Study designs: Cross-sectional studies, ecologic studies (and confidence intervals)

1
Study designs Cross-sectional studies, ecologic
studies (and confidence intervals)
Principles of Epidemiology for Public Health
(EPID600)
Victor J. Schoenbach, PhD home page Department of
EpidemiologyGillings School of Global Public
HealthUniversity of North Carolina at Chapel
Hill www.unc.edu/epid600/
2
Signs from around the world

• In a Copenhagen airline ticket office
• We take your bags and send them in all
  directions.

3
Signs from around the world

• In a Norwegian cocktail lounge
• Ladies are requested not to have children in the
  bar.

4
Signs from around the world

• Rome laundry Ladies, leave your clothes here
  and spend the afternoon having a good time.

5
Faster keyboarding - 1

• I cdnuolt blveiee taht I cluod aulaclty
  uesdnatnrd waht I was rdanieg. The phaonmneal
  pweor of the hmuan mnid, aoccdrnig to a
  rscheearch at Cmabrigde Uinervtisy. It dn'seot
  mttaer in waht oredr the ltteers in a wrod are,
  the olny iprmoatnt tihng is taht the frist and
  lsat ltteer be in the rghit pclae. The rset can
  be a taotl mses and you can sitll raed it wouthit
  a porbelm.
• Gary C. Ramseyer's First Internet Gallery of
  Statistics Jokes http//davidmlane.com/hyperstat/h
  umorf.html (162)

6
Faster keyboarding - 2

• Most of my friends could read this with
  understanding and rather quickly I might add.
  Then I had them read a statistical bit of
  literature
• Miittluvraae asilyans sattes an idtenossiy
  ctuoonr epilsle is the itternoiecsno of a panle
  pleralal to the xl-yapne and the sruacfe of a
  btiiarave nmarol dbttiisruein.
• Gary C. Ramseyer's First Internet Gallery of
  Statistics Jokes http//davidmlane.com/hyperstat/h
  umorf.html (162)

7
Study designs Cross-sectional studies, ecologic
studies (and confidence intervals)
Principles of Epidemiology for Public Health
(EPID600)
Victor J. Schoenbach, PhD home page Department of
EpidemiologyGillings School of Global Public
HealthUniversity of North Carolina at Chapel
Hill www.unc.edu/epid600/
8
Today outline

• Cross-sectional studies (and sampling)
• Ecologic studies
• Confidence intervals

9
Cross-sectional studies

• Cross-sectional studies include surveys
• People are studied at a point in time, without
  follow-up.
• Can combine a cross-sectional study with
  follow-up to create a cohort study.
• Can conduct repeated cross-sectional studies to
  measure change in a population.

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Cross-sectional studies

• Number of uninsured Americans rises to 50.7
  million. (USA Today, 9/17/2010 data from Census
  Bureau)
• In 2007-2008, almost one in five children older
  than 5 years was obese. (Health, United States,
  2010 data from the National Health and Nutrition
  Examination Survey)
• 35 (7.4 million) of births to U.S. women during
  the preceding 5 years were mistimed or unwanted
  (2002 National Survey of Family Growth, Series
  23, No. 25, Table 21)
• Source www.cdc.gov/nchs/

11
Cross-sectional studies

• Incidence information is not available from a
  typical cross-sectional study
• Sometimes can reconstruct incidence from
  historical information
• Example the incidence proportion of quitting
  smoking, called the quit ratio
  ex-smokers / ever-smokersis calculated from
  survey data.

12
Measure prevalence at point in time

• Snapshot of a population, a still life
• Can measure attitudes, beliefs, behaviors,
  personal or family history, genetic factors,
  existing or past health conditions, or anything
  else that does not require follow-up to assess.
• The source of most of what we know about the
  population

13
Population census

• A cross-sectional study of an entire population
• Provides the denominator data for many purposes
  (e.g., estimation of rates, assessing
  generalizability, projecting from smaller
  studies)
• A huge effort people can be difficult to find
  and to count may not want to provide data
• Some countries maintain accurate and current
  registries of the entire country

14
National surveys conducted by NCHS

• National Health Interview Survey (NHIS)
  household interviews
• National Health and Nutrition Examination Survey
  (NHANES) interviews and physical examinations
• National Survey of Family Growth (NSFG)
  household interviews
• National Health Care Survey (NHCS) medical
  records

15
National surveys

• Designed to be representative of the entire
  country
• Modes household interview, telephone, mail
• Employ complex sampling designs to optimize
  efficiency (tradeoff between information and
  cost)
• Logistically challenging (answering machines,
  cellphones, . . .)
• See presentation by Dr. Anjani Chandra at
  www.minority.unc.edu/institute/2003/materials/slid
  es/Chandra-20030522.ppt

16
Example National Health Interview Survey

• Conducted every year in U.S. by National Center
  for Health Statistics (CDC)
• Stratified, multistaged, household survey that
  covers the civilian noninstitutionalized
  population of the United States
• Redesigned every decade to use new census

17
multistaged

• Improves logistical feasibility and reduces costs
  (though reduces precision)
• 1. Divide population into primary sampling units
  (PSUs)PSU primary sampling unit
  metropolitan statistical area, county, group of
  adjacent counties

18
multistaged

• 2. Select sample of census block groups (SSUs)
  within each selected PSU
• 3. Map each selected census block group or
  examine building permits
• 4. Select one cluster of 4-8 housing units
  dispersed evenly throughout the block
• NCHS draws a new representative sample for each
  weeks interviews

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stratified

• US divided into 1,900 PSUs
• Largest 52 PSUs are self-representing
• Rest of PSUs divided into 73 categories
  (strata), based on socioeconomic and
  demographic variables
• Sampling takes place separately within each
  category (stratum)

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Sample size and Precision
21
Weighted sampling
22
stratified

• Also place census blocks into categories and
  sample within each
• Oversample some strata

23
Defined population

• Studies, especially cross-sectional studies, are
  easiest to interpret when they are based in a
  population that has some existence apart from the
  study itself (defined population)
• 1. Political subdivision (city, county, state)
• 2. Institutional (HMO, employer, profession)
• Probability sampling enables statistical
  generalizability to the defined population

24
Surveys of sentinel populations

• HIV seroprevalence survey in three county STD
  clinics in central NC in 1988
• 3,000 anonymous, unlinked, leftover sera
• Anonymous questionnaire for demographics and risk
  factors
• Schoenbach VJ, Landis SE, Weber DJ, Mittal
  M, Koch GG, Levine PH. HIV seroprevalence in
  sexually transmitted disease clients in a
  low-prevalence southern state. Ann Epidemiol
  19933281-288

25
HIV seroprevalence

• Schoenbach VJ, Landis SE, Weber DJ, Mittal
  M, Koch GG, Levine PH. HIV seroprevalence in
  sexually transmitted disease clients in a
  low-prevalence southern state. Ann Epidemiol
  19933281-288

26
Seroprevalence ( HIV) by risk factors

• Schoenbach VJ, Landis SE, Weber DJ, Mittal M,
  Koch GG, Levine PH. HIV seroprevalence in
  sexually transmitted disease clients in a
  low-prevalence southern state. Ann Epidemiol
  19933281-288

27
Interpretation

• Measures prevalence if incidence is our real
  interest, prevalence is often not a good
  surrogate measure
• Studies only survivors and stayers
• May be difficult to determine whether a cause
  came before an effect (exception genetic
  factors)

28
Other points

• Can choose by exposure or overall
• Can choose by disease may not be
  distinguishable from a case-control study with
  prevalent cases

29
Outline

• Cross-sectional studies (and sampling)
• Ecologic studies
• Confidence intervals

30
Ecologic studies

• Most study designs cross-sectional,
  case-control, cohort, intervention trials can
  be carried out with individuals or with groups
• Group-level studies which use routinely collected
  data are easier and less costly
• Group-level studies that involve interventions
  may not be easier or less costly

31
Types of group-level variables

• Summary of individual-level variable (e.g.,
  median household income, with high school
  diploma)
• Property of the aggregate (e.g., neighborhood
  grocery stores, seat belt legislation, community
  competence)

32
Interpretation

• Link between summary exposure variable and
  individual-level outcome must be inferred
• Inference from group to individual is not always
  sound

33
Example Male Circumcision and HIV
(Slope indicates strength of relationship r
indicates linearity)

• Source Bongaarts J, et al. The relationship
  between male circumcision and HIV infection in
  African populations. AIDS 1989 3(6) 373-7.

34
Outline

• Cross-sectional studies (and sampling)
• Ecologic studies
• Confidence intervals

35
Confidence intervals

• Provide a plausible range for the quantity being
  estimated
• Width indicates the precision of an estimate for
  a given level of confidence
• Confidence intervals quantify only random error
  from sampling variation, not systematic error
  from nonresponse, study design, etc.

36
Confidence level vs. precision

• The more vague my estimate, the more confident I
  can be that it includes the population parameter
  I am 100 confident that the prevalence of HIV
  is between 0 and 100.
• The more specific my estimate, the lower my
  confidence I am 0 confident that the
  prevalence of HIV is 5.23

37
Confidence intervals interpretation

• Simple interpretations are typically not precise
• Precise interpretations are typically not simple

38
Simple but imprecise

• There is 95 confidence that the interval
  contains the true value True, but begs the
  question how to define confidence

39
Simple but imprecise

• There is a 95 probability that the interval
  contains the true value Not quite correct
  probability (as conventionally defined) applies
  to a process, not to a single instance

40
Probability applies to a process example

• A 95 confidence interval can be viewed as a
  measurement or estimation process that will be
  correct (the interval includes the true value of
  the parameter) 95 of the time and incorrect 5
  of the time.
• Let us make up another estimation process that
  will be correct (about) 95 of the time.

41
Why probability applies to a process

• Estimate your gender by flipping a coin 5 times -
  if the result is 5 heads estimate
  your gender to be its opposite otherwise
  estimate your gender to be what you think it is
  now.
• Probability that estimate will be correct is(1
  Probability of 5 heads) 0.97 97
• Probability that estimate will be incorrect is 3

42
Why probability applies to a process

• So we now have a measurement process that will be
  correct 97 of the time. We will use it to
  measure your gender.
• Flip the coin 5 times, and suppose you get 5
  heads
• Is there a 97 probability that you are of the
  opposite sex?

43
Precise but not simple

• A 95 confidence interval is
• 1. obtained by using a procedure that will
  include the population parameter being estimated
  95 of the time
• 2. the set of all population values which are
  likely to yield a sample like the one we
  obtained

44
Suppose that this line represents the value of
the parameter we are trying to estimate
True value
45
Possible estimates of that parameter in N
identical studies (shows sampling variation)
Study estimates
True value
46
One possible true value and how it would
manifest, on average, in N identical studies
True value
95 of the distribution
47
Estimate from one study of a given size
?
Estimate
48
A possible true value with lt 2.5 chance of
being observed at or beyond the estimate
?
Estimate
95 of the distribution
49
A possible true value with gt 2.5 probability of
being observed at or beyond the estimate
?
Estimate
95 of the distribution
50
A possible true value with gt 2.5 probability of
being observed at or beyond the estimate
?
Estimate
95 of the distribution
51
A possible true value with lt 2.5 probability of
being observed at or beyond the estimate
?
Estimate
95 of the distribution
52
What the confidence interval represents
?
95 confidence interval
53
What the confidence interval represents
95 confidence interval
54
One possible true value and how it would
manifest, on average, in N identical studies
True value
1.96 x s.e. 1.96 x s.e.
55
Confidence intervals another take
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56
One possible population
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57
Another possible population
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58
A 3rd possible population
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59
A 4th possible population
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60
A 5th possible population
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61
A 6th possible population
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O
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62
etc.
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O
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63
There are 1.6 x 1060 possible populations (no
cases all cases)
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O
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64
Suppose this is the population
(prevalence 15)
O
O
O
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O
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65
Take a sample (n10)
O
O
O
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O
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O
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O
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O
O
66
The sample
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O
O
67
Make point estimate of prevalence
?
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?

?
O
O
68
Interval estimate

• What are all the possible populations that would
  be expected to yield this prevalence in a sample
  of size 10?

69
This one is not possible
O
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? ????????????????????????? ??????????????????????
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70
Possible, but VERY UNLIKELY
O
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O
71
Not quite 2.5 probability (2.1, in fact)
O
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????? ????????????????????????? ??????????????????
???????
O
O
O
O
72
Yields just about 2.5 (3, actually) probability
of selecting 2 (or more) cases in 10
O
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? ????????????????????????? ??????????????????????
??? ????????????????????????? ????????????????????
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???????
O
O
O
O
O
73
One possible true value and how it would
manifest, on average, in N identical studies
True value
95 of the distribution
74
Just above 2.5 (actually 2.6) probability of
selecting 2 (or fewer) cases in 10
O
O
O
O
O
O
O
O
O
O
O
O
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? ????????????????????????? ??????????????????????
??? ????????????????????????? ????????????????????
????? ????????????????????????? ??????????????????
???????
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
75
Just below 2.5 (actually 2.4) probability of
selecting 2 (or fewer) cases in 10
O
O
O
O
O
O
O
O
O
O
O
O
O
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? ????????????????????????? ??????????????????????
??? ????????????????????????? ????????????????????
????? ????????????????????????? ??????????????????
???????
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
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O
O
O
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O
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O
O
O
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O
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O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
76
Interval estimate for 2/10

• Lower bound 2.5 (5 cases)
• Upper bound 55 (110 cases)
• Meaning Our sample of 10 with 2 cases provides
  evidence to exclude, at conventional error
  tolerance, populations with fewer than 5 cases or
  more than 110 cases. Populations with 5-110
  cannot be excluded as likely sources for this
  sample.

77
Interval estimate for 2/10

• Actual population prevalence was 15, which in
  fact is between 2.5 and 55.
• 2.5 to 55 is a very wide interval, i.e., a very
  imprecise estimate
• To make it more precise, we need a larger sample

78
Signs from around the world Germany

• A sign posted in Germany's Black Forest It is
  strictly forbidden on our black forest camping
  site that people of different sex, for instance,
  men and women, live together in one tent unless
  they are married with each other for that
  purpose.

79
Signs from around the world Finland

• On the faucet in a Finnish washroom
• To stop the drip, turn cock to right.