February 12, 2015

Hazard ratio, and other stat stuff

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I have written about hazard ratio in the context of Provectus's pivotal Phase 3 trial. For example, see:

The projected hazard ratio of Provectus' upcoming pivotal Phase 3 trial (a registration study) for locally advanced cutaneous melanoma is unknown.

Assumption: Let's assume this number is 0.545 or thereabouts, which derives from past Phase 3 trial design information publicly provided by the company. See below from 2013:
Click to enlarge. Provectus corporate presentation, March 15, 2013
This figure of 0.545 could be traced back further, such as to 2012:
Click to enlarge. June 2012 blog post Pivotal MM Phase 3 Trial Design: Study Size Dramatically Reduced.
Note: While the above company slides are from 2012-2013, Eric presented preliminary metastatic melanoma Phase 2 trial results at SMR 2010, and final results at ESMO 2012.

Wikipedia notes about hazard ratio: "If the analogy of a race is applied, the hazard ratio is equivalent to the odds that an individual in the group with the higher hazard reaches the end of the race first. The probability of being first can be derived from the odds, which is the probability of being first divided by the probability of not being first: HR = P/(1 − P); P = HR/(1 + HR)."

In the case of Provectus' pivotal trial, and using the race analogy above, race entrant number 1 is PV-10 (the trial's treatment arm), and entrant number 2 is chemotherapy (the comparator or control arm). Hazard ratio, or HR, is the probability of PV-10 being first — an event or hazard (i.e., progression of disease) occurring in the treatment arm before it occurs in the control one.

Calculation: The probability of PV-10 being first is 0.545 / (1 + 0.545), or ~35%.

Another way of putting it, "...hazard ratio compares two treatments. If the hazard ratio is 2.0, then the rate of [events or hazards] in one treatment group is twice the rate in the other group." In the case of Provectus' pivotal trial, if the projected hazard ratio is 0.545, the rate of events or hazards in PV-10 treatment arm is projected to be about half the rate in the chemotherapy control arm.

Progression-free survival for chemotherapy (dacarbazine ["DTIC"] or temozolomide ["TMZ"] in Provectus' Phase 3 trial) is approximately 2-3 months (e.g., Middleton et al. (2000), Patel et al. (2011) [see footnote 13], Hauschild et al. (2012) [see reference 1], etc.). According to Eric, "[t]he performance of DTIC and TMZ are well documented and generally yield a normal distribution of events (for example, refer to Middleton et al.)."

 Let's assume most patients in the company's Phase 3 trial's chemotherapy comparator or control arm have their disease progress after 2-3 months (about 8-13 weeks). PFS assessments will be made every 12 weeks (i.e., t = 12 weeks, 24 weeks, etc.) up to 18 months.

Provectus observed (see the ESMO 2012 poster) Stage 3 patients in the company's Phase 2 trial achieved PFS of 9.7+ months (mean) as measured by modified RECIST (9.8 months (mean) on the ESMO 2014 poster). Eric reported PFS as measured by RECIST 1.1 (according to Peter), which is the approach or convention by which tumor progression will be measured in the Phase 3 trial, on ClinicalTrials.gov as 3.7 months (median). PFS was measured for 12 months (or 52 weeks).

Eric has not disclosed PFS for the subset of patients in the Phase 2 trial who had all of their disease treated. This all disease treated subgroup formed the basis of Provectus' denied breakthrough therapy designation application), and the Phase 3 trial solely will comprise these patients. Stage 3 patients as a group appear to have achieved a 37% complete response ("CR") and an objective response rate ("ORR") of 63%, while all disease treated Stage 3 patients achieved 50% and 71%, respectively (an improvement of 35% and 13%, respectively). See original data, and 95% confidence intervals on the ESMO 2014 poster.

 Let's assume the Phase 3 trial's PFS for PV-10 is at least 3.7 months (as reported for all Stage 3 patients from the Phase 2 trial). Or perhaps it is higher, like 4.2 months (13% above 3.7) or 5.0 months (35% above 3.7). Or perhaps it is much higher, like there is no event because there is no progression because (i) all of their disease is treated with PV-10 and (ii) PV-10 will be injected until the tumors achieve CR (or progress, and thus an event or hazard occurs).

So, at the first assessment period of 12 weeks:
  • Most if not all patients receiving chemotherapy would have progressed: 2-3 months ~< 12 weeks, and
  • Most if not all patients receiving PV-10 would have not: 3.7 to 4.2-5.0 to never > 12 weeks.
Assumption: Let's assume the probability of chemo patients progressing after 12 weeks is 80-90%, and the probability of PV-10 patients progressing after 12 weeks is 0-10%.

Calculation: The actual hazard ratio of the Phase 3 trial — the probability of an event in the PV-10 treatment arm divided by the probability of an event in the chemotherapy control arm — may range from 0 (0% / 90%: not going to happen) to 0.13 (10% / 80%).

A projected trial hazard ratio of 0.545 and an 80-90% probability of progression in the control arm would imply a 44-49% probability of progression in the PV-10 treatment arm. Provectus likely expects the actual hazard ratio (on the order of .13'ish) to handily beat the projected hazard ratio (of 0.545).

Provectus' focus may not be on whether the Phase 3 trial outcome is successful, but rather on how many enrolled and treated patients (and their presumed successful outcomes) are needed for the outcome to reach clinical (statistical) significance as quickly as possible.

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