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ANALYSIS OF SURVIVAL

ANALYSIS OF SURVIVAL. S URVIVAL. The probability that an individual will survive (not die from) the cancer. M ORTALITY. Probability of death from cancer within the population. S URVIVAL.

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ANALYSIS OF SURVIVAL

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  1. ANALYSIS OF SURVIVAL

  2. SURVIVAL The probability that an individual will survive (not die from) the cancer MORTALITY Probability of death from cancer within the population

  3. SURVIVAL For chronic disease, the proportion of patients cured is usually approximated by estimates of the net probability of survival at regular intervals after diagnosis

  4. MORTALITY Mortality from a disease is a measure of the frequency of death caused by the disease among the entire population at risk; it is influenced by both by the incidence of the disease and by survival from it

  5. CASE DEFINITION Define the subjects for whom calculations are to be made 1. Cancer type (site and histology) 2. Period of diagnosis 3. Sex 4. Stage of disease What to do about DCO cases or cases diagnosed at autopsy (survival time = 0)? Usually omitted, but if DCO% substantial, we will overestimate survival

  6. STARTING DATE Date from which we calculate survival time 1. Population based registry - date of diagnosis 2. Hospital registry – date of admission 3. Clinical trial – date of randomisation

  7. Women diagnosed with breast cancer (stage 1 or 2) in hospital Q during the years 1989-1993

  8. OUTCOME Date to which we calculate survival time 1. Death 2. Recurrence (“disease-free survival time”) ENDPOINT must be a binary variable (Yes/No only possible conditions)

  9. FOLLOW UP • PASSIVE: Notification via vital statistics system. • Usually involves linkage of registry and death certificates Cases that have not died are assumed to be alive (tends to overestimate survival, since some patients will have emigrated from surveillance area) 2. ACTIVE: Contact the patients not known to have died

  10. SURVIVAL FROM CANCER: Active follow-up methods • Review of clinical records (hospitals/hospices) • Reply paid postal enquiries • Telephone enquiries • Home visits Results in cases “LOST TO FOLLOW UP” In survival calculations by the ACTUARIAL METHOD, these subjects are assumed to have been present for half the time between the last and previous contact

  11. SURVIVALFROM CANCER The information needed • patient details • disease details • treatment details • date of diagnosis (start date) • date of death • date of LFU

  12. Women diagnosed with breast cancer (stage 1 or 2) in hospital Q during the years 1989-1993 FOLLOW-UP From 1/1/89 to end of 1995

  13. Diagram illustrating how follow-up data from 8 of the 40 women with breast cancer can be presented • by calendar year of diagnosis • by time since entry into the study (A = alive; D = dead)

  14. The data ordered by length of observed survival time, with (D) representing dead and (A) alive at the end of the follow-up period.

  15. DIRECT METHOD What proportion of subjects are alive at the end of a defined time period eg, 2 years BUT, in our data, six women are not under observation for 2 years, so they would have to be omitted from the analysis

  16. 10 dead 34 24 alive Tree diagram illustrating the two possible outcome for the 34 patients who completed a two-years follow-up period TWO YEAR SURVIVAL (direct method) = 24/34 = 0.71 = 71%

  17. The DIRECT method does not use all available information 6 subjects did have information on outcome, but we did not use it It is common, especially in population-based studies, for patients to be withdrawn from observation before the end of follow-up, or occurrence of the outcome of interest (death) CENSORED observations The ACTUARIAL METHOD makes use of all observations, including those censored during , for example, in the 2-year follow up

  18. CENSORED OBSERVATIONS Normally, we just know that an individual is lost to follow up at some time during the interval since the previous contact, but not exactly when. We assume that, on average, we observed each censored patent for HALF the follow-up period, without any deaths occurring among them If we calculate survival for just a single follow-up interval (eg. 2 years), we adjust the denominator for the censored subjects 2-year survival = 24/[34 + (6/2)] = 24/37 = 73%

  19. Use of several intervals (especially one year intervals) instead of one Allows comparisons between different groups of subjects, without the need to agree on a single interval Gives more information, for example, on the pattern of deaths in the cohort Example of data from table, laid out with results of follow-up each of first 3 years

  20. Calculate probability of surviving each year. Eg, year 1, 7/40 die (17.5%), so 82.5% survive Year 2 = 3/[33-(6/2)] = 3/30 subjects die (10%), so 90% survive

  21. THE ACTUARIAL LIFE TABLE qi = di / ri pi = 1 - qi pi = pi xpi-1

  22. FIVE YEAR SURVIVAL (actuarial method) = 0.328 = 32.8% This is the OBSERVED survival (from all causes of death) Results can be shown as a SURVIVAL CURVE

  23. CORRECTED/NET SURVIVAL Observed survival – probability of surviving ANY cause of death We are more likely to be interested in the probability of surviving the disease of interest (breast cancer, in our example) In our example, there were 4 deaths NOT due to breast cancer, and 3 of these contributed to the five-year survival calculation

  24. >5 years

  25. CORRECTED/NET SURVIVAL If cause of death is available, deaths due to OTHER causes are treated as withdrawals (at the date of death) CORRECTED/NET 5-YEAR SURVIVAL = 43.7%(32.8% observed)

  26. CORRECTED/NET SURVIVAL Important if we are comparing groups that differ with respect to sex, age, socio-economic status etc, that will influence the probability of dying from OTHER causes of death BUT Information on cause of death may be • Unavailable • Unreliable • Not comparably assigned between the groups being compared Use of RELATIVE SURVIVAL

  27. RELATIVE SURVIVAL The ratio of OBSERVED survival to that EXPECTED in a group of people in the general population, similar to the patient group with respect to sex, age, socio-economic status etc, AND year of observation (ie same probability of dying from OTHER causes of death EXPECTED survival is obtained from an appropriate LIFE TABLE

  28. LIFE TABLE FOR THAILAND (2000) - Females nqx the probability of dying between age x and the next age in the table

  29. For patient 5 (age 62at diagnosis), the expected probability of surviving 5 years is: 0.98667 x 0.98667 x 0.98667 x 0.979536 x 0.979536 = 0.92163

  30. RELATIVE SURVIVAL For the entire patient group, the expected survival is the sum of the individual five-year survival probabilities, divided by the total number of subjects (ie, the simple MEAN) Suppose this is 0.906 RELATIVE survival = OBSERVED survival EXPECTED survival RELATIVE survival = 32.8 0.906 36.2%

  31. RELATIVE SURVIVAL Note – calculation does not require information on CAUSE OF DEATH It does assumes the population has the same chance of death as that of the lifetable used

  32. THE KAPLAN-MEIER METHOD ACTUARIAL METHOD does not require knowledge of exact date of death, just the status of each subject at the end of the intervals studied (usually, for cancer, each year) If exact times of death are known, the survival probabilities can be estimated after each individual death, without the need to aggregate the data into intervals (of a year)

  33. Calculation of observed survival by the Kaplan-Meier method

  34. Survival curve produced by the Kaplan-Meier method for the 40 breast cancer patients (x indicates censoring times.) The last death occurs at 5.1 years, the curve remains flat after that It is useful (as here) to show the number of patients under the graph, or to show confidence intervals, to help interpretation of the curve

  35. Net (corrected) survival curves can be prepared by the Kaplan-Meier method, by assuming that deaths from unrelated causes are treated as censored observations

  36. COMPARISON OF SURVIVAL CURVES Kaplan-Meier survival curves for patients with breast cancer by stage of the tumour at the time of diagnosis • group 1 = tumour without lymph node involvement or metastasis; • group 2 = tumour with lymph node involvement and/ or regional or distant metastasis The numbers on the survival curves represent censored observations

  37. Two examples of comparative survival curves – the value of inspecting curves, rather than using a single measure (5-year survival)

  38. OTHER OUTCOMES We can calculate “survival” (or “failure” times) to outcomes other than death Clinical trials often use time to recurrence, or other specifed complication, as well as (or instead of ) death Probability of (a) overall survival; (b) of remaining free from local recurrence; and (c) of remaining free from regional of distant metastasis for 381 breast cancer patients according to type of postoperative treatment (RT = postoperative radiotherapy to the breast; RT= no further treatment)

  39. STANDARD ERROR of SURVIVAL (RATE) For observed survival s.e.(p) = (p(1-p)/n) = (0.71 x 0.29)/34 = 0.078 95% confidence interval = p + 1.96 (s.e. (p)) = 0.71 + 1.96 x 0.078 = 0.56 – 0.86

  40. STANDARD ERROR of ACTUARIAL SURVIVAL (RATE) s.e.(p) =   Greenwood’s formula = 0.074 ri (ri (ri – di)

  41. Standard error of relative survival Standard error of observed survival Expected survival = 0.074 0.906 = 0.082 95% confidence interval of relative survival 0.362 + (1.96 x 0.082) = 0.20 – 0.52

  42. COMPARISON OF SURVIVAL (RATES) Single point estimate of survival: probability of difference in two proportions – z statistic LOGRANK test (Breslow) Uses differences throughout the period of follow-up Comparison of survival should take account of confounding variables 1. Standardisation (eg, for age) 2. Stratification on the confounding factors – Mantel-Haenszel test 3. Modelling (Cox proportional hazards model)

  43. Fatality ( M:I) Ratio An approximate guide to survival M:I ratio  1 - survival e.g. survival = 0.05 (5%) = M:I ratio of 0.95 (95%) The cases and deaths do not refer to the same individuals, but if survival is fairly constant, the M:I ratio gives an approximate indication of survival

  44. SURVIVAL DATA CLINICAL TRIALS Randomized groups Single variable considered (treatment) HOSPITAL DATA Selected subjects (one institution) Comparison over time, between services, of treatment Comparison groups non-random POPULATION DATA Average outcome for entire population Result of many factors: stage of diagnosis (screening) treatment availability outcome of treatment

  45. SURVIVAL DATA EVALUATION OF CANCER CONTROL PROGRAMMES Effectiveness of Treatment in delaying/preventing death BUT, consider other factors influencing survival especially earlier diagnosis

  46. Survival ∝ Effectiveness of Treatment BUT, consider other factors influencing survival especially stage of disease (early/late diagnosis)

  47. PROGNOSTIC FACTOR Those factors whose subcategories reveal significant differences in survival e.g.: Stage, Age, Histology, Symptom

  48. FACTORS INFLUENCING SURVIVALFROM CANCER Disease: Natural history Clinical extent Definitions Treatment: Availability Access Quality Host: Age Sex SES Comorbidity Behaviour Early Detection: Early clinical detection Screening

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