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association rules and analysis

An Introduction to Survival Analysis

Course : Biostatistics Modules : An Introduction to Survival Analysis Lecturer: Bandit Thinkhamrop, PhD. Period: 9.00-12.00 Date : 6 August 2007 Objectives : After completion of this modules, fellows should be able to:

1. describe concept of survival analysis 2. calculate and interpret survival probability from a given data set 3. interpret survival curve 4. describe situation where survival analysis could be applied 6. perform data analysis using most common command of STATA.

Study materials:

1. Slide 2. Published article that used survival analysis

Teaching and learning activities :

1. Read the materials in Parts 1 and 2 as listed above 2. Attend a brief lecture and demonstration of using computer 3. Practice using computer as instructed in the study material Part 1 4. Discuss the problem faced during the practice session

Evaluation: Formative evaluation will be done by observation of participants' responses to

questions given while conducting the session as well as active participation and discussion in all learning activities. Summative evaluation will be based on the exercise.

Reference:

Hosmer, D.E., and Lemeshow, S. (1999). Applied survival analysis. New York. John Wiley & Sons.

Kleinbaum, D.G. (1996). Survival analysis: A self-learning text. New York: Springer-Verlag.

StataCorp. (1999). Stata statistical software: Release 6.0. College Station. TX: Stata Corporation.

1SURVIVAL ANALYSIS

Event

Dead, infection, relapsed, etc

Cured, improved, conception, discharged, etc

Smoking cessation, ect

Negative

Positive

Neutral

Time to event

General: event-free durationrelapse-free survival timeremission durationprogression-free survival

SURVIVAL TIME

Time to event

Failed: event occurred at time of observation

Censored: event have not occurred at time of observation

2CensoringEvent-free duration cannot be determined

Event have not yet occurred

Lost to follow-up

Competing event

Accrual, Follow-up, and EventID 2540 2541 2542 2543

Begin the study End of the study

Start of accrual End of accrual End of follow-up

123456

Recruitment period Follow-up period

Time since the beginning of the studyID

0 1 2 3 4

DeadDead

123456

48 months22 months14 months40 months26 months13 months

The data : >48 >22 14 40 >26 >13

3DATA

1 48 Still alive at the end of the study Censored2 22 Dead due to accident Censored3 14 Dead caused by the disease under investigation Dead4 40 Dead caused by the disease under investigation Dead5 26 Still alive at the end of the study Censored6 13 Lost to follow-up Censored

ID SURVIVAL TIME OUTCOME AT THE END EVENT(Months) OF THE STUDY

DATA

1 48 Censored2 22 Censored3 14 Dead4 40 Dead5 26 Censored6 13 Censored

ID TIME EVENT

1 48 02 22 03 14 14 40 15 26 06 13 0

ID TIME EVENT

ANALYSIS

1 48 02 22 03 14 14 40 15 26 06 13 0

ID TIME EVENT

Prevalence = 2/6

Incidence density = 2/163 person-months

Proportion of surviving at month t

Median survival time

4

5. listid time event

1. 1 48 02. 2 22 03. 3 14 14. 4 40 15. 5 26 06. 6 13 0

. stset time, failure(event)failure event: event ~= 0 & event ~= .

obs. time interval: (0, time]exit on or before: failure-------------------------------------------------------------------

6 total obs.0 exclusions

-------------------------------------------------------------------6 obs. remaining, representing2 failures in single record/single failure data

163 total analysis time at risk, at risk from t = 0earliest observed entry t = 0

last observed exit t = 48

. stsumfailure _d: event

analysis time _t: time| incidence no. of |------ Survival time -----|| time at risk rate subjects 25% 50% 75%

---------+---------------------------------------------------------------------total | 163 .0122699 6 40 40 .

. cii 163 0.0122699 , p-- Poisson Exact --

Variable | Exposure Mean Std. Err. [95% Conf. Interval]---------+-------------------------------------------------------------

| 163 .0122699 .0086762 .0014888 .0443053

. stquantNumber of deads = 2Number of ties = 0+---------------------------------------------------------------------------+| 50 percentile 95% Confidence Interval || survival time = 40.000 19.650 60.350 (Large Sample Approx.) || 14.000 48.000 (Brookmeyer-Crowley) |+---------------------------------------------------------------------------+

6. sts list, at(12, 24, 36, 48)failure _d: event

analysis time _t: timeBeg. Survivor Std.

Time Total Fail Function Error [95% Conf. Int.]-------------------------------------------------------------------------------

12 0 0 1.0000 . . .24 4 1 0.8000 0.1789 0.2038 0.969236 3 0 0.8000 0.1789 0.2038 0.969248 1 1 0.4000 0.2966 0.0114 0.8290

-------------------------------------------------------------------------------Note: Survivor function is calculated over full data and evaluated at

indicated times; it is not calculated from aggregates shown at left.

. sts g, at riskfailure _d: event

analysis time _t: time

Kaplan-Meier survival estimate

analysis time0 20 40 60

0.00

0.25

0.50

0.75

1.00 6

4

1

RESULTS

1 48 02 22 03 14 14 40 15 26 06 13 0

ID TIME EVENT

Incidence density = 1.2 per100 person-months(95%CI: 0.1 to 4.4)

Proportion of surviving at 24 month = 80%(95%CI: 20 to 97)

Median survival time = 40 Months (95%CI: 14 to 48)

Kaplan-Meier methods

Time tj

Number at risk

nj

Dead dj

Censored qj

Survival probability S(tj)

13 6 0 1 6/6 = 1.0 14 6-1 = 5 1 0 [(5-1)/5]1.0 = 0.8 22 5-1 = 4 0 1 [(4-0)/4]0.8 = 0.8 26 4-1 = 3 0 1 [(3-0)/3]0.8 = 0.8 40 6-1 = 2 1 0 [(2-1)/2]0.8 = 0.4 48 2-1 = 1 0 1 [(1-0)/1]0.4 = 0.4

Kaplan-Meier survival curve

ID TIME DEAD 1 48 0 2 22 0 3 14 1 4 40 1 5 26 0 6 13 0

ID TIME DEAD 6 13 0 3 14 1 2 22 0 5 26 0 4 40 1 1 48 0

Data sorted by time Original Data

0.5

S(t) 1.0

0 13 14 22 26 40 48

Survi

val p

robab

ility

Time (months)

Survival analysis

Computing notes and Exercises

Summer School in Modern Methods in Biostatistics and EpidemiologyVeneto, Italy

2328 June, 2003

http://www.pauldickman.com/teaching/veneto2003/

Contents

1 Survival analysis using Stata 2

2 Exercises using Stata 3

3 Splitting on two time scales and calculating SMRs 9

4 The Finnish Cancer Registry 12

References 12

1

1 Survival analysis using Stata

In order to analyse survival data it is necessary to specify (at a minimum) a variablerepresenting survival time and a variable specifying whether or not the event of interestwas observed (called the failure variable). Instead of specifying a variable representingsurvival time we can specify the entry and exit dates.

In many statistical software programs (such as SAS), these variables must be specifiedevery time a new analysis is performed. In Stata, these variables are specified once usingthe stset command and then used for all subsequent survival analysis (st) commands(until the next stset command). For example

. use melanoma

. stset surv_mm, failure(status==1)

The above code shows how we would stset the skin melanoma data in order to analysecause-specific survival with survival time in completed months (surv_mm) as the timevariable. Of the four possible values of status, we have specified that only code 1 indicatesan event (death due to melanoma). If we wanted to analyse observed survival (where alldeaths are considered to be events) we could use the following command

. stset surv_mm, failure(status==1,2)

Some of the Stata survival analysis (st) commands relevant to this course are given below.Further details can be found in the manuals or online help.

stset Declare data to be survival-time datastsplit Split time-span recordsstdes Describe survival-time datastsum Summarize survival-time datasts Generate, graph, list, and test the survivor and cumulative

hazard functionsstir Report incidence-rate comparisonstrate Tabulate failure ratestptime Calculate person-time at risk and failure ratesstcox Estimate Cox proportional hazards modelstphtest Test of Cox proportional hazards assumptionstphplot Graphical assessment of the Cox prop. hazards assumptionstcoxkm Graphical assessment of the Cox prop. hazards assumptionstreg Estimate parametric survival models

Once the data have been stset we can use any of these commands without having tospecify the survival time or failure time variables. For example, to plot the estimatedcause-specific survivor function by sex and then fit a Cox proportional hazards modelwith sex and calendar period as covariates

. sts graph, by(sex)

. stcox sex year8594

2

2 Exercises using Stata

1. Using hand calculation (i.e. using a spreadsheet program or pen, paper, and a cal-culator) estimate the cause-specific survivor function for the sa

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