The study by van Duijvendijk and colleagues²⁰¹ compares the HRQoL of colectomy and IRA versus proctocolectomy and IPAA in patients receiving major prophylactic surgery for FAP, as well as HRQoL in patients from the general population. Quality of life was measured using the SF-36 questionnaire. The authors report the number of patients in each group, their mean age (and the standard deviation of their age), and the mean values and standard deviations in the eight main categories in the SF-36 questionnaire (Table 140) and the health transition category.

TABLE 140

Short Form questionnaire-36 items categories

Ara and Brazier²²⁸ describe a methodology to calculate utility scores from SF-36 category scores. Their methodology is described by seven models, of which models 1–5 and 7 are special cases of model 6, the most general model supplied, in which all eight categories have corresponding coefficients, as do age and age squared and also the squared values of four categories (PF, SF, MH, BP). Models 4–7 require the squared values of some variables.

The utility score for a single patient, denoted i, is calculated by

where α is the intercept, x_i is the vector of questionnaire results and patient characteristics,

and β is the set of coefficients derived and published in the paper.

The mean utility for a set of patients is calculated by

where n is the number of patients. By linearity of expectation, this can be written as

where $\overline{\mathbf{x}}$ is the vector of mean values across all patients. Note that the mean value of Age² is not generally equal to the square of the mean value of Age (this may explain the discrepancy between our calculated values and those of Dinh and colleagues⁵⁵), but as standard deviations and patient numbers are provided we can calculate the appropriate mean values of these squared variables. If s is the sample standard deviation of a variable x and we want to calculate E[x²] = ∑(x²)/n we make use of the following formula for s:

to calculate that

and therefore

Using this formula we calculated the additional information (Table 141) necessary to apply all the models in the study by Ara and Brazier²²⁸ to calculate utility scores for the three groups.

TABLE 141

Additional calculations necessary for calculation of utility scores

With this information we computed the utility scores for the three groups using the seven different models, and therefore the utility decrement for the two types of surgery using each model (Table 142).

TABLE 142

Estimated utility scores