1/26/09 1 community health assessment in small populations: tools for working with “small...
Post on 28-Dec-2015
220 Views
Preview:
TRANSCRIPT
1/26/09 1
Community Health Assessment in Small Populations: Tools for Working With “Small
Numbers”
Community Health Assessment in Small Populations: Tools for Working With “Small
Numbers”Region 2 Quarterly Meeting
January 26, 2009
1/26/09 New Mexico Department of Health 2
OutlineOutline
Description of the Problem– Random variation– Survey samples versus complete count
datasets– Observed events versus underlying risk
Statistical Tools– Confidence intervals – Combining data– SMR
1/26/09 3
Small Numbers: The Problem
Small Numbers: The Problem
1/26/09 New Mexico Department of Health 4
Random VariationRandom Variation
Exercise:– Select a sample– Calculate the median age
State of New Mexico Median age1
– 36.0
Why are they different?
1. 2007 American Community Survey, U.S. Census Bureau. Downloaded on 1/21/09 from http://factfinder.census.gov
1/26/09 New Mexico Department of Health 5
Random Variation and Sample Size
Random Variation and Sample Size
What if we had a sample of New Mexico residents that was:– Randomly selected– n=5,000
Would it better match the state Census Bureau estimate?
1/26/09 New Mexico Department of Health 6
Size MattersSize Matters
The larger sample helps to “cancel out” the effects of random variation. – Some sample subjects are older than the
median.– Some sample subjects are younger than the
median.– As you increase the number of sample
subjects, the differences cancel out, and you get closer to the median.
1/26/09 New Mexico Department of Health 7
Reliability and ValidityReliability and Validity
The term "accuracy" is often used in relation to validity, while the term, "precision" is used to describe reliability.
1/26/09 New Mexico Department of Health 8
Numerator vs. DenominatorNumerator vs. Denominator
A large sample size means we have a large denominator, but the numerator also matters.
Some methods use a “Poisson distribution,” which considers ONLY the numerator size when assessing precision.
If we have only 1 event in one year, and 2 the next year, the addition of a single event doubles the rate of occurrence.
1/26/09 New Mexico Department of Health 9
Random Variation and Complete Count Datasets
Random Variation and Complete Count Datasets
What are some “complete count” datasets?
How do we use them for community health assessment?
1/26/09 New Mexico Department of Health 10
All-cause Deaths by Year, New Mexico, 1999-2006
0
5,000
10,000
15,000
20,000
1999 2000 2001 2002 2003 2004 2005 2006
Nu
mb
er o
f D
eath
s
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
Po
pu
lati
on
(P
erso
n-y
ears
at
Ris
k)
All-cause Deaths Person-years at Risk
1/26/09 New Mexico Department of Health 11
All-cause Deaths by Year, Santa Fe County, 1999-2006
0
200
400
600
800
1,000
1999 2000 2001 2002 2003 2004 2005 2006
Nu
mb
er o
f D
eath
s
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
160,000
Po
pu
lati
on
(P
erso
n-y
ears
at
Ris
k)
All-cause Deaths Person-years at Risk
1/26/09 New Mexico Department of Health 12
All-cause Deaths by Year, Union County, 1999-2006
0
20
40
60
1999 2000 2001 2002 2003 2004 2005 2006
Nu
mb
er o
f D
eath
s
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
Po
pu
lati
on
(P
erso
n-y
ears
at
Ris
k)
All-cause Deaths Person-years at Risk
1/26/09 New Mexico Department of Health 13
Diabetes Deaths by Year, Union County, 1999-2006
0
5
10
15
20
1999 2000 2001 2002 2003 2004 2005 2006
Nu
mb
er o
f D
eath
s
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
Po
pu
lati
on
(P
erso
n-y
ears
at
Ris
k)
Diabetes Deaths Person-years at Risk
Note: Diabetes deaths include deaths w ith an underlying cause coded w ith ICD-10 E10-E14. Data dow nloaded f rom http://ibis.state.health.nm.us on 1/21/09.
1/26/09 New Mexico Department of Health 14
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
20
40
60
80
100
120
140
160
180
200
1999 2000 2001 2002 2003 2004 2005 2006
Dea
ths
per
100
,000
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 15
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
20
40
60
80
100
120
140
160
180
200
1999 2000 2001 2002 2003 2004 2005 2006
Dea
ths
per
100
,000
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 16
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
20
40
60
80
100
120
140
160
180
200
1999 2000 2001 2002 2003 2004 2005 2006
Dea
ths
per
100
,000
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 17
Summary of the ProblemSummary of the Problem
Measurements are subject to sampling variability, also known as random error.
Even complete count datasets are subject to random error because we use them as a reflection of the underlying disease risk or rate.
1/26/09 New Mexico Department of Health 18
Summary of the ProblemSummary of the Problem
• A larger sample (denominator, population size) helps to “cancel out” the effects of random variation.
• Size matters, in both the numerator and the denominator.
• A measure that is relatively free from the effects of random variation is called “precise,” “reliable,” and “stable.” Those terms are synonymous.
1/26/09 19
Small Numbers: Statistical Tools
Small Numbers: Statistical Tools
1/26/09 New Mexico Department of Health 20
Tool #1. Confidence Intervals
Tool #1. Confidence Intervals
Use confidence intervals to help you decide whether the rate is stable.
Won’t solve the problem, but will provide information to help you interpret the rates.
The stability of an observed rate is important when comparing areas or assessing whether disease risk has increased or decreased.
1/26/09 New Mexico Department of Health 21
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
20
40
60
80
100
120
140
160
180
200
1999 2000 2001 2002 2003 2004 2005 2006
Dea
ths
per
100
,000
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 22
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
20
40
60
80
100
120
140
160
180
200
1999 2000 2001 2002 2003 2004 2005 2006
De
ath
s p
er
10
0,0
00
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 23
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
20
40
60
80
100
120
140
160
180
200
1999 2000 2001 2002 2003 2004 2005 2006
De
ath
s p
er
10
0,0
00
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 24
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
50
100
150
200
250
1999 2000 2001 2002 2003 2004 2005 2006
De
ath
s p
er
10
0,0
00
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 25
Calculation of 95% C.I.Calculation of 95% C.I.
The 95% confidence interval is calculated as 1.96 x Standard Error of the estimate (s.e.).
s.e. is calculated as
So the 95% C.I. is 1.96
1/26/09 New Mexico Department of Health 26
The “Normal” DistributionThe “Normal” Distribution
1/26/09 New Mexico Department of Health 27
Poisson DistributionPoisson Distribution
1/26/09 New Mexico Department of Health 28
Calculation of 95% C.I.Calculation of 95% C.I. p stands for “probability.” It is the rate
without the multiplier (e.g., 100,000 for deaths). q is the complement of the probability (1 minus P).
In Union County, there were 2 diabetes deaths among the 4,470 population, for a probability of 0.00045 (45 in 100,000)
1/26/09 New Mexico Department of Health 29
Calculation of 95% C.I.Calculation of 95% C.I. Formula: 1.96
p=0.00045, q=0.99955, n=4,470
(pq)/n = .000447 / 4470 = 0.000000100051
√(pq)/n = ………………… = 0.000316
1.96√(pq)/n = 1.96 x 0.000316 = 0.00062
Then we need to add the multiplier back in, so the confidence interval is:
+ 100,000*0.00062 = + 62
1/26/09 New Mexico Department of Health 30
Calculation of 95% C.I.Calculation of 95% C.I. The diabetes death rate was 44.7 per 100,000.
The confidence interval statistic is applied both above and below the rate.
C.I. LL (lower limit) is: 44.7- 62 = -17.3, and since we cannot have a negative rate, we’ll call it “0”
C.I. UL (upper limit) is: 44.7 + 62 = 106.7
The diabetes death rate for Union County in 2006 was 44.7 per 100,000 (95% C.I., 0 to 106.7)
1/26/09 New Mexico Department of Health 31
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
44.7 (0 - 106.7)
0
50
100
150
200
250
1999 2000 2001 2002 2003 2004 2005 2006
De
ath
s p
er
10
0,0
00
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 32
1/26/09 New Mexico Department of Health 33
1/26/09 New Mexico Department of Health 34
Confidence Interval FactoidsConfidence Interval Factoids
The confidence interval may be thought of as the range of probable true values for a statistic.
The confidence interval is an indication of the precision (stability, reliability) of the estimate.
A confidence interval is typically expressed as a symmetric value (e.g., "plus or minus 5%"). But for percentages, when the point estimate is close to 0% or 100%, a confidence interval with an asymmetric shape can be used.
1/26/09 New Mexico Department of Health 35
More Confidence Interval Factoids
More Confidence Interval Factoids
The 95% confidence interval (calculated as 1.96 times the standard error of a statistic) indicates the range of values within which the statistic would fall 95% of the time if the researcher were to calculate the statistic from an infinite number of samples of the same size drawn from the same base population. Unless otherwise stated, a confidence interval will be the "95% confidence interval."
1/26/09 New Mexico Department of Health 36
More Confidence Interval Factoids
More Confidence Interval Factoids
The 90% confidence interval, also commonly used, is calculated as 1.65 times the standard error of the estimate.
To calculate a confidence interval when the number of health events = 0, you may use 0 as the lower confidence limit, and for the upper confidence limit, assume a count of 3 health events in the same population.
1/26/09 New Mexico Department of Health 37
Tool #2. Combine DataTool #2. Combine Data
Combine years
Combine geographic areas (e.g., use the regional estimate rather than the county estimate)
Use a broader age group
1/26/09 New Mexico Department of Health 38
Diabetes Deaths by Year, New Mexico, Santa Fe County and Union County, 1999-2006
0
20
40
60
80
100
120
140
160
180
200
1999 2000 2001 2002 2003 2004 2005 2006
Dea
ths
per
100
,000
Po
pu
lati
on
State
Santa Fe Cnty
Union Cnty
1/26/09 New Mexico Department of Health 39
Diabetes Deaths by Year, Union County, 1999-2006
0
50
100
150
200
250
1999 2000 2001 2002 2003 2004 2005 2006 1999-2006
De
ath
s p
er
10
0,0
00
Po
pu
lati
on
1/26/09 New Mexico Department of Health 40
Diabetes Deaths, New Mexico, Santa Fe and Union Counties, 1999-2006
41.3
20.4
30.4
0
10
20
30
40
50
60
70
New Mexico Santa Fe Cnty Union Cnty
De
ath
s p
er
10
0,0
00
Po
pu
lati
on
1/26/09 New Mexico Department of Health 41
Interpretation of Diabetes Deaths in Union County
Interpretation of Diabetes Deaths in Union County
Union County’s diabetes death rate (1999-2006) was higher than the state, overall rate, but was not statistically significantly higher.
In other words, the Union County rate was “marginally higher” than the New Mexico state rate.
Was it higher than Santa Fe County?
1/26/09 New Mexico Department of Health 42
Differences Between Two Rates
Differences Between Two Rates
Statistical significance of a change in a rate from time1 to time2
Statistical significance of the difference between two rates in one time period (e.g., Union County versus Santa Fe County).
**Test of Proportions**
1/26/09 New Mexico Department of Health 43
Test of ProportionsTest of Proportions
Proportion1: 1999-2006 Union County diabetes death rate: 41.3/100,000 = .000413
Proportion 2: 1999-2006 Santa Fe County diabetes death rate: 20.4/100,000 = .000204
Difference between the two proportions:
.000413 - .000204 = .000209
1/26/09 New Mexico Department of Health 44
Test of Proportions (cont’d)Test of Proportions (cont’d) The difference between the two rates (0.00026)
must be considered in the context of the standard error of the difference between two rates (pooled standard error), computed as:
If the difference between the two rates, 0.000209, is greater than 1.96 x s.e.diff, then the difference is considered statistically significant.
Bruning, J.L., and Kintz, B.L. (1977) Computational Handbook of Statistics. Scott, Foresman and Company: London.
1/26/09 New Mexico Department of Health 45
Calculation of s.e.diffCalculation of s.e.diff
Union County:– p1=0.000413– q1=0.999587– n1=33,929
Santa Fe County: – p2=0.000204 – q2=0.999796 – n2=1,092,565
p=proportion, q=(1-p), n is the person-years at risk, or the sum of the population counts across all eight years.
1/26/09 New Mexico Department of Health 46
Calculation of s.e.diffCalculation of s.e.diff
1/26/09 New Mexico Department of Health 47
Evaluation of the DifferenceEvaluation of the Difference Union County: 41.3/100,000 = .000413
Santa Fe County: 20.4/100,000 = .000204
Difference: .000413 - .000204 = .000209
s.e.diff = .0001111
1.96 * s.e.diff = .000218
Is .000209 greater than .000218?
No. Union County’s rate is greater than Santa Fe County’s rate, but the difference is NOT statistically significant.
1/26/09 New Mexico Department of Health 48
Tool #3. SMR and ISRTool #3. SMR and ISR
Standardized Mortality (or Morbidity) Ratio (SMR)– Estimates the number of deaths (or health
events) one would EXPECT, based on …• The age- and sex-specific rates in a standard
population (e.g., New Mexico rate)• The age and sex distribution of the index area.
Indirectly Standardized Rates– Use SMR to perform age adjustment when
the number of cases is less than 20.
1/26/09 New Mexico Department of Health 49
Standardized Mortality RatioStandardized Mortality Ratio
The all-cause death rate in New Mexico in 2006 was 757.5 deaths per 100,000 population.
All other things being equal, we should expect the same death rate in Union County.
1/26/09 New Mexico Department of Health 50
Standardized Mortality RatioStandardized Mortality Ratio BUT all other things are NOT equal.
– 2006, % of population over age 65 was• 18.9% in Union County, compared with• 12.3% statewide.
In an older population, we would expect a higher death rate.
1/26/09 New Mexico Department of Health 51
Standardized Mortality RatioStandardized Mortality Ratio And Union County’s death rate is higher:
1364.6 deaths per 100,000.
IF we adjust the New Mexico death rate to account for Union County’s older population, THAT is how many deaths we should EXPECT.
1/26/09 New Mexico Department of Health 52
Sex Age Group
New Mexico, 2006 Age- & Sex-
specific All-Cause Mortality Rates
Union County Population Estimates
EXPECTED Number of
Union County Deaths
OBSERVED Number of
Union County Deaths
Standardized Mortality Ratio
(Observed/ Expected)
Male Less than 1 year 656.9 21 0.1Male 1-4 years 32.3 104 0.0Male 5-14 years 22.5 279 0.1Male 15-24 years 140.2 328 0.5Male 25-34 years 228.2 184 0.4Male 35-44 years 350.9 247 0.9Male 45-54 years 571.7 400 2.3Male 55-64 years 1035.5 282 2.9Male 65-74 years 2224.3 200 4.4Male 75-84 years 5796.5 125 7.2Male 85+ years 13167.3 41 5.4Female Less than 1 year 505.8 21 0.1Female 1-4 years 23.9 105 0.0Female 5-14 years 16.4 269 0.0Female 15-24 years 59.9 295 0.2Female 25-34 years 89.7 167 0.1Female 35-44 years 161 235 0.4Female 45-54 years 324.6 383 1.2Female 55-64 years 607.6 304 1.8Female 65-74 years 1466.6 242 3.5Female 75-84 years 4184.2 170 7.1Female 85+ years 12976 68 8.8
47.7 61 1.28
SMR (Observed/Expected)
(Rate x Pop) / 100,000
Standardized Mortality Ratio for 2006 Union County, All-cause Mortality
Standardized Mortality Ratio for 2006 Union County, All-cause Mortality
1/26/09 New Mexico Department of Health 53
SMR, Union CountySMR, Union County An SMR <1.0 indicates less-than-expected
mortality.
An SMR >1.0 indicates greater-than-expected mortality (also known as “excess mortality).
Union County’s SMR was 1.28, so the county had excess mortality in 2006.
Was it significantly more than expected?
1/26/09 New Mexico Department of Health 54
Indirect Age-StandardizationIndirect Age-Standardization You should not use direct age adjustment when
there are fewer than 20 (some say 25) health events. If you multiply the New Mexico crude rate by the Union County SMR, you get the indirectly age-adjusted rate for Union County.– Union Co. crude all-cause death rate: 1364.6– NM crude all-cause death rate: 757.5– Union County SMR: 1.28– Union County indirectly age-standardized rate: 969.6
(still higher than the state rate, but the effects of Union County’s age distribution have been removed).
1/26/09 New Mexico Department of Health 55
Confidence Interval for SMRConfidence Interval for SMR Observed deaths: 61 (# deaths from Vital Records data)
Expected deaths: 47.7 (# expected from SMR calculation)
SMR: 1.28 (observed / expected)
StdErr for SMR: 0.16 (SQRT(observed)) / expected
95% Confidence Interval: 0.32 (1.96 x StdErr)
Significance Test Does the 95% confidence interval include 1.0?– If "yes" -> not significant– If "no" -> statistically significant
1/26/09 New Mexico Department of Health 56
Summary: Statistical ToolsSummary: Statistical Tools
Use confidence intervals assess the stability of a rate.
Use C.I. to see if your local rate is significantly different from the state rate.
A statistic called a “Test of Proportions” uses the “pooled standard error” to test whether two local rates are significantly different.
1/26/09 New Mexico Department of Health 57
Summary: Statistical ToolsSummary: Statistical Tools
Combine data to improve the stability of your rate.– Combine persons (e.g., broader age group)– Combine place (larger area)– Combine time (more years)
1/26/09 New Mexico Department of Health 58
Summary: Statistical ToolsSummary: Statistical Tools
Use the Standardized Mortality (Morbidity) Ratio (SMR) to compare a local rate to a standard population (e.g., state overall).
The SMR “expected” can be used for indirect age-adjustment when the number of health events is fewer than 20, or if the age-specific death rates are not known.
1/26/09 59
Thanks!Thanks!
Lois M. Haggard, PhD
Community Health Assessment Program, NMDOH
lois.haggard@state.nm.us
http://ibis.health.state.nm.us
top related