Table 2 on page 2152 gives point and confidence interval estimates of the RR for different groups of people and different types of activities. Consider the characteristic of gait speed, which is broken down into 3 categories: slow, middle, and fast. Why are the RR's for the middle category all exactly 1?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Section4.6: Applications And The Perron-frobenius Theorem
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Table 2 on page 2152 gives point and confidence interval estimates of the RR for different groups of people and different types of activities. Consider the characteristic of gait speed, which is broken down into 3 categories: slow, middle, and fast. Why are the RR's for the middle category all exactly 1?

TABLE 2-Rate Ratios for Falls During 4 Categories of Activity by Baseline Characteristics and Location of Fall: MOBILIZE Boston, September 2005-December 2009
Indoor Falls
Outdoor Falls
Transitioning/Not
Moving, R
(95% CI)
Ascending or
Descending Stairs,
RR (95% CI)
Walking,
AR (95% CI)
Vigorous Activity,
RR (95% CI)
Transitioning/Not
Moving,
RR (95% CI)
Ascending or
Descending Stairs,
RR (95% C)
Walking,
RR (95% CI)
Vigorous Activity,
RR (95% CI)
Baseline Characteristics
Age, per 5 y
1.27 (1.09, 1.48)
0.82 (0.67, 0.99)
1.13 (0.96, 1.31)
1.37 (0.99, 1.88)
1.28 (0.94, 1.73)
0.96 (0.79, 1.17)
0.87 (0.76, 1.00)
0.54 (0.37, 0.79)
Female
1.15 (0.79, 1.68)
0.69 (0.45, 1.06)
1.17 (0.83, 1.67)
1.88 (0.76, 4.63)
0.63 (0.33, 1.21)
0.93 (0.59, 1.47)
0.84 (0.62, 1.14)
0.39 (0.19, 0.82)
Falls in year before baseline, no.
1.26 (1.12, 1.41)
1.10 (1.02, 1.19)
1.38 (1.24, 1.53)
1.35 (1.04, 1.77)
1.18 (0.95, 1.46)
1.07 (0.96, 1.20)
1.23 (1.10, 1.38)
1.53 (1.17, 2.00)
Body mass inder, kg/m?
< 25.0
25.0-29.9 (Ref)
1.04 (0.68, 1.61)
0.86 (0.54, 1.38)
1.01 (0.68, 1.51)
0.89 (0.36, 2.21)
1.48 (0.69, 3.16)
1.07 (0.64, 1.79)
1.10 (0.79, 1.52)
0.94 (0.42, 2.13)
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
2 30.0
1.35 (0.87, 2.08)
0.46 (0.25, 0.82)
1.33 (0.88, 1.99)
0.72 (0.26, 1.98)
1.17 (0.50, 2.72)
1.00 (0.58, 1.74)
0.46 (0.31, 0.70)
0.32 (0.12, 0.87)
Berg Balance Scale score
251.0 (Rel)
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
48.0-50.9
1.19 (0.77, 1.85)
1.23 (0.76, 1.99)
2.76 (1.88, 4.04)
0.49 (0.16, 1.49)
1.10 (0.50, 2.42)
1.28 (0.78, 2.11)
1.52 (1.09, 2.12)
0.58 (0.24, 1.39)
< 48.0
3.18 (2.14, 4.74)
0.71 (0.40, 1.29)
3.40 (2.30, 5.03)
1.47 (0.59, 3.64)
1.19 (0.53, 2.70)
0.93 (0.51, 1.68)
0.66 (0.43, 0.99)
0.21 (0.07, 0.61)
Unable to stand from a chair
2.08 (1.14, 3.78)
0.20 (0.05, 0.88)
1.97 (1.11, 3.48)
1.32 (0.31, 5.63)
0.62 (0.13, 2.93)
0.36 (0.11, 1.23)
0.45 (0.22, 0.90)
0.47 (0.10, 2.25)
without using arms
Gait speed, m/sec
Slow (< 0.60)
2.44 (1.45, 4.12)
0.25 (0.07, 0.84)
1.95 (1.15, 3.29)
0.72 (0.14, 3.64)
2.05 (0.77, 5.42)
0.74 (0.31, 1.76)
0.39 (0.20, 0.77)
0.59 (0.15, 2.35)
Middle (0.60-1.29; Ref)
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Fast (21.30)
0.89 (0.46, 1.72)
0.81 (0.41, 1.63)
1.77 (0.93, 3.38)
0.52 (0.20, 1.34)
0.81 (0.44, 1.51)
0.92 (0.50, 1.70)
1.53 (0.76, 3.09)
0.74 (0.31, 1.78)
2.83 (1.84, 4.33)
1.00 (0.59, 1.69)
2.18 (0.67, 7.09)
2.25 (0.87, 5.80)
7.36 (2.54, 21.28)
Vision worse than 40/100
0.34 (0.04, 2.94)
0.74 (0.20, 2.72)
0.39 (0.08, 1.80)
Some difficulty with or inability
2.66 (1.83, 3.86)
1.09 (0.66, 1.80)
1.90 (1.30, 2.77)
1.52 (0.61, 3.75)
1.70 (0.83, 3.51)
0.82 (0.47, 1.44)
0.75 (0.51, 1.09)
0.28 (0.10, 0.79)
to perform ADLS
Comorbidities, no.
1.29 (1.15, 1.44)
1.06 (0.92, 1.21)
1.15 (1.04, 1.28)
1.21 (0.95, 1.53)
1.32 (1.09, 1.59)
1.05 (0.91, 1.21)
0.93 (0.84, 1.02)
0.82 (0.65, 1.04)
>4 medications
1.76 (1.17, 2.66)
0.78 (0.50, 1.22)
1.12 (0.67, 1.87)
1.40 (0.97, 2.02)
0.58 (0.26, 1.30)
1.04 (0.51, 2.14)
0.56 (0.36, 0.87)
0.61 (0.45, 0.83)
0.41 (0.19, 0.86)
Psychotropic medication
Falls Efficacy Scale score < 90°
2.09 (1.40, 3.13)
1.67 (1.14, 2.46)
1.36 (0.55, 3.36)
1.31 (0.61, 2.84)
0.96 (0.56, 1.67)
1.11 (0.78, 1.60)
0.55 (0.21, 1.44)
0.12 (0.02, 0.64)
2.42 (1.55, 3.78)
0.95 (0.51, 1.77)
0.89 (0.45, 1.77)
1.85 (1.19, 2.90)
1.09 (0.35, 3.45)
2.37 (1.06, 5.31)
0.94 (0.49, 1.80)
0.70 (0.44, 1.12)
Impaired cognition, MMSE
1.25 (0.73, 2.13)
1.13 (0.67, 1.90)
0.21 (0.03, 1.76)
0.91 (0.31, 2.61)
0.62 (0.28, 1.39)
0.67 (0.41, 1.12)
0.26 (0.06, 1.06)
score 18-24
Fair/poor self-rated health
2.21 (1.40, 3.48)
0.62 (0.31, 1.24)
1.88 (1.21, 2.92)
1.57 (0.56, 4.44)
1.61 (0.68, 3.83)
0.88 (0.45, 1.71)
0.80 (0.51, 1.26)
0.12 (0.02, 0.62)
Physical activity, PASE score < 55°
1.98 (1.35, 2.91)
0.89 (0.53, 1.49)
1.82 (1.25, 2.64)
1.47 (0.61, 3.52)
1.98 (1.00, 3.93)
0.81 (0.47, 1.40)
0.54 (0.36, 0.79)
0.32 (0.12, 0.84)
Note. ADL - activities of daily living Cl = confidence interval; MMSE = Mini-Mental State Examç PACE = Physical Activity Scale for the Elderly; RR = rate ratio. Results are from binomial regression models with number of falls per year as the
outcome.
*Possible score, 0-56.
"Possible score, 10-100.
"Possible score,0-30; score of 18-24 indicates impaired cognition.
"Possible score, 0-361; < 55 is lowest quartile.
Transcribed Image Text:TABLE 2-Rate Ratios for Falls During 4 Categories of Activity by Baseline Characteristics and Location of Fall: MOBILIZE Boston, September 2005-December 2009 Indoor Falls Outdoor Falls Transitioning/Not Moving, R (95% CI) Ascending or Descending Stairs, RR (95% CI) Walking, AR (95% CI) Vigorous Activity, RR (95% CI) Transitioning/Not Moving, RR (95% CI) Ascending or Descending Stairs, RR (95% C) Walking, RR (95% CI) Vigorous Activity, RR (95% CI) Baseline Characteristics Age, per 5 y 1.27 (1.09, 1.48) 0.82 (0.67, 0.99) 1.13 (0.96, 1.31) 1.37 (0.99, 1.88) 1.28 (0.94, 1.73) 0.96 (0.79, 1.17) 0.87 (0.76, 1.00) 0.54 (0.37, 0.79) Female 1.15 (0.79, 1.68) 0.69 (0.45, 1.06) 1.17 (0.83, 1.67) 1.88 (0.76, 4.63) 0.63 (0.33, 1.21) 0.93 (0.59, 1.47) 0.84 (0.62, 1.14) 0.39 (0.19, 0.82) Falls in year before baseline, no. 1.26 (1.12, 1.41) 1.10 (1.02, 1.19) 1.38 (1.24, 1.53) 1.35 (1.04, 1.77) 1.18 (0.95, 1.46) 1.07 (0.96, 1.20) 1.23 (1.10, 1.38) 1.53 (1.17, 2.00) Body mass inder, kg/m? < 25.0 25.0-29.9 (Ref) 1.04 (0.68, 1.61) 0.86 (0.54, 1.38) 1.01 (0.68, 1.51) 0.89 (0.36, 2.21) 1.48 (0.69, 3.16) 1.07 (0.64, 1.79) 1.10 (0.79, 1.52) 0.94 (0.42, 2.13) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2 30.0 1.35 (0.87, 2.08) 0.46 (0.25, 0.82) 1.33 (0.88, 1.99) 0.72 (0.26, 1.98) 1.17 (0.50, 2.72) 1.00 (0.58, 1.74) 0.46 (0.31, 0.70) 0.32 (0.12, 0.87) Berg Balance Scale score 251.0 (Rel) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 48.0-50.9 1.19 (0.77, 1.85) 1.23 (0.76, 1.99) 2.76 (1.88, 4.04) 0.49 (0.16, 1.49) 1.10 (0.50, 2.42) 1.28 (0.78, 2.11) 1.52 (1.09, 2.12) 0.58 (0.24, 1.39) < 48.0 3.18 (2.14, 4.74) 0.71 (0.40, 1.29) 3.40 (2.30, 5.03) 1.47 (0.59, 3.64) 1.19 (0.53, 2.70) 0.93 (0.51, 1.68) 0.66 (0.43, 0.99) 0.21 (0.07, 0.61) Unable to stand from a chair 2.08 (1.14, 3.78) 0.20 (0.05, 0.88) 1.97 (1.11, 3.48) 1.32 (0.31, 5.63) 0.62 (0.13, 2.93) 0.36 (0.11, 1.23) 0.45 (0.22, 0.90) 0.47 (0.10, 2.25) without using arms Gait speed, m/sec Slow (< 0.60) 2.44 (1.45, 4.12) 0.25 (0.07, 0.84) 1.95 (1.15, 3.29) 0.72 (0.14, 3.64) 2.05 (0.77, 5.42) 0.74 (0.31, 1.76) 0.39 (0.20, 0.77) 0.59 (0.15, 2.35) Middle (0.60-1.29; Ref) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Fast (21.30) 0.89 (0.46, 1.72) 0.81 (0.41, 1.63) 1.77 (0.93, 3.38) 0.52 (0.20, 1.34) 0.81 (0.44, 1.51) 0.92 (0.50, 1.70) 1.53 (0.76, 3.09) 0.74 (0.31, 1.78) 2.83 (1.84, 4.33) 1.00 (0.59, 1.69) 2.18 (0.67, 7.09) 2.25 (0.87, 5.80) 7.36 (2.54, 21.28) Vision worse than 40/100 0.34 (0.04, 2.94) 0.74 (0.20, 2.72) 0.39 (0.08, 1.80) Some difficulty with or inability 2.66 (1.83, 3.86) 1.09 (0.66, 1.80) 1.90 (1.30, 2.77) 1.52 (0.61, 3.75) 1.70 (0.83, 3.51) 0.82 (0.47, 1.44) 0.75 (0.51, 1.09) 0.28 (0.10, 0.79) to perform ADLS Comorbidities, no. 1.29 (1.15, 1.44) 1.06 (0.92, 1.21) 1.15 (1.04, 1.28) 1.21 (0.95, 1.53) 1.32 (1.09, 1.59) 1.05 (0.91, 1.21) 0.93 (0.84, 1.02) 0.82 (0.65, 1.04) >4 medications 1.76 (1.17, 2.66) 0.78 (0.50, 1.22) 1.12 (0.67, 1.87) 1.40 (0.97, 2.02) 0.58 (0.26, 1.30) 1.04 (0.51, 2.14) 0.56 (0.36, 0.87) 0.61 (0.45, 0.83) 0.41 (0.19, 0.86) Psychotropic medication Falls Efficacy Scale score < 90° 2.09 (1.40, 3.13) 1.67 (1.14, 2.46) 1.36 (0.55, 3.36) 1.31 (0.61, 2.84) 0.96 (0.56, 1.67) 1.11 (0.78, 1.60) 0.55 (0.21, 1.44) 0.12 (0.02, 0.64) 2.42 (1.55, 3.78) 0.95 (0.51, 1.77) 0.89 (0.45, 1.77) 1.85 (1.19, 2.90) 1.09 (0.35, 3.45) 2.37 (1.06, 5.31) 0.94 (0.49, 1.80) 0.70 (0.44, 1.12) Impaired cognition, MMSE 1.25 (0.73, 2.13) 1.13 (0.67, 1.90) 0.21 (0.03, 1.76) 0.91 (0.31, 2.61) 0.62 (0.28, 1.39) 0.67 (0.41, 1.12) 0.26 (0.06, 1.06) score 18-24 Fair/poor self-rated health 2.21 (1.40, 3.48) 0.62 (0.31, 1.24) 1.88 (1.21, 2.92) 1.57 (0.56, 4.44) 1.61 (0.68, 3.83) 0.88 (0.45, 1.71) 0.80 (0.51, 1.26) 0.12 (0.02, 0.62) Physical activity, PASE score < 55° 1.98 (1.35, 2.91) 0.89 (0.53, 1.49) 1.82 (1.25, 2.64) 1.47 (0.61, 3.52) 1.98 (1.00, 3.93) 0.81 (0.47, 1.40) 0.54 (0.36, 0.79) 0.32 (0.12, 0.84) Note. ADL - activities of daily living Cl = confidence interval; MMSE = Mini-Mental State Examç PACE = Physical Activity Scale for the Elderly; RR = rate ratio. Results are from binomial regression models with number of falls per year as the outcome. *Possible score, 0-56. "Possible score, 10-100. "Possible score,0-30; score of 18-24 indicates impaired cognition. "Possible score, 0-361; < 55 is lowest quartile.
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