Research method
Cox Proportional Hazards Model
The Cox proportional-hazards model estimates how a covariate shifts the instantaneous rate of an event — death, cancer recurrence, incident depression, a cardiovascular composite — without having to specify the baseline hazard. The headline number is a hazard ratio: HR 0.80 means about 20% lower hazard in that group, holding the model's other covariates fixed, provided the proportional-hazards assumption is close enough to true. Time-to-event methods also let investigators keep people who are censored (lost to follow-up, end of study) in the risk set until they leave.
Researchers reach for Cox models when the outcome is not a yes/no at a fixed week but whether and when something happens in a cohort or a trial. It answers 'is this exposure associated with a different event rate over follow-up?' Its main limitation is that a hazard ratio from an observational cohort is not a randomised treatment effect, and when events are rare even a large trial can return an HR near 1 that is hard to read as proof of equivalence.
Evidence
What the evidence shows
Drawn from 16 studies in this library. Each finding starts with a plain-language takeaway, then the denser detail. Supports means evidence for a finding; Challenges means evidence against a stated position; Qualifies marks scope with a short note on each study’s contribution. Challenged positions are labeled — they are not findings.
In observational cancer and sleep cohorts, Cox models turn deprivation, education and disease severity into excess-hazard or event-rate contrasts. ONS Longitudinal Study analyses found less-deprived areas had lower excess hazard for prostate cancer (EHR 0.80) and that absolute net-survival gaps between extreme individual SES profiles were 29.6% in the most deprived areas versus 9.1% in the least; an OSA sleep-lab cohort of 10,149 patients had 11.5% composite events over a median 68 months, with higher AHI linked to higher hazard (e.g. univariate HR 1.49 for high versus low AHI).
Study Role Design N Population Outcome Individual SES and cancer survival Supports CohortONS Longitudinal Study; excess mortality models by SES markers N=9276 · 1522 men + 1237 women colorectal; 3044 prostate; 3473 breast (ONS Longitudinal Study analysis cohort) People with colorectal, prostate, or breast cancer in the ONS Longitudinal Study Excess mortality / net-survival gaps by area deprivation and individual SES OSA severity and cardiovascular risk Supports CohortDiagnostic polysomnography cohort linked to administrative CV outcomes N=10149 · 10,149 of 11,596 first diagnostic sleep studies linked to admin data (88%) Adults undergoing diagnostic polysomnography Composite cardiovascular events and mortality Diet and alcohol papers in this set report HRs for incident depression or CVD that are threshold-like or beverage-specific rather than strictly linear. Low-to-moderate alcohol (>5–15 g/day) had HR 0.72 for incident depression among 5,505 older Mediterranean adults; each extra 10 g/day olive oil in PREDIMED participants had HR 0.87 for major CVD events; higher diet-quality quintiles had depression HRs around 0.74–0.78.
A randomised trial can still use Cox (or a closely related survival contrast) as the primary analysis. Patients undergoing curative breast-cancer surgery randomised to propofol versus sevoflurane had five-year overall survival around 92% in both arms, with a hazard ratio near 1 and no statistically significant difference in intention-to-treat or per-protocol analyses.
When depression is not the trial's original primary endpoint, a Cox HR below 1 is easy to over-read. PREDIMED's merged Mediterranean-diet HR for incident depression was 0.85 and not significant; a nuts-arm benefit appeared in a diabetes subgroup after 224 cases over a median 5.4 years.
Open questions
Tensions and limits
Some items are genuine disagreements on the same question. Others mark different assays, populations, or outcomes — limits on how far one study travels — not a forced fight between papers.
The same modelling family is asked to do two different jobs: describe inequalities and exposures in cohorts, versus test a randomised intervention. The SES-cancer and OSA papers cannot name a single causal mechanism or a treatment that would close the HR gap, whereas the propofol–sevoflurane trial can say the assigned anaesthetic did not shift 5-year survival under its protocol. Reading every HR as if it were that trial overclaims the observational papers and underclaims the trial's design.
- Individual SES and cancer survival
- OSA severity and cardiovascular risk
- Propofol vs sevoflurane and breast cancer survival
Study Role Design N Population Outcome Individual SES and cancer survival Supports CohortONS Longitudinal Study; excess mortality models by SES markers N=9276 · 1522 men + 1237 women colorectal; 3044 prostate; 3473 breast (ONS Longitudinal Study analysis cohort) People with colorectal, prostate, or breast cancer in the ONS Longitudinal Study Excess mortality / net-survival gaps by area deprivation and individual SES OSA severity and cardiovascular risk Supports CohortDiagnostic polysomnography cohort linked to administrative CV outcomes N=10149 · 10,149 of 11,596 first diagnostic sleep studies linked to admin data (88%) Adults undergoing diagnostic polysomnography Composite cardiovascular events and mortality Propofol vs sevoflurane and breast cancer survival Supports RCT1:1 propofol vs sevoflurane for anaesthesia maintenance in curative primary breast cancer surgery N=1670 · ITT: 841 propofol, 829 sevoflurane Patients undergoing curative primary breast cancer surgery 5-year overall survival Null and protective HRs are not interchangeable with 'safe' or 'preventive.' The anaesthetic trial's HR near 1 is limited by rare mortality and differing opioid co-analgesia; the alcohol paper's HR 0.72 cannot prove drinking prevents depression; the antidepressant-adverse-event cohort links several drugs to more falls versus non-use, which may still be confounding by indication.
- Propofol vs sevoflurane and breast cancer survival
- Wine, alcohol, and depression
- Antidepressant adverse events cohort
Study Role Design N Population Outcome Propofol vs sevoflurane and breast cancer survival Supports RCT1:1 propofol vs sevoflurane for anaesthesia maintenance in curative primary breast cancer surgery N=1670 · ITT: 841 propofol, 829 sevoflurane Patients undergoing curative primary breast cancer surgery 5-year overall survival Wine, alcohol, and depression Supports CohortObservational analysis within PREDIMED participants N=5505 · Older Mediterranean adults; 443 incident depression cases Older adults in the PREDIMED Mediterranean cohort Incident depression by baseline alcohol/wine intake (Cox HRs) Antidepressant adverse events cohort Supports CohortUK primary-care database; newly diagnosed depression followed for adverse events N=238963 · Final eligible cohort; 87.7% received antidepressants during follow-up Adults aged 20–64 with newly diagnosed depression in UK primary care Adverse outcomes (including falls) by antidepressant class/drug vs non-use
Common misconceptions
A hazard ratio is the same thing as a relative risk at the end of follow-up.
It is a ratio of instantaneous event rates over time, under a proportional-hazards assumption. Absolute gaps can look very different from the HR, as in the cancer-survival paper's 29.6% versus 9.1% net-survival gaps by SES profile despite a prostate EHR of 0.80 for area deprivation.
If a large trial's HR is about 1, the two treatments have been proven equivalent.
The propofol versus sevoflurane breast-cancer trial analysed 1,670 patients and still could not prove equivalence for a rare mortality outcome; opioid co-analgesia also differed by arm.
An HR below 1 from a food or alcohol cohort means that exposure was shown to prevent the disease.
Those analyses remain observational (olive oil within a trial cohort; alcohol and diet-quality scores in follow-up studies) and the PREDIMED depression analysis was not even the trial's original primary endpoint.
Exam-style questions
Short-answer questions that ask you to explain or compare, not recall.
What does a Cox model add that a simple chi-square of 'event yes/no' at the end of a study does not, and why does that matter for the OSA cohort?
It uses time to the event and keeps censored people in the risk set until they leave, so a 68-month median follow-up with 11.5% composite events can still estimate how AHI shifts the hazard rather than collapsing everyone to a yes/no at a common calendar date. People diagnosed later or lost sooner still contribute follow-up time.
Contrast the propofol–sevoflurane HR near 1 with the olive-oil HR of 0.87. Which is a randomised treatment contrast, and what is each number still not allowed to claim?
Anaesthetic assignment was randomised; olive-oil intake was an observational contrast inside PREDIMED. The trial HR near 1 does not prove equivalence for rare deaths or for cancers other than primary breast surgery. The olive-oil HR does not mean olive oil was itself randomised, and residual confounding remains possible.
Why is PREDIMED's merged Mediterranean-diet HR of 0.85 for depression a weak basis for a dietary prescription against depression?
Depression was not the original primary endpoint, the merged-diet HR was not significant, and the clearer nuts-arm signal was a diabetes subgroup among 224 cases. Subgroup HRs after a non-significant main contrast are easy to overfit.
How can a 'protective' alcohol HR of 0.72 and an antidepressant-falls signal both be true in Cox models without telling a student what to drink or which pill to avoid?
Both are observational rate ratios. Moderate alcohol may mark a healthy-user pattern rather than a causal antidepressant; extra falls on named drugs may reflect who is prescribed them (confounding by indication). Cox organises the time-to-event comparison; it does not by itself identify the mechanism or the right clinical action.
The studies
16 studies in this library bear on Cox Proportional Hazards Model, ordered by citations. The first 8 are shown.
- Night shifts and type 2 diabetes risk
Longer rotating night-shift work associated with higher type 2 diabetes risk in two large female nurse cohorts.
- OSA severity and cardiovascular risk
In >10,000 sleep-study patients, higher apnea–hypopnea burden predicted cardiovascular events and death over years of follow-up.
- Healthy lifestyle and multimorbidity risk
Healthier lifestyle scores tracked lower CVD and diabetes risk and lower multimorbidity transitions.
- Mediterranean diet and depression risk
Overall Mediterranean diet assignment did not significantly reduce depression; a nuts arm suggested benefit in diabetes subgroup analyses.
- Olive oil intake and CVD risk
Higher olive oil intake tracked lower major CVD events and cardiovascular death in PREDIMED participants.
- How broadly does smoking raise heart and vessel disease risk?
In a large Australian cohort, current smoking raised risk across nearly all CVD subtypes—especially peripheral arterial disease—and quitting lowered risk.
- Shingles vaccine cut zoster by about half
In older US adults, herpes zoster vaccination showed ~48% effectiveness against incident zoster and ~59–62% against post-herpetic neuralgia.
- Diet quality and depression risk
In the SUN cohort, higher adherence to Mediterranean, pro-vegetarian, and AHEI-2010 diet scores tracked with lower risk of incident depression over about 8.5 years.
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- Wine, alcohol, and depression
In PREDIMED adults, low-to-moderate alcohol—especially wine—associated with lower incident depression risk versus abstaining, while heavy drinking looked riskier.
- Antidepressant adverse events cohort
In 238,963 adults aged 20–64 with depression, most used antidepressants and several common agents associated with higher fall rates versus non-use.
- Widening NSW cancer survival gaps
Among 651,245 NSW cancer cases, people in more disadvantaged areas had higher cancer death risk, and disparities appeared to widen over time.
- ANXA1 in breast cancer prognosis
ANXA1-positive breast tumors clustered with poor-prognosis features (high grade, basal/TN, BRCA1/2) and worse outcomes in some high-risk subgroups such as HER2+.
- Does socioeconomic status change cancer survival?
In Norwegian women, lower education and income predicted worse cancer survival until stage and smoking were accounted for.
- Individual SES and cancer survival
UK linked-data analysis shows both area deprivation and individual SES shape cancer survival, with wider absolute gaps in the most deprived areas.
- Propofol vs sevoflurane and breast cancer survival
In the CAN randomised trial, five-year overall survival after primary breast cancer surgery was essentially the same with propofol or sevoflurane maintenance anaesthesia.
- Screening and breast cancer equity in NZ
Screen-detected cancers were less common in Māori women, and crude survival was worse, but survival gaps narrowed among screen-detected cases.
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