The Nottingham Health Profile (NHP38) is a generic measure of subjective health status developed in Great Britain in the 1970s and extensively used in Europe 1. It contains 38 items with a 'yes/no' response format, describing problems on six health dimensions (Energy, Pain, Emotional Reactions, Sleep, Social Isolation and Physical Mobility). The Spanish version of the questionnaire was obtained through a process of precise translation (using translation and back-translation procedures), aimed at achieving conceptual equivalence 13. It has proved to be valid and reliable in several groups of patients 15. The authors of the original version weighted each NHP38 item, to offset the differences in the scope of the problems described by each item. For each dimension (scale), the items were weighted by the paired comparison method proposed by Thurstone 16. The NHP38 weighting has likewise been applied to the Swedish 17, French 18 and Spanish 19 versions of the questionnaire in order to assess cross-cultural equivalence and validate the process of adaptation. However, the use of an unweighted NHP38 scoring has been recommended for the Spanish version 19. To such ends, the scores are obtained by adding together the number of affirmative answers for each scale in the questionnaire and expressing the number as a percentage, ranging from 0 (best health status) to 100 (worst health status).

Data collection, intended for use in a common database covering all of the studies that have included the Spanish version of the NHP38 since its release in 1987, is described elsewhere 2021. The studies were identified by searches on Medline and the Spanish Medical Index from 1987 to 1995 (Key terms: Nottingham Health Profile, NHP, quality of life, measure of health status, questionnaire, reliability, validity, Spanish, and Spain). Other studies were identified from the Spanish NHP38 "cession of use" registry, kept by one of the authors (JA) since 1987. Of the 119 studies identified, data were available from 45, covering a total of 9,419 individuals. The Spanish version of the NHP38 had been used in all the studies (all respondents reporting on their own HRQOL).

Selected variables from these 45 studies were collected in a common data base (i. e. responses to NHP38 items, gender, age, self-reported general health status, and study population).

The 38 items of the original Nottingham Health Profile (NHP38) were subject to item analysis, using standard statistical procedures 1718. The classical index of discrimination was obtained by calculating the corrected item-total correlation coefficients (r) for each item with its hypothetical scale 3. Endorsement indices were also determined for each item by calculating the proportion (p) of people choosing to answer 'Yes'. First of all, the NHP38 items with a r (<0.4) and a low (<0.20) or high p (>0.80) were excluded 22. Exploratory Factor Analysis (EFA), employing Principal Axis Factor extraction and Promax rotation, was performed on the remaining items. EFA deleted all cases with missing values listwise (only cases with nonmissing values for all the items involved were used). A secondary reduction was then performed by deleting those items showing a low portion of the test score variance associated with the variance on the common factors (Communality < 0.3), as well as those items showing its highest factor loading on the main factor to be lower than 0.4, and those items with similar (difference ≤ 0.1) loadings on different factors.

Cronbach's alpha coefficient 23 was calculated on the scales (factors) resulting from the EFA, to estimate the internal-consistency reliability of each new composite score. Following the basics assumptions of CTT 34, a summary score of the reduced questionnaire was obtained by summing and averaging the scores of their component dimensions. The reliability of the summary score was estimated using the formula proposed by Nunnally and Bernstein (pp. 268) 3. Additional EFA, based on principal component extraction, was used to determine whether the new dimensions could be reduced to a unique summary score.

Through log-odds, the Rasch model specifies that the probability of response of person n to item i is governed by location B_n for the subject (person measure) and location D_i for the item (item calibration), along a common continuum of measurement:

Log [P_ni1/P_ni0] = B_n - D_i

where, P_ni1 is the probability of a "Yes" response to item i and P_ni0 is the probability of a "No" response. When B_n >D_i, there is more than 50% chance of a "Yes" response. When B_n = D_i, the chance for a "Yes" response is 50%. When B_n <D_i, the probability is less than 50%. Each facet in the model (B, D) is a separate parameter. Estimates of one of the sets of parameters are not affected by the other. This mathematical property enables "test-free" and "person-free" measurement. This property implies that the parameter that characterize an item does not depend on the ability distribution of the examinees and the parameter that characterize a subject does not depend on the set of test items.

Item calibration defines the hierarchical order of severity ("difficulty") of the items along the health continuum. Item calibration is expressed in log-odd units (logits), positioned along a hierarchical scale. A logit is defined as the natural log of an odds ratio. Logits of greater magnitude represent increasing item severity. One logit is the distance along the health continuum that increases the odds of observing the event specified in the measurement model by a factor of 2.718, the value of e, the base of natural or Napierian logarithms used for the calculation of "log-" odds. All logits are the same length with respect to this change in the odds of observing the indicative event.

The unidimensionality of a scale can be evaluated by the pattern of item goodness-of-fit statistics and by a formal test of the assumption of local independence 5910.

The original NHP38 was consecutively analyzed with the Rasch dichotomous response model. The Rasch analysis was performed with Version 2.7.3 of the BIGSTEPS computer program 25. To avoid negative values, and to express the resulting scores on a 0 (best health status) to 100 (worst health status) scale score, the initial BIGSTEPS estimates were rescaled in all analysis, setting a new origin (49.73 units) and spacing (11.84 units/1 logit) for the scale 9. In order to determine the precision of each estimate, an associated standard error (SE) was calculated for each item and person in the sample. The person separation index (PSEP) was also calculated. The PSEP is a ratio of standard deviation that describes the number of performance levels the test measures in a particular sample. It is equal to the square root of true person variance divided by the error variance due to person measurement imprecision (PSEP = (True Variance_N / Error Variance_N)^1/2. The test reliability (R) of the person separation index (PSEP) can be expressed as R = (PSEP)²/(1 + PSEP)² 2021. Hence, the separation index has to exceed 2 (or 3) in order to attain the desired level of reliability of at least 0.80 (or 0.90). If statistically distinct levels of person ability are defined as ability strata with centers three measurement errors apart, then the PSEP can be translated into the number of statistically distinct person strata identified by the test (Person Strata = [4·PSEP + 1]/3). A Person Strata of, "3" (the minimum level to attain a reliability of 0.90) implies that three different levels of performance can be consistently identified by the test for samples like that tested.

Chi-square fit statistics were used to determine how well each NHP38 item contributed to defining a common health variable (Goodness-of-fit test) 910. The most commonly used chi-squares are known as Oufit and Infit. They are reported as Mean-Squares (MNSQ), that is, the chi-square statistics divided by their degrees of freedom (so that they have a ratio-scale form with expectation 1 and range 0 to + ∝.). Outfit is based on the conventional sum of squared standardized residuals. If X is an observation, E its expected value based on Rasch parameter estimates, and σ² its modeled variance of expectation, then the squared standardized residual is: z² = (X - E)²/σ². Oufit is Σ (z²)/N, where N is the sum of the number of observations. Outfit is sensitive to unexpected responses made by persons for whom item i is far too "easy" or far too "difficult". Infit is an information-weighted sum in which each square residual is weighed by its variance (σ²). Infit can be calculated as Σ(z²σ²)/Σ (σ²) = Σ (X - E)²/Σ (σ²). Since variance is smallest for persons furthest from items i, the contribution to Infit of their responses is reduced. An item with an Outfit or Infit MNSQ near 0 indicates that the sample is responding to it in an overly predictable way. Item Outfit or Infit MNSQ values of about 1 are ideal by Rasch model specifications, and indicate local independence. Items with Outfit or Infit MNSQ values greater than 1.3 are usually diagnosed as potential misfits to Rasch model conditions and considered for deletion from the assessed sequence (More information about this issue is provided by Smith et al. (1998)24). Successive Rasch analyses were performed until a final set of items satisfied the model fit requirements.

Since Rasch analysis places both persons and items along the same latent dimension, one can ask whether there is a substantial number of persons who actually do respond as predicted by the Rasch model. For this reason, person fit statistics, based on Infit and Outfit mean-square statistics, were also calculated for the new short-form obtained by the Rasch approach.

In order to minimize the loss of sensitivity of the new short questionnaire, two additional scoring options were taken into account. Considering previous experience with the questionnaire 1526, the 38 items of the NHP38 were regrouped into two new, different scales before Rasch analysis was performed: a Physical scale (containing Energy, Pain and Physical Mobility dimensions) – 19 items – and a Psychological scale (containing Emotional Reactions, Sleep and Social Isolation) – 19 items. Separate Rasch analysis were performed with the Physical and Psychological scales. For this purpose, the item calibrations obtained when all items were analyzed together were used as anchor (fixed) values. The displacement (divergence) of the local estimate away from the anchored value was provided for each Physical and Psychological item (results not shown).

In order to perform a validation study of the stability of the results obtained by the two different strategies for the reduction of the questionnaire, the subjects in the initial common database were randomly divided into two independent sub-samples. The analysis described above was performed on sub-sample A (85%, n = 8,015), and independently repeated for sub-sample B (15%, n = 1,404)(15% was an arbitrary percentage which ensured that sub-sample B was representative of the age and study population sub-groups)

In order to compare the performance of the reduced versions, the following analyses were carried out: 1) Pearson and Spearman's coefficient of correlation was calculated comparing the original NHP38 and the CTT and Rasch analysis reduced scales; 2) Reliability estimates and item-total correlation coefficients were obtained for the Rasch analysis reduced scales and compared with the estimates obtained for the scales resulting form the CTT analysis; 3) the items and scales reduced by CTT were Rasch analyzed, and the results compared with those obtained by the Rasch reduction of the original questionnaire; 4) distribution patterns of scores and measures were described for each reduced questionnaire. Principal component extraction was also used to determine whether the Physical and Psychological Rasch scales could be reduced to a single summary score. The unidimensionality of the whole Rasch reduced version was further explored through the examination of the residual correlation matrix of a one-factor exploratory factor analysis of the items (Principal Axis Factor extraction).