The Use of Epidemiological Measures to Estimate the
Effects of Adverse Factors and Preventive Interventions
by
Lawrence S. Mayer
Good Samaritan Regional Medical Center, Phoenix ,
School of Hygiene and Public Health, Johns Hopkins University, and
Department of Economics, Arizona State University
Epidemiological studies conducted by researchers in medicine and public health may appear, at first blush, to be empirically based, statis-tic-ally analyzed, experimental and observational studies of the frequency of disease, injury or death. They do indeed fit this description but they have additional defining characteristics. Epidemiological studies are defined by their role in the testing of hypotheses regarding the mechanism of disease, injury or death. An epidem-io-logical study is a statistical study that focuses on testing a hypothesis that arises from the consideration of a disease process and must be designed in a manner that sheds light on that process. A study which characterizes the relative frequency of people with different color eyes and tests the hypothesis that the different colors occur with equal probability is not an epidemiological study unless eye color is being tested as a risk factor or outcome variable in a disease process.
Epidemiology studies are probably unique among statistical studies in the degree of attention given to choosing the dependent variable or outcome variable, as it is usually labeled in epidemiology. In epidem-iology, the outcome variable is almost always a rate related to the fre-quen-cy of disease, injury or death. The outcome variable adopted should be the vari-able that the experimenter consid-ers most likely to shed light on the hypothesis about the mechanism of disease, injury or death.
In epidemiology, the choice of the outcome variable (frequency of disease, injury or death) depends heavily on the mechanism hypoth-es-ized for the transmission of disease or the cause of injury or death.
Once a measure of the frequency of disease is chosen, a measure of effect must be chosen. This measure is used to summarize the difference between two populations (or among several populations). After the measure of the frequency of disease, the measure of effect is the next most critical choice in designing, running and interpreting an epidemiological study. For example in looking at the effects of radiation on workers at a nuclear plant, we might use the risk of death from cancer as the measure of the frequency of death. To compare nuclear workers to workers in another plant in the same community we might use the risk ratio, the measure of effect.
Once the measure of the rate of disease/injury/death and a measure of effect are selected, the data collection, whether experimental or observational, can be structured. The design of an epidemiological study must provide a test of the difference between two or more populations with regard to the chosen measure of effect applied to the chosen measure of the frequency of disease.
In this paper I discuss the problem of measuring the rate of bird mortality for Wind Resource Areas and the effect of the wind resource development on the risk of death for members of a particular species of bird. I comment on the problems of designing data collec-tion efforts that estimate and test the effects of the wind resource development or pre-ven-tive interventions on the rate of mortality. I close with a discus-sion and some comments on the implications of epidemiology for the study of avian mortality.
2. Measuring the Frequency of Disease, Injury or Death
Epidemiological studies are central to the study of the welfare of human populations. They are statistical studies that analyze the fre-quen-cy of disease, injury or death (usually abbreviated as the frequency of disease) in order to make statistical inferences about the process under-lying the disease, the etiology of the disease, or the causal path involved in the occurrence of the disease (Lilienfeld and Lilienfeld 1980; Klein-baum et al. 1982; Rothman 1986; Hennekens and Buring 1987; Kahn and Sempos 1989).
Statistically, the purposes of epidemiologic studies are to character-ize the frequency of disease, injury or death for a population and to test the impact of potentially adverse exposures or preventive interventions on the frequency. The guiding principles are descrip-tion and hypothesis testing.
The starting point for any epidemiological study is to quantify the frequency of disease. The simplest measure of disease frequency is the count of newly affected individuals or the count of all affected individuals. But count data by themselves have limited value in epidemiological studies. To investigate the distribution and determinants of the frequency of disease, the raw measures must be expressed as relative measures or ratios. Such expressions are called standardizations or rates; I prefer the latter term. Results expressed as rates allow comparison of two or more populations with regard to the frequency of disease. The differences among rates for these populations are the basis for epidemiological inferences about the process that underlies the disease.
Care is required in defining a rate suitable for use as a measure of disease frequency. Consider a simple hypothetical example. Suppose City A has 100 new cases of Tuberculosis while city B has 50. The statement, "City A has twice the frequency of Tuberculosis as City B" is true but may not be important as a scientific statement because it fails to control for the population sizes of the cities. Suppose City A has 100,000 residents and City B has 25,000. The ratio of the number of new cases to the population size, which is referred to as the incidence or incidence rate of the disease, is a standardized measure of disease fre-quency. The incidence for City A is 0.001 and for City B it is 0.002. Thus, while City A has more new cases, after controlling for the size of the city, City B has twice the incidence of Tuberculosis.
Suppose we learn that the count for City A is for two years and the count for City B is for one year. To compare the two cities we might adjust for both the size of city and the length of the reporting period. The annual incidence rate for City A is 0.0005 and for City B it is 0.002. Con-trol-ling for city size and reporting time, City B has four times the annual incidence rate of Tuberculosis.
These comparisons, while better than the comparison of the raw counts, are only sound if the standardization is appropriate on theoretical grounds. The standardization is only appropriate if it gives insights into the transmission, cause, or course of Tuberculosis.
This type of measure of disease frequency, a rate defined by the size of the population or by the person-years covered, is the most commonly used in epidemiology. It works well for chronic disease morbidity or mortality but may not work well for injury or death.
Suppose we knew that only a small fraction of the population of each city was at risk for contracting Tuberculosis and then only while doing certain activities. We might want to standardize the comparison of disease frequency by using rates standardized by the person-hours of exposure at these activities. We might hypothesize that this standardiz-a-tion or rate would give us more insight into the disease process. This type of standardization is not feasible with most chronic diseases but does point out the importance of considering that a rate is only as good as its denominator. A good epidemiological study considers the denomin-ator of the rate of disease as closely as it considers the numerator.
Turning to the problem of defining rates for studies of mortality, suppose we want to compare two types of aircraft, the Boeing 747 and the Beaver 36, a 19 passenger prop-driven commuter aircraft, in terms of risk of death. We could count the deaths that have occurred in a given year in each type of aircraft. Suppose that 1000 people died in Boeing 747 accidents and 500 died in Beaver 36 accidents. (Note: All such numbers are artificial.) We could state that the 747 has twice the frequency of deaths of the Beaver 36, but the statement would have little meaning because we have not standardized the counts. We could standardize the death counts in a variety of ways. The denominator might be the number of aircraft of each type; the number of passengers flown by each type of aircraft in a given year; or the number of passenger miles flown by each type in a given year. We might also standardize by the difficulty of the types of flights undertaken by each type of aircraft.
The best choice for the denominator depends on the purpose of the study. If the study is designed to test hypotheses about the relative safety of traveling on different types of equipment, then the natural denominator might be the number of passengers carried or the number of passenger miles. If it is to analyze the risk for pilots then it might be reasonable to standardize by the number of flights. If it is to estimate the actuarial risk of piloting the aircraft then it might reasonable to standardize by the hours of flight. In any case the appropriate standard-iza-tion is obtained from theoretical analysis of the process of death under consideration.
Suppose the Boeing 747 fleet carried 10,000,000 passengers in a year while the Beaver 36 carried 100,000 passengers. Then the annual mortality rate for the Boeing 747 is 1000/10,000,000 or 1 death per 10,000 passengers or 0.0001 while the annual mortality rate for the Beaver 36 is 500/100,000 or 5 deaths per 1000 passengers or 0.005. Using the rate of death per passenger, the mortality rate is 50 times greater on the Beaver 36.
But suppose the Boeing 747 fleet covered 10,000,000,000 passenger miles in the year while the Beaver 36 fleet covered 10,000,000 passenger miles. On a passenger mile basis, the mortality rate for the 747 would be 1000/10,000,000,000 or 1 death per 10,000,000 passenger miles or 0.0000001, while for the Beaver 36 it would be 500/10,000,000 or 500 deaths per 10,000,000 passenger miles or 0.00005. Based on the rate of death per passenger mile, the mortality rate is 500 times greater on the Beaver 36.
The choice between these two measures is a matter of debate. Both are widely used in epidemiology. But in some epidemiological contexts other types of disease frequency seem more natural than either of these measures.
For example, suppose the purpose of the study of death per aircraft is to focus on the major risk to the aircraft and its passengers, the risk of take-off and landing. In order to compare the Boeing 747 to the Beaver 36, the rate of death per take-off (or landing) could be used. Suppose the 747 fleet makes 20,000 take-offs per year and the Beaver 36 fleet makes 40,000 take-offs per year (it often carries no passengers on take-off). Then the mortality rate for the Boeing 747 is 1000/20,000 or 1 death per 20 take-offs or 0.0001 while the mortality rate for the Beaver 36 is 500/40,000 or 1 death per 80 take-offs or 0.00005. Using deaths per take-off, the mortality rate is four times greater on the Boeing 747.
Note that the mortality rate for the Beaver 36 is 500 or 50 or 0.25 times the mortality rate for the Boeing 747 depending on the standardiza-tion of the frequency of disease. The issue of which type of aircraft is safer can only be answered relative to a selected measure of mortality rate, which in turn depends on the hypothesis under study.
The effect of standardization is that it makes two or more popula-tions comparable except for the hypothesis under study. We never believe the two populations are identical but we try to ensure that they are similar enough, given the standardization, to allow unbiased assessment of the hypothesis under consideration.
Clearly standardization has limits. For example, the safest way to travel, per passenger mile, is by elevator. However, no type of standardization provides a reasonable basis for comparison of the safety of elevators and the safety of aircraft. The underlying processes are simply too dissimilar.
The best measure is the one that comes closest to the causal process while still being feasible. For example, in comparing the adverse health impacts of drinking water in two cities, we could measure the rate of disease associated with drinking water and then divide it by the number of residents in each city, or divide it by the number of children in the city if the disease predominantly affects children, or by the total number of glasses of water drunk by children in a year. The choice of the best denominator for the mortality rate is a scientific choice, not a statistical choice. Statistically, no one choice is preferable to another. The choice arises from the preliminary understanding of the process of disease, injury or death, an understanding that must be developed before definitive statistical research can be done.
Turning to the occupational setting, additional issues of standard-iza-tion arise (Check-oway et al. 1989). Work-related injuries and accidental deaths are difficult frequencies to standardize. Consider Plant A in which workers cut hardwood boards with a potentially dangerous machine, a large circular saw. Suppose that there were 10 significant accidents (serious cuts or amputations) in a given year and that the 100 workers in the plant work 20,000 days in the year. The injury rate is 1 per 10 workers or 1 per 2000 days worked.
Suppose Plant B has 100 workers who also worked 20,000 days cutting hardwood boards with the same type of circular saw with an additional safety shield attached. Suppose they had 20 accidents for a rate of 2 per 10 workers or 2 per 2000 days worked. By either measure Plant B has twice the injury rate of Plant A. The safety shield does not appear to protect the workers from serious injury.
But before we conclude that the safety shield fails we might want to isolate the actual risk behavior, cutting the boards. Suppose we learn that in Plant A the average worker cuts 500 boards a day but that in Plant B the average worker, in part because of the added margin of safety from the shield, cuts 2000 boards a day. Then the rate of significant accidents per board cut in Plant A is twice the risk in Plant B.
The chosen measure of the rate of serious accidents dramatically affects the comparison the two plants. Which plant is safer? It depends on how you measure the rate of injury.
In most epidemiological studies the choice of the measure-ment of disease frequency has a stronger impact on the analysis then does the difference between the populations being studied. In other words, the treatment effect usually is small compared to the variability that would arise from allowing alternative measures of disease frequency.
3. Applying these Measures to Avian Mortality
Suppose we want to estimate the frequency of death for Platinum Eagles in a given Wind Resource Area. And suppose we can count the number of deaths of Platinum Eagles in the area in the year. One standardized measure of the frequency of death is the number of deaths divided by the total number of birds that live in the area. Suppose there are 100 deaths and 1000 birds. Then the mortality rate can be expressed as 100/1000 or 1 death per 10 birds or 0.1.
Suppose we decide to compare the Wind Resource area to another area, the Control Area. Suppose the Control Area has about the same size and terrain as the Wind Resource Area and supports the same number of Platinum Eagles. Suppose this area has 50 deaths and thus a mortality rate of 50/1000 or 1 death per 20 birds or 0.05. For this measure of the frequency of death, the Wind Resource has twice the mortality per Platinum Eagle. But is the comparison appropriate? It depends on the purpose of the study.
Suppose the Wind Resource Area has a better prey base for Plat-inum Eagles than does the Control Area, and consequently has a higher utilization intensity than the Control Area. Suppose that, on the average, an eagle entering the Wind Resource area spends eight hours per day, but that, on average, an eagle entering the Control Area spends only two hours per day. Then the Control Area has twice the rate of mortality per eagle hour as does the Wind Resource Area. The Wind Resource Area has a higher frequency of death but a lower mortality rate per bird hour of usage. In this example, an apparent contradiction is explained by the fact that the development of the Wind Resource Area changes the utilization intensity.
4. Testing the Effect of External Factors on Avian Mortality
The measure of disease frequency, once chosen, is used to describe the distribution of disease in the population. Epidemiology focuses attention on description of the distribution of disease because this distribution may give insight into the cause or transmission of the disease. For example, the fact that Tuberculosis rates are highest among HIV patients, the homeless, Hispanic Americans, detention officers, and health care workers may give insight into the cause of the recent sharp increase in the incidence rate of Tuberculosis.
The second use of the measure of disease frequency is in a designed experiment or observational study that tests the effect of a potentially adverse exposure or a preventive or therapeutic intervention on the rate of disease or injury or death. For this use a second type of measure, the measure of effect, is used in conjunction with the measure of disease frequency. The measure of effect indicates the impact of an external factor on the measure of disease frequency. These external factors are usually potentially adverse exposures, such as exposure to a contagious disease or exposure to a toxin; or an intervention (preventive or thera-peutic), such as a vaccine to prevent childhood disease or a medication to reduce the impact of hepatitis C on the liver.
In the case of avian mortality the external factor could be the presence of wind tur-bines, which could be considered a potentially adverse exposure; or the removal of all perches from the turbines, which could be considered a preventive intervention.
The ideal situation for testing the effect of an external factor is to find or construct two populations that are comparable on all key parameters except that one population, the expos-ed, is influenced by the external factor of interest. The other population, the control, is known not to be influenced by the external factor. Often the experimental population serves as its own control. We compare the population before and after an intervention as if they were two different populations. This is a powerful design provided the potential confounding variables do not change over time. We compare the two popula-tions with regard to the chosen measure of the frequency of death. If they differ significantly we conclude that the external factor contributes to the death of the species.
Suppose we consider the wind turbines as a potentially adverse exposure and want to the test the hypothesis that they contribute to the death of Platinum Eagles. Suppose we can locate a Wind Resource Area, called Area A, that supports a population of Platinum Eagles, and a similar area, Area B, that resembles Area A on several critical parameters and supports a similar population of Platinum Eagles.
As a measure of the frequency of death, the rates given above the number of deaths per bird per year or the number of deaths per bird per hour of utilization per year can be used. Or, by analogy to the example of two plants that cut boards, if the behavior at issue is crossing the planes of the blades, then we could measure the rate of death per crossing of these planes.
Ideally, we might record every bird flight in Area A that cuts through the plane of an operating turbine blade and every flight in Area B that cuts through an equivalent plane. We might choose to measure the frequency of death in terms of "deaths per bird passing through these critical planes". This rate is a third measure of the frequency of death and is an alternative to the two given above.
Suppose that 100 Platinum Eagles die passing through the critical plane in Area A and that 1 Platinum Eagle dies during equivalent flights in Area B. Furthermore, suppose that Area A has 10,000 critical pass-ings but that Area B has 20,000 critical passings. The mortality rate for Area A is 100 out of 10,000 or 1 death per 100 critical bird passings or 0.01 and the mortality rate for area B is 1 out of 2000 or 5 deaths per 10,000 or 0.0005.
Regardless of the measure of the frequency of death chosen, a measure of the size of effect must be chosen if the two populations are to be compared. The choice of the measure of effect is independent of the choice of the measure of the frequency of death.
The oldest measure of effect is the risk difference, which is the difference in mortality rates. Using the mortality rate defined by the number of deaths per passing through the critical planes, the risk difference is 1 out of a hundred minus 5 out of a 10,000 which is 95 out of 10,000. The risk of death while passing through the planes of the blades is increased by 95 out of 10,000. This difference could be tested for statistical significance.
If the difference is significantly greater than zero, we conclude that the presence of the turbines increases the risk of death per passing through a critical plane, and thus within the Wind Resource Area generally. The next task is to hypothesize a mechanism of death, blunt trauma perhaps, and design an experiment to test the mechanism.
A more common measure of effect is the risk ratio or the relative risk, which is the ratio of the mortality rates, 0.01 divided by 0.0005 or 20. The relative risk of death is 20 times higher if a randomly chosen bird on a randomly chosen critical passing is in the Wind Resource Area vs. the Control Area.
For diagnostic purposes, the relative risk has proved useful. It focuses on the relative increased risk, which is valuable in determining the diagnosis or cause of death for an individual patient. It allows the clinician to update his or her degree of suspicion of a certain diagnosis or cause of death.
5. Attributable Risks and Prevented Fractions
In public health we are concerned with the implications of disease, injury or death for an entire population, not just the individual at risk. Thus we use different measures of effect.
For public health purposes a measure of effect that has proved very useful is the attributable risk. It combines the relative risk with the likelihood that a given individual is exposed to the external factor. It is the proportional increase in the risk of disease, injury or death assignable, or attributable to the external factor.
Let P(D), P(D E) and P(D E) be the probabilities of death for the entire population, the probability of death for the exposed population, and the probability of death for the unexposed population, respectively. For exposure E, the attributable risk is
AR(E) = [ P(D) - P(D | E) ] / P(D)
For example, suppose that, for a Platinum Eagle living in the general vicinity of the Wind Resource Area, the probability of flying through the plane of the blades during the year is 1 out of 10 or 0.1. The probability that a randomly chosen Platinum Eagle dies is 0.1 x 0.01 + 0.9 x 0.0005 = 0.01045. The probability that a Platinum Eagle in the control area dies crossing the theoretical blade plane without the presence of blades is 0.0005. The attributable risk is ( 0.01045 - 0.0005) / 0.01045 = 0.95. About 95 percent of the risk of dying while crossing the blade plane is attributable to the presence of the turbine. This large percentage makes sense as it is rather unlikely that the bird would die while crossing the critical plane if there are no blades present.
It could be argued that it is this large attributable risk that gives conservatio-ists, regulators and the public concern, even if the number of bird deaths is relatively small.
Note that the relative risk treats doubling the count as doubling the risk regardless of the size of the risk. The attributable risk tends to down-play small risks because they are less critical for the health of the population.
Turning to testing a preventive, or therapeutic, intervention, the same issues arise. The risk difference can be used to compare two populations, as can the risk ratio. Suppose we removed the perches from one-tenth of the turbines in a Wind Resource Area and decided to use deaths per bird as a measure of mortality. Suppose that 1000 Platinum Eagles live in the Wind Resource area and 200 of them live in the area where the perches were removed. Suppose that 100 Platinum Eagles die in a year and that 10 of them died in the area of the turbines without perches.
The mortality rate for the birds living around the turbines with perches is 90 out of 800 or about 1 out of 10 or 0.1. The mortality rate for the birds living around turbines without perches is 10 out of 200 or 0.05. The risk difference is 0.05 and the risk ratio is two. Removing the perches appears to reduce the risk of death by cutting a small risk in half.
For a second measure of effect, the attributable risk can be adapted for the case of a preventive intervention by defining the preventable fraction as the proportion of the cases that would be removed if all individuals got the preventive intervention (in our avian example, if all perches were removed).
The preventable fraction is defined by considering the preventive intervention as removing the adverse exposure (in the avian example, perches) and then calculating the attributable risk. For intervention I, the preventable fraction is
PLF(I) = [ P(D) - P(D | I) ] / P(D)
where P(D) and P(D I) are the probability of disease/injury/death and that probability given the intervention.
For the Platinum Eagles in the Wind Resource Area the mortality rate for the pop-u-la-tion is 100 out of 1000 or 1 out of 10 or 0.1. For those living in the area without perches the mortality rate is 10 out of 200 or 0.05. The preventable fraction is 0.05 / 0.1 = 0.5. About 50 percent of the risk would be removed if all perches were removed.
A third measure of effect is the prevented fraction, which is the actual reduction in mortality that has occurred from the preventive intervention as implemented. For intervention I, the prevented fraction is
PF(I) = [ P(D | I) - P(D) ] / P(D | I)
where P(D) and P(D| I) are, respectively, the probability of disease/injury/death in the population and the probability of disease in the absence of the intervention.
For the Platinum Eagles in the Wind Resource Area, the mortality rate for the popula-tion is 100 out of 1000 or 1 out of 10 or 0.1 and for those living in the area with perches it is 90 out of 800 or 0.1125. The prevented fraction is 0.0125 / 0.1125 = 0.11. About 11 percent of the risk of death has been removed by removing 10 percent of the perches.
These three measures of effect, the attributable risk, the preventable fraction and the prevented fraction, remove emphasis from the risk to individual and place emphasis on the risk to the population.
6. Estimating Mortality From Data
Ideally the contribution of the wind turbines to mortality of Platinum Eagles might be assessed by comparing the Wind Resource Area and a similar Control Area in terms of the risk of death to a Platinum Eagle flying through the plane of the blades. In practical terms several problems arise in trying to make this comparison.
We cannot match the Wind Resource Area and a Control Area as regards all potential confounders. Confounders are differences between the areas that, if not controlled, reduce the validity of comparisons of the mortality rates. In practice, we match the areas on the most critical confounders, statistically control for other major confounders by using methods such as blocking, stratification or analysis of covariance. We assign the lesser confounders to the statistical error term.
Once we match the Wind Resource Area and a Control Area, the second problem is to choose a measure of the mortality rate. It is practically impossible to record each time a Platinum Eagle crosses the plane of a turbine blade. There is no simple technology available for making this measurement. The cost would be prohibitive. So we have two courses. We can revert to defining the mortality rate as the number of deaths divided by the population size. Or we can try to choose a surrogate variable for the number of crossings of the planes of the blades. A surrogate variable is defined as a variable that can replace the outcome variable in a statistical study without significant loss in the validity or power of the study. For example, polyps in the colon are often used as a surrogate for colon cancer in studies of preventive interventions such as a high fibre diet. One possible surrogate in the eagle/wind power study would be number of hours of utilization of the two areas by the Platinum Eagles. The mortality rate would be the number of deaths per hour of utilization.
Utilization is a rough indicator of the level of at-risk behavior. If we adopt a measure of utilization, we are implicitly assuming that the higher the utilization the higher the level of at-risk behavior.
Suppose the measure of mortality used is the number of deaths per unit of utilization. One anomalous result may arise. The risk to the birds as measured by mortality rate may be lowered by wind resource develop-ment while the frequency of death actually increases. For example, suppose the development of the Wind Resource Area increases the food supply or the number of premium perches for the eagles. Suppose these changes quadruple the utilization rate of the Area and double the frequency of death. The mortality rate would be halved even though the raw number of deaths is doubled. This calculation helps clarify the distinction between the frequency of death and the mortality.
Once a mortality rate is chosen, a measure of effect must be chosen. This measure could be the risk ratio, as used in most clinical trials, or one of the public health measures such as the attributable risk.
The use of the attributable risk implies that the importance of the risk is going to be weighted by the absolute size of the risk. The risk ratio ignores the absolute size of the risk. Whether the absolute size of the risk should be embraced or ignored should be a matter of debate among experts on avian behavior and wind resource development. Again, the choice between the measures of effect may shape the results of the entire epidemiological study.
Having chosen two or more areas to compare, a mortality rate that measures the frequency of death, and a measure of effect, we must design the experiment or data collec-tion effort.
The most obvious experimental design is to compare two areas, the Wind Resource Area and a Control Area, that are virtually identical in all major con-found-ing variables except for the presence of the wind resource development. This design is covered in any standard text on statistical methods.
A second common design is the standard single population before-and-after design. In this design the mortality rate is measured before and after an adverse affect is implemented. The Resource Area observed before the development of the wind resource is used as the Control Area. The effect of wind power development on the mortality of Platinum Eagles for the Wind Resource Area could be assessed by measuring the mortality rate before developing the area and then measured after development. The measure of effect would be used to calculate the effect of the presence of the turbines on mortality. In order to be valid study several key assumptions must be made. Most importantly, the before-and-after comparison assumes that the study area is the same, aside from the presence of the wind development, during the before and after periods. This design can be confounded (biased) by failure to control for changes in external factors such as weather, prey bases, availability of water, or natural fluctuations in the underlying population. The study may be invalid if one year has a drought and the next has record rainfall.
Two additional designs, which are rather unique to epidemiology, are worth mentioning. In the case-controlled design, cases of death are sampled and then the population membership for each case is determined. Case-controlled designs are excellent for studies of mortality when the risk of death is small.
For a case-controlled study, dead Platinum Eagles might be sampled at random from two areas, the Wind Resource Area (Area A) and the Control Area (Area B). In addition, the number of Platinum Eagles living in each area would be estimated. The natural measure of disease/injury/death frequency for the case-controlled study is the odds of death (the prob-ability of dying divided by the probability of surviving) and the natural measure of effect is the odds ratio (the odds for Area A divided by the odds for Area B). With human popula-tions, case-controlled studies are the most practical way of testing hypotheses about the mechanism of death when death is rare. This may be a good design for assessing avian mortality.
Finally, proportional mortality studies might be helpful. Suppose that the sampling mechanism used to sample deaths from the Wind Resource Area and Control Area are almost identical but that both are quite incomplete. Suppose that necropsies could be used to determine the cause of death for each bird, with the pathologist being unaware of the area in which each bird died ("blind"). Better yet, the pathologist could be unaware of the entire nature of the study. We could examine the necropsies and classify each bird by cause of death, creating a distribution of death by cause. If the Wind Resource Area causes a large number of deaths by turbine strikes, then the Wind Resource Area should have a larger pro-por-tion of deaths from blunt trauma. Testing the equality of the death-by-cause distribu-tions in the two areas would give statistical insight into the hypothesis that the turbines, via blunt trauma, are responsible for a significant proportion of the deaths.
7. Comments and Discussion
In designing a study of the impact of a potentially adverse exposure or a preventive inter-vention on the risk of disease, injury or death, the first task is to isolate the hypothesis of mechanism that is being tested. The second task is to choose a measure of disease fre-quen-cy that best isolates the hypothesis being tested. The two components of this choice are to choose a disease count to use as a numerator and a base count to use as a denominator. The third task is to choose a measure of effect that uses the measure of disease frequency and isolates the hypothesis of interest. The fourth task is to design a study that compares two or more groups using the measure of effect applied to the measure of disease frequency chosen.
The logic is sequential and nested. Each choice depends on the choice made before.
In the case of avian mortality the first task is to isolate the process and hypothesis of interest. No single study can isolate both the impact of the development of the Wind Resource on the Platinum Eagle population and the physical risk of a turbine to an individual eagle traversing the plane of a turbine. The second task is to decide whether the hypothesis is most easily examined by the mortality rate as defined as death per bird, death per bird year, death per hour in the wind resource area, death per mile of flight, death per crossing of the planes of the turbines, or death per other suitable denominator. The third task is decide whether the relative risk, the attributable risk or another measure of effect should be used in comparing populations of Platinum Eagles living in different areas. The fourth task is to design a study that isolates the effect, controls for potential confounding factors, and allows a test of the critical hypothesis
For example our hypothesis might be that wind resource develop-ment increases the utilization of the Area and therefore increases the fre-quency of death but does so in such a way that the death per unit of utilization is not increased. We might design a before and after study to test whether the development increases the utilization rate and use a case-control study or proportional mortality study to estimate the risk of death from various causes including blunt trauma from the turbines.
If we see that the rate of utilization is increased by development and that the risk of death is also increased then we might ask if we can design and test preventive interventions that would reduce the death count without significantly reducing the utilization rate.
A final comment: If the underlying hypothesis is that there is an epidemic of death occurring in the Wind Resource area then the problem is epidemiological regardless of the fact that the deaths are non-human. Epidemiology is often applied to the study of disease among animals, but usually in an effort to learn about the disease among people. The study of AIDS related viruses in primates is a good example. The use of epidemiology to study the mortality of animal species is very exciting. Applying the principles of epidemiology may lead to a more clearly defined data collection effort where the relationships among the data, the hypothesis, the measure of disease frequency, the measure of effect, the disease process, and alternative policies are isolated before any analysis is attempted.
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There were several questions and comments about the most appropriate basis for stan-dard-ization. One attendee suggested that "birds/turbineˇyear" is questionable because large and small turbines may not be comparable. It was noted that the best measure will depend on identifying the behavior that places the birds at risk, and the hypothesis being tested. Several attendees suggested that researchers report results using a variety of potentially relevant measures, not just one of them. This could facilitate across-study comparisons and use of the data to address additional questions.
There was some discussion of the possibility of using "per kilowatt-hour", or some relat-ed measure, as a basis of standardization. One reason for doing so is that it would allow comparisons of risk across widely varying technologies for power generation.
