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Santé & Médecine

Survival Analysis

Pravin KolekarSuivre

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- Short Talk : Life Table &Kaplan-Meier Method PG Student : Dr.Pravin PG Guide : Dr.Todkar sir Activity Guide : Dr.Jatti sir
- Purpose 1.There has been short notes on Life Tables & Kaplan-Meier Method in PG exams 2. Short Talk is presented so that all the PGs will be well acquainted with topic
- Contents : 1.Introduction – Natural history of disease 2. Five approaches of expressing prognosis 3.Life Tables 4.Kaplan-Meier Method
- Natural History of Disease The disease results from complex interaction between man, an agent ( or cause of disease ) and environment Natural history of disease signifies the way in which a disease evolves over time from the earliest stage of its prepathogenesis phase to termination as recovery, disability or death ,in the absence of treatment or prevention It is described as consisting of two phases : Prepathogenesis (i.e. Process in environment ) & Pathogenesis ( Process in man ) .
- 1. Prepathogenesis Phase : In this phase the disease agent has not entered the human ,but factors favouring its interaction with human host are already existing in the environment. 2. Pathogenesis phase begins with the entry of disease agent in the susceptible human host . In case of infectious diseases, the agent multiplies & induces tissue physiological changes ,the disease progresses through period of incubation later through early & late pathogenesis . The final outcome of disease may be recovery disability or death.
- NATURAL HISTORY OF DISEASE
- Natural history of disease in quantitative terms : Importance : 1.To describe severity of disease to establish priorities for clinical services & public health programmes . 2.Quantification is important to establish baseline for natural history , so that as new treatments become available, the effects can be compared. 3. It is important to identify different treatments or management strategies for different stages of disease. 4. Patients are often concerned about prognosis.
- • Five approaches of expressing prognosis • I. Case-fatality • II. 5-year survival • III. Observed Survival • IV. Median survival Time • V. Relative survival
- Case- Fatality: • It is defined as the number of people who die of disease by number of people who have the disease • Case Fatality = No. of people who die of disease/ No. of people who have disease× 100
- Person years It is total sum of number of years that each member in study population is under observation. The individuals are observed for different periods of time ,the unit used for counting the observation time is person –year.
- Person years : • Limitations: person –years : Each person year is assumed to be equivalent to every other person year (i.e. the risk is same in any person- year observed ) • Despite this issue , Person –years are useful as denominators of rates of events in many situations, as randomized trials , cohort studies
- Five-Year Survival The 5 –year survival is the percentage of patients who are alive 5 years after treatment begins or 5 years after diagnosis.
- Median Survival Time: It is defined as the length of time that half (50%) of the study population survives. Mean survival time is average of survival times Advantages: Median survival time is less affected by extremes , where as mean survival times can be significantly affected by even single outlier In case of median survival , we would only have to observe the deaths of half of the group under observation & in case mean survival have to observe all deaths in study population.
- Relative survival: It is defined as the ratio of observed survival in people with the disease to expected survival if the disease were absent.
- Life Tables (Observed survival ) • The actual observed survival of patients followed over time, based on knowledge the interval within which event has occurred. • Life Tables are used for this purpose • It is peculiar type of cohort analysis.
- Hypothetical study of Treatment results (2000-2004) Followed to 2005 ( None lost to Follow –Up) Yr of Treat ment No. of Patients treated NO. ALIVE ON ANNIVERSARY OF TREATMENT 2001 2002 2003 2004 2005 2000 84 44 21 13 10 8 2001 62 31 14 10 6 2002 93 50 20 13 2003 60 29 16 2004 76 43
- • Survival analysis in Patients Treated (2000-2004) Yr of Treat ment No. of Patients treated NO. ALIVE AT END OF YEAR 1st Yr 2nd Yr 3rd Yr 4th Yr 5th Yr 2000 84 44 21 13 10 8 2001 62 31 14 10 6 2002 93 50 20 13 2003 60 29 16 2004 76 43 Total 375 197 71 36 16 8
- Probability Of Survival For Each Year Of The Study Total no. of patients who were alive 1 year after initiation of treatment / Total number of patients who started treatment 1. Probability of Surviving 1st year (P1) = 197/375 =0.525 2. Probability of Surviving 2nd year (P2) = 71/197-43 = 0.461 3. Probability of Surviving 3rd year (P3) = 36/71-16 = 0.655 4. Probability of Surviving 4th year (P4) = 16/36-13 = 0.696 5. Probability of Surviving 5th year (P5) = 8/16-6 = 0.800
- Cumulative Probabilities of Surviving Different Lengths of Time : 1. Probability of Surviving 1 year = P1 = 0.525 = 52.5 % 2. Probability of Surviving 2 years = P1×P2 =0.525×0.461 = =0.242 3.Probablity of Surviving 3 years = P1×P2×P3 = 0.525×0.461×0.655 =0.159 4.Probablity of Surviving 4 years = P1×P2×P3×P4 = 0.525×0.461×0.655×0.696 =0.800 5. Probability of Surviving 5 years = P1×P2×P3×P4×P5 = 0.525× 0.461× 0.655 ×0.696 ×0.800 = 0.088
- • Survival curve for hypothetical example of patients treated from 2000-2004 & followed until 2005
- Calculating Life Table Interval since beginning treatment Alive at begining of interval Died during interval Withdrew during interval No.at risk of dying during interval Col 2- 1/2 col4 Proportion who died during interval Col3/col5 Proportion who didn’t die during interval 1- Col.6 Cumu lative surviv al x IX dx Wx I’x qx px Px 1st yr 375 178 0 375 0.475 0.525 0.525 2nd yr 197 83 43 175.5 0.473 0.527 0.277 3rd yr 71 19 16 63 0.302 0.698 0.193 4th yr 36 7 13 29.5 0.237 0.763 0.147 5th yr 16 2 6 13 0.154 0.846 0.124
- • Life Table uses : 1.Finding out expectancy of life at birth or any age 2.Estimating no. of males who can marry and hence become target group for family planning methods Similarly number of children requiring high school education facilities , number of old people requiring social support can be estimated 3.Life insurance companies to fix their premiums and polices. 4.Estimating survival rates after radiotherapy or neurosurgery or anti malignancy treatment in the patients
- Kaplan –Meier Method Kaplan –Meier method also known as product limit method is statistical method used in analysis of time to event data Kaplan –Meier method is simplest way of computing the survival over time in spite of all difficulties associated with subjects or situations It is one of the best options to be used for measuring the fraction of subjects living after treatment
- In the Kaplan-Meier method predetermined intervals ,as done in Life tables, are not used. The exact point in time when each death or the event of interest, occurred is identified so that each death or event terminates the previous interval & new interval is started & For this new row is used in the Kaplan- Meier table. Survival probability for each time interval is calculated as the number of subjects surviving divided by number of patients at risk .
- • Hypothetical example of study of six patients analyzed by Kaplan-Meier method
- • Calculating Survival Using Kaplan-Meier Method Times to Deaths from starting Rx (Months ) No. Alive at Each Time of death(Inclu ding those who died at that time) No . Who Died at Each Time Proportion who died at That Time (Col.3/Col.2 ) Proportion who survived at That Time (1-Col.4) Cumulativ e survival 4 6 1 0.167 0.833 0.833 10 4 1 0.250 0.750 0.625 14 3 1 0.333 0.667 0.417 24 1 1 1.000 0.000 0.000
- Kaplan- Meier Method uses : • It is used to estimate survival function based on time to the occurrence of the event • Life tables are less commonly used nowadays and have been replaced with the Kaplan-Meier method.
- Assumptions made is using Life tables & Kaplan-Meier Method There has been no change in the effectiveness of treatment or in survivorship over calendar time. Participants are lost to follow up. If large proportion of the study population is lost to follow up, the findings of study will be less valid Third assumption is related with use of predetermined intervals as in case of traditional life tables
- • References : • 1.Gordis Epidemiology • 2.Park’s Textbook of Preventive & Social Medicine
- Thank You

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