APPENDIX : How to weigh the CAMCOG items to arrive at an interval level test score
After recoding of items with more than two response categories, an IRT (extension of Rasch)-model weighted CAMCOG-47 sum score S can be obtained by multiplying each CAMCOG-47 item i, coded 0 (wrong) or 1 (correct answer), with item discrimination weight ai and sum the results (Table A):
The weighted CAMCOG test score S (range 0-154) is a sufficient statistic for cognitive ability measure in logit units, i.e. the score most likely to occur given a subjects latent (not directly observable) cognitive ability (Table B). The cognitive ability measures are on the same logit scale as are the item difficulty calibrations. For extreme scores, the associated estimates of might be somewhat biased (see column “Bias”).
In order to transform a logit unit cognitive ability measure , into the predicted probability p of a correct answer to a particular CAMCOG-47 item with difficulty (see Table 2 article) and discrimination ai, the following formula can be used:
where exp denotes the exponential mathematical function base 2.7183.
For example, patients with ability score S = 93 points, 0.22 logit (Table B). These patients have a 50% probability of a correct response to Q148 with the same logit difficulty value, a 75 % probability of a correct answer to the less difficult item Q159 with = - 0.15 and ai = 3, and a 10 % probability of a correct answer to the more difficult item Q146 with = 0.77 and ai = 4.
Table A. Item weights of the CAMCOG-47 and recoding of items with more than two response categories
Question / Description / Weightai / Scores
recoded
to ‘0’ / Scores
recoded
to ‘1’
Q120 / Orientation: time (day of the week) / 3
Q121 / Orientation: time (date - day) / 3
Q122 / Orientation; time (date-month) / 4
Q123 / Orientation: time (date - year) / 5
Q124 / Orientation: time (season) / 3
Q126 / Orientation: place (town or village) / 4
Q127 / Orientation: place (which province or county) / 5
Q128 / Orientation: place (ward or floor) / 4
Q129 / Orientation: place (building or home address) / 4
Q130 / Understanding: motor response (nod once) / 2
Q131 / Understanding: motor response (ear, left hand) / 3
Q132 / Understanding: motor response (floor, ceiling) / 3
Q133 / Understanding: motor response (2 finger shoulder) / 3
Q135 / Understanding: verbal response (cities or towns) / 3
Q136 / Understanding: verbal response (radio before TV) / 4
Q138 / Expression: naming photos / 4 / 0-5 / 6
Q139 / Expression: naming animals / 4 / 0-3 / 4-6
Q141 / Expression: definitions (pharmacist) / 4
Q144 / Expression: repetition (sentence) / 2
Q146 / Memory: remembering items question 138 / 4 / 0-2 / 3-6
Q147 / Memory: recognition objects question 138 / 3 / 0-2 / 3-6
Q148 / Memory: retrieval: past (World War I) / 3
Q149 / Memory: retrieval: past (World War II) / 5
Q150 / Memory: retrieval: past (German leader WW II) / 4
Q151 / Memory:retrieval: past (Russian leader WW II) / 3
Q153 / Memory: retrieval: past (Pilot with kidnapped son) / 3
Q154 / Memory retrieval: recent (Queen) / 4
Q155 / Memory retrieval: recent (heir to throne) / 3
Q156 / Memory: retrieval: recent (Prime minister) / 4
Q157 / Memory: retrieval: recent (news) / 4
Q159 / Concentration (counting backwards from 20) / 3 / 0-1 / 2
Q160 / Concentration: repeatedly subtracting 7 / 2 / 0-4 / 5-6
Q162 / Reading: (close your eyes) / 3
Q163 / Reading (50+ hands behind head) / 3
Q165 / Drawing (spiral) / 2
Q166 / Drawing (3D house) / 3
Q167 / Drawing (clock) / 4 / 0-2 / 3
Q170 / Co-ordination: ideas (put sheet in envelope) / 2
Q171 / Writing: dictation (address) / 4 / 0-1 / 2
Q173 / Co-ordination: ideomotoric (scissors) / 2 / 0-1 / 2
Q174 / Co-ordination: ideomotoric: (toothbrush) / 3 / 0-1 / 2
Q175 / Perception: tactile (coins) / 2 / 0-1 / 2
Q177 / Arithmetic (change) / 3
Q178 / Memory: recall (address) / 5 / 0-4 / 5
Q182 / Abstract thinking: (living things) / 2 / 0 / 1-2
Q183 / Perception: visual (picture of Queen, Pope) / 3 / 0-1 / 2
Q184 / Perception: visual (photos from unusual angles) / 1 / 0-2 / 3-6
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Table B. IRT (Rasch model) weighted score S and interval scale cognitive ability measure
S / / Bias / S / / Bias0 / -2.158 / .246 / 77 / .045 / .000
1 / -1.817 / .085 / 78 / .055 / .000
2 / -1.628 / .033 / 79 / .066 / .000
3 / -1.499 / .013 / 80 / .077 / .000
4 / -1.400 / .004 / 81 / .088 / .000
5 / -1.321 / .000 / 82 / .099 / .000
6 / -1.254 / -.002 / 83 / .110 / .000
7 / -1.197 / -.002 / 84 / .121 / .000
8 / -1.146 / -.002 / 85 / .132 / .000
9 / -1.101 / -.002 / 86 / .143 / .000
10 / -1.060 / -.002 / 87 / .154 / .000
11 / -1.022 / -.002 / 88 / .165 / .000
12 / -.987 / -.001 / 89 / .176 / .000
13 / -.954 / -.001 / 90 / .188 / .000
14 / -.923 / -.001 / 91 / .199 / .000
15 / -.894 / -.001 / 92 / .210 / .000
16 / -.867 / -.001 / 93 / .222 / .000
17 / -.840 / .000 / 94 / .233 / .000
18 / -.815 / .000 / 95 / .245 / .000
19 / -.791 / .000 / 96 / .256 / .000
20 / -.768 / .000 / 97 / .268 / .000
21 / -.745 / .000 / 98 / .280 / .000
22 / -.723 / .000 / 99 / .292 / .000
23 / -.702 / .000 / 100 / .304 / .000
24 / -.682 / .000 / 101 / .316 / .000
25 / -.662 / .000 / 102 / .329 / .000
26 / -.642 / .000 / 103 / .341 / .000
27 / -.623 / .000 / 104 / .354 / .000
28 / -.605 / .000 / 105 / .366 / .000
29 / -.587 / .000 / 106 / .379 / .000
30 / -.569 / .000 / 107 / .392 / .000
31 / -.552 / .000 / 108 / .405 / .000
32 / -.535 / .000 / 109 / .418 / .000
33 / -.518 / .000 / 110 / .432 / .000
34 / -.501 / .000 / 111 / .445 / .000
35 / -.485 / .000 / 112 / .459 / .000
36 / -.469 / .000 / 113 / .473 / .000
37 / -.454 / .000 / 114 / .487 / .000
38 / -.438 / .000 / 115 / .501 / .000
39 / -.423 / .000 / 116 / .516 / .000
40 / -.408 / .000 / 117 / .531 / .000
41 / -.393 / .000 / 118 / .545 / .000
42 / -.379 / .000 / 119 / .560 / .000
43 / -.365 / .000 / 120 / .576 / .000
44 / -.351 / .000 / 121 / .591 / .000
45 / -.337 / .000 / 122 / .607 / .000
46 / -.323 / .000 / 123 / .623 / .000
47 / -.309 / .000 / 124 / .639 / .000
48 / -.296 / .000 / 125 / .655 / .000
49 / -.283 / .000 / 126 / .672 / .000
50 / -.270 / .000 / 127 / .689 / .000
51 / -.257 / .000 / 128 / .706 / .000
52 / -.244 / .000 / 129 / .724 / .000
53 / -.231 / .000 / 130 / .742 / .000
54 / -.219 / .000 / 131 / .760 / .000
55 / -.206 / .000 / 132 / .779 / .000
56 / -.194 / .000 / 133 / .798 / .000
57 / -.182 / .000 / 134 / .818 / .000
58 / -.170 / .000 / 135 / .839 / .000
59 / -.158 / .000 / 136 / .860 / .000
60 / -.146 / .000 / 137 / .882 / .000
61 / -.134 / .000 / 138 / .905 / .001
62 / -.123 / .000 / 139 / .929 / .001
63 / -.111 / .000 / 140 / .954 / .001
64 / -.100 / .000 / 141 / .981 / .001
65 / -.088 / .000 / 142 / 1.009 / .001
66 / -.077 / .000 / 143 / 1.039 / .002
67 / -.066 / .000 / 144 / 1.071 / .002
68 / -.054 / .000 / 145 / 1.106 / .002
69 / -.043 / .000 / 146 / 1.144 / .002
70 / -.032 / .000 / 147 / 1.186 / .001
71 / -.021 / .000 / 148 / 1.233 / .000
72 / -.010 / .000 / 149 / 1.288 / -.002
73 / .001 / .000 / 150 / 1.352 / -.007
74 / .012 / .000 / 151 / 1.430 / -.017
75 / .023 / .000 / 152 / 1.532 / -.038
76 / .034 / .000 / 153 / 1.677 / -.083
154 / 1.930 / -.209
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