## BPSA Response as Surrogate for Survival

The best PSA outcome was determined for each patient, and hierarchically ordered as [28]:

Complete response (CR) if the PSA level was at least 20 ng/mL at baseline, returned to normal (< 4 ng/mL) at any time, and remained normal for at least 28 days

Partial response (PR) if the PSA level was at least 20 ng/mL at baseline, decreased by at least 50% from the baseline level, and remained under 50% of the baseline level for at least 28 days

No change (NC) if the PSA level was at least 20 ng/mL at baseline, and fluctuated between 50% below and 50% above the baseline level for at least 28 days

Progressive disease (PD) if no other response category applied, and if PSA was at least equal to 10ng/mL

Not evaluable (NE), if none of the above applied

A patient was defined as having a PSA response if his best PSA outcome was either PR or CR. Hence the biomarker is binary here, and the clinical endpoint is a (possibly censored) survival time.

At the individual level, PSA response was a very strong predictor of survival (Fig. 2a). Because PSA response is binary and survival is censored, the normal theory coefficient of determination (R2) discussed earlier does not apply, and another measure of association between PSA response and survival is needed. One way to express the impact of PSA response on survival is as follows [8]: consider the odds of surviving beyond time t for PSA responders and for nonresponders; the ratio of these odds is a survival odds ratio. Although the odds of surviving beyond time t decrease in time for both responders and nonresponders, in our model the ratio of these odds is assumed constant. This survival odds ratio is equal to 5.5 (95% confidence interval = 2.7-8.2), which means that at any point in time the odds of surviving beyond that time are more than five times higher for patients with a PSA response as compared to patients without such a response. The strong prognostic impact of PSA response can be explained in at least three plausible ways:

PSA response and survival are largely determined by a common set of prognostic factors, so that patients who are likely to have a response are also those who are potentially long survivors.

Patients who survive a long time are more likely to have a PSA response because of length-biased sampling [29].

There is a true causal relationship between the achievement of a PSA response and a prolongation of survival.

The first and second explanations are amenable, at least in part, to statistical investigations, the first through adjustments of the comparison of responders and nonresponders for all known prognostic factors, and the second through a landmark analysis [30]. When these investigations fail to explain a large portion of the prognostic impact of PSA response, then there is indirect evidence that PSA response truly results in a survival improvement [7].

At the group level, the effects of liarozole on PSA response and on survival were poorly correlated, with a coefficient of determination R2ial = 0.05 (standard error = 0.13) (Fig. 2b).

Figure 2 (a) The survival of patients with a PSA response differs substantially from that of patients without a PSA response. At any point in time the odds of surviving beyond that time are more than five times higher for patients with a PSA response as compared to patients without such a response (see text). (b) The treatment effects on survival and on PSA response show no correlation in advanced prostate cancer (R^ = 0.05). Each circle shows treatment effects estimated in one of the countries in which the trials were conducted. (The size of the circle is proportional to the number of patients.)

Figure 2 (a) The survival of patients with a PSA response differs substantially from that of patients without a PSA response. At any point in time the odds of surviving beyond that time are more than five times higher for patients with a PSA response as compared to patients without such a response (see text). (b) The treatment effects on survival and on PSA response show no correlation in advanced prostate cancer (R^ = 0.05). Each circle shows treatment effects estimated in one of the countries in which the trials were conducted. (The size of the circle is proportional to the number of patients.)

There was no overall significant benefit of liarozole over control for either response or survival: the PSA response rate was 16% and 11%, respectively, for liarozole and control (p = 0.11), while median survival was 11.3 and 10.9 months, respectively, for liarozole and control (p = 0.71).