Measures of disease frequency

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1 Measures of disease frequency Madhukar Pai, MD, PhD McGill University, Montreal 1

2 Overview Big picture Measures of Disease frequency Measures of Association (i.e. Effect) Measures of Potential Impact 2

3 3

4 Measures of Disease Frequency The importance of understanding the numerator and the denominator [proportions, rates, ratios] Defining the numerator [ case ] Defining the denominator [ population at risk ] Quantifying occurrence is usually done using: Incidence Prevalence Incidence: Cumulative incidence [incidence risk, incidence proportion] Incidence density [incidence rate; sometimes hazard rate] Prevalence: Point prevalence Period prevalence 4

5 Rates, Ratios, Proportions Three general classes of mathematical parameters. Often used to relate the number of cases of a disease [numerator] or health outcome to the size of the source population [denominator] in which they occurred. Numerator ( case ) has to be defined Denominator ( population size ) has to be defined Epidemiologists have been referred to as people in search of the denominator! 5

6 Ratio Obtained by dividing one quantity by another. These quantities may be related or may be totally independent. Usually expressed as: Example: Number of stillbirths per thousand live births. # stillbirths # live births x 10 y n 1000 Ratio is a general term that includes Rates and Proportions. Dictionary: The value obtained by dividing one quantity by another. [Porta 2008] Kleinbaum et al. ActivEpi 6

7 Proportion A ratio in which the numerator (x) is included in the denominator (y) x 10 y n Expressed as: where, 10 n is often 100. Example: The number of fetal deaths out of the total number of births. # of fetal deaths 100 live births + fetal deaths Answer often read as a percent. Dictionary: A type of ratio in which the numerator in included in the denominator. [Porta 2008] Kleinbaum et al. ActivEpi 7

8 Rate A measure of how quickly something of interest happens. Expressed as: x 10 y n Example: The number of new cases of Parkinson s disease which develops per 1,000 person-years of follow-up. # of new cases of Parkinson's disease Total time disease - free subjects observed 1000 Time, place and population must be specified for each type of rate. In a rate, numerator is not a subset of the denominator Rate is not a proportion Kleinbaum et al. ActivEpi 8

9 Measures of Disease Frequency Incidence (I): Measures new cases of a disease that develop over a period of time. Dictionary: The number of new health-related events in a defined population within a specified period of time. May be measured as a frequency count, a rate or a proportion. [Porta 2008] Very helpful for etiological/causal inference Difficult to estimate Implies follow-up over time (i.e. cohort design) Prevalence (P): Measures existing cases of a disease at a particular point in time or over a period of time. Dictionary: A measure of disease occurrence: the total number of individuals who have an attribute or disease at a particular time (or period) divided by the population at risk of having the disease at that time or midway through the period. It is a proportion, not a rate. [Porta 2008] Very helpful for quantifying disease burden (e.g. public health) Relatively easy to estimate Implies a cross-sectional design Kleinbaum et al. ActivEpi 9

10 Prevalence vs. Incidence Prevalence can be viewed as describing a pool of disease in a population. Incidence describes the input flow of new cases into the pool. Deaths and cures reflects the output flow from the pool.

11 11 Kleinbaum et al. ActivEpi

12 Risk Probability that an individual with certain characteristics such as: Age Race Sex Smoking status will experience a health status change over a specified follow-up period (i.e. risk period) Dictionary: Probability that an event will occur within a stated period of time. [Porta 2008] Assumes: Does not have disease at start of follow-up. Does not die from other cause during follow-up (no competing risks). Risk is often used for prediction at the individual level 12

13 Risk 0 RISK 1 0% percentage 100% Specify risk period Example: The 10-year risk that a 45-year-old male will develop prostate cancer is 5%. Risk can be estimated from: 1. Cumulative Incidence (directly) [note: cumulative incidence is also called incidence risk ] 2. Incidence density (indirectly via life tables, etc) 13

14 Cumulative Incidence CI = I N I = # of new cases during follow-up N = # of disease-free subjects at start of follow-up Measures the frequency of addition of new cases of disease and is always calculated for a given period of time (e.g. annual incidence) Must always state the time period (since time is not automatically captured in CI) Dictionary: Incidence expressed as a proportion of the population at risk. A measure of risk. The proportion of a closed population at risk for a disease that develops the disease during a specified interval. [Porta 2008] 14

15 Prevalent cases must be excluded before follow-up 15

16 Example Kleinbaum et al. ActivEpi 16

17 Cumulative Incidence Most common way to estimate risk Always a proportion (bounded between 0 and 1) Assumes a fixed or closed cohort (no exits allowed) For brief specified periods of time, e.g. an outbreak, commonly called an Attack Rate - In reality, attrition is a huge problem (losses to follow-up, deaths, competing risks) - Formula does not reflect continually changing population size for dynamic cohorts (open populations). - Does not allow subjects to be followed for different time periods. - In real life, one has to deal with losses, competing risks, attrition, dynamic cohorts, and differential follow-up time!! 17 - So, rate becomes more relevant

18 In epidemiology, we generally measure average rates [instantaneous rates are difficult to estimate, but hazard function 18 comes close] Kleinbaum et al. ActivEpi

19 Rate Describes how rapidly health events are occurring in a population of interest. In epidemiologic studies, we typically measure the average rate at which a disease is occurring over a period of time. Rate is always non-negative, but has no upper bound (0 < Rate < infinity) Rate is not a proportion bounded between 0 and 1 Example: 50 new cases per 10,000 person-years Interpretation: An average of 50 cases occurs for every 10,000 years of disease free follow-up time observed on a cohort of subjects. This type of rate is not easy to use for individual risk prediction [they are useful at the population level] Dictionary: The rate at which new events occur in a population. [Porta 2008] Kleinbaum et al. ActivEpi

20 Incidence density (incidence rate) IR = I PT I = # of new cases during follow-up PT = total time that disease free individuals in the cohort are observed over the study period (total person-time experience of the cohort). Synonyms: hazard rate*, incidence density rate, person-time incidence. Dictionary: The average person-time incidence rate [Porta, 2008] Measures the rapidity with which new cases are occurring in a population Most sophisticated form of measuring incidence [most difficult as well] - Accounts for losses, competing risks, dynamic turn-over, differential follow-up time, changes in exposures over time - *hazard function (in survival analysis) is the event rate at time t conditional on survival until time t [hazard rate is something like an instantaneous rate] 20 Kleinbaum et al. ActivEpi

21 Incidence density : new cases that occur in the total population-time Numerator Morgenstern IJE 1980 Denominator = Area under the curve = aggregate of personmoments [total population-time] 21

22 Example Hypothetical cohort of 12 initially disease-free subjects followed over a 5-year period from 1990 to Kleinbaum et al. ActivEpi 22

23 Example, cont. IR = I PT = 5 25PY = 0.20 = 20 new cases per 100 person - years or 200 new cases per 1000 person - years Study questions: 1) Is the value of 0.20 a proportion? 2) Does the value of 0.20 represent an individual s risk of developing disease? Kleinbaum et al. ActivEpi 23

24 Confusing Risk with Rate The term Rate is often been used incorrectly to describe a measure of risk (cumulative incidence). e.g., Attack Rate Death Rate Case-Fatality Rate When reading Epidemiologic literature, one should be careful to determine the actual measure being reported. Kleinbaum et al. ActivEpi 24

25 Risk vs Rate RISK E.g. Cumulative incidence Proportion (always between 0 and 1) Probability that an individual will develop a disease during a specific period Use for individual prognosis More assumptions Cannot handle variable followup times, attrition, competing risks Easy to compute in a fixed cohort with few losses; but gets difficult with open populations with longer follow up and losses RATE E.g. Incidence density Non-negative and no upper bound Describes how rapidly new events occur in a specific population Use for etiological comparisons Fewer assumptions Can handle variable follow-up times, attrition, competing risks Can be computed even with open populations with losses and longer follow up 25

26 Risk vs Odds Dictionary: Odds is the ratio of the probability of occurrence of an event to that of non-occurrence. [Porta, 2008] 26 Source: Silva 1999

27 Risk vs Odds To go from Probability to Odds: Effective Clinical Practice May/June 2000 Volume 3 Number 3 Odds = P / (1 P) E.g. If P = 0.20, Odds = 0.20 / 0.80 = 0.25 To go from Odds to Probability: Probability = Odds / (1 + Odds) E.g. If Odds = 0.25, P = 0.25 / 1.25 =

28 28

29 29

30 Prevalence Measures existing cases of a health condition Inherently biased towards inclusion of survivors Primary outcome of a cross-sectional study (e.g. sample surveys) Two types of Prevalence Point prevalence Period prevalence 30

31 Point Prevalence P = C N C = # of observed cases at time t N = Population size at time t Measures the frequency of disease at a given point in time Dictionary: A measure of disease occurrence: the total number of individuals who have an attribute or disease at a particular time (or period) divided by the population at risk of having the disease at that time or midway through the period. It is a proportion, not a rate. [Porta 2008] 31

32 Point Prevalence Example Suppose there are 150 individuals in a population and, on a certain day, 15 are ill with the flu. What is the estimated prevalence for this population? P = 15 = % Kleinbaum et al. ActivEpi 32

33 Prevalence Useful for: Assessing the health status of a population. Planning health services. Often the only measure possible with chronic diseases where incident cases cannot be easily detected (e.g. prevalence of hypertension) Not very useful for: Identifying risk factors (etiology): confusion between risk factors for survival vs. risk factors for developing disease Makes no sense for conditions that are acute and short duration (e.g. diarrhea) Kleinbaum et al. ActivEpi 33

34 Period Prevalence PP = C + N I C = the # of prevalent cases at the beginning of the time period. I = the # of incident cases that develop during the period. N = size of the population for this same time period. Example: one year prevalence: proportion of individuals with the disease at any time during a calendar year. It includes cases arising before 34 and during the year. Denominator is total population during the time period.

35 Prevalence: example Point prevalence at time t 1 = 2/10 = 20% Point prevalence at time t 2 = 3/8 = 38% Period prevalence between t 1 and t 2 : 6/10 = 60% 35 Source: Silva 1999

36 What impacts prevalence estimation? GAINS In-migration Prevalence All new cases Cases existing at one point in time Early deaths Cures LOSES Out-migration 36

37 What factors can increase prevalence? Prevalence Longer duration Prolongation of life without cure Increased incidence In-migration of cases Out-migration of healthy people In-migration of susceptible people Better diagnosis/reporting Source: Beaglehole,

38 What factors can decrease prevalence? Prevalence Shorter duration High case fatality Decreased incidence In-migration of healthy people Out-migration of cases Improved cure rates Source: Beaglehole,

39 Relation between measures of disease frequency Relationship between prevalence and incidence: Prevalence = Incidence Rate X Average Duration* *Assumptions: steady state population and rare disease Relationship between incidence risk and rate: Risk = Incidence Rate X Duration of the period of risk 39

40 Key issue to understand: all measures are estimates [subject to error] 40

41 Therefore, all estimates must be reported with a confidence intervals 41

42 What are 95% confidence intervals? The interval computed from the sample data which, were the study repeated multiple times, would contain the true effect 95% of the time Incorrect Interpretation: "There is a 95% probability that the true effect is located within the confidence interval." This is wrong because the true effect (i.e. the population parameter) is a constant, not a random variable. Its either in the confidence interval or it's not. There is no probability involved (in other words, truth does not vary, only the confidence interval varies around the truth). Useful reading: Primer on 95% CI by American College of Physicians 42

43 Crude vs. adjusted rates Crude rates are useful, but not always comparable across populations Example: crude death rate in Sweden is higher than in Panama [Rothman text] Why? Confounding by age Age standardization is nothing but adjustment for confounding by age Rothman KJ,

44 Example from Kleinbaum: Kleinbaum et al. ActivEpi 44

45 Example from Kleinbaum: Kleinbaum et al. ActivEpi 45

46 Example from Kleinbaum: Kleinbaum et al. ActivEpi 46

47 Example from Kleinbaum: Kleinbaum et al. ActivEpi 47

48 Example from Kleinbaum: Kleinbaum et al. ActivEpi 48

49 Example from Kleinbaum: Kleinbaum et al. ActivEpi 49

50 Example from Kleinbaum: Kleinbaum et al. ActivEpi 50

51 Example from Kleinbaum: Kleinbaum et al. ActivEpi 51

52 Readings for this week Rothman text: Chapter 3: Measuring disease occurrence and causal effects Gordis text: Chapter 3: Measuring the occurrence of disease: morbidity Chapter 4: Measuring the occurrence of disease: mortality 52

53 53

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