racusum: Risk-adjusted CUSUM Charts
In cusum: Cumulative Sum (CUSUM) Charts for Monitoring of Hospital Performance
Description
Usage
Arguments
Examples
Description
Calculate risk-adjusted CUSUM charts for performance data
Usage
1
2
3
Arguments
patient_risks
Double. Vector of patient risk scores (individual risk of adverse event)
patient_outcomes
Integer. Vector of binary patient outcomes (0,1)
limit
Double. Control limit for signalling performance change
weights
Double. Optional vector of weights, if empty, standard CUSUM weights are calculated with weights_t
odds_multiplier
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases)
reset
Logical. Reset the CUSUM after a signal to 0; defaults to TRUE
limit_method
"constant" or "dynamic"
Examples
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
# Patients risks are usually known from Phase I.
# If not, these risk scores can be simulated.
# define possible patient risk scores
risks <- c(0.001, 0.01, 0.1, 0.002, 0.02, 0.2)
# sample risk population of size n = 100
set.seed(2046)
patient_risks <- sample(x = risks, size = 100, replace = TRUE)
# control limit can be obtained with racusum_limit_sim(),
# here it is set to an arbitrary value (2.96),
# or dynamic control limits with racusum_limit_dpcl()
##### RA-CUSUM of in-control process
# simulate patient outcome for performace as expected
set.seed(2046)
patient_outcomes <- as.logical(rbinom(
n = 100,
size = 1,
prob = patient_risks
))
racusum(patient_risks,
patient_outcomes,
limit = 2.96
)
#### RA-CUSUM of out-of-control process
# simulate patient outcome for deviating performance
set.seed(2046)
patient_outcomes <- as.logical(rbinom(n = 100, size = 1, prob = patient_risks * 2))
#'
racusum(patient_risks,
patient_outcomes,
limit = 2.96
)
Example output
t p ct signal limit
1 1 0.100 0.00000000 0 0
2 2 0.002 0.00000000 0 0
3 3 0.002 0.00000000 0 0
4 4 0.001 0.00000000 0 0
5 5 0.010 0.00000000 0 0
6 6 0.010 0.00000000 0 0
7 7 0.001 0.00000000 0 0
8 8 0.002 0.00000000 0 0
9 9 0.100 0.59783700 0 0
10 10 0.200 0.41551544 0 0
11 11 0.010 0.40556511 0 0
12 12 0.001 0.40456561 0 0
13 13 0.010 0.39461528 0 0
14 14 0.010 0.38466495 0 0
15 15 0.100 0.28935477 0 0
16 16 0.010 0.27940444 0 0
17 17 0.010 0.26945411 0 0
18 18 0.001 0.26845461 0 0
19 19 0.001 0.26745511 0 0
20 20 0.010 0.25750478 0 0
21 21 0.100 0.16219460 0 0
22 22 0.020 0.14239197 0 0
23 23 0.001 0.14139247 0 0
24 24 0.010 0.13144214 0 0
25 25 0.020 0.11163951 0 0
26 26 0.020 0.09183689 0 0
27 27 0.200 0.00000000 0 0
28 28 0.020 0.00000000 0 0
29 29 0.200 0.51082562 0 0
30 30 0.200 0.32850407 0 0
31 31 0.010 0.31855374 0 0
32 32 0.010 0.30860341 0 0
33 33 0.200 0.81942903 0 0
34 34 0.020 0.79962640 0 0
35 35 0.002 0.79762840 0 0
36 36 0.002 0.79563040 0 0
37 37 0.001 0.79463090 0 0
38 38 0.002 0.79263289 0 0
39 39 0.010 0.78268256 0 0
40 40 0.010 0.77273223 0 0
41 41 0.020 0.75292960 0 0
42 42 0.001 0.75193010 0 0
43 43 0.200 0.56960855 0 0
44 44 0.100 0.47429837 0 0
45 45 0.100 0.37898819 0 0
46 46 0.010 0.36903786 0 0
47 47 0.010 0.35908753 0 0
48 48 0.002 0.35708952 0 0
49 49 0.200 0.17476797 0 0
50 50 0.020 0.15496534 0 0
51 51 0.010 0.14501501 0 0
52 52 0.001 0.14401551 0 0
53 53 0.010 0.13406518 0 0
54 54 0.001 0.13306568 0 0
55 55 0.002 0.13106767 0 0
56 56 0.002 0.12906967 0 0
57 57 0.020 0.10926704 0 0
58 58 0.100 0.01395686 0 0
59 59 0.001 0.01295736 0 0
60 60 0.020 0.00000000 0 0
61 61 0.200 0.00000000 0 0
62 62 0.002 0.00000000 0 0
63 63 0.002 0.00000000 0 0
64 64 0.002 0.00000000 0 0
65 65 0.010 0.00000000 0 0
66 66 0.100 0.00000000 0 0
67 67 0.020 0.00000000 0 0
68 68 0.100 0.00000000 0 0
69 69 0.020 0.00000000 0 0
70 70 0.001 0.00000000 0 0
71 71 0.020 0.00000000 0 0
72 72 0.100 0.00000000 0 0
73 73 0.002 0.00000000 0 0
74 74 0.020 0.00000000 0 0
75 75 0.010 0.00000000 0 0
76 76 0.001 0.00000000 0 0
77 77 0.002 0.00000000 0 0
78 78 0.010 0.00000000 0 0
79 79 0.200 0.00000000 0 0
80 80 0.100 0.00000000 0 0
81 81 0.100 0.00000000 0 0
82 82 0.001 0.00000000 0 0
83 83 0.100 0.00000000 0 0
84 84 0.002 0.00000000 0 0
85 85 0.002 0.00000000 0 0
86 86 0.020 0.00000000 0 0
87 87 0.100 0.00000000 0 0
88 88 0.200 0.51082562 0 0
89 89 0.200 0.32850407 0 0
90 90 0.020 0.30870144 0 0
91 91 0.001 0.30770194 0 0
92 92 0.200 0.81852756 0 0
93 93 0.001 0.81752806 0 0
94 94 0.020 0.79772544 0 0
95 95 0.001 0.79672594 0 0
96 96 0.100 0.70141576 0 0
97 97 0.002 0.69941775 0 0
98 98 0.200 0.51709620 0 0
99 99 0.002 0.51509819 0 0
100 100 0.100 0.41978801 0 0
t p ct signal limit
1 1 0.100 0.00000000 0 0
2 2 0.002 0.00000000 0 0
3 3 0.002 0.00000000 0 0
4 4 0.001 0.00000000 0 0
5 5 0.010 0.00000000 0 0
6 6 0.010 0.00000000 0 0
7 7 0.001 0.00000000 0 0
8 8 0.002 0.00000000 0 0
9 9 0.100 0.59783700 0 0
10 10 0.200 0.41551544 0 0
11 11 0.010 0.40556511 0 0
12 12 0.001 0.40456561 0 0
13 13 0.010 0.39461528 0 0
14 14 0.010 0.38466495 0 0
15 15 0.100 0.28935477 0 0
16 16 0.010 0.27940444 0 0
17 17 0.010 0.26945411 0 0
18 18 0.001 0.26845461 0 0
19 19 0.001 0.26745511 0 0
20 20 0.010 0.25750478 0 0
21 21 0.100 0.16219460 0 0
22 22 0.020 0.14239197 0 0
23 23 0.001 0.14139247 0 0
24 24 0.010 0.13144214 0 0
25 25 0.020 0.11163951 0 0
26 26 0.020 0.09183689 0 0
27 27 0.200 0.00000000 0 0
28 28 0.020 0.00000000 0 0
29 29 0.200 0.51082562 0 0
30 30 0.200 0.32850407 0 0
31 31 0.010 0.31855374 0 0
32 32 0.010 0.30860341 0 0
33 33 0.200 0.81942903 0 0
34 34 0.020 0.79962640 0 0
35 35 0.002 0.79762840 0 0
36 36 0.002 0.79563040 0 0
37 37 0.001 0.79463090 0 0
38 38 0.002 0.79263289 0 0
39 39 0.010 0.78268256 0 0
40 40 0.010 0.77273223 0 0
41 41 0.020 0.75292960 0 0
42 42 0.001 0.75193010 0 0
43 43 0.200 0.56960855 0 0
44 44 0.100 0.47429837 0 0
45 45 0.100 0.37898819 0 0
46 46 0.010 0.36903786 0 0
47 47 0.010 0.35908753 0 0
48 48 0.002 0.35708952 0 0
49 49 0.200 0.17476797 0 0
50 50 0.020 0.15496534 0 0
51 51 0.010 0.14501501 0 0
52 52 0.001 0.14401551 0 0
53 53 0.010 0.13406518 0 0
54 54 0.001 0.13306568 0 0
55 55 0.002 0.13106767 0 0
56 56 0.002 0.12906967 0 0
57 57 0.020 0.10926704 0 0
58 58 0.100 0.01395686 0 0
59 59 0.001 0.01295736 0 0
60 60 0.020 0.00000000 0 0
61 61 0.200 0.00000000 0 0
62 62 0.002 0.00000000 0 0
63 63 0.002 0.00000000 0 0
64 64 0.002 0.00000000 0 0
65 65 0.010 0.00000000 0 0
66 66 0.100 0.00000000 0 0
67 67 0.020 0.00000000 0 0
68 68 0.100 0.59783700 0 0
69 69 0.020 1.27118155 0 0
70 70 0.001 1.27018205 0 0
71 71 0.020 1.25037943 0 0
72 72 0.100 1.15506925 0 0
73 73 0.002 1.15307124 0 0
74 74 0.020 1.13326862 0 0
75 75 0.010 1.12331829 0 0
76 76 0.001 1.12231879 0 0
77 77 0.002 1.12032078 0 0
78 78 0.010 1.11037045 0 0
79 79 0.200 0.92804890 0 0
80 80 0.100 0.83273872 0 0
81 81 0.100 0.73742854 0 0
82 82 0.001 0.73642904 0 0
83 83 0.100 0.64111886 0 0
84 84 0.002 0.63912085 0 0
85 85 0.002 0.63712285 0 0
86 86 0.020 0.61732022 0 0
87 87 0.100 0.52201004 0 0
88 88 0.200 1.03283567 0 0
89 89 0.200 0.85051411 0 0
90 90 0.020 0.83071148 0 0
91 91 0.001 0.82971198 0 0
92 92 0.200 1.34053761 0 0
93 93 0.001 1.33953811 0 0
94 94 0.020 1.31973548 0 0
95 95 0.001 1.31873598 0 0
96 96 0.100 1.22342580 0 0
97 97 0.002 1.22142780 0 0
98 98 0.200 1.03910624 0 0
99 99 0.002 1.03710824 0 0
100 100 0.100 1.63494524 0 0
cusum documentation built on Oct. 2, 2019, 5:03 p.m.
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Description Usage Arguments Examples
Description
Calculate risk-adjusted CUSUM charts for performance data
Usage
1 2 3 |
Arguments
patient_risks |
Double. Vector of patient risk scores (individual risk of adverse event) |
patient_outcomes |
Integer. Vector of binary patient outcomes (0,1) |
limit |
Double. Control limit for signalling performance change |
weights |
Double. Optional vector of weights, if empty, standard CUSUM weights are calculated with weights_t |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
reset |
Logical. Reset the CUSUM after a signal to 0; defaults to TRUE |
limit_method |
"constant" or "dynamic" |
Examples
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 | # Patients risks are usually known from Phase I.
# If not, these risk scores can be simulated.
# define possible patient risk scores
risks <- c(0.001, 0.01, 0.1, 0.002, 0.02, 0.2)
# sample risk population of size n = 100
set.seed(2046)
patient_risks <- sample(x = risks, size = 100, replace = TRUE)
# control limit can be obtained with racusum_limit_sim(),
# here it is set to an arbitrary value (2.96),
# or dynamic control limits with racusum_limit_dpcl()
##### RA-CUSUM of in-control process
# simulate patient outcome for performace as expected
set.seed(2046)
patient_outcomes <- as.logical(rbinom(
n = 100,
size = 1,
prob = patient_risks
))
racusum(patient_risks,
patient_outcomes,
limit = 2.96
)
#### RA-CUSUM of out-of-control process
# simulate patient outcome for deviating performance
set.seed(2046)
patient_outcomes <- as.logical(rbinom(n = 100, size = 1, prob = patient_risks * 2))
#'
racusum(patient_risks,
patient_outcomes,
limit = 2.96
)
|
Example output
t p ct signal limit
1 1 0.100 0.00000000 0 0
2 2 0.002 0.00000000 0 0
3 3 0.002 0.00000000 0 0
4 4 0.001 0.00000000 0 0
5 5 0.010 0.00000000 0 0
6 6 0.010 0.00000000 0 0
7 7 0.001 0.00000000 0 0
8 8 0.002 0.00000000 0 0
9 9 0.100 0.59783700 0 0
10 10 0.200 0.41551544 0 0
11 11 0.010 0.40556511 0 0
12 12 0.001 0.40456561 0 0
13 13 0.010 0.39461528 0 0
14 14 0.010 0.38466495 0 0
15 15 0.100 0.28935477 0 0
16 16 0.010 0.27940444 0 0
17 17 0.010 0.26945411 0 0
18 18 0.001 0.26845461 0 0
19 19 0.001 0.26745511 0 0
20 20 0.010 0.25750478 0 0
21 21 0.100 0.16219460 0 0
22 22 0.020 0.14239197 0 0
23 23 0.001 0.14139247 0 0
24 24 0.010 0.13144214 0 0
25 25 0.020 0.11163951 0 0
26 26 0.020 0.09183689 0 0
27 27 0.200 0.00000000 0 0
28 28 0.020 0.00000000 0 0
29 29 0.200 0.51082562 0 0
30 30 0.200 0.32850407 0 0
31 31 0.010 0.31855374 0 0
32 32 0.010 0.30860341 0 0
33 33 0.200 0.81942903 0 0
34 34 0.020 0.79962640 0 0
35 35 0.002 0.79762840 0 0
36 36 0.002 0.79563040 0 0
37 37 0.001 0.79463090 0 0
38 38 0.002 0.79263289 0 0
39 39 0.010 0.78268256 0 0
40 40 0.010 0.77273223 0 0
41 41 0.020 0.75292960 0 0
42 42 0.001 0.75193010 0 0
43 43 0.200 0.56960855 0 0
44 44 0.100 0.47429837 0 0
45 45 0.100 0.37898819 0 0
46 46 0.010 0.36903786 0 0
47 47 0.010 0.35908753 0 0
48 48 0.002 0.35708952 0 0
49 49 0.200 0.17476797 0 0
50 50 0.020 0.15496534 0 0
51 51 0.010 0.14501501 0 0
52 52 0.001 0.14401551 0 0
53 53 0.010 0.13406518 0 0
54 54 0.001 0.13306568 0 0
55 55 0.002 0.13106767 0 0
56 56 0.002 0.12906967 0 0
57 57 0.020 0.10926704 0 0
58 58 0.100 0.01395686 0 0
59 59 0.001 0.01295736 0 0
60 60 0.020 0.00000000 0 0
61 61 0.200 0.00000000 0 0
62 62 0.002 0.00000000 0 0
63 63 0.002 0.00000000 0 0
64 64 0.002 0.00000000 0 0
65 65 0.010 0.00000000 0 0
66 66 0.100 0.00000000 0 0
67 67 0.020 0.00000000 0 0
68 68 0.100 0.00000000 0 0
69 69 0.020 0.00000000 0 0
70 70 0.001 0.00000000 0 0
71 71 0.020 0.00000000 0 0
72 72 0.100 0.00000000 0 0
73 73 0.002 0.00000000 0 0
74 74 0.020 0.00000000 0 0
75 75 0.010 0.00000000 0 0
76 76 0.001 0.00000000 0 0
77 77 0.002 0.00000000 0 0
78 78 0.010 0.00000000 0 0
79 79 0.200 0.00000000 0 0
80 80 0.100 0.00000000 0 0
81 81 0.100 0.00000000 0 0
82 82 0.001 0.00000000 0 0
83 83 0.100 0.00000000 0 0
84 84 0.002 0.00000000 0 0
85 85 0.002 0.00000000 0 0
86 86 0.020 0.00000000 0 0
87 87 0.100 0.00000000 0 0
88 88 0.200 0.51082562 0 0
89 89 0.200 0.32850407 0 0
90 90 0.020 0.30870144 0 0
91 91 0.001 0.30770194 0 0
92 92 0.200 0.81852756 0 0
93 93 0.001 0.81752806 0 0
94 94 0.020 0.79772544 0 0
95 95 0.001 0.79672594 0 0
96 96 0.100 0.70141576 0 0
97 97 0.002 0.69941775 0 0
98 98 0.200 0.51709620 0 0
99 99 0.002 0.51509819 0 0
100 100 0.100 0.41978801 0 0
t p ct signal limit
1 1 0.100 0.00000000 0 0
2 2 0.002 0.00000000 0 0
3 3 0.002 0.00000000 0 0
4 4 0.001 0.00000000 0 0
5 5 0.010 0.00000000 0 0
6 6 0.010 0.00000000 0 0
7 7 0.001 0.00000000 0 0
8 8 0.002 0.00000000 0 0
9 9 0.100 0.59783700 0 0
10 10 0.200 0.41551544 0 0
11 11 0.010 0.40556511 0 0
12 12 0.001 0.40456561 0 0
13 13 0.010 0.39461528 0 0
14 14 0.010 0.38466495 0 0
15 15 0.100 0.28935477 0 0
16 16 0.010 0.27940444 0 0
17 17 0.010 0.26945411 0 0
18 18 0.001 0.26845461 0 0
19 19 0.001 0.26745511 0 0
20 20 0.010 0.25750478 0 0
21 21 0.100 0.16219460 0 0
22 22 0.020 0.14239197 0 0
23 23 0.001 0.14139247 0 0
24 24 0.010 0.13144214 0 0
25 25 0.020 0.11163951 0 0
26 26 0.020 0.09183689 0 0
27 27 0.200 0.00000000 0 0
28 28 0.020 0.00000000 0 0
29 29 0.200 0.51082562 0 0
30 30 0.200 0.32850407 0 0
31 31 0.010 0.31855374 0 0
32 32 0.010 0.30860341 0 0
33 33 0.200 0.81942903 0 0
34 34 0.020 0.79962640 0 0
35 35 0.002 0.79762840 0 0
36 36 0.002 0.79563040 0 0
37 37 0.001 0.79463090 0 0
38 38 0.002 0.79263289 0 0
39 39 0.010 0.78268256 0 0
40 40 0.010 0.77273223 0 0
41 41 0.020 0.75292960 0 0
42 42 0.001 0.75193010 0 0
43 43 0.200 0.56960855 0 0
44 44 0.100 0.47429837 0 0
45 45 0.100 0.37898819 0 0
46 46 0.010 0.36903786 0 0
47 47 0.010 0.35908753 0 0
48 48 0.002 0.35708952 0 0
49 49 0.200 0.17476797 0 0
50 50 0.020 0.15496534 0 0
51 51 0.010 0.14501501 0 0
52 52 0.001 0.14401551 0 0
53 53 0.010 0.13406518 0 0
54 54 0.001 0.13306568 0 0
55 55 0.002 0.13106767 0 0
56 56 0.002 0.12906967 0 0
57 57 0.020 0.10926704 0 0
58 58 0.100 0.01395686 0 0
59 59 0.001 0.01295736 0 0
60 60 0.020 0.00000000 0 0
61 61 0.200 0.00000000 0 0
62 62 0.002 0.00000000 0 0
63 63 0.002 0.00000000 0 0
64 64 0.002 0.00000000 0 0
65 65 0.010 0.00000000 0 0
66 66 0.100 0.00000000 0 0
67 67 0.020 0.00000000 0 0
68 68 0.100 0.59783700 0 0
69 69 0.020 1.27118155 0 0
70 70 0.001 1.27018205 0 0
71 71 0.020 1.25037943 0 0
72 72 0.100 1.15506925 0 0
73 73 0.002 1.15307124 0 0
74 74 0.020 1.13326862 0 0
75 75 0.010 1.12331829 0 0
76 76 0.001 1.12231879 0 0
77 77 0.002 1.12032078 0 0
78 78 0.010 1.11037045 0 0
79 79 0.200 0.92804890 0 0
80 80 0.100 0.83273872 0 0
81 81 0.100 0.73742854 0 0
82 82 0.001 0.73642904 0 0
83 83 0.100 0.64111886 0 0
84 84 0.002 0.63912085 0 0
85 85 0.002 0.63712285 0 0
86 86 0.020 0.61732022 0 0
87 87 0.100 0.52201004 0 0
88 88 0.200 1.03283567 0 0
89 89 0.200 0.85051411 0 0
90 90 0.020 0.83071148 0 0
91 91 0.001 0.82971198 0 0
92 92 0.200 1.34053761 0 0
93 93 0.001 1.33953811 0 0
94 94 0.020 1.31973548 0 0
95 95 0.001 1.31873598 0 0
96 96 0.100 1.22342580 0 0
97 97 0.002 1.22142780 0 0
98 98 0.200 1.03910624 0 0
99 99 0.002 1.03710824 0 0
100 100 0.100 1.63494524 0 0
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