Common Misunderstandings of Survival Time Analysis

Home , Censoring (statistics)

Milensu Shanyinde

Centre for Statistics in Medicine University of Oxford

2nd April 2012

C S M Outline

. Introduction

. Essential features of the Kaplan-Meier survival curves

. Median survival times

. Median follow-up times

. Forest plots to present outcomes by subgroups

C S M Introduction

. Survival data is common in cancer clinical trials

. Survival analysis methods are necessary for such data

. Primary endpoints are considered to be time until an event of interest occurs

. Some evidence to indicate inconsistencies or insufficient information in presenting survival data

. Poor presentation could lead to misinterpretation of the data

C S M 3

. Paper by DG Altman et al (1995)

. Systematic review of appropriateness and presentation of survival analyses in clinical oncology journals

. Assessed; - Description of data analysed (length and quality of follow-up) - Graphical presentation

C S M 4

. Cohort sample size 132, paper publishing survival analysis

. Results; - 48% did not include summary of follow-up time - Median follow-up was frequently presented (58%) but method used to compute it was rarely specified (31%)

Graphical presentation; - 95% used the K-M method to present survival curves - Censored observations were rarely marked (29%) - Number at risk presented (8%)

C S M 5 . Paper by S Mathoulin-Pelissier et al (2008)

. Systematic review of RCTs, evaluating the reporting of time to event end points in cancer trials

. Assessed the reporting of; - Number of events and censoring information - Number of patients at risk - Effect size by median survival time or Hazard ratio - Summarising Follow-up

C S M 6 . Cohort sample size 125

. Results; - Survival analysis cited with K-M method (92%) - Censoring was less defined (47%) - Number of patients at risk was less defined (45%) - Median Follow-up was reported (71%), but method used was not specified in almost all the papers

C S M 7

Presenting Kaplan Meier survival curves

C S M 8 Case 1: Presenting K-M survival curves

. Patients with first relapse of acute lymphoblastic leukaemia aged 1-18 years

. Experiencing two types of relapse, isolated or combined relapse

. Cohort size N = 123, of which 80 (65%) had i-CNS relapse

. 58 patients experienced the event (death)

C S M 9 Case 1 :- Presenting K-M survival curves

. Assess overall survival by type of relapse (isolated and combined relapse)

. K-M method estimates survival probability in both groups

. Graphical display of the survival curves using the K-M method

. To effectively display an informative plot as recommended

C S M 10

Isolated CNS Combined CNS Isolated CNS Combined CNS

1.00

0.75

0.50

0.25

Overall survival probabilitysurvivalOverall Overall survival proportion survival Overall

0.25 Log rank p = 0.3026 0.00 0 12 24 36 48 60 Log rank p = 0.3026

0.00 Time (months) 0 12 24 36 48 60 Number at risk Time (months) Isolated CNS 80 53 38 25 12 10 Combined CNS 43 28 20 12 9 4 Number at risk Isolated CNS 80 53 38 25 12 10 Combined CNS 43 28 20 12 9 4

Median survival times

C S M 12 Median Survival time

. Effect size is sometimes determined using Median survival time, if incorrectly presented could mislead results

. Median survival time : - Time when half of the patients are event free

. Median survival time estimated from the K-M survival curves.

. Takes into account patients who have been censored, so all patients are included

C S M 13 Case 2: Median Survival time

- Retrospective study of patients newly diagnosed with Hodgkin Lymphoma (HL)

- Cohort size N=224, data collected from 1997 – 2010 from five hospitals

- Patients comprising of 93 (42%) HIV+ patients

- 31 events (deaths) of which 15(48%) were HIV+ patients

- To compare overall survival of patients according to HIV status

C S M 14 Case 2: Median Survival time

Principal Investigator proposed summary of observed survival times excluding censored patients

“16 HIV– and 15 HIV + patients have died at a median time of 32 months (range: 5-97) and 9 months (range: 1-75) respectively, p= xx”

C S M 15 Case 2: Median Survival time

“16 HIV– and 15 HIV + patients have died at a median time of 32 months (range: 5-97) and 9 months (range: 1-75) respectively, p= xx”

“Five-year overall survival (OS) was 81% (95%CI: 69-89) and 88% (95%CI:80-93) for HIV positive and negative patients respectively.“

HIV+ HIV-

HIV+ HIV- 0.30

1.00

0.20

0.75

0.50

0.10

Cumulative percentage Cumulative

0.25

Overall survival probabilitysurvivalOverall 0.00 0 5 10 15 log rank p=0.148 Time (years) 0.00 Number at risk 0 5 10 15 HIV+ 93 28 8 0 Time (years) HIV- 131 70 28 0 Number at risk HIV+ 93 28 8 0 HIV- 131 70 28 0

C S M 16

Median follow-up

C S M 17 Median follow-up

. Quantify length of follow-up of patients

. The median follow-up is an indicator of how ‘mature’ your survival data is (e.g. how many months on ‘average’ the patients were followed since randomisation into the study).

. Interpretation depends greatly on the time frame in which the study was carried out i.e. did we observe enough events

. Several methods (yielding different results) could be used and need to report method used in analysis

C S M 18 Method 1: Median follow-up

Method 1 - Median follow-up using all patients - Have data on date of event or date patient last seen - Estimated from observed follow-up times

- Advantages; - Includes all patients

Disadvantages - Unstable and biased towards patients with short follow-up - Directly affected by times of observed events

C S M 19

Method 2: Median follow-up

Method 2 - Median follow-up for censored patients or survivors - Estimated from observed follow-up times, excluding patients with events

- Advantages; - We are not aware of how long we could have followed the patient if they had not experienced the event

- Disadvantages; - Loss of information - Unstable estimate when number of survivors is small C S M 20 Method 3: Median follow-up

Method 3 - Reverse K-M method - Estimated from the from K-M method, but events are reversed - The event of interest here becomes being alive and death is censored

Advantages; - Analogous to the K-M estimator - Robust Disadvantages; - Challenging to understand C S M 21 Case 3: Median follow-up

. Patients with first relapse of acute lymphoblastic leukaemia.

. Two types of relapse, isolated or combined relapse

. Cohort size N = 123, of which 80 (65%) had i-CNS relapse

. To summarise median follow-up for the whole cohort

C S M 22 Case 3: Median follow-up

Method Median follow-up estimate

All patients 33.9 months Censored patients only 36.3 months

Reverse K-M 39.5 months (95%CI; 36.0 - 48.5)

. Depending on which method you use different results are obtained. Consider this in your analysis.

C S M 23

Forest plots

C S M 24 Forest Plots

. Recently used method of displaying lots of information in small space and getting the bigger picture across groups

. We present Relative Risk, but could also be used to present Hazard Ratios or Odd Ratios

C S M 25 Case 4: Forest plot

. Patients with first relapse of acute lymphoblastic leukaemia, aged 1-18 years . Some concerns that age at relapse might have a big effect on Figure 3B

outcome 1.00 <10 ≥10 0.75

0.50

0.25 Overall survival probability survival Overall

Log rank p = 0.0108 0.00 0 12 24 36 48 60

Time (months)

Number at risk <10 78 57 40 28 15 10 ≥10 45 24 18 9 6 4 C S M 26

28 Summary

. Some recommended essential features when graphically displaying the survival curves

. Median survival times and what it actually means

. Report method used to obtain median follow-up

. Graphical display of subgroups using Forest Plots to present outcomes

C S M 29 References

. DG Altman et al (1995), Review of survival analyses published in cancer journals. British Journal of Cancer 72:511-518 . S Mathoulin-Pelissier et al (2008) Survival End Point Reporting in Randomized Cancer Clinical Trials: A Review of Major Journals. J Clin Oncol 26:3721-3726 . I Zweiner et al (2011), Survival Analysis. Medicine 108:163-169 . M Schemper and TL Smith (1996), A Note on Quantifying Follow- up Studies of Failure Time. Controlled Clinical Trials 17: 343-346

C S M 30 Acknowledgements

Sharon Love Senior Statistician Centre for Statistics in Medicine, University of Oxford

Dr Saha Vaskar CRUK Professor of Paediatric Oncology Academic Unit of Paediatric and Adolescent Oncology, Manchester

Dr Silvia Montoto Clinical Senior Lecturer/ Honorary Consultant Barts Cancer Institute- a CR-UK Centre of Excellence, Queen Mary University

C S M 31