Survival Analysis: From Square One to Square Two .


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Address structure. Essential conceptsKaplan-Meier analysisCox regressionComputer rehearse. What\'s in a name?. time-to-occasion datafailure-time datacensored information (in secret result). Sorts of blue penciling. misfortune to catch up amid the study period study conclusion. Illustrations of survival examination. 1. Conjugal status
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Survival Analysis: From Square One to Square Two Yin Bun Cheung, Ph.D. Paul Yip, Ph.D. Readings

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Lecture structure Basic ideas Kaplan-Meier examination Cox relapse Computer rehearse

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time-to-occasion information disappointment time information controlled information (imperceptibly result) What\'s in a name?

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misfortune to catch up amid the review time frame ponder conclusion Types of blue penciling

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Examples of survival examination 1. Conjugal status & mortality 2. Therapeutic medicines & tumor repeat & mortality in disease patients 3. Measure during childbirth & formative points of reference in newborn children

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Censoring (time of occasion not watched) Unequal follow-up time Why survival examination ?

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What is time? What is the root of time? In the study of disease transmission: Age (birth as time 0) ? Date-book time since a benchmark study ?

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What is the source of time? In clinical trials: Since randomisation ? Since treatment starts ? Since onset of presentation ?

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The decision of starting point of time Onset of ceaseless introduction Randomisation to treatment Strongest impact on the risk

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Types of survival examination 1. Non-parametric strategy Kaplan-Meier examination 2. Semi-parametric strategy Cox relapse 3. Parametric technique

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Square 1 to square 2 This address concentrates on two ordinarily utilized strategies Kaplan-Meier strategy Cox relapse show

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KM survival bend * d=death, c=censored, surv=survival

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KM survival bend

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No. of expected passings Expected demise in gathering An at time i, accepting balance in survival: E Ai =no. at hazard in gathering An i  demise i add up to no. at hazard i Total expected demise in gathering An: E A =  E Ai

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Log rank test A correlation of the quantity of expected and watched passings. The bigger the inconsistency, the less conceivable the invalid theory of uniformity.

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A guess The log rank test measurement is frequently approximated by X 2 = (O A - E A ) 2/E A + (O B - E B ) 2/E B, where O A & E An are the watched & expected number of passings in gathering An, and so forth

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1 .8 .6 S(t) S(t) .4 .2 0 5 10 15 20 0 5 10 15 20 Time Proportional peril suspicion Log rank test favored (PH genuine ) Breslow test favored (non-PH)

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Risk, contingent hazard, danger

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Another look of PH Hazard 0 5 10 15 20 0 5 10 15 20 Time Log rank test favored (PH genuine ) Breslow test favored (non-PH)

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Cox relapse display Handles 1 introduction factors. Covariate impacts given as Hazard Ratios. Semi-parametric: just expect corresponding danger.

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Cox demonstrate on account of a solitary variable . h i (t) = h B (t)  exp( B X i ) . h j (t) = h B (t)  exp( B X j ) . h i (t)/h j (t) =exp[B( X i - X j )] exp(B) is a Hazard Ratio

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Test of relative risk suspicion Scaled Schoenfeld residuals Grambsch-Therneau Test for treatment  period association Example: mortality of dowagers

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Computer rehearse A clinical trial of stage I bladder tumor Thiotepa versus Control Data from StatLib

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Data structure Two most critical factors: Time to repeat (>0) Indicator of disappointment/editing (0=censored; 1=recurrence) (coding relies on upon programming)

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KM gauges Thiotepa Control

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Log rank test chi2(1) = 1.52 Pr>chi2 = 0.22

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Cox relapse models

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Test of PH supposition Grambsch-Therneau test for PH in model II Thiotepa P=0.55 Number of tumor P=0.60

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Major References (Examples) Ex 1. Cheung. Int J Epidemiol 2000;29:93-99. Ex 2. Sauerbrei et al . J Clin Oncol 2000;18:94-101. Ex 3. Cheung et al . Int J Epidemiol 2001;30:66-74.

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Major References (General) Allison. Survival Analysis utilizing the SAS ® System . Collett. Demonstrating Survival Data in Medical Research . Fisher, van Belle. Biostatistics: A Methodology for the Health Sciences .

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