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Common measures and statistics in epidemiological literature

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The document provides an introduction to common measures and statistics used in epidemiological literature. It defines measures of frequency such as risk, rate, and prevalence which characterize the occurrence of health outcomes in a population. Risk ratios and odds ratios are presented as measures of the strength of association between an exposure and outcome. The null value in epidemiological studies is 1.0 for risk ratios, rate ratios, and odds ratios, representing no association. Confidence intervals are discussed as a measure of precision of an estimate. Crude and adjusted values are also explained as ways to account for confounding factors.

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Common Measures and Statistics in Epidemiological Literature Dr. Mohammed Jawad
Introduction • For the non-epidemiologist or non- statistician, understanding the statistical nomenclature presented in journal articles can sometimes be challenging, particularly since multiple terms are often used interchangeably, and still others are presented without definition. • This lecture will provide a basic introduction to the terminology commonly found in epidemiological literature.
Measures of frequency
Measures of frequency • Measures of frequency characterize the occurrence of health outcomes, disease, or death in a population. • These measures are descriptive in nature and indicate how likely one is to develop a health outcome in a specified population. • The three most common measures of health outcome or frequency are risk, rate, and prevalence.
Risk • Risk, also known as incidence, cumulative incidence, incidence proportion, or attack rate (although not really a rate at all) is a measure of the probability of an unaffected individual developing a specified health outcome over a given period of time. For a given period of time (i.e.: 1 month, 5 years, lifetime): • A 5-year risk of 0.10 indicates that an individual at risk has a 10% chance of developing the given health outcome over a 5-year period of time.
Risk ratio and rate ratio Risk ratios or rate ratios are commonly found in cohort studies and are defined as: the ratio of the risk in the exposed group to the risk in the unexposed group or the ratio of the rate in the exposed group to the rate in the unexposed group
Risk ratio and rate ratio • Risk ratios and rate ratios are measures of the strength of the association between the exposure and the outcome. • How is a risk ratio or rate ratio interpreted? • A risk ratio of 1.0 indicates there is no difference in risk between the exposed and unexposed group. • A risk ratio greater than 1.0 indicates a positive association, or increased risk for developing the health outcome in the exposed group. • A risk ratio of 1.5 indicates that the exposed group has 1.5 times the risk of having the outcome as compared to the unexposed group. • Rate ratios can be interpreted the same way but apply to rates rather than risks.
Risk ratio and rate ratio • A risk ratio or rate ratio of less than 1.0 indicates a negative association between the exposure and outcome in the exposed group compared to the unexposed group. • In this case, the exposure provides a protective effect. • For example, a rate ratio of 0.80 where the exposed group received a vaccination for Human Papillomavirus (HPV) indicates that the exposed group (those who received the vaccine) had 0.80 times the rate of HPV compared to those who were unexposed (did not receive the vaccine).
Risk ratio and rate ratio • One of the benefits the measure risk difference has over the risk ratio is that it provides the absolute difference in risk, information that is not provided by the ratio of the two. • A risk ratio of 2.0 can imply both a doubling of a very small or large risk, and one cannot determine which is the case unless the individual risks are presented.
Odds ratio Another measure of association is the odds ratio (OR). The formula for the OR is:
Odds ratio • The odds ratio is used in place of the risk ratio or rate ratio in case-control studies. • In this type of study, the underlying population at risk for developing the health outcome or disease cannot be determined because individuals are selected as either diseased or non-diseased or as having the health outcome or not having the health outcome. • An odds ratio may approximate the risk ratio or rate ratio in instances where the health outcome prevalence is low (less that 10%) and specific sampling techniques are utilized, otherwise there is a tendency for the OR to overestimate the risk ratio or rate ratio.
Odds ratio • The odds ratio is interpreted in the same manner as the risk ratio or rate ratio with an OR of 1.0 indicating no association, an OR greater than 1.0 indicating a positive association, and an OR less than 1.0 indicating a negative, or protective association.
The null value • The null value is a number corresponding to no effect, that is, no association between exposure and the health outcome. In epidemiology, the null value for a risk ratio or rate ratio is 1.0, and it is also 1.0 for odds ratios and prevalence ratios (terms you will come across). A risk ratio, rate ratio, odds ratio or prevalence ratio of 1.0 is obtained when, for a risk ratio for example, the risk of disease among the exposed is equal to the risk of disease among the unexposed.
The null value • Statistical testing focuses on the null hypothesis, which is a statement predicting that there will be no association between exposure and the health outcome (or between the assumed cause and its effect), i.e. that the risk ratio, rate ratio or odds ratio will equal 1.0. • If the data obtained from a study provide evidence against the null hypothesis, then this hypothesis can be rejected, and an alternative hypothesis becomes more probable.
The null value • For example, a null hypothesis would say that there is no association between children having cigarette smoking mothers and the incidence of asthma in those children. • If a study showed that there was a greater incidence of asthma among such children (compared with children of nonsmoking mothers), and that the risk ratio of asthma among children of smoking mothers was 2.5 with a 95% confidence interval of 1.7 to 4.0, we would reject the null hypothesis. • The alternative hypothesis could be expressed in two ways: 1) children of smoking mothers will have either a higher or lower incidence of asthma than other children, or 2) children of smoking mothers will only have a higher incidence of asthma.
The null value • The first alternative hypothesis involves what is called a "two-sided test" and is used when we simply have no basis for predicting in which direction from the null value exposure is likely to be associated with the health outcome, or, in other words, whether exposure is likely to be beneficial or harmful. • The second alternative hypothesis involves a "one-sided test" and is used when we have a reasonable basis to assume that exposure will only be harmful (or if we were studying a therapeutic agent, that it would only be beneficial).
Measures of significance
The p-value • The "p" value is an expression of the probability that the difference between the observed value and the null value has occurred by "chance", or more precisely, has occurred simply because of sampling variability. • The smaller the "p" value, the less likely the probability that sampling variability accounts for the difference.
The p- value • Typically, a "p" value less than 0.05, is used as the decision point, meaning that there is less than a 5% probability that the difference between the observed risk ratio, rate ratio, or odds ratio and 1.0 is due to sampling variability. • If the "p" value is less than 0.05, the observed risk ratio, rate ratio, or odds ratio is often said to be "statistically significant." However, the use of 0.05 as a cut-point is arbitrary.
The p- value • The exclusive use of "p" values for interpreting results of epidemiologic studies has been strongly discouraged in the more recent texts and literature because research on human health is not conducted to reach a decision point (a "go" or "no go" decision), but rather to obtain evidence that there is reason for concern about certain exposures or lifestyle practices or other factors that may adversely influence the health of the public.
The p- value • Statistical tests of significance, (such as p- values) were developed for industrial quality- control purposes, in order to make a decision whether the manufacture of some item is achieving acceptable quality. We are not making such decisions when we interpret the results of research on human health. • The lower bound of the 95% confidence interval is also often utilized to decide whether a point estimate is statistically significant, i.e. whether the measure of effect (e.g. the ratio 2.5 with a lower bound of 1.8) is statistically different than the null value of 1.0.
Measures of precision
Confidence interval • A confidence interval expresses the extent of potential variation in a point estimate (the mean value or risk ratio, rate ratio, or odds ratio). • This variation is attributable to the fact that our point estimate of the mean or risk ratio, rate ratio, or odds ratio is based on some sample of the population rather than on the entire population.
Confidence interval • For example, from a clinical trial, we might conclude that a new treatment for high blood pressure is 2.5 times as effective as the standard treatment, with a 95% confidence interval of 1.8 to 3.5. • 2.5 is the point estimate we obtain from this clinical trial. But not all subjects with high blood pressure can be included in any study, thus the estimate of effectiveness, 2.5, is based on a particular sample of people with high blood pressure.
Confidence interval • If we assume that we could draw other samples of persons from the same underlying population as the one from which subjects were obtained for this study, we will obtain a set of point estimates, not all of which would be exactly 2.5. Some samples would be likely to show an effectiveness less than 2.5, and some greater than 2.5. • The 95% CI is an interval that would contain the true, real (population) parameter value 95% of the time if you repeated the experiment/study. • So if we were to repeat the experiment/study, 95 out of 100 intervals would give an interval that contains the true risk ratio, rate ratio or odds ratio value.
Confidence interval • Remember, that you can only interpret the CI in relation to talking about repeated sampling. • Thus we can also say that the new treatment for high blood pressure is 2.5 times as effective as the standard treatment, but this measure could range from a low of 1.8 to a high of 3.5.
Confidence interval • The confidence interval also provides information about how precise an estimate is. • The tighter, or narrower, the confidence interval, the more precise the estimate. • Typically, larger sample sizes will provide a more precise estimate. • Estimates with wide confidence intervals should be interpreted with caution.
Other terms
Crude and adjusted values • There are often two types of estimates presented in research articles, crude and adjusted values. • Crude estimates refer to simple measures that do not account for other factors that may be driving the estimate. • For instance, a crude death rate would simply be the number of deaths in a calendar year divided by the average population for that year. • This may be an appropriate measure in certain circumstances but could become problematic if you want to compare two or more populations that vary on specific factors known to contribute to the death rate.
Crude and adjusted values • For example, you may want to compare the death rate for two populations, one of which is located in a high air pollution area, to determine if air pollution levels affect the death rate. • The high air pollution population may have a higher death rate, but you also determine that it is a much older population. As older individuals are more likely to die, age may be driving the death rate rather than the pollution level.
Crude and adjusted values • To account for the difference in age distribution of the populations, one would want to calculate an adjusted death rate that adjusts for the age structure of the two groups. • This would remove the effect of age from the effect of air pollution on mortality.
Crude and adjusted values • Adjusted estimates are a means of controlling for confounders or accounting for effect modifiers in analyses. Some factors that are commonly adjusted for include gender, race, socioeconomic status, smoking status, and family history.
Practice Questions 1. Based on the following table, calculate the requested measures. Also provide the definition for each measure in one sentence. a. The risk ratio comparing the exposed and the unexposed study participants b. The risk difference between the exposed and the unexposed study participants c. The prevalence of the disease among the entire study sample, assuming the disease is a long-term, chronic disease with no cure and assuming no study participants have died.
Common measures and statistics in epidemiological literature
Practice Questions 2. Interpret the following risk ratios in words. a. A risk ratio= 1.0 in a study where researchers examined the association between consuming a certain herbal supplement (the exposure) and developing arthritis. b. A risk ratio= 2.6 in a study where researchers examined the association between ever having texted while driving (the exposure) and being in a car accident. c. A risk ratio = 0.75 in a study where researchers examined the association between ≥ 30 minutes of daily exercise (the exposure) and heart disease.
References Alexander LK, Lopes B, Ricchetti-Masterson K, Yeatts KB. Common Measures and Statistics in Epidemiological Literature. Epidemiologic Research and Information Center (ERIC) Notebook. Second Edition. 2015.

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Common measures and statistics in epidemiological literature

  • 1. Common Measures and Statistics in Epidemiological Literature Dr. Mohammed Jawad
  • 2. Introduction • For the non-epidemiologist or non- statistician, understanding the statistical nomenclature presented in journal articles can sometimes be challenging, particularly since multiple terms are often used interchangeably, and still others are presented without definition. • This lecture will provide a basic introduction to the terminology commonly found in epidemiological literature.
  • 4. Measures of frequency • Measures of frequency characterize the occurrence of health outcomes, disease, or death in a population. • These measures are descriptive in nature and indicate how likely one is to develop a health outcome in a specified population. • The three most common measures of health outcome or frequency are risk, rate, and prevalence.
  • 5. Risk • Risk, also known as incidence, cumulative incidence, incidence proportion, or attack rate (although not really a rate at all) is a measure of the probability of an unaffected individual developing a specified health outcome over a given period of time. For a given period of time (i.e.: 1 month, 5 years, lifetime): • A 5-year risk of 0.10 indicates that an individual at risk has a 10% chance of developing the given health outcome over a 5-year period of time.
  • 6. Risk ratio and rate ratio Risk ratios or rate ratios are commonly found in cohort studies and are defined as: the ratio of the risk in the exposed group to the risk in the unexposed group or the ratio of the rate in the exposed group to the rate in the unexposed group
  • 7. Risk ratio and rate ratio • Risk ratios and rate ratios are measures of the strength of the association between the exposure and the outcome. • How is a risk ratio or rate ratio interpreted? • A risk ratio of 1.0 indicates there is no difference in risk between the exposed and unexposed group. • A risk ratio greater than 1.0 indicates a positive association, or increased risk for developing the health outcome in the exposed group. • A risk ratio of 1.5 indicates that the exposed group has 1.5 times the risk of having the outcome as compared to the unexposed group. • Rate ratios can be interpreted the same way but apply to rates rather than risks.
  • 8. Risk ratio and rate ratio • A risk ratio or rate ratio of less than 1.0 indicates a negative association between the exposure and outcome in the exposed group compared to the unexposed group. • In this case, the exposure provides a protective effect. • For example, a rate ratio of 0.80 where the exposed group received a vaccination for Human Papillomavirus (HPV) indicates that the exposed group (those who received the vaccine) had 0.80 times the rate of HPV compared to those who were unexposed (did not receive the vaccine).
  • 9. Risk ratio and rate ratio • One of the benefits the measure risk difference has over the risk ratio is that it provides the absolute difference in risk, information that is not provided by the ratio of the two. • A risk ratio of 2.0 can imply both a doubling of a very small or large risk, and one cannot determine which is the case unless the individual risks are presented.
  • 10. Odds ratio Another measure of association is the odds ratio (OR). The formula for the OR is:
  • 11. Odds ratio • The odds ratio is used in place of the risk ratio or rate ratio in case-control studies. • In this type of study, the underlying population at risk for developing the health outcome or disease cannot be determined because individuals are selected as either diseased or non-diseased or as having the health outcome or not having the health outcome. • An odds ratio may approximate the risk ratio or rate ratio in instances where the health outcome prevalence is low (less that 10%) and specific sampling techniques are utilized, otherwise there is a tendency for the OR to overestimate the risk ratio or rate ratio.
  • 12. Odds ratio • The odds ratio is interpreted in the same manner as the risk ratio or rate ratio with an OR of 1.0 indicating no association, an OR greater than 1.0 indicating a positive association, and an OR less than 1.0 indicating a negative, or protective association.
  • 13. The null value • The null value is a number corresponding to no effect, that is, no association between exposure and the health outcome. In epidemiology, the null value for a risk ratio or rate ratio is 1.0, and it is also 1.0 for odds ratios and prevalence ratios (terms you will come across). A risk ratio, rate ratio, odds ratio or prevalence ratio of 1.0 is obtained when, for a risk ratio for example, the risk of disease among the exposed is equal to the risk of disease among the unexposed.
  • 14. The null value • Statistical testing focuses on the null hypothesis, which is a statement predicting that there will be no association between exposure and the health outcome (or between the assumed cause and its effect), i.e. that the risk ratio, rate ratio or odds ratio will equal 1.0. • If the data obtained from a study provide evidence against the null hypothesis, then this hypothesis can be rejected, and an alternative hypothesis becomes more probable.
  • 15. The null value • For example, a null hypothesis would say that there is no association between children having cigarette smoking mothers and the incidence of asthma in those children. • If a study showed that there was a greater incidence of asthma among such children (compared with children of nonsmoking mothers), and that the risk ratio of asthma among children of smoking mothers was 2.5 with a 95% confidence interval of 1.7 to 4.0, we would reject the null hypothesis. • The alternative hypothesis could be expressed in two ways: 1) children of smoking mothers will have either a higher or lower incidence of asthma than other children, or 2) children of smoking mothers will only have a higher incidence of asthma.
  • 16. The null value • The first alternative hypothesis involves what is called a "two-sided test" and is used when we simply have no basis for predicting in which direction from the null value exposure is likely to be associated with the health outcome, or, in other words, whether exposure is likely to be beneficial or harmful. • The second alternative hypothesis involves a "one-sided test" and is used when we have a reasonable basis to assume that exposure will only be harmful (or if we were studying a therapeutic agent, that it would only be beneficial).
  • 18. The p-value • The "p" value is an expression of the probability that the difference between the observed value and the null value has occurred by "chance", or more precisely, has occurred simply because of sampling variability. • The smaller the "p" value, the less likely the probability that sampling variability accounts for the difference.
  • 19. The p- value • Typically, a "p" value less than 0.05, is used as the decision point, meaning that there is less than a 5% probability that the difference between the observed risk ratio, rate ratio, or odds ratio and 1.0 is due to sampling variability. • If the "p" value is less than 0.05, the observed risk ratio, rate ratio, or odds ratio is often said to be "statistically significant." However, the use of 0.05 as a cut-point is arbitrary.
  • 20. The p- value • The exclusive use of "p" values for interpreting results of epidemiologic studies has been strongly discouraged in the more recent texts and literature because research on human health is not conducted to reach a decision point (a "go" or "no go" decision), but rather to obtain evidence that there is reason for concern about certain exposures or lifestyle practices or other factors that may adversely influence the health of the public.
  • 21. The p- value • Statistical tests of significance, (such as p- values) were developed for industrial quality- control purposes, in order to make a decision whether the manufacture of some item is achieving acceptable quality. We are not making such decisions when we interpret the results of research on human health. • The lower bound of the 95% confidence interval is also often utilized to decide whether a point estimate is statistically significant, i.e. whether the measure of effect (e.g. the ratio 2.5 with a lower bound of 1.8) is statistically different than the null value of 1.0.
  • 23. Confidence interval • A confidence interval expresses the extent of potential variation in a point estimate (the mean value or risk ratio, rate ratio, or odds ratio). • This variation is attributable to the fact that our point estimate of the mean or risk ratio, rate ratio, or odds ratio is based on some sample of the population rather than on the entire population.
  • 24. Confidence interval • For example, from a clinical trial, we might conclude that a new treatment for high blood pressure is 2.5 times as effective as the standard treatment, with a 95% confidence interval of 1.8 to 3.5. • 2.5 is the point estimate we obtain from this clinical trial. But not all subjects with high blood pressure can be included in any study, thus the estimate of effectiveness, 2.5, is based on a particular sample of people with high blood pressure.
  • 25. Confidence interval • If we assume that we could draw other samples of persons from the same underlying population as the one from which subjects were obtained for this study, we will obtain a set of point estimates, not all of which would be exactly 2.5. Some samples would be likely to show an effectiveness less than 2.5, and some greater than 2.5. • The 95% CI is an interval that would contain the true, real (population) parameter value 95% of the time if you repeated the experiment/study. • So if we were to repeat the experiment/study, 95 out of 100 intervals would give an interval that contains the true risk ratio, rate ratio or odds ratio value.
  • 26. Confidence interval • Remember, that you can only interpret the CI in relation to talking about repeated sampling. • Thus we can also say that the new treatment for high blood pressure is 2.5 times as effective as the standard treatment, but this measure could range from a low of 1.8 to a high of 3.5.
  • 27. Confidence interval • The confidence interval also provides information about how precise an estimate is. • The tighter, or narrower, the confidence interval, the more precise the estimate. • Typically, larger sample sizes will provide a more precise estimate. • Estimates with wide confidence intervals should be interpreted with caution.
  • 29. Crude and adjusted values • There are often two types of estimates presented in research articles, crude and adjusted values. • Crude estimates refer to simple measures that do not account for other factors that may be driving the estimate. • For instance, a crude death rate would simply be the number of deaths in a calendar year divided by the average population for that year. • This may be an appropriate measure in certain circumstances but could become problematic if you want to compare two or more populations that vary on specific factors known to contribute to the death rate.
  • 30. Crude and adjusted values • For example, you may want to compare the death rate for two populations, one of which is located in a high air pollution area, to determine if air pollution levels affect the death rate. • The high air pollution population may have a higher death rate, but you also determine that it is a much older population. As older individuals are more likely to die, age may be driving the death rate rather than the pollution level.
  • 31. Crude and adjusted values • To account for the difference in age distribution of the populations, one would want to calculate an adjusted death rate that adjusts for the age structure of the two groups. • This would remove the effect of age from the effect of air pollution on mortality.
  • 32. Crude and adjusted values • Adjusted estimates are a means of controlling for confounders or accounting for effect modifiers in analyses. Some factors that are commonly adjusted for include gender, race, socioeconomic status, smoking status, and family history.
  • 33. Practice Questions 1. Based on the following table, calculate the requested measures. Also provide the definition for each measure in one sentence. a. The risk ratio comparing the exposed and the unexposed study participants b. The risk difference between the exposed and the unexposed study participants c. The prevalence of the disease among the entire study sample, assuming the disease is a long-term, chronic disease with no cure and assuming no study participants have died.
  • 35. Practice Questions 2. Interpret the following risk ratios in words. a. A risk ratio= 1.0 in a study where researchers examined the association between consuming a certain herbal supplement (the exposure) and developing arthritis. b. A risk ratio= 2.6 in a study where researchers examined the association between ever having texted while driving (the exposure) and being in a car accident. c. A risk ratio = 0.75 in a study where researchers examined the association between ≥ 30 minutes of daily exercise (the exposure) and heart disease.
  • 36. References Alexander LK, Lopes B, Ricchetti-Masterson K, Yeatts KB. Common Measures and Statistics in Epidemiological Literature. Epidemiologic Research and Information Center (ERIC) Notebook. Second Edition. 2015.