An application of the new irt command in Stata

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Stephen Rodgers
5 years ago
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Center (ARC), Department of Neurobiology, Health Care Sciences and Society,

1 An application of the new irt command in Stata Giola Santoni 2015 Nordic and Baltic Stata Users Group meeting, Stockholm September 4, 2015 Aging Research Center (ARC), Department of Neurobiology, Health Care Sciences and Society, Karolinska Institutet, and Stockholm Gerontology Research Center, Stockholm, Sweden

2 What we would like to do: Be able to measure the health status of a person 60 years old or older. What we can do: measure several indicators of health 2

3 What we can do: measure... Cognitive functioning: MMSE test - bounded variable - integer values - skewed to the left MMSE 3

4 What we can do: measure... Cognitive functioning: MMSE test - bounded variable - integer values - skewed to the left Physical functioning: gait speed - only positive values - not really continuos Density MMSE Gait speed (m/sec) 4

5 What we can do: measure... Morbidities: # of chronic diseases - bounded variable - integer values - skewed to the right Number of chronic diseases 5

6 What we can do: measure... Morbidities: # of chronic diseases - bounded variable - integer values - skewed to the right Disability: personal- instrumentalactivities of daily living (PADL IADL) - bounded - zero inflated Number of chronic diseases 6

7 Aim: Create an health index Problem: How to treat the available variables? Which cut-offs to use? Solution: Use nominal response model 1) items can have different number of categories 2) no order is given to the categories 3) it allows us to find the cut-off points for each item that results in the best test 7

8 Item Information Curve Question: Is the patient s gait speed fast? Given the patient s health status, what is the patient s probability of answering yes? Probability Health status 8

9 Item Characteristic Curve Question: Is the patient s gait speed fast? Given the patient s health status, what is the patient s probability of answering yes? Item characteristic curve Probability Discrimination Health status 9

10 Item Characteristic Curve Question: Is the patient s gait speed fast? Given the patient s health status, what is the patient s probability of answering yes? Item characteristic curve 10

11 Item Characteristic Curve Question: Is the patient s gait speed a) slow, b) medium, or c) fast? Given the patient s health status, what is the patient s probability of answering a), b), or c)? 1.00 Item characteristic curve a) b) c) Health status 11

12 Item Characteristic Curve Question: Is the patient s gait speed a) slow, b) medium, or c) fast? Given the patient s health status, what is the patient s probability of answering a), b), or c)? Item characteristic curve Item characteristic curve 1.00 a) b) c) 1.00 a) c) Probability b) Health status Health status 12

13 Item Information Curve The item information curve is a function of the descriminant and the probability of the answer Item characteristic curve 1.00 Item information curve ap(1-p) Information Health status Health status 13

14 Health Index Requirements for the health index: 1) differentiate people across the different levels of health. a. Difficulty values for questions with three or more categories in order. b. Difficulty values evenly distributed across the latent trait. 2) discriminate people of similar level of health and be precise over a large range of the latent trait. a) High discriminant values. b) Large information function. 14

15 irt nrm PADL IADL Gait MMSE Morb, intpoints(50) Nominal response model Number of obs = 3,363 Log likelihood = Coef. Std.Err. z P>z [95% Conf. Interval] PADL Discrim 1 vs Diff 1 vs IADL Discrim 1 vs Diff 1 vs Gait Discrim 1 vs vs vs Diff 1 vs vs vs MMSE1 Discrim 1 vs vs Diff 1 vs vs Morb Discrim 1 vs vs Diff 1 vs vs

16 Health Index irtgraph icc PADL IADL, /// blocation plocation irtgraph icc Gait, /// blocation plocation 1.0 Boundary Characteristic Curves 1.0 Boundary Characteristic Curves 0.5 Probability 0.5 Pr(PADL=1) Pr(IADL=1) Pr(Gait 1) Pr(Gait 2) Pr(Gait=3) Theta Theta PADL Discrim 1 vs Diff 1 vs IADL Discrim 1 vs Diff 1 vs Gait Discrim 1 vs vs vs Diff 1 vs vs vs

17 Health Index 1.0 Category Characteristic Curves Probability Theta Pr(Gait=0) Pr(Gait=1) Pr(Gait=2) Pr(Gait=3) irtgraph icc Gait, ccc 17

18 Health Index 1.0 Category Characteristic Curves Probability Theta Pr(Gait=0) Pr(Gait=1) Pr(Gait=2) Pr(Gait=3) Diff = (Diffi-Diffi-1)/(Discrimi-Discrimi-1) Coef. Std. Err. z P> z [95% Conf. Interval] A B C

19 Health Index 1.0 Category Characteristic Curves Probability Theta Pr(Gait=0) Pr(Gait=1) Pr(Gait=2) Pr(Gait=3) 1.0 Category Characteristic Curves 1.0 Category Characteristic Curves 0.5 Probability Theta Pr(MMSE=0) Pr(MMSE=1) Pr(MMSE=2) Theta Pr(Morb=0) Pr(Morb=1) 20 Pr(Morb=2)

20 Health Index irtgraph tif, data(a,replace) merge using A irtgraph iif PADL IADL Gait MMSE Morb, range(-3 3) addplot(line tif theta) 40 Item Information Functions Information Theta PADL IADL Gait MMSE Morb 21

21 Health Index irtgraph tcc, range(-3 3) scorelines( , lwidth(medthick) lcolor(gs8)) 9 8 Test Characteristic Curve Theta 22

22 Health Index Health index by sex and age Health Index % 50% 10% Men Women Age (years) 23

23 Health Index Area under the receiver operating characteristic (ROC) curve in predicting time to death within 5 years Health index Multi Prognostic Index ROC Area 95%CI ROC Area 95%CI p-value All 0.82 (0.79, 0.84) 0.77 (0.75, 0.80) < (0.69, 0.77) 0.69 (0.65, 0.73) (0.71, 0.78) 0.71 (0.67, 0.75) 28 24

Item Analysis: Classical and Beyond

Item Analysis: Classical and Beyond SCROLLA Symposium Measurement Theory and Item Analysis Modified for EPE/EDP 711 by Kelly Bradley on January 8, 2013 Why is item analysis relevant? Item analysis provides