The AMC Linear Disability Score project in a population requiring residential care: psychometric properties
 Rebecca Holman^{1}Email author,
 Robert Lindeboom^{1},
 Marinus Vermeulen^{2} and
 Rob J de Haan^{1}
DOI: 10.1186/14777525242
© Holman et al; licensee BioMed Central Ltd. 2004
Received: 22 June 2004
Accepted: 03 August 2004
Published: 03 August 2004
Abstract
Background
Currently there is a lot of interest in the flexible framework offered by item banks for measuring patient relevant outcomes, including functional status. However, there are few item banks, which have been developed to quantify functional status, as expressed by the ability to perform activities of daily life.
Method
This paper examines the psychometric properties of the AMC Linear Disability Score (ALDS) project item bank using an item response theory model and full information factor analysis. Data were collected from 555 respondents on a total of 160 items.
Results
Following the analysis, 79 items remained in the item bank. The remaining 81 items were excluded because of: difficulties in presentation (1 item); low levels of variation in response pattern (28 items); significant differences in measurement characteristics for males and females or for respondents under or over 85 years old (26 items); or lack of model fit to the data at item level (26 items).
Conclusions
It is conceivable that the item bank will have different measurement characteristics for other patient or demographic populations. However, these results indicate that the ALDS item bank has sound psychometric properties for respondents in residential care settings and could form a stable base for measuring functional status in a range of situations, including the implementation of computerised adaptive testing of functional status.
Background
It is now widely accepted that examining quality of life is an important aspect in the treatment and evaluation of many conditions. Functional status is seen as an important determinant of quality of life. A wide variety of instruments have been developed to quantify functional status [1]. These instruments tend to have a fixed length and all items are administered to the whole group of patients under scrutiny. However, currently interest is moving towards the more flexible framework offered by item banks. An item bank is a collection of items, for which the measurement properties of each item are known [2, 3]. When using an item bank, it is not essential for all respondents to be examined using all items. This enables the burden of testing to be considerably reduced for both patients and researchers. It is even possible to select the 'best' items for individual patients using computerised adaptive testing algorithms [4]. Furthermore, results from studies using different selections of items from an item bank can be directly compared. Item banks, measuring concepts such as quality of life [2, 5], the impact of headaches [6] or functional status [7, 8], have been developed.
The AMC Linear Disability Score (ALDS) project item bank was developed to quantify functional status [7, 9]. The ALDS item bank covers a large number of activities, which are suitable for assessing respondents with a very wide range of functional status and many types of chronic condition. The item bank is particularly suitable for use in the Netherlands. The ALDS items were obtained from a systematic review of generic and disease specific functional health instruments [1]. Five psychometric aspects of the ALDS item bank need to be considered before it can be implemented. These are: (a) there needs to be enough variation in the response categories used for each item [9]; (b) estimates of the item response theory model parameters should not depend on patient characteristics such as age or gender [10, 11]; (c) estimates of the item response theory model parameters, which are stable across different subsets of items from the instrument and based on a sufficiently large sample [12] of respondents, should be available [9]; (d) an examination of the extent to which the ALDS items represent a single construct; and (e) testing whether a simpler item response theory model is suitable for the set of items.
This paper examines these five aspects of the ALDS item bank using the responses given by residents of supported housing schemes, residential care and nursing homes in and around Amsterdam, the Netherlands. This, mainly elderly, population has been chosen because they generally experience some level of functional restriction and consume a large amount of health care services.
Methods
Data collection
This paper considers 160 items, which were considered to be applicable in a residential care setting. Each item has two response categories: 'I could carry out the activity' and 'I could not carry out the activity'. If a respondent had never had the opportunity to experience an activity 'not applicable' was recorded. In the analysis, responses in the category 'not applicable' were treated as if the individual items had not been presented to the individual respondents [13]. It was felt that presenting all 160 items to each respondent would place an unnecessary and unacceptable burden on those responding to the items. Therefore, the data described in this paper were collected using an incomplete, anchored calibration design [7, 9, 14, 15] with four sets of 80 items. Item sets A and B have half their items in common, as do item sets B and C, item sets C and D and item sets A and D. The items in common between two sets of items are known as 'anchors' and allow all items and patients to be calibrated on the same scale. The patterns of missing data in this type of design are, in statistical terms, ignorable [16]. The item sets were administered randomly to 150 respondents (item set A), 143 respondents (item set B), 138 respondents (item set C) and 124 respondents (item set D).
Respondents
A total of 555 residents of supported housing, residential care and nursing homes were interviewed. The median age was 84 years (range 37 to 101 years), while 444 (80%) were female. Since the respondents were interviewed 'at home', accurate data on medical conditions were not available. All respondents gave informed consent. The study was approved by the medical ethics committee in our hospital.
The item response theory models
In this paper the data were analysed using the twoparameter logistic item response theory model [7, 9, 17, 18]. In this model, the probability, P _{ ik }, that patient k responds to item i in the category 'can' is modelled using
where θ _{ k }denotes the ability of patient k to perform activities of daily life. The discrimination parameter (α _{ i }) and difficulty parameter (β _{ i }) describe the measurement characteristics of item i. The larger the value of β _{ i }, the more difficult item i is. In addition, the larger the value of α _{ i }, the better an item is a distinguishing between abilities above and below β _{ i }. If the values of α _{ i }are constrained to be equal for all items, the model in equation 1 becomes the oneparameter logistic item response theory model [19]. The model in equation 1 can be extended to test whether the values of β _{ i }for, say males and females, are significantly different. If the values of β _{ i }for different groups of respondents are significantly different, then there is evidence of differential item functioning. Fullinformation factor analysis also uses an extension of the model in equation 1. These approaches are described in mathematical terms in the Appendix. In this paper, estimates of α _{ i }and β _{ i }were obtained using a marginal maximum likelihood based procedure [20]. This method assumes that the ability parameters (θ _{ k }) follow a Normal distribution and can account for incomplete designs, as described in the Appendix. Expected a posteriori methods were used to estimate θ _{ k }[21].
Statistical analysis
To achieve the objectives of this study, there were five steps in the statistical analysis. In step (a), the amount of variation in the response categories used for each item [9] was considered and items demonstrating too little variation were removed. Items were excluded from further analysis if fewer than 10% or more than 90% of the patients responded in the category 'cannot'. In step (b), the items were examined to investigate whether the value of the item difficulty parameter (β _{ i }) was similar for male and female patients and for patients younger than 85 years and those aged 85 or older. The model is described in depth in the Appendix. Items were excluded from further analysis if the value of the item difficulty parameter was significantly different (1% level) between gender or aged based groups. In this step, the fit of the model to the data from each item was not assessed. In step (c), estimates of the item parameters (α _{ i }and β _{ i }) were obtained. The fit of the model to the data from each item was assessed using G^{2} statistics [22]. Items, for which the fit statistic had a pvalue of less than 0.01, were excluded from the item bank. In addition, the stability of the estimates of the item parameters over different sets of items was examined using the model from step (b). Items were excluded from further analysis if the value of the item difficulty parameter was significantly different (1% level) between item sets A and B, B and C, C and D or A and D. Furthermore, a KolmogornovSmirnov test was carried out to examine whether the ability parameters (θ _{ k }) were Normally distributed. In step (d), the dimensionality of the item bank was examined using item response theory based full information factor analysis [18, 22, 23]. The number of latent roots greater than 1 is regarded as an indicator of the number of factors in the data set. This method is described in more depth in the Appendix. Four exploratory factor analyses were carried out, one on each of the anchors between item sets A and B (293 respondents), B and C (281 respondents), C and D (262 respondents) or A and D (274 respondents). A fifth, confirmatory, factor analysis was carried out on the whole data set (555 respondents). In addition, Cronbach's coefficient alpha was calculated for each anchor and the whole data set [24, 25]. In step (e) the oneparameter logistic item response theory model was fitted to the remaining items. The differences between the 2log likelihoods of this model and the twoparameter model fitted in step (c) was tested using a χ^{2} test. The analysis in steps (a), (b), (c) and (e) was carried out in Bilog, version 3.0 [22]. The analysis in step (d) was carried out using TESTFACT, version 4.0 [22].
Results
The number of items proceeding to each step of the analysis The number of and examples of items removed at each stage of the psychometric analysis.
Stage of analysis  Number of items removed  Reason for removal  Examples 

1  Concerns about the way the item was presented  
(a)  28  < 10% or > 90% of responses in 'cannot'  Reaching for a cup and taking a sip of water Combing hair at a sink Cycling on a heavily laden bicycle 
(b)  26  Significant difference between M and F and/or under and over 85 years  Washing up (easier for older respondents) Crossing the street (easier for younger respondents Preparing a warm meal (easier for female respondents) 
(c)  26  Item fit pvalue < 0.01 or estimates of β _{ i }not stable  Taking oral medication Cycling Getting money out of the bank using an ATM 
In item bank  79  See Table 2  
Total  160 
The 79 items remaining in the calibrated item bank. The items remaining in the calibrated item bank. The number of respondents, to whom the item was offered (Offered to), the number responding in the category 'not applicable' (NA), the number responding in the category 'can' (can) and the number responding in the category 'cannot' (cannot) are given. The discrimination (β) and difficulty (β) parameters are given along with their standard errors in parentheses.
Description of item content  Offered to  Item response category  Location parameter (β)  Discrimination parameter (α)  

NA  can  cannot  
Walking up stairs with a bag  262  0  19  243  3.607  (2.404)  1.122  (0.892) 
Mopping a flight of stairs  262  5  16  241  2.830  (1.708)  0.447  (0.411) 
Cleaning the top of a high cupboard  281  2  27  252  2.816  (1.946)  0.480  (0.393) 
Cleaning a bathroom  293  1  37  255  2.621  (2.061)  0.323  (0.338) 
Vacuuming  274  0  33  241  2.408  (1.844)  0.287  (0.280) 
Going for a walk in the woods  281  0  31  250  2.343  (1.636)  0.362  (0.340) 
Fetching groceries for 3–4 days  293  0  36  257  2.262  (1.623)  0.353  (0.343) 
Mopping the floor  281  2  41  238  2.225  (1.902)  0.339  (0.374) 
Caring for plants on a balcony  262  1  32  229  2.108  (1.616)  0.314  (0.325) 
Travelling by bus or tram  281  0  44  237  2.093  (1.835)  0.308  (0.370) 
Walking up two flights of stairs  274  0  39  235  1.921  (1.532)  0.277  (0.298) 
Cleaning a fridge  293  2  64  227  1.406  (1.464)  0.171  (0.236) 
Going to a restaurant  293  3  60  230  1.335  (1.238)  0.159  (0.188) 
Carrying a tray  281  1  75  205  1.304  (1.774)  0.222  (0.326) 
Going for a long walk (15+ minutes)  281  0  72  209  1.290  (1.629)  0.178  (0.277) 
Going to the dentist  293  18  75  200  1.283  (1.881)  0.205  (0.299) 
Sweeping the floor  262  1  70  191  1.239  (1.902)  0.196  (0.313) 
Cutting toe nails  262  0  45  217  1.175  (0.786)  0.136  (0.144) 
Walking up a hill or bridge  281  3  73  205  1.133  (1.425)  0.137  (0.198) 
Walking up one flight of stairs  274  2  67  205  1.127  (1.382)  0.155  (0.222) 
Going to a concert  262  0  57  205  0.996  (0.860)  0.113  (0.128) 
Going to the pharmacist  262  2  75  185  0.976  (1.572)  0.131  (0.201) 
Hanging a load of washing out  293  10  84  199  0.960  (1.514)  0.144  (0.240) 
Going to the post office or bank  274  0  88  186  0.948  (1.881)  0.151  (0.248) 
Going to a party  281  1  69  211  0.924  (0.878)  0.109  (0.129) 
Filling an official form in  281  1  68  212  0.896  (0.790)  0.106  (0.119) 
Using a washing machine  281  6  95  180  0.851  (1.743)  0.153  (0.244) 
Visiting an outpatients' clinic  293  0  95  198  0.815  (1.317)  0.112  (0.161) 
Taking bottles to the bottle bank  281  5  108  168  0.675  (1.840)  0.153  (0.312) 
Short walk (less than 15 minutes)  274  0  95  179  0.645  (1.358)  0.108  (0.166) 
Putting a rubbish bag outside  293  5  108  180  0.573  (1.338)  0.116  (0.198) 
Reaching into a high cupboard  274  0  95  179  0.569  (1.097)  0.099  (0.172) 
Using a dustpan and brush  262  2  103  157  0.537  (1.865)  0.135  (0.335) 
Opening and closing a high window  281  0  140  141  0.078  (1.290)  0.096  (0.166) 
Fetching groceries for one day  262  0  128  134  0.043  (1.373)  0.099  (0.184) 
Using a public toilet  293  5  159  129  0.139  (1.835)  0.110  (0.241) 
Putting flowers in a vase  293  2  162  129  0.169  (1.787)  0.107  (0.240) 
Frying an egg  281  3  154  124  0.178  (1.982)  0.115  (0.261) 
Warming up a tin of soup  293  1  164  128  0.203  (1.919)  0.113  (0.232) 
Cleaning a toilet  262  0  149  113  0.308  (1.528)  0.105  (0.203) 
Putting socks and lace up shoes on  281  1  167  113  0.314  (1.165)  0.093  (0.157) 
Changing the bulb in a table light  281  1  177  103  0.533  (1.541)  0.116  (0.174) 
Cleaning a bathroom sink  281  5  170  106  0.564  (2.089)  0.126  (0.302) 
Cutting finger nails  262  0  168  94  0.605  (1.337)  0.114  (0.173) 
Rubbing lotion into whole body  262  4  164  94  0.627  (1.469)  0.115  (0.184) 
Reaching into a low cupboard  274  0  184  90  0.672  (1.131)  0.106  (0.152) 
Picking something up off the floor  262  0  172  90  0.712  (1.466)  0.129  (0.198) 
Making porridge  293  2  191  100  0.714  (1.704)  0.119  (0.216) 
Getting in and out of a car  281  3  185  93  0.738  (1.656)  0.132  (0.209) 
Shaking a tablecloth out  274  2  190  82  0.906  (1.438)  0.125  (0.204) 
Making a bed  281  0  193  88  1.003  (2.028)  0.152  (0.292) 
Preparing breakfast or lunch  262  1  186  75  1.117  (1.729)  0.169  (0.279) 
Using the lift in a public building  262  2  199  61  1.208  (1.299)  0.158  (0.186) 
Putting an alarm clock right  281  4  216  61  1.319  (1.431)  0.165  (0.199) 
Pulling a blanket up  293  0  253  40  1.485  (0.898)  0.167  (0.149) 
Visiting the neighbours  293  1  231  61  1.548  (1.685)  0.221  (0.252) 
Travelling as a passenger in a car  274  3  230  41  1.592  (1.126)  0.222  (0.192) 
Shaving face or applying make up  274  1  233  40  1.593  (1.075)  0.180  (0.164) 
Watering a house plant  262  3  204  55  1.600  (1.681)  0.226  (0.259) 
Opening and closing a window  262  0  201  61  1.735  (2.137)  0.246  (0.343) 
Putting trousers on  293  2  224  67  1.821  (2.372)  0.295  (0.406) 
Making coffee or tea  293  0  235  58  1.832  (1.936)  0.237  (0.290) 
Peeling an apple  281  1  233  47  1.859  (1.631)  0.226  (0.219) 
Making a bowl of cereal  281  1  225  55  1.860  (1.921)  0.222  (0.256) 
Eating a meal at the table  293  0  255  38  2.081  (1.509)  0.253  (0.225) 
Hanging clothes up in a cupboard  262  0  203  59  2.105  (2.595)  0.344  (0.481) 
Opening and closing curtains  262  0  216  46  2.129  (1.958)  0.366  (0.357) 
Moving between two dining chairs  281  0  237  44  2.214  (1.905)  0.389  (0.375) 
Putting a scarf and gloves on  293  1  259  33  2.364  (1.617)  0.306  (0.246) 
Making a cheese sandwich  281  1  243  37  2.416  (1.856)  0.392  (0.333) 
Moving to sit on the edge of a bed  262  1  231  30  2.457  (1.658)  0.309  (0.244) 
Putting a coat on  274  0  227  47  2.463  (2.323)  0.425  (0.395) 
Putting a shirt or blouse on  262  0  228  34  2.495  (1.842)  0.360  (0.287) 
Washing upper body at a sink  274  0  243  31  2.705  (1.875)  0.420  (0.327) 
Answering the front door  274  1  233  40  2.792  (2.373)  0.481  (0.449) 
Getting out of bed into a chair  262  0  232  30  3.019  (2.132)  0.581  (0.448) 
Washing lower body at sink  293  1  241  51  3.037  (3.098)  0.722  (0.761) 
Putting a Tshirt on  293  2  257  34  3.440  (2.664)  0.718  (0.630) 
Locking a door  262  0  230  32  3.366  (2.512)  0.970  (0.749) 
Discussion
In this study, the psychometric properties of the item bank have been examined using a sample of 555 respondents and an incomplete calibration design. Each item was presented to between 262 and 293 respondents. These figures are above the minimum, of 200 respondents, regarded as necessary to implement the models used in this paper [12]. It could be argued that it would have been desirable for all respondents to be presented with all items, but this would have placed an unacceptable burden on the, often frail, population in this study. Incomplete calibration designs are regularly implemented in the development and maintenance of item banks used in educational testing [4, 14] and have gained some recognition in health related applications [15]. Developments in psychometric theory mean that it is now possible to perform the same types of analysis on data resulting from incomplete designs, as is performed on data from complete calibration designs [22, 23, 25]. The number of items in the anchors following the analysis, indicate that the design was still amply linked [9].
One of the major assumptions underlying the use of the item response theory models described in this paper is that the items reflect a single latent trait (θ). This has been examined using item response theory based fullinformation factor analysis. Part of the fullinformation factor analysis was performed on subsets of the data, as exploratory analyses on incomplete designs may lead to instable results. However, the confirmatory factor analysis was performed on all data. The results, together with the high level of internal consistency, as measured by Cronbach's alpha, and the acceptable fit of the twoparameter logistic item response theory model to the data indicate that the items presented in this paper probably represent a unidimensional construct in a population of respondents requiring residential care.
Another important assumption when using item response theory models in conjunction with marginal maximum likelihood estimation procedures is that the values of the latent trait (θ) follow a prespecified, usually Normal, distribution. In this study, there was no evidence that these values did not follow a Normal distribution. This is in contrast to many previously published studies into health and quality of life outcomes, where a strongly skewed distribution was found. The authors feel that there are two reasons for this contrast. Firstly, in this study, the respondents all had some level of restriction in their ability to perform activities of daily life. Secondly, the item bank includes items well above and well below the level of functional status enjoyed by the respondents. This means that the item bank did not have a ceiling or floor effect with respect this this population.
In this study, 81 (51%) of 160 items were removed from the item bank because they did not conform to the psychometric standards required of the item bank. This is a much higher level than would be expected in the calibration of an item bank for use in educational measurement. However, when the results are examined more carefully, 28 items were removed because they were too difficult or too easy for the population in this study. In addition, 26 items were removed because they had different item parameters for different groups of respondents. These problems would have been identified much earlier in an educational item bank. Hence, only 26 (25%) of 106 items were removed due to item misfit. The number of items retained in the item bank may have been higher if a more flexible model, based on, for example, nonparametric smoothing techniques had been used [26]. However, this type of model is less suitable as a base for implementing modern testing algorithms, such as computerised adaptive testing. In addition, it is possible that more items could be made available if the items demonstrating differential item functioning were included in the item bank with different item location parameters (β _{ i }) for males and females or for younger and older respondents. This may seem complicated, but is straightforward in the framework of a computerised item bank.
This paper has concentrated on the twoparameter logistic item response theory model. However, the oneparameter logistic item response theory model was also fitted to the 79 items remaining in the item bank. This model fitted the data significantly less well than the twoparameter model, even after 3 items demonstrating misfit at the item level were removed. This confirms the choice of the twoparameter model. This model was chosen because it allows the probability of responding in the category 'can' to be modelled more flexibly than when the oneparameter logistic model is used. This enables a more realistic model for the data to be built than when the more restrictive approach associated with the oneparameter model is chosen [18].
This paper has examined the calibration of the ALDS item bank in a population requiring residential care. It has been shown that the item bank has sound psychometric properties and could form a stable base for a wide range of applications. However, it is possible that the items will have different measurement characteristics for patients requiring treatment for specific chronic conditions or in other countries. Hence, it is important that the ALDS item bank is tested carefully before it is used to assess the functional status in other groups of respondents or in other countries.
Conclusions
Now that the measurement properties of the ALDS item bank have been examined carefully, the item bank can be used as a foundation for quantifying functional status. If modern algorithms, such as computerised adaptive testing, are implemented, it will be possible to obtain accurate measurements, whilst keeping the burden of testing on respondents and interviewers to a minimum. Items can be selected for use in further research, for allocation individuals to appropriate care settings and for calculating institutional funding based on the actual care load. It is hoped that the ALDS item bank will play an important part in the implementation of computerised adaptive testing of functional status.
Appendix
Differential item functioning
The model in equation 1 can be extended to test whether different groups of respondents to have different values of β _{ i }. This is known as differential item functioning. For instance, if interest is in possible differences in β _{ i }between males and females, then the probability, P _{ ik }, that patient k responds to item i in the category 'can' is written as
where β _{ iM }is the item difficulty for male respondents, β _{ iFM }is the difference between the item difficulty for males and for females and I _{ k }is an indicator variable taking the value 0 if respondent k is male and the value 1 if respondent k is female. The hypothesis H_{0} : β _{ iFM }= 0 can be tested to examine whether item i has the same measurement characteristics for males and for females.
Item parameter estimation in incomplete designs
In this study, the item parameters (α _{ i }and β _{ i }) were estimated using marginal maximum likelihood methods. The likelihood, L, over n items and K (K = 555) respondents can be written as
where I _{ ik }is an indicator variable taking the value 1 if respondent k was offered item i and the value 0 otherwise and where J _{ ik }is an indicator variable taking the value 1 if respondent k responded to item i in the category 'can' and the value 0 otherwise. Furthermore, the probability, P _{ ik }, that respondent k responded to item i in the category 'can' is as in equation 1, or, where appropriate, as in equation 2 or 4. In the estimation process, the values of θ _{ k }or θ _{ km }were assumed to follow a Normal distribution with mean equal to 0 and unknown variance, σ^{2}, and were integrated out of the likelihood to obtain the marginal likelihood. The marginal likelihood was maximised using an EM algorithm [20].
Full information factor analysis
Full information factor analysis is a technique based on multidimensional item response theory models where the ability is represented by M variables, denoted θ _{ km }where m = 1, 2,..., M [22, 23]. The model, in equation 1, for the probability, P _{ ik }, that person k responds to item i in the category 'can' can be extended to
where θ _{ km }denotes the value of the latent variable θ _{ m }associated with person k and α _{ im }denotes the discrimination parameter for item i with respect to the latent variable θ _{ m }. Furthermore, δ _{ i }is a difficulty type parameter. The loading, a _{ im }of item i on factor m can be calculated using
The value of the standard difficulty parameter, (β _{ i }), can be calculated using
Generally, the parameters α _{ im }and δ _{ i }are estimated using marginal maximum likelihood methods.
Funding
RH and RL were supported by a grant from the Anton Meelmeijer fonds, a charity supporting innovative research in the Academic Medical Center, Amsterdam, The Netherlands.
Authors contributions
RL conceived the study and supervised the data collection. RH prepared the first draft and carried out the analyses. RL, MV and RJdH critically reviewed the manuscript. RH prepared the final version.
Abbreviations
 ALDS:

AMC Linear Disability Score
Declarations
Authors’ Affiliations
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