The methodology used for estimating survival curves for the alternative treatments is as follows:

• Derive a baseline survival curve for MP. This curve is derived by calculating the event probability for each time interval, by calculating a weighted average of the trial MP arms using number of participants in the trial as a weight.
• Derive HRs for each of the treatments versus MP at different time points for each trial. Combine HRs for treatments with more than one trial.
• Construct the baseline survival curves for MP using the event probability for each time interval.
• Construct the survival curves for other treatments by using the event probability for each time interval, i.e. event probability for MP multiplied by HR.

For MP treatment, OS and PFS at regular time points were estimated for each of the included studies from our meta-analysis of the clinical trials. The data from the trials were combined to form baseline MP, OS and PFS curves through a weighted average, using number of patients in the trials as the weight. We estimated the hazard rate for MP for each 6-monthly period (Table 52). The hazard rate for death for MP per cycle is estimated for each time point t_i:

TABLE 52

Baseline MP OS curve and derived death rate.

The treatment effects for the other interventions compared with MP were taken from our clinical review (see Chapter 4, Assessment of effectiveness). As the HR of the treatments versus MP varied over time, a constant HR was not appropriate. A similar methodology was used for estimating OS and PFS; however, only OS is described in this appendix.

We derived the HR for each 6-monthly period for each of the treatments versus MP.

The hazard rate for death for each of the treatments per cycle is estimated for each time point t_i:

where s(t) is the survival function over time t.

The HR (HR) for each intervention j versus MP at each time point t_i is:

The HR was assumed to be constant after 36 months for OS as there were few patients with more than this length of follow-up in the trials. This HR was estimated for each of the treatments versus MP at 36 months' follow-up for OS.

The hazard rate for death for each of the treatments per cycle was also assumed to be constant after 36 months and is given by:

where s(t) is the survival function and t is 36 months (26.1 cycles).

The methodology is illustrated for OS for VMP with data from the VISTA trial. Table 53 shows the hazards and the HRs derived from the VISTA trial for OS.

TABLE 53

Hazards and HR for VMP vs MP for OS from the VISTA trial.

To generate the survival curves for each of the treatments the baseline death rate in each time period for MP was multiplied by the HR to give the new death rate for the alternative treatment. This method provided a closer fit to the trial data than approximations, such as fitting distributions.

The survival curves were constructed by multiplying the survival in the previous time point by the proportion who survived in the current time interval, using the estimated hazards for MP and the HR for the other interventions.

Thus the survival function s(t) is given by:

To demonstrate the fit from this method we derive the VMP survival curves using the trial MP curves and compare with the original trial curves. Figure 16 shows the MP and VMP survival curves derived for the model against the trial data from the VISTA trial. As can be seen in the figure, the derived survival curves in the model closely match both treatments during the trial period.

FIGURE 16

MP and VMP survival curves derived for the model against trial data from the VISTA trial.

In the model, instead of using the MP trial data, the MP baseline data are used with the same method as described above. Figure 17 shows the MP and VMP survival curves derived for the model using the baseline combined MP curves.

FIGURE 17

Melphalan + prednisolone/prednisone (MP) and VMP survival curves for the model using combined baseline MP curves.