline. Statistical methodology applied in this branch of Medicine is increasing day by day both in teaching and in practice. In this context, papers related to epidemiology are usually presented with a large amount of numerical information that can be obscure and difficult to understand for many readers of biomedical science journals. Moreover, complex tools related to statistical modeling have helped to darken this matter even more for biologists, physicians or other non-mathematical professionals.(1)
On the other hand, medical students and practitioners often consider themselves skeptical about the utility of statistics in clinical research, while other students face this matter even with fear. Statistical concepts such as probability or random variable are sometimes difficult to teach mainly because they are abstract and you can not present them in a simple way. Moreover, the notation and terminology is often confusing and misleading.(2) Teaching statistics to non- specialists has forced statisticians to manage this subject as non-mathematically as possible, only introducing formulae when absolutely necessary.(3) However, these efforts are not always effective since they often fail to establish a clear link between the process of statistical inference and the use of data from experimental or non-experimental research.4 In epidemiology, it is essential to keep in mind this link in order to understand concepts related to random error and systematic error that are connected to precision and validity.
Risk Ratio and Odds Ratio
Risk Ratio (RR) can be computed as the risk or probability of an outcome among individuals who have a given specific characteristic divided by the risk or probability among individuals who lack this characteristic. Then, it is a ratio of risk or, in epidemiological terms, a ratio of the cumulative incidence rates of an outcome in a given period of time. RR can not be computed in a retrospective studies since the number of diseased and diseased-free subjects are fixed by the investigator in this design. On the other hand, odds ratio (OR) can be computed in a prospective study and it represents the odds that an health-related outcome will occur in individuals who have a specific characteristic to the odds of individuals who lack this characteristic.
RR and OR are the most common measures of comparative risk in epidemiological research. They provide a quantitative assessment of the magnitude of the association between a exposure variable and the outcome that usually is a disease status. RR can be computed directly in prospective studies and OR can be computed both in prospective and retrospective studies. It has been demonstrated that the exposure OR in cases versus controls equals the disease OR for exposed versus unexposed. This OR approximates the ratio of proportions of subjects who develops the disease in a specific period of time among exposed and unexposed, when the disease is rare.(5) Therefore, in absence of systematic bias, it would be valid to calculate OR from a case-control design as an approximation for RR. Moreover, in a incidence-density sampling, the OR approximates the ratio of instantaneous disease incidence rates, even without the assumption of rarity.(6)
Using ORINTA
ORINTA is a small software program that runs under Microsoft Windows and it is written in Visual Basic 4.0 - 16-bit.(7) It has an unique screen that correspond to the simple 2 X 2 contingency table used in prospective studies in epidemiological research. Both exposure and disease status are encoded as dichotomous variables. ORINTA computes the sum of the totals, for odds and the cumulative incidence rate for exposed and unexposed groups. It also presents a simple chi-square statistic with one degree of freedom together its p-value. The estimations of OR and RR are shown with their 95% confidence intervals which were computed with the methods of Woolf and Kaltz respectively.(8)
Students can use ORINTA interactively by moving the four scrolls that correspond to the four cells in the contingency table. Likewise, teachers could use ORINTA showing this screen to the whole class. When a cell is changed in the table, totals in rows and columns also change, and all statistics are recalculated instantaneously. Without any calculation by hand, the student can experiment by him or herself (or guided by the teacher) 1) The exposure OR in cases versus controls equals the disease OR for exposed versus unexposed 2) OR approximates the RR in prospective studies when the disease is rare 3) The asymmetry of the confidence intervals for OR and RR and 4) The effect of the sample size on the p-value of the chi-square statistic and confidence intervals.
As an example, the student could start with the table of cancer death and smoking history provided in the book of Kahn and Sempos (8) (page 68) (Figure 1). As death from cancer is a rare event, the point estimations of the OR and RR are quite similar (1.27 and 1.25 respectively).
Another example in the same book (page 67) Figure 2 provides a table for coronary heart disease status (not a rare event) and systolic blood pressure as an exposure factor. Here, the RR and OR differ in a greater magnitude.
The most interesting thing for students is that they can see with ORINTA how the estimations of OR and RR change from one example to another by moving the scrolls with the mouse without having to make calculations, allowing them to focus on the underlying concept. In fact, they can explore any situation and confirm the concepts previously aquired in class. From a statistical point of view, ORINTA, for example, could be used by the teacher to explain the asymmetry in the confidence intervals. Finally, it shows in an easy way how confidence intervals are narrower when the figures in the cell increases.
References
1. Appleton DR. What Do we Mean by a Statistical Model? Statistics in Medicine 1995; 14: 185 - 197.
2 Watts DG. Why Is Introductory Statistics Difficult to Learn? and What Can we Do to Make it Easier?. The American Statistician 1991; 45: 290 - 291.
3. Simpson JM. Teaching Statistics to Non- Specialist. Stat.Med. 1995; 14: 199 - 208.
4. Yilmaz MR. The Challenge of Teaching Statistics to Non-Specialist. J.Stat.Edu 1996; Vol. 4. Num. 1.
5. Greenland S, Thomas DC. On the need for the Rare Disease Assumption in Case- Control Studies. Am.J.Epidemiol. 1982; 116: 547 - 553.
6. Breslow EN. Statistics in Epidemiology: The Case-Control Study. J.Am.Stat.Assoc. 1996; 91: 14 - 28.
7. Microsoft Visual Basic Programming System for Windows. Programmer´s Guide. Version 4.0. Microsoft Corporation, 1995.
8. Kahn HA, Sempos CT. Statistical Methods in Epidemiology. New York: Oxford University Press, 1989.
Adress correspondence:
José Luis Santos Martín
Department of Nutritional Epidemiology.
Institute of Nutrition and Food Technology (INTA)
University of Chile.
Macul 5540
Comuna de Macul
Santiago, Chile.
Phone: (56 2) 678 14 54
Fax: (56 2) 221 40 30
Email: jsantos@uec.inta.uchile.cl