{"id":1633,"date":"2025-10-27T13:46:48","date_gmt":"2025-10-27T13:46:48","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=1633"},"modified":"2026-03-26T18:40:50","modified_gmt":"2026-03-26T18:40:50","slug":"cancer-survival-rates-are-misleading","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2025\/10\/27\/cancer-survival-rates-are-misleading\/","title":{"rendered":"Cancer Survival Rates Are Misleading"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>UPDATE: I submitted a more formal version of this article to the UMAP Journal (Undergraduate Mathematics and Its Applications), which publishes articles that use mathematical modeling for real-world problems, often with a pedagogical or expository angle. A preprint is available on arXiv at: <a href=\"https:\/\/arxiv.org\/abs\/2603.19945\">https:\/\/arxiv.org\/abs\/2603.19945<\/a><\/em><\/p>\n<\/blockquote>\n\n\n\n<p>Five-year survival might be the most misleading statistic in medicine. For example, suppose 5-year survival for a hypothetical cancer is<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>91% among patients diagnosed early, while the tumor is <strong>localized<\/strong> at the primary site,<\/li>\n\n\n\n<li>74% among patients diagnosed later, when the tumor has spread <strong>regionally<\/strong> to nearby lymph nodes or adjacent organs, and<\/li>\n\n\n\n<li>16% among patients diagnosed late, when the tumor has spread to <strong>distant<\/strong> organs or lymph nodes.<\/li>\n<\/ul>\n\n\n\n<p>What can we infer from these statistics?<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>If a patient is diagnosed early, it is tempting to think the probability is 91% that they will survive five years after diagnosis.<\/li>\n\n\n\n<li>Looking at the difference in survival between early and late detection, it is tempting to conclude that more screening would save lives.<\/li>\n\n\n\n<li>In a case where a patient is diagnosed late and dies of cancer, it is tempting to say that they would have survived if their cancer had been caught early.<\/li>\n\n\n\n<li>And if 5-year survival increases over time, it is tempting to conclude that treatment has improved.<\/li>\n<\/ol>\n\n\n\n<p>In fact, <strong>none of these inferences are correct<\/strong>.<\/p>\n\n\n\n<p>Let\u2019s take them one at a time.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Particularization<\/h2>\n\n\n\n<p>Here\u2019s the first incorrect inference:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>If a patient is diagnosed early, and 5-year survival is 91%, it is tempting to think the probability is 91% that they will survive five years after diagnosis.<\/p>\n<\/blockquote>\n\n\n\n<p>This is <em>almost<\/em> correct in the sense that it applies to the past cases that were used to estimate the survival rate \u2013 of all patients in the dataset who were diagnosed early, 91% of them survived at least five years.<\/p>\n\n\n\n<p>But it is misleading for two reasons:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Because it is based on past cases, it doesn\u2019t apply to present cases if (1) the effectiveness of treatment has changed or \u2013 often more importantly \u2013 (2) diagnostic practices have changed.<\/li>\n\n\n\n<li>Also, before interpreting a probability like this, which applies in general, it is important to <strong>particularize<\/strong> it for a specific case.<\/li>\n<\/ul>\n\n\n\n<p>Factors that should be taken into account include the general health of the patient, their age, and the mode of detection. Some factors are <strong>causal<\/strong> \u2013 for example, general health directly improves the chance of survival. Other factors are less obvious because they are <strong>informational<\/strong> \u2013 for example, the mode of detection can make a big difference:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If a tumor is discovered because it is causing symptoms, it is more likely to be larger, more aggressive, and relatively late for a given stage \u2013 and all of those implications decrease the chance of survival.<\/li>\n\n\n\n<li>If a tumor is not symptomatic, but discovered during a physical exam, it is probably larger, later, and more likely to cause mortality, compared to one discovered by high resolution imaging or a sensitive chemical test.<\/li>\n\n\n\n<li>Conversely, tumors detected by screening are more likely to be slow-growing because of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Length_time_bias\">length-biased sampling<\/a> \u2013 the probability of detection depends on the time between when a tumor is detectable and when it causes symptoms.<\/li>\n<\/ul>\n\n\n\n<p>Taking age into account is complicated because it might be both causal and informational, with opposite implications. A young patient might be more robust and able to tolerate treatment, but a tumor detectable in a younger person is likely to have progressed more quickly than one that could only be discovered after more years of life. So the implication of age might be negative among the youngest and oldest patients, and positive in the middle-aged.<\/p>\n\n\n\n<p>For some cancers, the magnitude of these implications is large, so the probability of 5-year survival for a particular patient might be higher than 91% or much lower.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Is More Screening Better?<\/h2>\n\n\n\n<p>Now let\u2019s consider the second incorrect inference.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>If 5-year survival is high when a cancer is detected early and much lower when it is detected late, it is tempting to conclude that more screening would save lives.<\/p>\n<\/blockquote>\n\n\n\n<p>For example, in a <a href=\"https:\/\/www.youtube.com\/watch?v=ph2ZeNooFLg\">recent video<\/a>, Nassim Taleb and Emi Gal discuss the pros and cons of cancer screening, especially full-body MRIs for people who have no symptoms. At one point they consider this table of survival rates based on stage at diagnosis:<a href=\"https:\/\/github.com\/AllenDowney\/ThinkBayes2\/raw\/master\/images\/cancer_table.png\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"775\" height=\"377\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-5.png\" alt=\"\" class=\"wp-image-1642\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-5.png 775w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-5-300x146.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-5-768x374.png 768w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-5-555x270.png 555w\" sizes=\"auto, (max-width: 775px) 100vw, 775px\" \/><\/figure>\n\n\n\n<p>They note that survival is highest if a tumor is detected while localized at the primary site, lower if it has spread regionally, and often much lower if it has spread distantly.<\/p>\n\n\n\n<p>They take this as evidence that screening for these cancers is beneficial. For example, <a href=\"https:\/\/youtu.be\/ph2ZeNooFLg?t=357\">at one point<\/a> Taleb says, \u201cLook at the payoff for pancreatic cancer \u2013 10 times the survival rate.\u201d<\/p>\n\n\n\n<p>And Gal adds, \u201cColon cancer, it\u2019s like seven times\u2026 The overarching insight is that you want to find cancer early\u2026 This table makes the case for the importance of finding cancer early.\u201d<\/p>\n\n\n\n<p>Taleb agrees, but this inference is incorrect: <strong>This table does not make the case that it is better to catch cancer early<\/strong>.<\/p>\n\n\n\n<p>Catching cancer early is beneficial only if (1) the cancers we catch would otherwise cause disease and death, <em>and<\/em> (2) we have treatments that prevent those outcomes, <em>and<\/em> (3) these benefits outweigh the costs of additional screening. This table does not show that any of those things is true.<\/p>\n\n\n\n<p>In fact, it is possible for a cancer to reproduce any row in this table, even if we have no treatment and detection has no effect on outcomes. To demonstrate, I\u2019ll use a model of tumor progression to show that a hypothetical cancer could have the same survival rates as colon cancer \u2013 <strong>even if there is no effective treatment at all<\/strong>.<\/p>\n\n\n\n<p>To be clear, I\u2019m not saying that cancer treatment is not effective \u2013 in many cases we know that it is. I\u2019m saying that we can\u2019t tell, just looking at a survival rates, whether early detection has any benefit at all.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Markov Model<\/h2>\n\n\n\n<p><a href=\"https:\/\/allendowney.github.io\/ThinkBayes2\/cancer.html\">The details of the model are here<\/a> and you can <a href=\"https:\/\/colab.research.google.com\/github\/AllenDowney\/ThinkBayes2\/blob\/master\/examples\/cancer.ipynb\">click here to run my analysis in a Jupyter notebook on Colab<\/a>.<\/p>\n\n\n\n<p>We\u2019ll model tumor progression using a Markov chain with these states:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>U1<\/code>, <code>U2<\/code>, and <code>U3<\/code> represent tumors that are undetected at each stage: local, regional, and distant.<\/li>\n\n\n\n<li><code>D1<\/code>, <code>D2<\/code>, <code>D3<\/code> represent tumors that were detected\/diagnosed at each stage.<\/li>\n\n\n\n<li>And <code>M<\/code> represents mortality.<\/li>\n<\/ul>\n\n\n\n<p>The following figure shows the states and transition rates of the model.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"442\" height=\"292\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-4.png\" alt=\"\" class=\"wp-image-1636\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-4.png 442w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-4-300x198.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/10\/image-4-409x270.png 409w\" sizes=\"auto, (max-width: 442px) 100vw, 442px\" \/><\/figure>\n\n\n\n<p>The transition probabilities are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>lams<\/code>, two values that represent transition rates between stages,<\/li>\n\n\n\n<li><code>kappas<\/code>, three values that represent detection rates at each state,<\/li>\n\n\n\n<li><code>mu<\/code> the mortality rate from <code>D3<\/code>,<\/li>\n\n\n\n<li><code>gamma<\/code> the effectiveness of treatment.<\/li>\n<\/ul>\n\n\n\n<p>If <code>gamma &gt; 0<\/code>, the treatment is effective by decreasing the probability of progression to the next stage. In the models we\u2019ll run for this example, <code>gamma=0<\/code>, which means that detection has no effect on progression. <\/p>\n\n\n\n<p>Overall, these values are within the range we observe in real cancers.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The transition rates are close to 1\/6, which means the average time at each stage is 6 simulated years.<\/li>\n\n\n\n<li>The detection rate is low at the first stage, higher at the second, and much higher at the third.<\/li>\n\n\n\n<li>The mortality rate is close to 1\/3, so the average survival after diagnosis at the third stage is about 3 years.<\/li>\n<\/ul>\n\n\n\n<p>In this model, death occurs only after a cancer has progressed to the third stage and been detected. That\u2019s not realistic \u2013 in reality deaths can occur at any stage, due to cancer or other causes.<\/p>\n\n\n\n<p>But adding more transitions would not make make the model better. The purpose of the model is to show that we can reproduce the survival rates we see in reality, even if there are no effective treatments. Making the model more realistic would increase the number of parameters, which would make it easier to reproduce the data, but that would not make the conclusion stronger. More realistic models are not necessarily better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Results<\/h2>\n\n\n\n<p id=\"codecell10\">We can simulate this model to compute survival rates and the distribution of stage at diagnosis<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the model, survival rates are 95% if localized, 72% if spread regionally, and 17% if spread distantly. For colon cancer, the rates from the SEER data are are 91%, 74%, and 16%. So the simulation results are not exactly the same, but they are close.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the model, 38% of tumors are localized when diagnosed, 33% have spread regionally, and 29% have spread distantly. The actual distribution for colon cancer is 38%, 38%, and 24%. Again, the simulation results are not exactly the same, but close.<\/li>\n<\/ul>\n\n\n\n<p>With more trial and error, I could probably find parameters that reproduce the results exactly. That would not be surprising, because even though the model is meant to be parsimonious, it has seven parameters and we are matching observations with only five degrees of freedom.<\/p>\n\n\n\n<p>That might seem unfair, but it makes the point that there is not enough information in the survival table \u2013 even if we also consider the distribution of stages \u2013 to estimate the parameters of the model precisely. <strong>The data don\u2019t exclude the possibility that treatment is ineffective<\/strong>, so they don\u2019t prove that early detection is beneficial.<\/p>\n\n\n\n<p>Again, it <em>might<\/em> be better to find cancer early, if the benefit of treatment outweighs the costs of false discovery and overdiagnosis \u2013 but that\u2019s a different analysis, and 5-year survival rates aren\u2019t part of it.<\/p>\n\n\n\n<p>That\u2019s why <a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC2733256\/\">this editorial<\/a> concludes, \u201cOnly reduced mortality rates can prove that screening saves lives\u2026 journal editors should no longer allow misleading statistics such as five year survival to be reported as evidence for screening.\u201d<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Counterfactuals<\/h2>\n\n\n\n<p>Now let\u2019s consider the third incorrect inference.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>In a case where a patient is diagnosed late and dies of cancer, it is tempting to say that they would have survived if their cancer had been caught early.<\/p>\n<\/blockquote>\n\n\n\n<p>For example, <a href=\"https:\/\/youtu.be\/ph2ZeNooFLg?t=836\">later in the previous video<\/a>, Taleb says, \u201cYour mother, had she had a colonoscopy, she would be alive today\u2026 she\u2019s no longer with us because it was detected when it was stage IV, right?\u201d And Gal agrees.<\/p>\n\n\n\n<p>That <em>might<\/em> be true, if treatment would have prevented the cancer from progressing. But this conclusion is not supported by the data in the survival table.<\/p>\n\n\n\n<p>If someone is diagnosed late and dies, it is tempting to look at the survival table and think there\u2019s a 91% chance they would have survived if they had been diagnosed earlier. But that\u2019s not accurate \u2013 and it might not even be close.<\/p>\n\n\n\n<p>First, remember what 91% survival means: among people diagnosed early, 91% survived five years after diagnosis. But among those survivors, an unknown proportion had tumors that would not have been fatal, even without treatment. Some might be non-progressive, or progress so slowly that they never cause disease or death. But in a case where the patient dies of cancer, we know their tumor was not one of those.<\/p>\n\n\n\n<p>As a simplified example, suppose that of all tumors that are caught early, 50% would cause death within five years, if untreated, and 50% would not. Now imagine 100 people, all detected early and all treated: 50 would survive with or without treatment; out of the other 50, 41 survive with treatment \u2013 so overall survival is 91%. But if we know someone is in the second group, their chance of survival is 41\/50, which is 82%.<\/p>\n\n\n\n<p>And if the percentage of non-progressive cancers is higher than 50%, the survival rate for progressive cancers is even lower, holding overall survival constant. So that\u2019s one reason the inference is incorrect.<\/p>\n\n\n\n<p>To see the other reason, let\u2019s be precise about the counterfactual scenario. Suppose someone was diagnosed in 2020 with a tumor that had spread distantly, and they died in 2022. Would they be alive in 2025 if they had been diagnosed earlier?<\/p>\n\n\n\n<p>That depends on when the hypothetical diagnosis happens \u2013 if we imagine they were diagnosed in 2020, five year survival <em>might<\/em> apply (except for the previous point). But if it had spread distantly in 2020, we have to go farther back in time to catch it early. For example, if it took 10 years to progress, catching it early means catching it in 2010. In that case, being \u201calive today\u201d would depend on 15-year survival, not 5-year.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">It&#8217;s a Different Question<\/h2>\n\n\n\n<p>The five-year survival rate answers the question, \u201cOf all people diagnosed early, how many survive five years?\u201d That is a straightforward statistic to compute.<\/p>\n\n\n\n<p>But the hypothetical asks a different question: \u201cOf all people who died [during a particular interval] after being diagnosed late, how many would be alive [at some later point] if the tumor had been detected early?\u201d That is a <em>much<\/em> harder question to answer \u2013 and five-year survival provides little or no help.<\/p>\n\n\n\n<p>In general, we don\u2019t know the probability that someone would be alive today, if they had been diagnosed earlier. Among other things, it depends on progression rates with and without treatment.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If many of the tumors caught early would not have progressed or caused death, even without treatment, the counterfactual probability would be low.<\/li>\n\n\n\n<li>In any case, if treatment is ineffective, as in the hypothetical cancer we simulated, the counterfactual probability is zero.<\/li>\n\n\n\n<li>At the other extreme, if treatment is perfectly effective, the probability is 100%.<\/li>\n<\/ul>\n\n\n\n<p>It might be frustrating that we can\u2019t be more specific about the probability of the counterfactual, but if someone you know was diagnosed late and died, and it bothers you to think they would have lived if they had been diagnosed earlier, it might be some comfort to realize that we don\u2019t know that \u2013 and it could be unlikely.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Comparing Survival Rates<\/h2>\n\n\n\n<p>Now let\u2019s consider the last incorrect inference.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>If 5-year survival increases over time, it is tempting to conclude that treatment has improved.<\/p>\n<\/blockquote>\n\n\n\n<p>This conclusion is appealing because if cancer treatment improves, survival rates improve, other things being equal. But if we do more screening and catch more cancers early, <strong>survival rates improve even if treatment is no more effective<\/strong>. And if screening becomes more sensitive, and detects smaller tumors, survival rates also improve.<\/p>\n\n\n\n<p>For many cancers, all three factors have changed over time: improved treatment, more screening, and more sensitive screening. Looking only at survival rates, we can\u2019t tell how much change in survival we should attribute to each.<\/p>\n\n\n\n<p>And the answer is different for different sites. For example, <a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/25417232\/\">this paper<\/a> concludes:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>In some cases, increased survival was accompanied by decreased burden of disease, reflecting true progress. For example, from 1975 to 2010, five-year survival for colon cancer patients improved \u2026 while cancer burden fell: Fewer cases \u2026 and fewer deaths \u2026, a pattern explained by both increased early detection (with removal of cancer precursors) and more effective treatment. In other cases, however, increased survival did not reflect true progress. In melanoma, kidney, and thyroid cancer, five-year survival increased but incidence increased with no change in mortality. This pattern suggests overdiagnosis from increased early detection, an increase in cancer burden.<\/p>\n<\/blockquote>\n\n\n\n<p>And <a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/10865276\/\">this paper<\/a> explains:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Screening detects abnormalities that meet the pathological definition of cancer but that will never progress to cause symptoms or death (non-progressive or slow growing cancers). The higher the number of overdiagnosed patients, the higher the survival rate.<\/p>\n<\/blockquote>\n\n\n\n<p>It concludes that \u201cAlthough 5-year survival is a valid measure for comparing cancer therapies in a randomized trial, our analysis shows that changes in 5-year survival over time bear little relationship to changes in cancer mortality. Instead, they appear primarily related to changing patterns of diagnosis.\u201d<\/p>\n\n\n\n<p>That conclusion might be stated too strongly. <a href=\"https:\/\/www.researchgate.net\/publication\/46555895_Are_Increasing_5-Year_Survival_Rates_Evidence_of_Success_Against_Cancer_A_Reexamination_Using_Data_from_the_US_and_Australia\">This response paper<\/a> concludes \u201cWhile the change in the 5-year survival rate is not a perfect measure of progress against cancer [\u2026] it does contain useful information; its critics may have been unduly harsh. Part of the long-run increase in 5-year cancer survival rates is due to improved [\u2026] therapy.\u201d<\/p>\n\n\n\n<p>But they acknowledge that with survival rates alone, we can\u2019t say what part \u2013 and in some cases we have evidence that it is small.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Summary<\/h2>\n\n\n\n<p>Survival statistics are misleading because they suggest inferences they do not actually support.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Survival rates from the past might not apply to the present, and for a particular patient, the probability of survival depends on (1) causal factors like general health, and (2) informational factors like the mode of discovery (screening vs symptomatic presentation).<\/li>\n\n\n\n<li>If survival rates are higher when tumors are discovered early, that doesn\u2019t mean that more screening would be better.<\/li>\n\n\n\n<li>And if a cancer is diagnosed late, and the patient dies, that doesn\u2019t mean that if it had been diagnosed early, they would have lived.<\/li>\n\n\n\n<li>Finally, if survival rates improve over time (or they are different in different places) that doesn\u2019t mean treatment is more effective.<\/li>\n<\/ul>\n\n\n\n<p>To be clear, all of these conclusions <em>can<\/em> be true, and in some cases we know they are true, at least in part. For some cancers, treatments have improved, and for some, additional screening would save lives. But to support these conclusions, we need other methods and metrics \u2013 notably randomized controlled trials that compare mortality. Survival rates alone provide little or no information, and they are more likely to mislead than inform.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>UPDATE: I submitted a more formal version of this article to the UMAP Journal (Undergraduate Mathematics and Its Applications), which publishes articles that use mathematical modeling for real-world problems, often with a pedagogical or expository angle. A preprint is available on arXiv at: https:\/\/arxiv.org\/abs\/2603.19945 Five-year survival might be the most misleading statistic in medicine. For example, suppose 5-year survival for a hypothetical cancer is What can we infer from these statistics? In fact, none of these inferences are correct. Let\u2019s&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2025\/10\/27\/cancer-survival-rates-are-misleading\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[103,47,104],"class_list":["post-1633","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-cancer","tag-length-biased-sampling","tag-medical-statistics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Cancer Survival Rates Are Misleading - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2025\/10\/27\/cancer-survival-rates-are-misleading\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cancer Survival Rates Are Misleading - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"UPDATE: I submitted a more formal version of this article to the UMAP Journal (Undergraduate Mathematics and Its Applications), which publishes articles that use mathematical modeling for real-world problems, often with a pedagogical or expository angle. A preprint is available on arXiv at: https:\/\/arxiv.org\/abs\/2603.19945 Five-year survival might be the most misleading statistic in medicine. For example, suppose 5-year survival for a hypothetical cancer is What can we infer from these statistics? In fact, none of these inferences are correct. Let\u2019s... 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If I have a tumor that I\u2019ve been told has a malignancy rate of 2% per year, does that compound? So after 5 years there\u2019s a 10% chance it will turn malignant? This turns out to be an interesting question, because the\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1145,"url":"https:\/\/www.allendowney.com\/blog\/2023\/12\/12\/smoking-causes-cancer-2\/","url_meta":{"origin":1633,"position":1},"title":"Smoking Causes Cancer","author":"AllenDowney","date":"December 12, 2023","format":false,"excerpt":"In the preface of Probably Overthinking It, I wrote: Sometimes interpreting data is easy. For example, one of the reasons we know that smoking causes lung cancer is that when only 20% of the population smoked, 80% of people with lung cancer were smokers. If you are a doctor who\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-1.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-1.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-1.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-1.png?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":1097,"url":"https:\/\/www.allendowney.com\/blog\/2023\/11\/07\/we-have-a-book\/","url_meta":{"origin":1633,"position":2},"title":"We Have a Book!","author":"AllenDowney","date":"November 7, 2023","format":false,"excerpt":"My copy of Probably Overthinking It has arrived! If you want a copy for yourself, you can get a 30% discount if you order from the publisher and use the code UCPNEW. You can also order from Amazon or, if you want to support independent bookstores, from Bookshop.org. The official\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":845,"url":"https:\/\/www.allendowney.com\/blog\/2023\/01\/19\/smoking-causes-cancer\/","url_meta":{"origin":1633,"position":3},"title":"Smoking causes cancer","author":"AllenDowney","date":"January 19, 2023","format":false,"excerpt":"Here's a question posted on Reddit's statistics forum: The Centers for Disease Control and Prevention states on its website that \u201cin the United States, cigarette smoking causes about 90% of lung cancers.\u201d If S is the event \u201csmokes cigarettes\u201d and L is the event \u201chas lung cancer,\u201d then the prob\u0002ability\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1221,"url":"https:\/\/www.allendowney.com\/blog\/2024\/02\/11\/the-political-gender-gap-is-not-growing\/","url_meta":{"origin":1633,"position":4},"title":"The Political Gender Gap is Not Growing","author":"AllenDowney","date":"February 11, 2024","format":false,"excerpt":"In a previous article, I used data from the General Social Survey (GSS) to see if there is a growing gender gap among young people in political alignment, party affiliation, or political attitudes. So far, the answer is no. Young women are more likely than men to say they are\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2024\/02\/ft_ideology_gap_us.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":169,"url":"https:\/\/www.allendowney.com\/blog\/2019\/02\/06\/the-marriage-strike-continues\/","url_meta":{"origin":1633,"position":5},"title":"The marriage strike continues","author":"AllenDowney","date":"February 6, 2019","format":false,"excerpt":"Last month The National Survey of Family Growth released new data from 5,554 respondents interviewed between 2015 and 2017. I've worked on several studies using data from the NSFG, so it's time to do some updates! 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