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Task 1 - CDD guidelines for plotting and interpreting public health data
One health (VET392)
Murdoch University
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Principles of Epidemiology in Public Health Practice, Third
Edition
An Introduction to Applied Epidemiology and Biostatistics
Lesson 4: Displaying Public Health Data
Section 3: Graphs
A graph (used here interchangeably with chart) displays numeric data in visual form. It can display patterns, trends, aberrations, similarities, and differences in the data that may not be evident in tables. As such, a graph can be an essential tool for analyzing and trying to make sense of data. In addition, a graph is often an effective way to present data to others less familiar with the data.
When designing graphs, the guidelines for categorizing data for tables also apply. In addition, some best practices for graphics include: Ensure that a graphic can stand alone by clear labeling of title, source, axes, scales, and legends; Clearly identify variables portrayed (legends or keys), including units of measure; Minimize number of lines on a graph; Generally, portray frequency on the vertical scale, starting at zero, and classification variable on horizontal scale; Ensure that scales for each axis are appropriate for data presented; Define any abbreviations or symbols; and Specify any data excluded.
In epidemiology, most graphs have two scales or axes, one horizontal and one vertical, that intersect at a right angle. The horizontal axis is known as the x-axis and generally shows values of the independent (or x) variable, such as time or age group. The vertical axis is the y-axis and shows the dependent (or y) variable, which, in epidemiology, is usually a frequency measure such as number of cases or rate of disease. Each axis should be labeled to show what it represents (both the name of the variable and the units in which it is measured) and marked by a scale of measurement along the line.
“Charts.. fulfill certain basic objectives: they should be: (1) accurate representations of the facts, (2) clear, easily read, and understood, and (3) so designed and constructed as to attract and hold attention.”( 12 )
— CF Schmid and SE Schmid
“Make the data stand out. Avoid superfluity.”( 13 )
— WS Cleveland
YearYear CasesCases
1950 319,
1951 530,
1952 683,
1953 449,
1954 683,
1955 555,
1956 612,
1957 487,
YearYear CasesCases
1970 47,
1971 75,
1972 32,
1973 26,
1974 22,
1975 24,
1976 41,
1977 57,
YearYear CasesCases
1990 27,
1991 9,
1992 2,
1993 312
1994 963
1995 309
1996 508
1997 138
In constructing a useful graph, the guidelines for categorizing data for tables by types of data also apply. For example, the number of reported measles cases by year of report is technically a nominal variable, but because of the large number of cases when aggregated over the United States, we can treat this variable as a continuous one. As such, a line graph is appropriate to display these data.
Try It: Plotting a Graph
Scenario:Scenario: Table 4 shows the number of measles cases by year of report from 1950 to 2003. The number of measles cases in years 1950 through 1954 has been plotted in Figure 4, below. The independent variable, years, is shown on the horizontal axis. The dependent variable, number of cases, is shown on the vertical axis. A grid is included in Figure 4 to illustrate how points are plotted. For example, to plot the point on the graph for the number of cases in 1953, draw a line up from 1953, and then draw a line from 449 cases to the right. The point where these lines intersect is the point for 1953 on the graph.
Your Turn:Your Turn: Use the data in Table 4 to plot the points for 1955 to 1959 and complete the graph in Figure 4.
Figure 4 Partial Graph of Measles by Year of Report — United States, 1950–1959Figure 4 Partial Graph of Measles by Year of Report — United States, 1950–
Image Description
Table 4 Number of Reported Measles Cases, by Year of Report — United States, 1950–2003Table 4 Number of Reported Measles Cases, by Year of Report — United States, 1950–
Image Description Source: Honein MA, Paulozzi LJ, Mathews TJ, Erickson JD, Wong L-Y. Impact of folic acid fortification of the US food supply on the occurrence of neural tube defects. JAMA 2001;285:2981–6. Figure 4 shows another example of an arithmetic-scale line graph. Here the y-axis is a calculated variable, median age at death of people born with Down’s syndrome from 1983–1997. Here also, we see the value of showing two data series on one graph; we can compare the mortality risk for males and females.
Figure 4 Median Age at Death of People withFigure 4 Median Age at Death of People with Down’s Syndrome by Sex — United States, 1983–Down’s Syndrome by Sex — United States, 1983– 19971997
Image Description Source: Yang Q, Rasmussen A, Friedman JM. Mortality associated with Down’s syndrome in the USA from 1983 to 1997: a population-based study. Lancet 2002;359:1019–25.
More About the X-axis and the Y-axis
When you create an arithmetic-scale line graph, you need to select a scale for the x- and y-axes. The scale should reflect both the data and the point of the graph. For example, if you use the data in Table 4 to graph the number of cases of measles cases by year from 1990 to 2002, then the scale of the x-axis will most likely be year of report, because that is how the data are available. Consider, however, if you had line-listed data with the actual dates of onset or report that spanned several years. You might prefer to plot these data by week, month, quarter, or even year, depending on the point you wish to make.
The following steps are recommended for creating a scale for the y-axis. Make the length of the y-axis shorter than the x-axis so that your graph is horizontal or “landscape.” A 5:3 ratio is often recommended for the length of the x-axis to y-axis. Always start the y-axis with 0. While this recommendation is not followed in all fields, it is the standard practice in epidemiology. Determine the range of values you need to show on the y-axis by identifying the largest value you need to graph on the y-axis and rounding that figure off to a slightly larger number. For example, the largest y-value in Figure 4 is 49 years in 1997, so the scale on the y-axis goes up to 50. If median age continues to increase and
YearYear
Rate perRate per 100,000100,
1955 336.
1956 364.
1957 283.
1958 438.
1959 229.
1960 246.
1961 231.
1962 259.
1963 204.
1964 239.
1965 135.
1966 104.
1967 31.
YearYear
Rate perRate per 100,000100,
1971 36.
1972 15.
1973 12.
1974 10.
1975 11.
1976 19.
1977 26.
1978 12.
1979 6.
1980 6.
1981 1.
1982 0.
1983 0.
YearYear
Rate perRate per 100,000100,
1987 1.
1988 1.
1989 7.
1990 11.
1991 3.
1992 0.
1993 0.
1994 0.
1995 0.
1996 0.
1997 0.
1998 0.
1999 0.
exceeds 50 in future years, a future graph will have to extend the scale on the y-axis to 60 years. Space the tick marks and their labels to describe the data in sufficient detail for your purposes. In Figure 4, five intervals of 10 years each were considered adequate to give the reader a good sense of the data points and pattern.
Exercise 4.
Using the data on measles rates (per 100,000) from 1955 to 2002 in Table 4:
Construct an arithmetic-scale line graph of rate by year. Use intervals on the y-axis that are appropriate for the range of data you are graphing.
Construct a separate arithmetic-scale line graph of the measles rates from 1985 to 2002. Use intervals on the y-axis that are appropriate for the range of data you are graphing.
Graph paper is provided at the end of this lesson.
Table 4 Rate (per 100,000 Population) of Reported Measles Cases by Year of Report — United States,Table 4 Rate (per 100,000 Population) of Reported Measles Cases by Year of Report — United States, 1955–20021955–
a constant multiple. Within a cycle, the ten tick-marks are spaced so that spaces become smaller as the value increases. Notice that the absolute distance from 1 to 2 is wider than the distance from 2 to 3, which is, in turn, wider than the distance from 8 to 9. This results from the fact that we are graphing the logarithmic transformation of numbers, which, in fact, shrinks them as they become larger. We can still compare series, however, since the shrinking process preserves the relative change between series.
Figure 4 Age-adjusted Death Rates for 5 of the 15Figure 4 Age-adjusted Death Rates for 5 of the 15 Leading Causes of Death — United States, 1958–Leading Causes of Death — United States, 1958– 20022002
Image Description Adapted from: Kochanek KD, Murphy SL, Anderson RN, Scott C. Deaths: final data for 2002. National vital statistics report; vol 53, no 5. Hyattsville, Maryland: National Center for Health Statistics, 2004. p. 9. Consider the data shown in Table 4. Two hypothetical countries begin with a population of 1,000,000. The population of Country A grows by 100,000 persons each year. The population of Country B grows by 10% each year. Figure 4. displays data from Country A on the left, and Country B on the right. Arithmetic-scale line graphs are above semilog-scale line graphs of the same data. Look at the left side of the figure. Because the population of Country A grows by a constant number of persons each year, the data on the arithmetic-scale line graph fall on a straight line. However, because the percentage growth in Country A declines each year, the curve on the semilog-scale line graph flattens. On the right side of the figure the population of Country B curves upward on the arithmetic-scale line graph but is a straight line on the semilog graph. In summary, a straight line on an arithmetic-scale line graph represents a constant change in the number or amount. A straight line on a semilog-scale line graph represents a constant percent change from a constant rate.
Table 4 Hypothetical Population Growth in Two CountriesTable 4 Hypothetical Population Growth in Two Countries
COUNTRY ACOUNTRY A (Constant Growth by 100,000)(Constant Growth by 100,000)
COUNTRY BCOUNTRY B
(Constant Growth by 10%)(Constant Growth by 10%)
YearYear PopulationPopulation Growth RateGrowth Rate PopulationPopulation Growth RateGrowth Rate
0 1,000,000 1,000,
1 1,100,000 10% 1,100,000 10%
2 1,200,000 9% 1,210,000 10%
3 1,300,000 8% 1,331,000 10%
4 1,400,000 7% 1,464,100 10%
5 1,500,000 7% 1,610,510 10%
6 1,600,000 6% 1,771,561 10%
7 1,700,000 6% 1,948,717 10%
8 1,800,000 5% 2,143,589 10%
9 1,900,000 5% 2,357,948 10%
10 2,000,000 5% 2,593,742 10%
11 2,100,000 5% 2,853,117 10%
12 2,200,000 4% 3,138,428 10%
13 2,300,000 4% 3,452,271 10%
14 2,400,000 4% 3,797,498 10%
15 2,500,000 4% 4,177,248 10%
16 2,600,000 4% 4,594,973 10%
17 2,700,000 3% 5,054,470 10%
18 2,800,000 3% 5,559,917 10%
19 2,900,000 3% 6,115,909 10%
20 3,000,000 3% 6,727,500 10%
To create a semilogarithmic graph from a data set in Analysis Module:
To calculate data for plotting, you must define a new variable. For example, if you want a semilog plot for annual measles surveillance data in a variable called MEASLES, under the VARIABLES section of the Analysis commands:
Select DeDefifinene. Type logmeasleslogmeasles into the Variable NameVariable Name box. Since your new variable is not used by other programs, the ScopeScope should be StandardStandard. Click on OKOK to define the new variable. Note that logmeasleslogmeasles now appears in the pull-down list of VariablesVariables. Under the VariablesVariables section of the Analysis commands, select AssignAssign.
Types of variables and class intervals are discussed in Lesson 2.
Image Description Source: Cortese M, Gerber S, Jones E, Fernandez J. A Salmonella Enteriditis outbreak in Chicago. Presented at the Eastern Regional Epidemic Intelligence Service Conference, March 23, 2000, Boston, Massachusetts.
Figure 4 Number of Cases ofFigure 4 Number of Cases of SalmonellaSalmonella Enteriditis Among Party Attendees by Date andEnteriditis Among Party Attendees by Date and Time of Onset — Chicago, Illinois, February 2000Time of Onset — Chicago, Illinois, February 2000
Image Description Source: Cortese M, Gerber S, Jones E, Fernandez J. A Salmonella Enteriditis outbreak in Chicago. Presented at the Eastern Regional Epidemic Intelligence Service Conference, March 23, 2000, Boston, Massachusetts. The most common choice for the x-axis variable in field epidemiology is calendar time, as shown in Figures 4–c. However, age, cholesterol level or another continuous-scale variable may be used on the x-axis of an epidemic curve.
Figure 4 Number of Cases ofFigure 4 Number of Cases of SalmonellaSalmonella Enteriditis Among Party Attendees by Date andEnteriditis Among Party Attendees by Date and Time of Onset — Chicago, Illinois, FebruaryTime of Onset — Chicago, Illinois, February 20002000
Image Description Source: Cortese M, Gerber S, Jones E, Fernandez J. A Salmonella Enteriditis outbreak in Chicago. Presented at the Eastern Regional Epidemic Intelligence Service Conference, March 23, 2000, Boston, Massachusetts.
In Figure 4, which shows a frequency distribution of adults with diagnosed diabetes in the United States, the x-axis displays a measure of body mass — weight (in kilograms) divided by height (in meters) squared. The choice of variable for the x-axis of an epidemic curve is clearly dependent on the point of the display. Figures 4, 4, or 4 are constructed to show the natural course of the epidemic over time; Figure 4 conveys the burden of the problem of overweight and obesity.
Six bars are captioned from under-weight to extreme obese. Percentages of population decrease after the overweight category to the extremely obese.
Figure 4 Distribution of Body Mass IndexFigure 4 Distribution of Body Mass Index Among Adults with Diagnosed Diabetes —Among Adults with Diagnosed Diabetes — United States, 1999–2002United States, 1999–
Image Description Data Source: Centers for Disease Control and Prevention. Prevalence of overweight and obesity among adults with diagnosed diabetes–United States, 1988-1994 and 1999-2002. MMWR 2004;53:1066–8. The component of most interest should always be put at the bottom because the upper component usually has a jagged baseline that may make comparison difficult. Consider the data on pneumoconiosis in Figure 4. The graph clearly displays a gradual decline in deaths from all pneumoconiosis between 1972 and 1999. It appears that deaths from asbestosis (top subgroup in Figure 4) went against the overall trend, by increasing over the same period. However, Figure 4 makes this point more clearly by placing asbestosis along the baseline.
Figure 4 Number of Deaths with Any DeathFigure 4 Number of Deaths with Any Death CertiCertifificate Mention of Asbestosis, Coal Worker’scate Mention of Asbestosis, Coal Worker’s Pneumoconiosis (CWP), Silicosis, andPneumoconiosis (CWP), Silicosis, and UnspeciUnspecifified/Other Pneumoconiosis Amonged/Other Pneumoconiosis Among Persons AgedPersons Aged ≥ 15 Years, by Year — United15 Years, by Year — United States, 1968–2000States, 1968–
Image Description Adapted from: Centers for Disease Control and Prevention. Changing patterns of pneumoconiosis mortality–United States, 1968-2000. MMWR 2004;53:627–31. This graph is similar to the one above except the variables in the stacks are arranged in a different order. It dramatizes the increase of asbestosis deaths over time.
Figure 4 Number of Deaths with Any DeathFigure 4 Number of Deaths with Any Death CertiCertifificate Mention of Asbestosis, Coal Worker’scate Mention of Asbestosis, Coal Worker’s Pneumoconiosis (CWP), Silicosis, andPneumoconiosis (CWP), Silicosis, and
Source: U. Census Bureau [Internet]. Washington, DC: IDB Population Pyramids [cited 2004 Sep 10]. Available from: census/ipc/www/idb/.
Figure 4 Population Distribution of SwedenFigure 4 Population Distribution of Sweden by Age and Sex, 1997by Age and Sex, 1997
Image Description Source: U. Census Bureau [Internet]. Washington, DC: IDB Population Pyramids [cited 2004 Sep 10]. Available from: census/ipc/www/idbpyr.html. While population pyramids are used most often to display the distribution of a national population, they can also be used to display other data such as disease or a health characteristic by age and sex. For example, smoking prevalence by age and sex is shown in Figure 4. This pyramid clearly shows that, at every age, females are less likely to be current smokers than males.
Figure 4 Percentage of PersonsFigure 4 Percentage of Persons ≥18 Years18 Years Who Were Current Smokers,Who Were Current Smokers,** by Age and Sexby Age and Sex — United States, 2002— United States, 2002
Image Description
- Answer “yes” to both questions: “Do you now smoke cigarettes everyday or some days?” and “Have you smoked at least 100 cigarettes in your entire life?” Data Source: Centers for Disease Control and Prevention. Cigarette smoking among adults– United States, 2002. MMWR 2004;53:427–31.
Frequency polygons
A frequency polygon, like a histogram, is the graph of a frequency distribution. In a frequency polygon, the number of observations within an interval is marked with a single point placed at the midpoint of the interval. Each point is then connected to the next with a straight line. Figure 4 shows an example of a frequency polygon over the outline of a histogram for the same data. This graph makes it easy to identify the peak of the epidemic (4 weeks).
Figure 4 Comparison ofFigure 4 Comparison of Frequency Polygon and HistogramFrequency Polygon and Histogram
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Image Description
A frequency polygon contains the same area under the line as does a histogram of the same data. Indeed, the data that were displayed as a histogram in Figure 4 are displayed as a frequency polygon in Figure 4.
Figure 4 Number of Deaths with Any DeathFigure 4 Number of Deaths with Any Death CertiCertifificate Mention of Asbestosis, Coal Worker’scate Mention of Asbestosis, Coal Worker’s Pneumoconiosis (CWP), Silicosis, andPneumoconiosis (CWP), Silicosis, and UnspeciUnspecifified/Other Pneumoconiosis Amonged/Other Pneumoconiosis Among Persons AgedPersons Aged ≥ 15 Years, by Year — United15 Years, by Year — United States, 1968–2000States, 1968–
Image Description Data Source: Centers for Disease Control and Prevention. Changing patterns of pneumoconiosis mortality–United States, 1968-2000. MMWR 2004;53:627–31. A frequency polygon differs from an arithmetic-scale line graph in several ways. A frequency polygon (or histogram) is used to display the entire frequency distribution (counts) of a continuous variable. An arithmetic-scale line graph is used to plot a series of observed data points (counts or rates), usually over time. A frequency polygon must be closed at both ends because the area under the curve is representative of the data; an arithmetic-scale line graph simply plots the data points. Compare the pneumoconiosis mortality data displayed as a frequency polygon in Figure 4 and as a line graph in Figure 4.
Figure 4 Number of Deaths with Any DeathFigure 4 Number of Deaths with Any Death CertiCertifificate Mention of Asbestosis, Coal Worker’scate Mention of Asbestosis, Coal Worker’s Pneumoconiosis (CWP), Silicosis, andPneumoconiosis (CWP), Silicosis, and UnspeciUnspecifified/Other Pneumoconiosis Amonged/Other Pneumoconiosis Among Persons AgedPersons Aged ≥ 15 Years, by Year — United15 Years, by Year — United States, 1968–2000States, 1968–
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Image Description Source: Kaydos-Daniels S, Bixler D, Colsher P, Haddy L. Symptoms following smallpox vaccination–West Virginia, 2003. Presented at 53rd Annual Epidemic Intelligence Service Conference, April 19-23, 2004, Atlanta, Georgia. A survival curve can be used with follow-up studies to display the proportion of one or more groups still alive at different time periods. Similar to the axes of the cumulative frequency curve, the x-axis records the time periods, and the y-axis shows percentages, from 0% to 100%, still alive.
The most striking difference is in the plotted curves themselves. While a cumulative frequency starts at zero in the lower left corner of the graph and approaches 100% in the upper right corner, a survival curve begins at 100% in the upper left corner and proceeds toward the lower right corner as members of the group die. The survival curve in Figure 4 shows the difference in survival in the early 1900s, mid-1900s, and late 1900s. The survival curve for 1900–1902 shows a rapid decline in survival during the first few years of life, followed by a relatively steady decline. In contrast, the curve for 1949– 1951 is shifted right, showing substantially better survival among the young. The curve for 1997 shows improved survival among the older population.
Figure 4 Percent Surviving by Age in Death-Figure 4 Percent Surviving by Age in Death- registration States, 1900–1902 and Unitedregistration States, 1900–1902 and United States, 1949–1951 and 1997States, 1949–1951 and 1997
Image Description Source: Anderson RN. United States life tables, 1997. National vital statistics reports; vol 47, no. 28. Hyattsville, Maryland: National Center for Health Statistics, 1999. Note that the smallpox scab separation data plotted as a cumulative frequency graph in Figure 4 can be plotted as a smallpox scab survival curve, as shown in Figure 4.
Figure 4 “Survival” of SmallpoxFigure 4 “Survival” of Smallpox Vaccination Scabs Among Primary VaccinesVaccination Scabs Among Primary Vaccines (n=29) and Revaccinees (n=328) — West(n=29) and Revaccinees (n=328) — West Virginia, 2003Virginia, 2003
Kaplan-Meier is a well accepted method for estimating survival probabilities.( 14 )
Image Description Source: Kaydos-Daniels S, Bixler D, Colsher P, Haddy L. Symptoms following smallpox vaccination–West Virginia, 2003. Presented at 53 Annual Epidemic Intelligence Service Conference, April 19-23, 2004, Atlanta, Georgia.
References (This Section)
Schmid CF, Schmid SE. Handbook of graphic presentation. New York: John Wiley & Sons, 1954.
Cleveland WS. The elements of graphing data. Summit, NJ: Hobart Press, 1994.
Brookmeyer R, Curriero FC. Survival curve estimation with partial non-random exposure information. Statistics in Medicine 2002;21:2671–83.
rd
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Lesson 4 Overview
Image DescriptionImage Description
Figure 4.
Description:Description: The Y-axis shows equal intervals of frequency (e. number of cases, percent, rate). The X-axis shows equal intervals of method of classification (e., time of illness onset, in days; year of report; age of cases, in years). Data are marked with a dot at the intersection of the X and Y axes. A straight line connects the dots. The line shows an increase and decrease of reported measles cases by year Return to text.
Figure 4.
Description:Description: Line graph showing the prevalence of neural tube defects over time. There is a slight decrease when folic acid fortification was optional, and a continuing decrease when folic acid was mandatory. Return to text.
Figure 4.
Description:Description: Line graph shows age at death on the Y-axis and year on the X-axis. Data for men is displayed with diamond data points and a dashed line. Data for women are displayed with a square data point and a solid line. The data for men and women can be easily compared. Return to text.
Figure 4.
Description:Description: A mumps vaccine was first licensed in December 1967. Because of the recommendation of two doses of measles-mumps-rubella vaccine and the continued high coverage rate in the United States, mumps incidence continues to be low, with 231 cases reported for 2003, thus meeting the Healthy People 2010 objective of less than 500 cases per year. In the graph, the Y-axis shows incidence per 100,000 population. The X-axis shows year. An increase between 1995 and 1997 is seen. Return to text.
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Figure 4.
Description:Description: A population pyramid. Horizontal bars indicate the population by age. The y-axis is in the middle. Bars indicating data for males is on one side, females on the other. A linear relationship between age and population is seen for both males and females. The overall shape is triangular. Return to text.
Figure 4.
Description:Description: A population pyramid. The overall shape is not triangular because there is no linear relationship between age and population. Return to text.
Figure 4.
Description:Description: A population pyramid showing 2 trends: the percentage of smokers (both male and female) increase by age and fewer females at all age groups smoke. Return to text.
Figure 4.
Description:Description: The same data is shown in 2 different formats. The histogram shows number of cases as columns. The Frequency polygon shows number of cases as data points connected by lines. The midpoints of intervals of the histogram intersect the frequency polygon. For the frequency polygon, the first data point is connected to the midpoint of the previous interval on the X-axis. The last data point is connected the mid-point of the following interval. Return to text.
Figure 4.
Description:Description: A frequency polygon showing the same data as Figure 4. Instead of columns with 4 different colors to indicate the number of deaths, a series of 4 lines represent the 4 sets data creating a smoother shape. The area under each line is colored to indicate the difference between each set of data. The lines at the beginning and end intersect the X-axis. Return to text.
Figure 4.
Description:Description: A line graph showing the same data as Figure 4. Instead of shaded areas, a series of 4 lines representing the 4 sets data creating a smoother shape. Each dataset has a different type of line, for example, dashed, dotted, or solid. The lines at the beginning and end do not intersect the X-axis. Return to text.
Figure 4.
Description:Description: A cumulative frequency graph showing 2 lines, one for revaccinees and 1 for primary vaccines. Both lines start at zero in the lower left corner of the graph and approaches 100% in the upper right corner. The data points at 50% frequency is seen. Return to text.
Figure 4.
Description:Description: A survival curve with 3 data sets indicated by different lines. All lines start at 100% on the left and decrease to 0% on the right. The graph is counter-intuitive because increased age at death is depicted by a declining curve. Return to text.
Figure 4.
Description:Description: The same data as figure 4 presented as a survival curve with both lines declining from the left to the right. Return to text.
Page last reviewed: May 18, 2012 (archived document) Content source: Deputy Director for Public Health Science and Surveillance, Center for Surveillance, Epidemiology, and Laboratory Services, Division of Scientific Education and Professional Development
Task 1 - CDD guidelines for plotting and interpreting public health data
Course: One health (VET392)
University: Murdoch University
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