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Session Guide
Sampling to
Study Drug Use
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
Sampling to Study Drug Use
SESSION GUIDE
PURPOSE AND CONTENT
The purpose of this session is to expose participants to the range of methods available
for sampling. Participants will be taught the underlying principles of sampling and will
undertake practical sampling exercises. Participants should understand that each
sampling method has different strengths and weaknesses, and can be used in different
circumstances.
To study drug use in health facilities may require the use of a range of sampling
techniques. Participants should also learn how to teach field staff to sample accurately
under varying field situations.
OBJECTIVES
[VA 1]
By the end of the session participants will be able to:
1. Describe the principles on which sampling is based.
2. Identify and describe different sampling methods.
3. Select a sample of health facilities from a list of such facilities using at least
two different methods.
4. Compare the results of the methods and discuss when each method might be
used in the field.
5. Instruct others how to sample when studying drug use.
FURTHER READINGS OR SOURCES
1. Designing and Conducting Health Systems Research Projects Vol. 2 Part 1
IDRC/WHO 1991 Available from IDRC, PO Box 8500, Ottawa, Ontario, Canada
K1G 3HG See Pages 196-220
2. Vaughan, J. P., and Morrow, R. H., Manual of Epidemiology for District Health
Management, WHO Geneva, 1989, p. 76-78.
3. Beaglehole, R., Bonita, R., Kjellström, T., Basic Epidemiology, WHO Geneva
1993, p. 46.
4. Lwanga, S. K., and Lemeshow, S., Sample Size Determination in Health Studies,
WHO Geneva, 1991.
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5. EPI INFO Version 6 Manual, p. 135-136, Plus using the program.
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Sampling to Study Drug Use
SESSION NOTES
INTRODUCTION
[VA 2]
Sampling is a process by which we study a small part of a population to make
judgments about that population. We sample as a part of our daily lives.
For example, if we want to know if Fruit Seller A is better than Fruit Seller B in a market,
we would go to Seller A and examine a number of his/her fruits for quality and price and
then repeat the process for Seller B. It would not be fair or accurate to base judgment
on a single fruit from each seller and it would be impractical to check every fruit in the
stall. The questions are: How do we select which fruit to examine, and how many to
examine? Obviously, if we only examine the fruit at the front of the stall we may get an
incorrect answer. So we need to find a sample method to check all the fruit by
examining a sample of the fruit.
Whenever we want to learn about health in the community or practices in the health
system, we need to draw samples since it would be impractical to collect data on every
person or event. In drug use surveys we need to draw samples to select facilities to
survey, prescriptions to study, or patients to observe.
If we wanted to know about prescribing in primary care facilities in a country we would
probably get the wrong impression of the real situation if we only surveyed the five
health centers closest to the central office of the Ministry of Health because these
would likely be better than the average. If we wanted to examine prescribing in a health
center we would be misled if we surveyed the first 20 cases attending on a Monday
morning. There may be an excess of men with hangovers from weekend drinking or
workers wanting sick notes to excuse them from going to work. So, to get a
representative sample we would need to ensure that all facilities or patients can be
included in the survey.
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[VA 3]
Sampling involves the selection of a number of study units
from a defined study population.
DEFINITIONS
[VA 4]
A study unit may be a person, a health facility, a prescription, or another such unit.
The study population, sometimes called the reference population, is the collection of
all possible study units. Again, this population may be people, health facilities,
prescriptions or other such units.
[VA 5]
A representative sample has all the important characteristics of the
population from which it is drawn.
SAMPLING METHODS
[VA6]
A sampling frame is a list of all of the available units in the study population. If a
complete listing is available, the sampling frame is identical to the study population.
There are two broad types of sampling methods. These are:
•
Non -- probability sampling
•
Probability sampling
The type of sampling depends whether there is a sampling frame available. If a
sampling frame exists, or if it can be created, probability sampling is used. If there is
none available, probability samplings cannot be used.
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It is always better to use probability sampling if this is possible. However, in some
situations, non-probability sampling is the only possible method. A sample drawn
using non-probability methods is likely to be less representative than a probability
sample so study results are less valid. When non-probability sampling is used in a
survey this fact should be included in any report.
[VA 7]
NON-PROBABILITY SAMPLING METHODS
If a sampling frame is not available or it cannot be created, a non-probability sampling
method will need to be used. There are two common methods. These are
convenience sampling and quota sampling.
Convenience sampling is a method by which, for convenience sake, the study units
that happen to be available at the time of data collection are selected in the sample.
This is the least representative sampling method.
Quota sampling is a method by
which different categories of
sample units are included to
ensure that the sample contains
units from these categories. For
example, a quota sample of
patients from a health center
might include 10 patients with
ARI, 10 with diarrhea, and 10
with malaria.
Both of these methods may be
used in drug use studies. When
measuring prescribing and
dispensing times or in assessing
patient understanding, a
convenience sample of patients
may be the only practical method. A quota sample may be used for males and females
to ensure that both genders are observed or interviewed. This may be important since
men are often treated with more respect and have higher literacy rates. Also, men may
be given priority over women or children and receive more thorough care.
Non-probability samples are not necessarily representative of the reference population.
However, we often need to use these methods when we have inadequate sample
frames or when a time constraint exists which forces us to use them.
PROBABILITY SAMPLING METHODS
[VA 8]
If a sampling frame (a list of the population units) exists then probability sampling may
be used.
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Probability sampling involves RANDOM selection procedures to ensure that
each sample unit is chosen on the basis of CHANCE.
Whenever possible use probability sampling to obtain results which are less biased.
There are a number of different methods.
[VA 9]
1. Simple Random Sampling
This is the simplest form of simple probability
sampling. A lottery is an example of a random
sample. The simple random sampling procedure is as
follows:
a) Make a numbered list of all units in the
reference population from which you will select
the sample (for example, a list all the health
centers in the country).
b) Decide on the size of the sample (for the WHO
Drug Use Indicators method this would be a
minimum of 20 facilities).
c) Choose the facilities to include by a lottery
method. (For example the numbers of all the
facilities can be placed in a box and drawn, a
random number table can be used, or random
numbers can be generated using a spreadsheet or calculator.)
This is the method used in Worksheet 1.1
[VA 10]
2. Systematic Sampling
In systematic sampling, sample units are selected from a numbered list of all units in
the study population by using a regular interval, starting from a random starting point.
To calculate the sampling interval, divide the size of the list by the desired sample
size. For example, if we want to select 20 health centers from a list of 46 in our
sampling frame, our sampling interval would be 46/20 = 2.3.
The first facility chosen in this case can be either 1, 2 or 3, which are all the possible
sampling units within the first sampling interval. This is selected by (1) choosing a
random number between 0 and 1 (with at least 3 digits after the decimal point), then (2)
multiplying this random number by the sampling interval, and (3) rounding this result
upward to get the number of the first facility. For example, if the random number
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chosen is 0.183, the first unit for the sample is 0.183 x 2.3 = 0.421 which rounds
upward to 1, so the first facility on the list is chosen for the sample.
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Later facilities are selected by adding the sampling interval to the previous result. If the
first result was 0.421. then the next facilities selected would be:
0.421 + 2.3 = 2.721 so
2.721 + 2.3 = 5.021 so
5.021 + 2.3 = 7.321 so
Facility 1
Facility 3
(Remember: always round upward)
Facility 6
Facility 8
and so forth.
If the first result had been 1.749, then the first facility would be Facility 2, and the next
facilities selected would be:
1.749 + 2.3 = 4.049 so
4.049 + 2.3 = 6.349 so
6.349 + 2.3 = 8.649 so
Facility 2
Facility 5
Facility 7
Facility 9
and so forth.
[VA11]
The method just described gives every unit an equal chance of being selected. This
method is used in Worksheet 1.2. This method can also be used with minor
modification to select units allowing for how large they are.
Sometimes it is desirable for clinics serving larger populations to have a greater chance
of being included in a sample. This method is called sampling with probability
proportional to size. This method is used in Worksheet 1.3 .
Systematic sampling is also useful when sampling prescriptions from a patient register.
If a register contains 100 pages each with 25 lines of prescriptions and you need to
select 30 prescriptions, the sampling interval would be:
100 x 25 = 83.3
30
Thus every 83rd prescription would be sampled. An alternative method described
below called multistage sampling could also be used to select a sample from a patient
register.
3. Stratified Sampling
[VA12]
Stratified sampling is used when the reference population contains different subpopulations, which should be considered separately.
For example, this might be the case in a study which included urban and rural facilities,
facilities with or without doctors, male or female patients.
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When stratified sampling is used, the sample frame (the list of the overall population) is
sorted into two or more groups. These different strata (groups) may then be sampled
either randomly or systematically.
In our fruit sellers example, we might want to check the quality and price of each of the
varieties of fruit sold.
The WHO manual, (p.59-60), recommends the use of stratified systematic sampling
methods for selecting facilities. For example, the sampling frame might include the
following list of facilities:
Facility Number
1
2
3
4
5
6
7
8
9
10
etc.
Type
Urban
Rural
Rural
Rural
Urban
Rural
Urban
Urban
Rural
Rural
etc.
This could then be grouped and sorted into 2 strata as follows:
1
5
7
8
Urban
Urban
Urban
Urban
Etc.
2
3
4
6
9
10
Rural
Rural
Rural
Rural
Rural
Rural
etc.
A sample would be selected separately from both the urban list and the rural list.
This is the method used in Worksheet 1.2, 1.4, 1.5, and 1.6.
4. Cluster Sampling
[VA 13]
In a cluster sample, a group of sample units is selected together, rather than each unit
being selected separately. This method may not be as representative as single unit
sampling, but for logistic reasons may be necessary. The recommended WHO
sampling procedure of selecting 30 groups of 7 children is a common cluster sampling
method.
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The main advantage of cluster sampling is that the method is easy to use and often
logistically simpler to organize. For example, when choosing houses in a community, it
is easier to walk between neighboring houses than all over the community. The
disadvantage is that the samples selected may be less representative especially when
the number of clusters selected is low. Thus, when the cluster method is used, try to
increase the sample size (by increasing the number of clusters sampled).
In drug use studies, cluster sampling may be used for selecting facilities when
distances are great. For example, a cluster of two facilities could be selected by
randomly selecting a single facility and then selecting the closest facility to the one
selected. This method might allow two facilities to be surveyed in a day when travel
time between facilities is significant. This method is used in Worksheet 1.7.
5. Multistage Sampling
[VA14]
In multistage sampling, the methods described above can be combined. For
example, we might wish to select 32 health facilities in a country containing 56 districts,
each of which contains a number of health facilities. From the 56 districts, 16 districts
would first be selected. In each district two health facilities would then be randomly
selected. This would be two-stage random sampling.
In the example above of selecting 30 prescriptions from a patient ledger of 100 pages
containing 25 prescriptions per page, we can use systematic sampling of the pages and
random selection of the prescription per page.
Thus we would calculate the sampling interval for the pages
100 ÷ 30 = 3.3
Randomly select the starting page from 1-4 as described above, then add 3.3
repeatedly to select the page numbers. Randomly select a number from 1-25 using a
calculator or a random number table to select which individual prescription would
actually be chosen on each page.
SAMPLE SIZE
[VA15]
The method of deciding the desirable sample size is described in the HSR manual p.
205-209 and Table 7.1 and in the WHO Manual of Epidemiology for District Health
Management on p.78. The EPI-INFO computer package contains a statistical
calculator which calculates minimum sample sizes based on different assumptions.
The appropriate sample size depends on:
•
Expected variation of the data. The more variation the larger sample required.
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•
The expected rate of the variable. For example, a smaller sample will be required
to obtain the same degree of accuracy if the rate of antibiotic prescribing is 20%
than if the rate is 50%.
•
The degree of accuracy required. Because the entire population is not studied,
every sample has some degree of uncertainty. The larger the sample, the less
the uncertainty. This certainty is often measured in terms of a 95% confidence
interval. For example, if we find a rate of 50% in a sample, how sure can we be
that this is the true rate in the reference population?
[VA16]
For a sample size of 50, the range of certainty will be 36% - 64% (95% CI)
100, the range will be 40% - 60%
200, the range will be 43% - 57%
500, the range will be 45% - 55%
1000, the range will be 47% - 53%
Increasing the size of the sample increases the certainty, but after a certain point the
value of the increase in certainty is not in proportion to the increase in effort and
resources to collect the data.
The appropriate sample size is usually a compromise between what is
STATISTICALLY DESIRABLE and what is FEASIBLE.
In general, a minimum sample size is 30
The WHO Manual on "How to Investigate Drug Use in Health Facilities" reflects the
experiences of a number of surveys carried out in Africa, Asia, and Latin America.
These surveys have shown that there is less variation in practice within health facilities
than between facilities. Thus to obtain reliable estimates, it is better to increase the
number of facilities included in the sample rather than emphasizing the number of
prescriptions surveyed or patients observed in each survey.
However the difficulty in doing these surveys is usually the logistic or transport problem
of getting to the health facilities.
The compromise which has been reached for a simple cross-sectional survey would be
30 prescriptions from 20 facilities.
When individual facilities are being studied or compared, a minimum of 100
prescriptions should be collected. If the event being studied is very unusual, e.g.
injection use in Bangladesh, or very frequent, e.g. generic use in Zimbabwe, this
number may need to be increased to obtain sufficiently precise estimates.
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When the indicators are used for supervision a method called Lot Quality Assurance
Sampling (LQAS) may be used. This is described in Annex 4 of the WHO Manual, p.
77-81.
SUMMARY
[VA17]
The principles underlying sampling should be understood by all people involved in drug
use surveys. The field workers, enumerators, and supervisors should understand that
any facility or any prescription or any patient attending could be included in the survey.
Every effort should be made to avoid bias (systematic error) in selecting sampled units
for study.
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[VA18]
ACTIVITY ONE
Sample Selection
RATIONALE
This is a small group or individual activity that will lead you through a process of
deciding on a sample for a prescribing study. There are different approaches to sample
selection. Each group will be asked to implement at least two different strategies. The
groups will then come together and compare the results of the different sampling
methods.
Summary information about the province to be studied is given to you on the bottom of
the table in the Summary Worksheet. Refer to Annex 1 of the Manual, p. 59, How to
Investigate Drug use in Health Facilities.
Your group will be assigned one or more methods of drawing a sample of 20 health
facilities, either
1.
simple random sampling (Worksheet 1.1)
2.
systematic sampling (Worksheet 1.2)
3.
systematic sampling with probability proportional to size (Worksheet 1.3)
4.
stratified sampling by location (Worksheet 1.4)
5.
stratified sampling by staffing (Worksheet 1.5)
6.
cluster sampling (worksheet 1.6)
A table of random numbers has been provided to draw the samples. When you have
completed your assigned method, you should choose one other method, and draw
another sample.
For each method, compute the values of two descriptive variables (% urban facilities, %
facilities staffed by physicians) as well as the values of the two indicators. Compare
your two sets of results and be prepared to discuss your experience in drawing the
sample and the differences in results. Enter your results into the Summary Worksheet
and compare your results with the true values given at the bottom of the Summary
table. Be prepared to discuss which method would be best in drawing an actual sample
and why.
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INSTRUCTIONS
CHOICE #1: A simple random sample (Worksheet 1.1)
Tear a sheet of paper into 52 pieces. Number them 1 to 52, crunch each up into a little
ball, and place in a paper bag. Shake the bag well. Randomly remove 20 numbers.
These 20 facilities are a simple random sample of the whole 52. Fill in the Summary
Table to show the results of the sampling.
CHOICE #2:
Systematic random sampling (Worksheet 1.2)
Use the method described in the Indicators Manual on p. 60, Step 3:
a. Calculate your sampling interval. This will be 52 ÷ 20 = _____.
b. Choose a random number from the random number table = _____.
c. Multiply the result in (a) by the random number selected in (b) = _____.
d. Round up this result and drop any numbers after the decimal point. This is
number of your first facility.
e. Add the sampling interval calculated in (a) to the result in (c) = _____.
f. Round up the number you calculated in (e). The result is the number of your
second facility.
g. Add the number you calculated in (e) to the sampling interval calculated in (a)
and use the results to choose another facility (remembering to round up).
h. Continue with this procedure until you have selected 20 facilities [i.e., (a), (f), (g),
plus 17 more].
i.
Fill in the Summary Table to show the results of the sampling.
CHOICE #3: Systematic Sampling proportional to size (Worksheet 1.3).
Order the list of facilities to be sampled in inverse order of their size, as in Worksheet
1.3, and calculate the cumulative population.
a. Calculate the sampling interval by dividing the cumulative population by the
number of facilities to be included in the sample. This will be 1,721,549 ÷ 20 =
___________.
b. Choose a random number from the random number table = _____.
c. Multiply the result in (a) by the random number selected in (b) = ___________.
d. Select for the sample the health facility whose cumulative total is the lowest one
greater than the result in (c).
e. Add the sampling interval calculated in (a) to the result in (c) = ___________.
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f. Select as the next facility the one whose cumulative total is greater than the new
result in (e). Note that it is possible for the same facility to be selected more than
once by this method. In this case, the sample in that facility would be increased
accordingly.
g. Continue with this procedure until you have chosen 20 facilities.
h. Fill in the Summary Table to show the results of the sampling.
CHOICE # 4-5:
Stratified Sampling (Worksheets 1.4, 1.5)
Use Worksheets 1.4 or 1.5 to sample facilities stratified by location (Worksheet 1.4) or
by staffing (Worksheet 1.5). Divide the 20 facilities to be chosen equally within the two
strata (10 facilities from each). You can use either simple random sampling (choice 1)
or systematic sampling (choice 2) to select facilities from within each stratum.
CHOICE # 6: Cluster Sampling
Use Worksheet 1.6 and Figure 1.1.
a. Select 10 facilities using a simple random sample.
b. For each facility selected, choose the closest facility (Figure 1.1) to also be
included in the sample, forming a “cluster” of two facilities. If one of these
“clustered” facilities is chosen in a later random selection, pick an alternative
facility.
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TABLE OF RANDOM NUMBERS
0.28181
0.72498
0.73725
0.52251
0.49285
0.86298
0.07287
0.58109
0.64009
0.29625
0.66929
0.66220
0.99302
0.18193
0.92831
0.49890
0.47829
0.63489
0.76565
0.45887
0.51128
0.82958
0.26826
0.30873
0.97455
0.96525
0.66284
0.65283
0.77644
0.00708
0.00456
0.79470
0.12438
0.85958
0.08906
0.42408
0.64120
0.88661
0.33995
0.32381
0.23257
0.59271
0.01073
0.72465
0.61465
0.42220
0.50486
0.06957
0.60827
0.76483
0.08029
0.93451
0.66671
0.82705
0.33302
0.37228
0.16365
0.36674
0.99228
0.97763
0.85545
0.47110
0.64983
0.65950
0.25651
0.45020
0.03074
0.27105
0.96124
0.82531
0.45179
0.91398
0.57483
0.04158
0.85490
0.23386
0.86688
0.32958
0.82493
0.80896
0.95771
0.26886
0.42753
0.31799
0.33788
0.03774
0.37183
0.03002
0.88968
0.23196
0.17683
0.96398
0.75046
0.28314
0.48483
0.94486
0.85873
0.84084
0.53865
0.66985
0.85179
0.90095
0.78970
0.87265
0.58291
0.50105
0.84170
0.99398
0.53512
0.92228
0.57912
0.80075
0.75099
0.46035
0.03565
0.69909
0.66783
0.90832
0.02986
0.22192
0.67320
0.86713
0.81196
0.80469
0.38245
0.94346
0.18294
0.10796
0.12440
0.23352
0.45849
0.90048
0.34620
0.05729
0.94829
0.33323
0.84855
0.94886
0.25914
0.24674
0.01712
0.42879
0.26207
0.08147
0.97829
0.88756
0.45596
0.53436
0.78177
0.70243
0.10376
0.61636
0.13122
0.91718
0.62576
0.02111
0.86360
0.66843
0.61691
0.94477
0.45562
0.00920
0.80484
0.20412
0.56143
0.68958
0.61691
0.79670
0.31113
0.59684
0.79149
0.44454
0.54806
0.56180
0.56570
0.32469
0.24865
0.93081
0.83379
0.75202
0.18090
0.35996
0.13794
0.69819
0.12238
0.36665
0.72498
0.14370
0.69521
0.64750
0.92647
0.27204
0.74311
0.00770
0.79796
0.46656
0.09531
0.96037
0.67877
0.02913
0.98787
0.63830
0.42029
0.76461
0.49438
0.17978
0.36590
0.68464
0.01725
0.56969
0.12674
0.27456
0.09152
0.35512
0.32333
0.94221
0.32937
0.51749
0.22256
0.45500
0.52418
0.18912
0.60885
0.46557
0.89203
0.75146
0.17375
0.88816
0.78345
0.75994
0.32292
0.46516
0.29774
0.58630
0.90772
0.77493
0.21989
0.76631
0.35466
0.12921
0.02041
0.31859
0.37045
0.52637
0.61276
0.27080
0.81381
0.30177
0.41056
0.22386
0.33997
0.53453
0.61351
0.08043
0.66141
0.08242
0.45106
0.28192
0.61149
0.23421
0.31418
0.81665
0.43712
0.23187
0.05931
0.91934
0.75016
0.62742
0.39834
0.77903
0.11711
0.33572
0.42376
0.42746
0.73458
0.73781
0.44204
0.61443
0.37379
0.02845
0.04473
0.89193
0.61618
0.19254
0.11625
0.55357
0.96248
0.59649
0.84159
0.02210
0.18668
0.73940
0.41397
0.84106
0.07765
0.95867
0.77079
0.19120
0.03718
0.69954
0.47300
0.51598
0.07515
0.14068
0.61879
0.38847
0.22035
0.60881
0.91990
0.84598
0.96374
0.08211
0.20302
0.40121
0.78577
0.17222
0.75848
0.03392
0.08040
0.05837
0.79615
0.29272
0.03856
0.66394
0.89791
0.55139
0.46294
0.10344
0.09858
0.83487
0.85167
0.38321
0.88336
0.49885
0.55009
0.88740
0.63831
0.50767
0.89957
0.36070
0.95815
0.46685
0.92520
0.04732
0.17528
0.87197
0.10954
0.98299
0.64286
0.26476
0.62750
0.64289
0.88960
0.34320
0.05009
0.15801
0.70049
0.51270
0.36109
0.45412
0.91120
0.47596
0.70473
0.69698
0.15379
0.54472
0.76638
0.10933
0.04316
0.23775
0.98373
0.62209
0.50972
0.56497
0.12685
0.12228
0.83086
0.84285
0.21149
0.71091
0.99088
0.05220
0.09493
0.18544
0.21911
0.24681
0.12357
0.26155
0.41118
0.62699
0.01418
0.39623
0.31389
0.22487
0.08780
0.47660
0.23950
0.44983
0.50313
0.98918
0.49158
0.45738
0.43658
0.61989
0.63616
0.64254
0.12260
0.12691
0.80597
0.69470
0.89381
0.30331
0.62498
0.00840
0.58307
0.31831
0.04971
0.12898
0.20795
0.69122
0.17834
0.73566
0.86054
0.53096
0.19030
0.40076
0.37797
0.16523
0.37903
0.05685
0.42250
0.81803
0.68689
0.06085
0.85354
0.67050
0.53116
0.37000
0.90315
0.96170
0.76316
0.03085
0.12392
0.85764
0.79473
0.64700
0.05156
0.00161
0.34031
0.85848
0.37644
0.30871
0.02263
0.92995
0.69914
0.41139
0.24985
0.65169
0.83446
0.24328
0.41650
0.30083
0.41456
0.52947
0.59728
0.42059
0.08680
0.72780
0.17830
0.29981
0.65694
0.64121
0.87283
0.08256
0.51521
0.09632
0.96991
0.01995
0.08538
0.60245
0.45925
0.83535
0.01621
0.13931
0.88096
0.91876
0.06729
0.29531
0.34718
0.30287
0.94694
0.03234
0.01685
0.44927
0.96743
0.77647
0.89795
0.70874
0.79766
0.27899
0.51682
0.29086
0.06674
0.55644
0.82617
0.42074
0.51122
0.07251
0.18400
0.42275
0.35605
0.71820
0.93333
0.90307
0.22131
0.56783
0.27218
0.79006
0.51330
0.72072
0.10695
0.46832
0.54752
0.42062
0.77207
0.92343
0.46015
0.25226
0.92989
0.39096
0.66306
0.54315
0.19732
0.93970
0.26452
0.01699
0.34247
0.40966
0.73553
0.07105
0.12381
0.22499
0.45461
0.89338
0.88220
0.32310
0.41270
0.27622
0.19192
0.14589
0.24460
0.90691
0.84366
0.00903
0.05829
0.96554
0.47328
0.71992
0.13625
0.20414
0.12008
0.62760
0.64833
0.32322
0.72038
0.72905
0.31476
0.52878
0.47862
0.78920
0.62424
0.37949
0.59325
0.26475
0.57841
0.53154
0.94293
0.59005
0.48267
0.33931
0.99890
0.41183
0.66202
0.96907
0.44813
0.10240
0.48133
0.69020
0.37108
0.58334
0.40350
0.84116
0.17939
0.13269
0.58245
0.35246
0.85754
0.44455
0.35954
0.47513
0.78685
0.72963
0.44966
0.08484
0.66328
0.53813
0.72375
0.00377
0.35268
0.71415
0.13459
0.69961
0.18580
0.39052
0.70874
0.01537
0.96905
0.00905
0.81310
0.07091
0.70279
0.35562
0.74295
0.09807
0.08923
0.92743
0.60295
0.36365
0.48653
0.61688
0.85134
0.19207
0.12405
0.36063
0.66066
0.11763
0.20335
0.50064
0.53612
0.20593
0.45736
0.58754
0.53659
0.17384
0.97663
0.88577
0.04209
0.81155
0.96738
0.86854
0.68577
0.97448
0.16354
0.51926
0.83935
0.90583
0.01143
0.71272
0.30522
0.81135
0.47764
0.48798
0.94535
0.75110
0.72068
0.83954
0.14708
0.29782
0.81229
0.64851
0.42981
0.82970
0.53078
0.93501
0.00701
0.49909
0.04041
0.65202
0.88068
0.70192
0.39129
0.72761
0.26746
0.45020
16
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
ACTIVITY ONE SUMMARY TABLE
Results of Different Sampling Methods
Sampling
Method
Number
Urban
% Urban
24
46%
Number
Physician
%
Physician
Avg. No.
Drugs
% with
Antibiotics
3.5
52%
1.1
Simple
Random
1.2
Systematic
1.3
Systematic
Proportional to
Size
1.4
Stratified
By
Location
1.5
Stratified
By
Staffing
1.6
Cluster
Sample
True
Figures in the
Population
35
73%
17
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
ACTIVITY ONE - WORKSHEET 1.1
52 Health Facilities Sorted by Facility ID for Simple Random Sampling
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
Location
Urban
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Rural
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Rural
Urban
Urban
Urban
Rural
Urban
Urban
Rural
Rural
Staffing
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
# of
Drugs
3.7
3.6
3.2
3.4
3.7
3.4
3.5
4.2
2.9
3.7
3.1
2.8
2.8
4.2
4.1
3.9
3.4
3.6
3.8
2.7
3.6
2.8
4.0
4.4
3.3
3.6
4.7
2.9
2.8
3.8
3.4
3.7
2.5
3.1
3.9
3.7
3.1
2.5
3.5
3.6
3.3
4.4
3.0
2.5
3.8
3.7
2.9
3.7
3.3
3.0
3.7
4.1
% with
Antibiotics
48%
34%
58%
31%
26%
67%
44%
69%
50%
46%
29%
61%
49%
27%
32%
27%
28%
38%
31%
26%
63%
31%
51%
70%
61%
66%
47%
62%
72%
60%
52%
46%
62%
51%
68%
57%
65%
59%
69%
53%
48%
58%
61%
43%
64%
85%
59%
51%
58%
64%
35%
70%
Population
47,175
43,073
20,715
24,882
22,498
27,735
29,438
32,294
42,160
28,628
39,951
18,563
34,123
29,829
37,888
29,835
30,471
32,388
22,645
17,727
16,944
27,213
35,295
18,037
24,099
35,280
24,921
57,819
23,927
28,269
22,859
37,702
79,203
48,567
28,506
39,573
32,530
28,733
25,441
23,206
89,121
20,141
33,617
39,395
24,510
28,266
78,483
12,211
38,660
27,118
43,391
16,494
Select
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
18
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
ACTIVITY ONE - WORKSHEET 1.2
52 Health Facilities Sorted by Facility ID for Stratified Sampling
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
Location
Urban
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Rural
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Rural
Urban
Urban
Urban
Rural
Urban
Urban
Rural
Rural
Staffing
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
# of
Drugs
3.7
3.6
3.2
3.4
3.7
3.4
3.5
4.2
2.9
3.7
3.1
2.8
2.8
4.2
4.1
3.9
3.4
3.6
3.8
2.7
3.6
2.8
4.0
4.4
3.3
3.6
4.7
2.9
2.8
3.8
3.4
3.7
2.5
3.1
3.9
3.7
3.1
2.5
3.5
3.6
3.3
4.4
3.0
2.5
3.8
3.7
2.9
3.7
3.3
3.0
3.7
4.1
% with
Antibiotics
48%
34%
58%
31%
26%
67%
44%
69%
50%
46%
29%
61%
49%
27%
32%
27%
28%
38%
31%
26%
63%
31%
51%
70%
61%
66%
47%
62%
72%
60%
52%
46%
62%
51%
68%
57%
65%
59%
69%
53%
48%
58%
61%
43%
64%
85%
59%
51%
58%
64%
35%
70%
Population
47,175
43,073
20,715
24,882
22,498
27,735
29,438
32,294
42,160
28,628
39,951
18,563
34,123
29,829
37,888
29,835
30,471
32,388
22,645
17,727
16,944
27,213
35,295
18,037
24,099
35,280
24,921
57,819
23,927
28,269
22,859
37,702
79,203
48,567
28,506
39,573
32,530
28,733
25,441
23,206
89,121
20,141
33,617
39,395
24,510
28,266
78,483
12,211
38,660
27,118
43,391
16,494
Select
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
19
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
ACTIVITY ONE - WORKSHEET 1.3
52 Health Facilities Sorted by Population for Sampling Probability Proportional to Size
ID
41
33
47
28
34
1
51
2
9
11
36
44
49
15
32
23
26
13
43
37
18
8
17
16
14
7
38
10
35
30
46
6
22
50
39
27
4
45
25
29
40
31
19
5
3
42
12
24
20
21
52
48
Location
Urban
Urban
Urban
Urban
Urban
Urban
Rural
Rural
Rural
Rural
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Urban
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Rural
Urban
Urban
Urban
Rural
Rural
Urban
Urban
Rural
Rural
Urban
Urban
Urban
Urban
Urban
Rural
Rural
Rural
Urban
Rural
Rural
Rural
Rural
Rural
Rural
Staffing
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Paramedic
Paramedic
Paramedic
Physician
Physician
Paramedic
Physician
Paramedic
Paramedic
Physician
Paramedic
Paramedic
Paramedic
# of
Drugs
3.3
2.5
2.9
2.9
3.1
3.7
3.7
3.6
2.9
3.1
3.7
2.5
3.3
4.1
3.7
4.0
3.6
2.8
3.0
3.1
3.6
4.2
3.4
3.9
4.2
3.5
2.5
3.7
3.9
3.8
3.7
3.4
2.8
3.0
3.5
4.7
3.4
3.8
3.3
2.8
3.6
3.4
3.8
3.7
3.2
4.4
2.8
4.4
2.7
3.6
4.1
3.7
% with
Antibiotics
48%
62%
59%
62%
51%
48%
35%
34%
50%
29%
57%
43%
58%
32%
46%
51%
66%
49%
61%
65%
38%
69%
28%
27%
27%
44%
59%
46%
68%
60%
85%
67%
31%
64%
69%
47%
31%
64%
61%
72%
53%
52%
31%
26%
58%
58%
61%
70%
26%
63%
70%
51%
Population
89,121
79,203
78,483
57,819
48,567
47,175
43,391
43,073
42,160
39,951
39,573
39,395
38,660
37,888
37,702
35,295
35,280
34,123
33,617
32,530
32,388
32,294
30,471
29,835
29,829
29,438
28,733
28,628
28,506
28,269
28,266
27,735
27,213
27,118
25,441
24,921
24,882
24,510
24,099
23,927
23,206
22,859
22,645
22,498
20,715
20,141
18,563
18,037
17,727
16,944
16,494
12,211
Cumulative
Population
89,121
168,324
246,807
304,626
353,193
400,368
443,759
486,832
528,992
568,943
608,516
647,911
686,571
724,459
762,161
797,456
832,736
866,859
900,476
933,006
965,394
997,688
1,028,159
1,057,994
1,087,823
1,117,261
1,145,994
1,174,622
1,203,128
1,231,397
1,259,663
1,287,398
1,314,611
1,341,729
1,367,170
1,392,091
1,416,973
1,441,483
1,465,582
1,489,509
1,512,715
1,535,574
1,558,219
1,580,717
1,601,432
1,621,573
1,640,136
1,658,173
1,675,900
1,692,844
1,709,338
1,721,549
Select
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
20
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
ACTIVITY ONE - WORKSHEET 1.4
52 Health Facilities Sorted by Location for Stratified Sampling
ID
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
27
44
48
51
52
1
25
26
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
45
46
47
49
50
Location
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Staffing
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Paramedic
# of
Drugs
3.6
3.2
3.4
3.7
3.4
3.5
4.2
2.9
3.7
3.1
2.8
2.8
4.2
4.1
3.9
3.4
3.6
3.8
2.7
3.6
2.8
4.0
4.4
4.7
2.5
3.7
3.7
4.1
3.7
3.3
3.6
2.9
2.8
3.8
3.4
3.7
2.5
3.1
3.9
3.7
3.1
2.5
3.5
3.6
3.3
4.4
3.0
3.8
3.7
2.9
3.3
3.0
% with
Antibiotics
34%
58%
31%
26%
67%
44%
69%
50%
46%
29%
61%
49%
27%
32%
27%
28%
38%
31%
26%
63%
31%
51%
70%
47%
43%
51%
35%
70%
48%
61%
66%
62%
72%
60%
52%
46%
62%
51%
68%
57%
65%
59%
69%
53%
48%
58%
61%
64%
85%
59%
58%
64%
Population
43,073
20,715
24,882
22,498
27,735
29,438
32,294
42,160
28,628
39,951
18,563
34,123
29,829
37,888
29,835
30,471
32,388
22,645
17,727
16,944
27,213
35,295
18,037
24,921
39,395
12,211
43,391
16,494
47,175
24,099
35,280
57,819
23,927
28,269
22,859
37,702
79,203
48,567
28,506
39,573
32,530
28,733
25,441
23,206
89,121
20,141
33,617
24,510
28,266
78,483
38,660
27,118
Select
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
21
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
ACTIVITY ONE - WORKSHEET 1.5
52 Health Facilities Sorted by Staffing for Stratified Sampling
ID
3
6
8
12
21
24
29
31
33
40
46
48
50
52
1
2
4
5
7
9
10
11
13
14
15
16
17
18
19
20
22
23
25
26
27
28
30
32
34
35
36
37
38
39
41
42
43
44
45
47
49
51
Location
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Urban
Urban
Urban
Rural
Urban
Rural
Urban
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Rural
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Rural
Urban
Urban
Urban
Rural
Staffing
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
# of
Drugs
3.2
3.4
4.2
2.8
3.6
4.4
2.8
3.4
2.5
3.6
3.7
3.7
3.0
4.1
3.7
3.6
3.4
3.7
3.5
2.9
3.7
3.1
2.8
4.2
4.1
3.9
3.4
3.6
3.8
2.7
2.8
4.0
3.3
3.6
4.7
2.9
3.8
3.7
3.1
3.9
3.7
3.1
2.5
3.5
3.3
4.4
3.0
2.5
3.8
2.9
3.3
3.7
% with
Antibiotics
58%
67%
69%
61%
63%
70%
72%
52%
62%
53%
85%
51%
64%
70%
48%
34%
31%
26%
44%
50%
46%
29%
49%
27%
32%
27%
28%
38%
31%
26%
31%
51%
61%
66%
47%
62%
60%
46%
51%
68%
57%
65%
59%
69%
48%
58%
61%
43%
64%
59%
58%
35%
Population
20,715
27,735
32,294
18,563
16,944
18,037
23,927
22,859
79,203
23,206
28,266
12,211
27,118
16,494
47,175
43,073
24,882
22,498
29,438
42,160
28,628
39,951
34,123
29,829
37,888
29,835
30,471
32,388
22,645
17,727
27,213
35,295
24,099
35,280
24,921
57,819
28,269
37,702
48,567
28,506
39,573
32,530
28,733
25,441
89,121
20,141
33,617
39,395
24,510
78,483
38,660
43,391
Select
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
22
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
ACTIVITY ONE - WORKSHEET 1.6
52 Health Facilities Sorted by Facility ID for Cluster Sampling
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
Location
Urban
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Rural
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Rural
Urban
Urban
Urban
Rural
Urban
Urban
Rural
Rural
Staffing
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Physician
Physician
Physician
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
Physician
Paramedic
# of
Drugs
3.7
3.6
3.2
3.4
3.7
3.4
3.5
4.2
2.9
3.7
3.1
2.8
2.8
4.2
4.1
3.9
3.4
3.6
3.8
2.7
3.6
2.8
4.0
4.4
3.3
3.6
4.7
2.9
2.8
3.8
3.4
3.7
2.5
3.1
3.9
3.7
3.1
2.5
3.5
3.6
3.3
4.4
3.0
2.5
3.8
3.7
2.9
3.7
3.3
3.0
3.7
4.1
% with
Antibiotics
48%
34%
58%
31%
26%
67%
44%
69%
50%
46%
29%
61%
49%
27%
32%
27%
28%
38%
31%
26%
63%
31%
51%
70%
61%
66%
47%
62%
72%
60%
52%
46%
62%
51%
68%
57%
65%
59%
69%
53%
48%
58%
61%
43%
64%
85%
59%
51%
58%
64%
35%
70%
Population
47,175
43,073
20,715
24,882
22,498
27,735
29,438
32,294
42,160
28,628
39,951
18,563
34,123
29,829
37,888
29,835
30,471
32,388
22,645
17,727
16,944
27,213
35,295
18,037
24,099
35,280
24,921
57,819
23,927
28,269
22,859
37,702
79,203
48,567
28,506
39,573
32,530
28,733
25,441
23,206
89,121
20,141
33,617
39,395
24,510
28,266
78,483
12,211
38,660
27,118
43,391
16,494
Select
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
23
SAMPLING TO STUDY DRUG USE
SESSION GUIDE
Figure 1.1: Geographical Distribution of Health Centers for Cluster Sampling
37
33
46
52
42
31
9
18
6
16
13
19
3
17
25
23
11
2
24
8
7
20
35
38
15
28
50
45
40
51
44
43
49
29
47
34
22
30
39
5
21
32
41
48
36
26
27
1
10
4
14
12
24