Dimension dependence
Two related questions are relevant if new dimensions are considered. (1) To what extent are the descriptive scores on the dimensions related (dependent)? (For example: the best level in mobility usually corresponds to best level in usual activities, or the level of self-care is never better than the lowest level of any of the other dimensions, a case of dominance or no relation beyond chance agreement.) (2) Are the contributions of the dimensions to the total utility score related? Note that two dimensions may be strongly related in a descriptive way, while they may still have independent roles in utility terms. Reversely, independent dimensions in a descriptive way may show strong interaction in utility terms, which may be cancelation or enhancement of the disutility associated with either of them. A new dimension at least should show both additional descriptive power and an independent utility role, preferably also at the non-extreme levels. This paper focuses on descriptive independence, question 1, and tentatively addresses question 2 by analysis of EQ-VAS data (see below). The EQ-VAS was used as a proxy of HRQL in this analysis.
To check descriptive dependence, we created cross tables between pairs of dimensions, specifically checking instances of dominance/subordination of the cognitive dimension. The following procedure was developed. We considered the profiles with level 3 (L3; extreme problems) on one dimension (A) and level 1 (L1; no problems) on another dimension (B). Then we defined ‘dominance of dimension A across B’ as the presence of less combinations of A-L3 and B-L1, than of A-L1 and B-L3, corrected for chance frequency of these combinations. This definition catches ‘negative’ dominance, defined as the mechanism that dysfunction in dimension A is paralleled by dysfunction in each other dimension, limiting the probability of a high level. In our context ‘positive’ dominance is of no interest, i.e., a high level of dimension A limits the presence of poor levels elsewhere. The authors formulated hypotheses regarding the dominance of domains through discussion. For the cognition domain, we hypothesized that cognition dominates self-care and usual activities. It was deemed plausible that severe cognitive problems co-occur with severe problems with self-care and usual activities, but not the other way around. The plausibility of the remaining domains combination falls outside the scope of this paper, and are therefore not further discussed.
In our data analysis, we first estimated the probability of all possible level 3 and level 1 dimension combinations under independence, based on multiplication of the marginal frequencies of the levels per dimension using the following formula:
$${\text{Probability (D1}}\_{\text{L1}}|{\text{ D2}}\_{\text{L3)}}\,=\,{\text{prevalence (D1}}\_{\text{L1)}} \times {\text{prevalence (D2}}\_{\text{L3)}},$$
where D1_L1 is dimension 1 (e.g., mobility) level 1 and D2_L3 is dimension 2 (e.g., self-care) level 3.
For instance, if mobility_L3 had a prevalence of 10% and usual activities_L1 had a prevalence of 60%, the estimated expected conditional probability of mobility_L3 and usual activities_L1 is 6%. Then we listed all prevalent EQ-5D + C profiles of our dataset, and selected among them the pairs with contrasting results (some pairs qualify for multiple contrasts, e.g., the profile 112,313 contains 6 L1–L3 contrasts). We compared the number of L1–L3 versus L1–L3 contrasts for dimension combinations with cognition as one of the two dimensions, and calculated the relative frequency of both contrasts, i.e., the observed frequencies relative to chance frequencies. E.g., cognition level 3 and pain/discomfort level 1 versus pain/discomfort level 3 and cognition level 1. The ratio of the relative frequencies (cognition L1 & dimension × L3 as denominator) decides on dominance: if it is 1.0 then dimensions are independent, if it is < 1.0 than cognition dominates, if > 1.0 then cognition is subordinate.
Dimension dependency was additionally investigated by calculating Spearman’s rank correlation coefficients between the six EQ-5D + C dimensions.
Explanatory power analysis of all dimensions
We then predicted the EQ-VAS score from the EQ-5D dimensions, the cognitive dimension, and the socio-demographic factors. Univariate and multivariate regression analysis was applied. All descriptive EQ-5D + C dimensions were dummy coded (= standard): ‘some problems’ and ‘severe problems’ with ‘no problems’ as reference category. Separate and combined analyses were performed for participants with reported full health (EQ-5D profile of 11111) and without full health because of the combined effect of many respondents reporting to be in full health and the non-linear relations in the upper part of the scale. Only complete responses of the EQ-5D, cognition question, and EQ-VAS were selected for analysis.
Firstly, we performed univariate regression analyses and predicted the EQ-VAS with the EQ-5D and cognition attributes. Subsequently, a multivariate regression analyses model was constructed including the original EQ-5D attributes. In the second step, the cognition attributes were added to the model in order to examine the additive effect. Multivariate regression analysis was also used to assess the explanatory power of any set of combinations of five of the six EQ-5D + C dimensions.
Secondly, the EQ-5D attributes, cognition attributes, and all socio-demographic characteristics were simultaneously offered (forced entry) to a multivariate regression model explaining the EQ-VAS score. The initial model contained first-degree interactions. The backward deletion strategy was employed, starting from a model with 16 variables. We deleted non-significant predictors from the model until only significant predictors remained (p < 0.05). The regression analyses were repeated for patients with specific injury categories to explore the effect of the cognition dimension among patients with and without traumatic brain injury (clinical known-group comparison).
All analyses were conducted using SPSS V.24 (Statistical Package for Social Sciences, Chicago, Illinois, USA).
The following hypotheses were formulated:
1.
There are no redundancies and dependency patterns in the domains of the EQ-5D-3L, but they may exist when cognition domain is added.
2.
There is no added descriptive value of cognitive information, i.e., the coefficient size of cognitive information (in cross-sectional explanatory analysis) is smaller than that of the least important EQ-5D3L domain, regardless whether socio-demographics are added.
3.
The explanatory power of the EQ-5D + C is higher compared to the EQ-5D in TBI patients due to specific cognitive symptoms after TBI.