SUPPLEMENTAL MATERIAL FOR
Use Rates of Free-standing Filters in an Asthma Intervention Study
Stuart Batterman,1* Liuliu Du,1 Edith Parker,2 Thomas Robins,1 Toby Lewis,1, 3 Bhramar
Mukherjee1, Erminia Ramirez,4 Zachary Rowe,5 Wilma Brakefield-Caldwell6
Statistical modeling
Several statistical models were fitted using general estimating equation (GEE) models to
identify factors affecting household weekly average filter use during both week-long intensive
periods and the longer non-intensive periods, and to account for repeated measures, i.e.,
multiple visits to a home. The full model (model 1) was:
Fi = β0 + β1 Periodi + β2 Week i + β3 Spri + β4 Sumi + β5 Falli +β6 ETSi
(1)
where Fi = weekly average filter use in house i (i=1, 2….89); Periodi = indicator variables
denoting visit type and number (baseline visit, intensive weeks 1 to 3, and non-intensive period
1 to 3); Weeki = indicator variables indicating week number following last intensive visit (1, 2,
3 ... 9, 10); Spri, Sumi and Falli = indicator variables for spring, summer and fall seasons
(spring was defined as March through May, summer as June through August; fall as September
through November); ETSi = detection of the ETS tracer; and β0 through β6 = estimated
parameters. To help confirm results, a similar model (model 2) was estimated using only nonintensive data. A third model (model 3) considered only the intensive weeks (baseline and
seasonal visits) and excluded the Week variable (which was not relevant). Only model 3
included the ETS variable since ETS measurements were not available for non-intensive
periods.
The weekly trends shown in the paper as Figure 3 were confirmed by GEE models that
included adjustments for season. Significant parameters in model 1 (encompassing both
intensive and non-intensive periods) included sampling period, week number and season
(Supplemental Table 1). This model shows that use increased in spring and summer seasons an
average of 9-10% compared to winter (the reference period), and declined by 12% in the week
immediately following each intensive, and then by 2-3% in the three subsequent weeks,
following trends in Figure 3. Similar trends were seen when only non-intensive data were
considered (model 2, Supplemental Table 1), although non-intensive period 3 did not attain
statistical significance, possibly due to a small sample (n=91 participant-weeks, 7 households).
In model 3 (including only the intensive periods; Supplemental Table 1), seasonal effects and
the presence of ETS were not significant predictors, suggesting that season affected use during
the non-intensive periods only. A variant of model 1 investigating whether filter use during the
non-intensive period changed in anticipation of the next intensive visits yielded negative results
(data not shown). In addition, daily data for the three weeks prior to the intensive visits were
examined. Again, no significant or consistent trend was observed.
Supplemental Table 1. GEE estimates of filter use during intensive and non-intensive periods
(model 1), non-intensive periods only (model 2) or intensive periods only (model 3).
Intercept
Seasonal Visit 3
Non-intensive 3
Seasonal Visit 2
Model 1 (N=2374)
β
SE
79.57
3.58
-35.47
11.62
-37.12
7.22
-23.22
5.14
Non-intensive 2
Seasonal Visit 1
Non-intensive 1
Baseline Visit
-35.31
4.64
-26.12
5.25
-29.02
4.18
Reference Reference
Spring
Summer
Fall
Winter
8.91
2.94
10.39
3.39
4.15
3.84
Reference Reference
Variable
Period
Season
Group
>10
6-10
Week
ETS
5
4
3
2
1
0
-25.14
-20.17
3.34
2.85
-20.48
2.72
-18.78
3.14
-15.43
2.80
-12.17
2.47
Reference Reference
Model 2 (N=2146)
β
SE
50.35
4.15
-8.42
-6.32
Model 3 (N=228)
β
SE
87.70
4.60
-37.16
15.10
5.16
-18.95
7.23
-17.25
7.01
3.18
Reference Reference
Reference Reference
9.72
3.01
11.38
3.46
4.69
4.37
Reference Reference
-25.37
-20.27
-8.53
7.56
-3.80
8.53
-9.04
6.14
Reference Reference
3.37
2.85
-20.59
2.70
-18.87
3.13
-15.50
2.78
-12.26
2.46
Reference Reference
Yes
SE: standard error. Bolded values are significant at α = 0.05.
1.11
4.93
Low
Medium
High
Turbo
100
80
60
40
20
Use during intensive visits (%)
000
20
40
60
80
100
Use during non-intensive periods (%)
Supplemental Figure 1. Individual level data on filter use for intensive (left) and non-intensive
(right) visits, sorted by total use fraction during intensive visits. Each bar represents a different
household and shows the average filter use and fan speed across the study period.
Supplemental Figure 2. Scatter plots for weekly filter use between intensive and non-intensive
periods. (Seasonal visits 3 and non-intensive 3 were not shown because of limited sample sizes).
Weekly trends and exponential models
Supplemental Figure 3 depicts weekly trends of filter use following the intensive visits to
the households. The plot combines measurements made during the baseline and seasonal
intensive weeks (n=228 visits or participant-weeks) and the non-intensive periods (n=2,146
participant-weeks). While the interquartile range shows significant variation, use tended to
decrease over a period of several weeks and then leveled off. Trends were similar following
baseline and seasonal visits (data not shown). The weekly median and means closely fit
exponential models:
U(t)average = 40.02 e−0.73t + 33.08
(2)
U(t)median = 74.05 e−0.84t + 18.81
(3)
where U(t) = filter use (%) at week t; and t=0 is the week of the baseline or seasonal visit. This
analysis indicates that use following an intensive visit drops for three to four weeks, at which
point use levels off (until the household is next visited for health and environmental
assessments). This pattern suggests that any effect of the home visits on use behavior is shortlived. A similar analysis was performed to see if families modified use during the nonintensive period in anticipation of an upcoming intensive visit by our staff, but no consistent
changes were observed.
The weekly trends in Supplemental Figure 3 were confirmed by GEE models that included
adjustments for season. Significant parameters in model 1 (encompassing both intensive and
non-intensive periods) included sampling period, week number and season (Supplemental
Table 1). This model shows that use increased in spring and summer seasons an average of 910% compared to winter (the reference period), and declined by 12% in the week immediately
following each intensive, and then by 2-3% in the three subsequent weeks, following trends
shown below. Similar trends were seen when only non-intensive data were considered (model
2, Supplemental Table 1), although non-intensive period 3 did not attain statistical significance,
possibly due to a small sample (n=91 participant-weeks, 7 households). In model 3 (including
only the intensive periods; Supplemental Table 1), seasonal effects and the presence of ETS
were not significant predictors, suggesting that season affected use during the non-intensive
periods only. A variant of model 1 investigating whether filter use during the non-intensive
period changed in anticipation of the next intensive visits yielded negative results (data not
shown). In addition, daily data for the three weeks prior to the intensive visits were examined.
Again, no significant or consistent trend was observed.
In summary, the trend analyses show that filter use rapidly decreased in the few weeks
following an intensive visit when the household was visited for health and environmental
assessments, and that use was somewhat higher in spring and summer seasons during the nonintensive periods.
100
Average
Average
Filter Use (%)
80
Median
Median
60
40
20
0
0
1
2
3
4
5
6
7
8
9
10
Week
Supplemental Figure 3. Filter use during intensive periods (week 0) and the following 10 weeks
during the non-intensive period. The plot combines measurements made during the baseline and
seasonal intensive weeks (n=228 visits or participant-weeks) and the non-intensive periods
(n=2,146 participant-weeks). (Seasonal visit 2 and non-intensive period 3 are omitted due to
limited sample size). Lines show fit to exponential models (see text).
100
A
High(n=24)
Medium(n=23)
Low(n=23)
Filter Use (%)
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
Hour of Day
100
B
High (n=134)
Medium (n=157)
8
14
Low (n=103)
Filter Use (%)
80
60
40
20
0
0
2
4
6
10
12
16
18
20
22
24
Hour of Day
Supplemental Figure 4. Filter use by the hour of day for intensive periods. A: Use by
household-study grouped by tertiles of average use among households with low (6-47%),
medium (48-72%) and high (73-94%) use groups after excluding households with little use
(≤5%, n=1) or near continuous use (≥95%, n=16). B. Use by household-day grouped by tertiles
of average daily use with low (6-33%), medium (34-64%) and high (65-94%) use groups after
excluding household-days households with little use (≤5%, n=235) or near continuous use
(≥95%, n=638).