If you're an investor in biotech and drug stocks, you've no doubt seen or heard of a Kaplan-Meier analysis, often referred to as "K-M curves." But do you know how these curves are used and why they can cause your favorite biotech stock to rise or fall?
Interpreting "K-M curves" correctly is an important tool for biotech investors.
In 1958, two medical statisticians, Edward Kaplan and Paul Meier, published a paper describing a new method for estimating patient survival rates in clinical trials. The "Kaplan-Meier estimator" is a mathematical formula which uses information about patients who die during a clinical trial along with information about patients who survive or drop out to calculate the probability of survival over time.
Kaplan-Meier "curves" are now ubiquitous in medical research, used to analyze all types of patient outcomes. As an investor, you'll likely come across K-M curves when drug companies present results from clinical trials at medical meetings. Often times, companies will try to get by with press releases that describe clinical trial results without actually providing the real data. I always ask companies to provide me with primary source material, including K-M curves. You should do the same.
The chart below depicts the K-M curves for a pivotal clinical trial comparing Bristol-Myers Squibb's (BMY) - Get Report checkpoint inhibitor nivolumab (brand name: Opdivo) against the chemotherapy docetaxel in patients with non-small cell lung cancer. The study was published in the New England Journal of Medicine. Bristol secured regulatory approval for Opdivo in second-line lung cancer based on data described in this chart.
The "y" or vertical axis measures the percentage of patients estimated to be alive in the clinical trial. The "x" or horizontal access tracks time, in this case measured in months. All patients enter the study alive (thankfully) so the K-M curves start at 100% for month 0.
The blue line represent lung cancer patients treated with nivolumab/Opdivo. The green line tracks similar patients in the study treated with docetaxel.
K-M curves are really not curves at all, they look more like a set of stairs. The lines step down when a patient(s) in the study dies. The height of the vertical step-downs and the length of the horizontal stairs are the graphical representation of the calculations used to determine the probability of survival over time. Ideally, you want to see a curve which looks like a long, flat set of stairs because that means relatively few patients are dying during the course of the clinical trial. Conversely, a steep, downward curve means patients are dying relatively quickly.
Plotting the probability of survival for both sets of patients in a trial on a single graph gives you the comparison needed to determine if the drug being studied -- Opdivo, in this example -- is helping patients live longer.
For the first six months, survival is actually trending in favor of docetaxel over Opdivo. At around six months, the curves cross, after which Opdivo survival starts beating docetaxel.
Between six and nine months, the survival benefit of Opdivo (blue line) over docetaxel (green line) becomes more apparent, as seen by the widening space between the K-M curves.
You'll often hear or read about "median overall survival" results from clinical trials. Median is middle, so median overall survival is the estimate for the length of time that half the patients in the study are still alive. Calculating median overall survival using the K-M curves is easy: Just find 50% overall survival on the y axis and draw a line across until you hit the curves. Then, draw vertical lines down to the x axis. That's your median overall survival.
In this Bristol study, the median overall survival for the Opdivo patients was 12.2 months compared to 9.4 months for the docetaxel patients.
Be careful not to over-interpret median overall survival results. In this case, lung cancer patients treated with Opdivo will not all live 2.8 months longer than if they had been treated with docetaxel. Remember, median is middle, so half the patients treated with Opdivo will live longer than 12.2 months but the other half will not.
A more accurate description of overall survival calculated from K-M curves is the hazard ratio. A hazard ratio (HR) measures the probability of an event occurring in the treatment arm compared to the control arm. In this example, the event is death, the treatment arrn is Opdivo and the control arm is docetaxel.
Interpreting hazard ratios can be tricky but here's an easy cheat sheet: The smaller the hazard ratio, the greater the relative difference (benefit) in the treatment effect being measured. A hazard ratio of 1.0 means the two arms of the study are the same - not good when trying to show an experimental drug is better than a placebo or control.
Looking at the KM curves from Bristol study again, the overall survival hazard ratio is 0.73.
A hazard ratio less than 1 means, the probability of death following treatment with Opdivo is lower than with docetaxel.
The "p value" on the HR analysis in the Bristol study was 0.002, meaning there is a .2 (two tenths) percent chance the overall survival benefit was not real. For most studies, the acceptable threshold for statistical significance is 5%, or a p value of 0.05.
To most people who are not bio-statisticians, the hazard ratio looks like gibberish, which is why drug companies and even physicians fall back on using median overall survival to explain clinical trial results.
Resist that temptation. Instead, think of a hazard ratio in terms of relative risk. Odds ratios are much easier for people to understand. In this example, treatment with Opdivo reduced the relative risk of death by 27% compared to docetaxel.
The relative risk calculation is simple -- subtract the reported hazard ratio from 1. In this study, 1 minus 0.73 (the reported hazard ratio) equals 0.27, or a 27% reduction in the risk of dying.
Remember the rule of thumb I offered above, smaller hazard ratios are better. You can see how this plays out in terms of relative risk. For argument's sake, let's say the hazard ratio in the Bristol lung cancer study was 0.45 -- smaller than the actual reported 0.73. That would translate into a 55% relative reduction in the risk of death for Opdivo over docetaxel (1 minus 0.45 equals 0.55) -- better than the reported 27%.
Relying on median overall survival instead of the hazard ratio can overstate the efficacy of a drug. Here's an example of that, culled from a study, published in the Journal of Clinical Oncology comparing the overall survival benefit of Exelixis' (EXEL) - Get Report cancer drug cabozantinib to the steroid prednisone in patients with prostate cancer.
The first thing you notice about these K-M curves is that the two lines are much closer together throughout the study. Just by looking at this chart, you should be able to tell that the drug arm in blue(cabozantinib) isn't showing much of a survival benefit over the comparator (prednisone) in yellow.
At the median, the overall survival for prostate cancer patients treated with cabozantinib is 11 months compared to 9.8 months for the prednisone-treated patients. That's a 1.2 month survival benefit favoring cabozantinib.
If you relied only on the median overall survival, you might conclude that cabozantinib performed well in this study. After all, isn't a survival benefit of one month better than nothing?
Perhaps, but look at the hazard ratio: 0.90. That's very close to 1, meaning the probability of death following treatment with cabozantinib is almost the same as it is with prednisone.
Said another way, treatment with cabozantinib reduced the relative risk of dying by just 10% compared to prednisone. That's not very effective. In fact, this Exelixis study failed. That tiny, questionable survival benefit was not statistically significant, with a "p value" of 0.213 -- or an unacceptably high 21% chance the small survival benefit was not real.
That's your bio-statistics lesson for the day. Understanding K-M curves and how to analyze them will make you a better, more informed biotech investor.
Editor's note: This column is a significantly revised version of an earlier column published by Adam Feuerstein on Yahoo! Finance in November 2014.
Adam Feuerstein writes regularly for TheStreet. In keeping with company editorial policy, he doesn't own or short individual stocks, although he owns stock in TheStreet. He also doesn't invest in hedge funds or other private investment partnerships. Feuerstein appreciates your feedback; click here to send him an email.