The Model
The 2 decision pathways, surgery and palliative care, are compared for their value. We define the value as the product of QOL and DOL in each pathway and use the severity of the symptoms as a surrogate for QOL. If duration and quality were depicted on the x and y axes of a graph (Figure 1), then the area under the curve would represent the collective value in each situation. Figure 2 shows the timeline and the different pathways with each decision. The value in each situation is calculated in relation to the full value, which is represented as the value of normal life (Vn), that is, life without disease and with normal life expectancy. The values of each decision pathway, the value of surgery (Vs) and the value of palliation (Vp), are then compared to define the benefit for each decision as follows:
If Vs/Vp > 1, the benefit is toward surgery;
If Vs/Vp < 1, the benefit is for palliative care.
Definitions
Both quality and duration of life are presented on a 1-10 scale, 1 being the lowest and 10 the highest value, to yield a product with a value of 100 in normal, disease-free life. Any lower value is presented as a percentage to represent the comparison to the full value. QOL is determined by degradation of full quality with the average level of symptoms. DOL is calculated as a lost time (period of time from death after a specific intervention [surgery or palliation] until death at normal life expectancy) in fraction of full life (death at life expectancy). The Vs is adjusted to exclude the nonsurvivors using the chance of survival (100 – POM risk).
For the DOL under any condition, a 10-year survival rate could be used as a surrogate in this formula. Compared to life expectancy value, using the 10-year survival rate simplifies the calculation since cardiac diseases are more prevalent in older age, close to or beyond the average life expectancy value.
Using the time intervals from the timeline in Figure 2:
dh = time interval from diagnosis to death at life expectancy
dg = time interval from diagnosis to death after successful surgery
df = time interval from diagnosis to death after palliative care
Duration for palliative care:
Duration for surgery:
Adjustment: This value is calculated for those who survive the surgery. To adjust for the POM, it is multiplied by the 100 − POM risk.
Since value is the base for comparison in this model, and it is the product of 2 equally important factors in the formula (severity and duration of symptoms), a factor of 10 was chosen to yield a value of 100, which represents 100% health or absence of symptoms for any duration.
After elimination of normal life expectancy, form the numerator and denominator:
To adjust for surgical outcomes in special circumstances where less than optimal or standard surgical results are expected (eg, in very rare surgeries, limited resource institutions, or suboptimal postoperative surgical care), an optional coefficient R can be added to the numerator (surgical value). This optional coefficient, with values such as 0.8, 0.9 (to degrade the value of surgery) or 1 (standard surgical outcome), adjusts for variability in interinstitutional surgical results or surgeon variability. No coefficient is added to the denominator since palliative care provides minimal differences between clinicians and hospitals. Thus, the final adjusted formula would be as follows:
