Understanding Statistics

A Patient Story

The following story is a fictional composite based on common patient experiences. It is not about any single individual.

Robert, 68, sat across from his radiation oncologist, staring at a graph in a research paper the doctor had printed out. Two curving lines swept across the page — one blue, one red — with numbers along the sides and tiny tick marks scattered along the curves. "This study shows that Treatment A gives you a better chance," the doctor said, pointing at the gap between the lines. Robert nodded politely, but inside he was lost. What did "hazard ratio 0.60" mean? What was a "confidence interval"? And when the doctor said "median survival was 5 years," did that mean he had 5 years to live?

He went home and told his wife: "I think it was good news, but honestly, I couldn't understand half of what he showed me."

This chapter is for Robert — and for every patient who has ever felt lost in the numbers.

Why This Chapter Matters

Throughout this book — and in conversations with your doctors — you will encounter statistics. Studies will report "overall survival," "progression-free survival," "hazard ratios," and "p-values." Your doctor may show you a survival curve or mention that a side effect was "Grade 2."

You do not need to become a statistician. But understanding a few key concepts will help you:

• Make sense of what your doctor is telling you
• Evaluate information you find online or in the news
• Participate more meaningfully in treatment decisions
• Avoid common misunderstandings that cause unnecessary fear — or false hope

Think of this chapter as a translator between the language of medical research and the language of everyday life.

Part 1: Measuring How Well Treatments Work

When researchers test a new cancer treatment, they need a way to measure whether it actually helps patients. These measurements are called endpoints. Different endpoints answer different questions.

Overall Survival (OS)

What it means: Overall survival is the length of time from the start of treatment (or from entering a study) until death from any cause.^[1][2]

Why it matters: This is considered the gold standard — the most important measurement in cancer research — because it answers the most fundamental question: does this treatment help people live longer?^[2] It is completely objective — there is no ambiguity about whether someone is alive or not.

The catch: Overall survival takes a long time to measure, especially in slow-growing cancers like many prostate cancers, where patients may live for many years regardless of treatment. It can also be "muddied" by treatments patients receive after the study treatment stops working, making it hard to know how much of the survival benefit came from the original treatment versus later treatments.^[1][3]

In plain language: If a study says "the 5-year overall survival was 90%," it means that out of 100 patients who started the treatment, about 90 were still alive 5 years later.

Progression-Free Survival (PFS)

What it means: Progression-free survival is the length of time from the start of treatment until the cancer grows, spreads, or the patient dies — whichever happens first.^[1][3]

Why it matters: PFS tells you how long a treatment keeps the cancer under control. It can be measured sooner than overall survival, which is why many clinical trials use it as their primary endpoint.^[3][4]

The catch: Living longer without your cancer growing does not always mean living longer overall. In some cancers, improvements in PFS translate into longer life; in others, they do not — especially when effective treatments are available after the cancer progresses.^[1][4] Also, PFS depends on how often doctors check for progression (with scans, blood tests, etc.), which can vary between studies.

In plain language: If a study says "median PFS was 24 months," it means that half the patients went at least 24 months before their cancer started growing again or they passed away.

Metastasis-Free Survival (MFS)

What it means: Metastasis-free survival is the time from the start of treatment until the cancer spreads to distant parts of the body (metastasizes) or the patient dies.^[5][6]

Why it matters: In prostate cancer specifically, MFS has become an extremely important endpoint. Research has shown that MFS correlates strongly with overall survival — meaning that treatments that delay metastasis tend to also help patients live longer.^[7][8] This is particularly important because prostate cancer can take many years to become life-threatening, and waiting for overall survival data could delay access to effective treatments by many years.

MFS was the primary endpoint in several landmark prostate cancer trials, including the EMBARK trial (enzalutamide for biochemical recurrence), the SPARTAN trial (apalutamide for non-metastatic castration-resistant prostate cancer), and others.^[5][6]

In plain language: If a study says "3-year MFS was 85%," it means that out of 100 patients, about 85 had no detectable cancer spread and were still alive at 3 years.

Biochemical Recurrence-Free Survival (bRFS) and Biochemical Recurrence (BCR)

What it means: In prostate cancer, "biochemical recurrence" means that after treatment (surgery or radiation), the PSA level starts rising again, suggesting the cancer may be coming back — even before anything shows up on scans or causes symptoms.^[9][10]

• After surgery (radical prostatectomy): BCR is typically defined as a PSA that rises above 0.2 ng/mL on two or more measurements.^[11]
• After radiation therapy: BCR is typically defined as a PSA rise of 2 ng/mL above the lowest point the PSA reached after treatment (called the "nadir"). This is known as the Phoenix definition.^[11]

Biochemical recurrence-free survival (bRFS) is the time from treatment until BCR occurs (or until death).

Why it matters: A rising PSA is often the first sign that cancer may be returning. However — and this is very important — not every PSA rise means the cancer will come back in a dangerous way. Many men with biochemical recurrence live for years or even decades without ever developing metastatic disease or dying from prostate cancer.^[9][10]

The catch: Research has shown that biochemical recurrence is not a strong surrogate for overall survival — meaning that treatments that improve bRFS do not always improve how long patients live.^[7][8] This is why doctors are cautious about making major treatment decisions based on PSA changes alone.

In plain language: If a study says "5-year bRFS was 80%," it means that 80 out of 100 patients still had their PSA under control at 5 years. The other 20 had a PSA rise — but that does not necessarily mean their cancer came back in a dangerous way.

Prostate Cancer-Specific Mortality (PCSM)

What it means: This measures deaths caused specifically by prostate cancer, as opposed to deaths from other causes (heart disease, other cancers, accidents, etc.).

Why it matters: Because prostate cancer often affects older men who may have other health conditions, many patients with prostate cancer ultimately die of something else entirely. PCSM helps researchers understand how deadly the cancer itself is, separate from other causes of death.

In plain language: If a study says "10-year PCSM was 3%," it means that out of 100 patients, only about 3 died specifically from prostate cancer over 10 years.

Part 2: Understanding "Median"

You will hear the word "median" constantly in cancer statistics. It is one of the most misunderstood concepts in medicine.

What "Median" Means

The median is the middle value in a group of numbers. If you line up all patients from shortest survival to longest survival, the median is the person exactly in the middle.

Example: Imagine 11 patients with survival times of: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, and 20 years. The median survival is 6 years — because 5 patients lived less than 6 years and 5 patients lived more than 6 years.

What "Median" Does NOT Mean

"Median survival is 5 years" does NOT mean you will live exactly 5 years.

It means that in a group of patients studied, half lived longer than 5 years and half lived less than 5 years. Some may have lived 2 years. Others may have lived 15 years. The median tells you about the middle of the group — it tells you nothing about where YOU will fall in that group.

Why Doctors Use Median Instead of Average

The average (mean) can be pulled in one direction by extreme values. If 9 patients live 2 years and 1 patient lives 50 years, the average survival is about 6.8 years — which does not represent anyone's actual experience. The median (2 years) gives a more realistic picture of what a "typical" patient experienced.

The Key Takeaway About Median

When your doctor says "the median survival is X years," remember:

• Half the patients did better than that number
• Some patients did much better
• You are an individual, not a statistic
• Your outcome depends on many factors specific to you

Part 3: Reading Survival Curves

Survival curves are the graphs you will see most often in cancer research. They may look intimidating, but they are actually telling a simple story: how many patients are still alive (or event-free) as time passes.

The Kaplan-Meier Curve

The most common type of survival curve is called a Kaplan-Meier curve, named after the two statisticians who developed it in 1958.^[12][13]

How to read it:

• The vertical axis (up and down) shows the percentage of patients who have not yet experienced the event (usually death, but sometimes cancer progression or metastasis). It starts at 100% (everyone is alive at the beginning) and decreases over time.
• The horizontal axis (left to right) shows time — usually in months or years.
• The curve itself is a staircase-like line that steps down each time a patient experiences the event. A steep drop means many events happened in a short time. A flat section means the treatment was keeping things stable during that period.
• Small vertical tick marks on the curve represent "censored" patients — people who left the study before it ended (perhaps they moved, or the study ended while they were still alive). These patients are not counted as having the event, but their time in the study still contributes to the analysis.^[12][13]
• Numbers at risk — a row of numbers below the graph shows how many patients were still being followed at each time point. As time goes on, this number gets smaller (because patients either had the event or were censored). When this number gets very small, the curve becomes less reliable.

Comparing two curves:

Most survival graphs show two or more curves — for example, one for a new treatment and one for the standard treatment. The curve that stays higher for longer represents the group that did better. If the curves are far apart, the difference between treatments is large. If they are close together or overlapping, the difference is small.^[12][14]

The Cumulative Incidence Curve

While Kaplan-Meier curves show the probability of not having an event (they start at 100% and go down), cumulative incidence curves show the probability of having an event (they start at 0% and go up).^[15][16]

Why does this matter?

In many situations, especially in prostate cancer where patients are often older, a patient might die of something other than prostate cancer — a heart attack, a stroke, another cancer. These are called competing risks — events that "compete" with the event you are studying because once they happen, the patient can no longer experience the event of interest.^[16][17]

The standard Kaplan-Meier method does not handle competing risks well. It tends to overestimate the actual risk of the event you are studying.^[17][18] For example, if you use Kaplan-Meier to estimate the risk of dying from prostate cancer, it might say 20% — but the actual risk might be only 14% because some of those patients would have died from heart disease first. Research has shown that Kaplan-Meier estimates can be about 1.4 times higher than the true risk when competing events are present.^[17]

The cumulative incidence function (sometimes called the "competing risks method") accounts for this by keeping track of all the different events that can happen, giving you a more accurate picture of the actual risk.^[16][19]

In plain language: When you see a cumulative incidence curve in a prostate cancer study, it is usually giving you a more realistic estimate of risk than a Kaplan-Meier curve would, especially for older patients who have other health conditions.

Part 4: Understanding Treatment Comparisons

When a study compares two treatments, the results are usually reported using several key numbers. Here is what they mean.

Hazard Ratio (HR)

What it is: The hazard ratio compares the rate at which events (like death or cancer progression) happen in one group versus another.^[14][20]

How to interpret it:

• HR = 1.0 means both treatments have the same rate of events — no difference.
• HR less than 1.0 means the new treatment is better (fewer events). For example, HR = 0.70 means the new treatment reduced the rate of events by 30%.
• HR greater than 1.0 means the new treatment is worse (more events).

A simple way to think about it: If the hazard ratio for death is 0.60 comparing Treatment A to Treatment B, it means that at any given point during the study, patients on Treatment A had about 40% less risk of dying compared to patients on Treatment B.^[21]

The catch: The hazard ratio assumes that the benefit of treatment stays constant over time (called the "proportional hazards assumption"). This is not always true — some treatments, like immunotherapy, may show little benefit early on but large benefits later.^[22]

Confidence Interval (CI)

What it is: A confidence interval gives you a range of values that likely contains the true result. Because studies are done on a sample of patients (not every patient in the world), there is always some uncertainty about the exact result.^[23][24]

How to interpret it: A 95% confidence interval means: if we repeated this study 100 times, about 95 of those times the true result would fall within this range.^[24][25]

Example: A study reports HR = 0.60 with a 95% CI of 0.44 to 0.80.^[21] This means:

• The best estimate is that the treatment reduced the risk by 40% (HR 0.60)
• But the true benefit could be as large as a 56% reduction (HR 0.44) or as small as a 20% reduction (HR 0.80)
• Because the entire range is below 1.0, we are confident the treatment truly helps

Key rule: For hazard ratios, if the confidence interval crosses 1.0 (for example, 0.85 to 1.15), it means the study could not confirm a real difference between treatments — the result is "not statistically significant."

P-Value

What it is: The p-value tells you how likely it is that the observed result happened by chance alone, assuming there is actually no difference between treatments.^[23][26]

How to interpret it:

• P 0.05 is the traditional threshold for "statistically significant" — meaning there is less than a 5% chance the result is due to random chance. Most researchers consider this strong enough evidence to conclude a real difference exists.^[23]
• P 0.001 means less than a 0.1% chance — very strong evidence.
• P = 0.19 (for example) means there is a 19% chance the result could have occurred by chance — not strong enough to conclude a real difference.

Important caution: A small p-value does not tell you how large or important the difference is — only that a difference probably exists. A treatment could have a statistically significant benefit (p 0.05) but the actual benefit could be tiny and clinically meaningless. Conversely, a study might show a large benefit but have a p-value above 0.05 simply because too few patients were enrolled.^[25]

In plain language: Think of the p-value as a measure of confidence. A very small p-value means "we are very confident this result is real, not just a fluke." A large p-value means "we are not sure — it might be real, or it might be chance."

Putting It All Together: Reading a Study Result

Here is a real example from the EMBARK trial in prostate cancer:^[21]

"The 8-year overall survival was 78.9% in the combination group and 69.5% in the leuprolide-alone group; the hazard ratio for death was 0.60 (95% CI, 0.44 to 0.80; P0.001)."

Translation: Patients who received enzalutamide plus leuprolide had about a 79% chance of being alive at 8 years, compared to about 70% for leuprolide alone. The combination treatment reduced the risk of death by about 40% (HR 0.60). The confidence interval (0.44 to 0.80) tells us the true benefit is somewhere between a 20% and 56% reduction in death risk — and because the entire range is below 1.0, we are confident the benefit is real. The p-value of less than 0.001 confirms this — there is less than a 0.1% chance this result happened by random chance.

Part 5: Grading Side Effects

When you read about treatment side effects in studies or hear your doctor mention them, they are usually graded on a standardized scale called the Common Terminology Criteria for Adverse Events (CTCAE), developed by the National Cancer Institute.^[27][28] This system is used worldwide in cancer clinical trials and helps doctors communicate about side effects using a common language.

The current version (CTCAE version 5.0) includes over 800 different possible side effects, each with its own grading criteria.^[29][30] But the basic grading system is simple:

^[27][28][31]

What This Means for You

• When a study says "Grade 3 or higher adverse events occurred in 25% of patients," it means that 1 in 4 patients experienced a severe, life-threatening, or fatal side effect.
• Grade 1 and 2 side effects are common with most cancer treatments and are generally manageable.
• Grade 3 side effects are serious and often require a change in treatment — dose reduction, treatment pause, or additional medications.
• Grade 4 side effects are emergencies.
• Doctors pay the most attention to Grade 3 and above when deciding whether a treatment's benefits outweigh its risks.

Patient-Reported Outcomes (PROs)

An important development in recent years is that researchers now also ask patients directly about their side effects, rather than relying only on the doctor's assessment. This is called PRO-CTCAE (Patient-Reported Outcomes version of the CTCAE).^[30] Research has shown that doctors may miss up to half of patients' symptoms when they are the only ones reporting — so patient self-reporting improves accuracy.^[30]

Part 6: Absolute vs. Relative Numbers

This is one of the most important — and most commonly misunderstood — distinctions in medical statistics.

Relative Risk Reduction

If a study says a treatment "reduces the risk of death by 50%," that sounds dramatic. But it depends on what the starting risk was.

• If your risk of dying from prostate cancer over 10 years was 40% and a treatment cuts it by 50%, your new risk is 20%. That is a huge benefit — 20 out of 100 patients are saved.
• If your risk was 2% and a treatment cuts it by 50%, your new risk is 1%. The relative reduction is the same (50%), but the absolute benefit is only 1 out of 100 patients.

Absolute Risk Reduction

The absolute risk reduction tells you the actual difference in percentages. In the first example above, the absolute risk reduction is 20% (40% minus 20%). In the second example, it is only 1% (2% minus 1%).

Number Needed to Treat (NNT)

This is perhaps the most patient-friendly statistic. The NNT tells you how many patients need to receive a treatment for one patient to benefit.

• NNT = 5 means you need to treat 5 patients for 1 to benefit — that is a very effective treatment.
• NNT = 100 means you need to treat 100 patients for 1 to benefit — the treatment helps, but most patients who take it will not personally benefit from it.

Why this matters: When your doctor discusses a treatment, ask about both the relative and absolute benefits. A "50% reduction in risk" means very different things depending on your starting risk.

Myth vs. Fact

Myth: "Median survival of 5 years means I will die in 5 years."

Fact: Median means half the patients lived longer — some much longer. It says nothing about any individual patient's outcome.

Myth: "If a study is 'statistically significant,' the treatment must be a big improvement."

Fact: Statistical significance only means the result is unlikely due to chance. The actual benefit could be large or small. Always look at the absolute numbers, not just the p-value.^[25]

Myth: "Grade 1 side effects are nothing to worry about."

Fact: Grade 1 side effects are mild, but they can still affect your quality of life, especially if they persist. Always report all side effects to your medical team, even mild ones.

Myth: "If a treatment improves progression-free survival, it must also help you live longer."

Fact: Not always. In some cancers, PFS improvements translate to longer life; in others, they do not — especially when effective later treatments are available.^[1][4]

Questions to Ask Your Doctor

• "When you say the survival rate is X%, is that overall survival or cancer-specific survival?"
• "Is that a median number? What is the range — what did the best and worst outcomes look like?"
• "What is the absolute benefit of this treatment — how many patients out of 100 would it actually help?"
• "What grade of side effects should I expect? How common are Grade 3 or higher side effects with this treatment?"
• "Is the benefit of this treatment based on overall survival data, or a surrogate endpoint like PFS or MFS?"
• "How does my individual situation compare to the patients in the studies you are referencing?"

Key Takeaways

• Overall survival is the gold standard endpoint — it measures how long patients live. Metastasis-free survival is a validated surrogate in prostate cancer that correlates strongly with overall survival.
• Median means the middle value — half did better, half did worse. It is not a prediction for any individual patient.
• Kaplan-Meier curves show survival over time. The higher the curve stays, the better. Cumulative incidence curves are more accurate when competing risks (like death from other causes) are present.
• Hazard ratio, confidence interval, and p-value work together: the HR tells you the size of the benefit, the CI tells you the range of uncertainty, and the p-value tells you how confident you can be that the result is real.
• Side effects are graded 1 to 5 — from mild to fatal. Grade 3 and above are considered serious and often require treatment changes.

Support Resources

• National Cancer Institute — Understanding Cancer Statistics: cancer.gov
• Prostate Cancer Foundation — Research Explainers: pcf.org
• NCCN Patient Guidelines: nccn.org/patients — includes simplified explanations of study results
• American Cancer Society — Understanding Your Diagnosis: cancer.org

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