Introduction
Methods
The 15D instrument
The original 15D valuation tasks and the original value algorithm estimation procedure
The new 15D valuation tasks and the new value algorithm estimation procedure

Step 1: For each dimension \(j\) and level \(i~\) (L2–L5 and “being dead”), compute the weighted means \(\overline {s} _{i}^{j}\) over the respondents’ raw VASscores from the within dimension tasks (Table 6 in Appendix 4).

Step 2: For each level \(i\) (L2–L5), estimate the level’s relative scores \(~{{S}_{j,i}}~\), within each dimension \(~j\), as \(~{\widehat {S}_{j,i}}~\mathop =\limits^{{{\text{def}}}} ~\frac{{100  \overline {s} _{i}^{j}}}{{100  \overline {s} _{{{\text{death}}}}^{j}}}\), resulting in within dimension disutility values (where \({\widehat {S}_{j,1}}=0\) since \(\overline {s} _{1}^{j}=100~\) by definition, see Table 7 in Appendix 4).

Step 3: Estimate the mean of the respondents’ empirically obtained scores for the pitsstate as \({\widehat {V}_{{\text{Pits}}}}\mathop =\limits^{{{\text{def}}}} ~\frac{{100  {{\overline {s} }_{{\text{Pits}}}}}}{{100  {{\overline {s} }_{{\text{death}}}}}}\), resulting in one disutility value for the pitsstate representing the estimated health state valuerange.

Step 4: Estimate the within dimension disutility table \({{T}_{j,i}}~\) (Table 1) by rescaling the level scores \({\widehat {S}_{j,i}}~\) by the rescaling factor \(\widehat {\omega }\mathop =\limits^{{def}} \frac{{{{\widehat {V}}_{{\text{Pits}}}}}}{{\mathop \sum \nolimits_{j} {{\widehat {S}}_{j,5}}}}: {{\widehat {T}}_{j,i}} \mathop=\limits^{{def}} {\widehat {\omega }}\mathop \cdot {{\widehat {S}}_{j,i}}\). This normalizing constant ensures that the final range of health state utilities is bounded by 1 for “perfect health” and \(1  {\widehat {V}_{{\text{Pits}}}}\) for the pitsstate.A 15D health state value \({V_{H~}}\left( \mathbf{l} \right)\) is a simple sum of fifteen of the disutility values presented in Table 1.
Mobility  Vision  Hearing  Breathing  Sleep  Eating  Speech  Elimination  Usual activities  Mental function  Discomfort  Depression  Distress  Vitality  Sexual activity  

Level 2  0.0357  0.0300  0.0304  0.0367  0.0327  0.0392  0.0386  0.0388  0.0331  0.0413  0.0382  0.0390  0.0367  0.0369  0.0297 
Level 3  0.0612  0.0625  0.0583  0.0612  0.0524  0.0721  0.0603  0.0729  0.0612  0.0687  0.0689  0.0625  0.0589  0.0569  0.0637 
Level 4  0.0876  0.0839  0.0830  0.0825  0.0774  0.0952  0.0847  0.0915  0.0831  0.0894  0.0899  0.0878  0.0831  0.0805  0.0849 
Level 5  0.1083  0.1012  0.0959  0.1008  0.0968  0.1061  0.0960  0.1038  0.1016  0.1022  0.1063  0.1039  0.0978  0.0976  0.0975 
The Norwegian valuation studies
Empirical performance of the Norwegian 15D health state values
Results
Descriptive statistics
Norwegian population (n = 3,937,847)  Unweighted sample (n = 2256)  

Gender  
Men  1,956,835 (50%)  1089 (48%) 
Women  1,981,012 (50%)  1167 (52%) 
Age  
18–24^{a}  575,921 (15%)  140 (6%) 
25–39  985,937 (25%)  433 (19%) 
40–59  1,331,512 (34%)  895 (40%) 
60–66  398,529 (10%)  360 (16%) 
Older than 67  645,948 (16%)  428 (19%) 
Education  
Elementary school  1,111,379 (28%)  472 (20%) 
High school  1,625,640 (41%)  960 (43%) 
University B.A.  811,360 (21%)  449 (20%) 
University M.A.  269,627 (7%)  318 (14%) 
No formal education  119,841 (3%)  57 (3%) 