survival analysis

ORIGINAL ARTICLE

Survival analysis

Robert Flynn

Aims and objectives. This paper describes when and why survival analysis is used and describes the use and interpretation of the

techniques most commonly encountered in medical literature. This is performed using examples taken from core medical

journals.

Background. Survival analysis is widely used in clinical and epidemiological research: in randomised clinical trials for com-

paring the efficacy of treatments and in observational (non-randomised) research to determine and test the existence of epi-

demiological association.

Design. This paper introduces the principles, practice and terminology of survival analysis.

Methods. References are made to examples from open-access medical journals.

Results. Survival analysis is a well-established series of methodologies that are widely encountered in medical literature for both

observational and randomised studies.

Conclusions. Survival analysis represents a more efficient use of clinical data than other forms of analysis which rely on fixed

time periods. One of the most widely used techniques is that developed by Kaplan and Meier. This involves the creation of life

tables and the plotting of survival curves with comparison made between two or more groups. The log-rank test is commonly

used to establish whether there is a statistically significant difference between these groups. The Multivariate Cox proportional

hazards extend this approach to give an estimate of effect size (the Hazards Ratio) and can adjust for any potential confounding

variables. In this model, the assumption of proportional hazards is of key importance and should always be checked. More

advanced techniques are the use of time-dependent variables and the less widely used parametric survival techniques. Care

should always be taken when considering the assumptions involved when using such methods.

Relevance to clinical practice. As survival analysis is widely used in clinical research, it is important that readers can critically

evaluate the use of this technique.

Key words: Cox proportional hazards models, Kaplan–Meier survival curves, statistics, survival analysis

Accepted for publication: 10 October 2011

Introduction

Survival analysis concerns the follow-up in time of individ-

uals from an initial experience or exposure until a discrete

event. It can be used to describe survival of a single group of

patients, but more interestingly, it can also be used to

compare the experience of different groups of patients or

subjects. Its use in contemporary medical literature is

widespread. This article will describe when and why

survival analysis is used, the nature of the data required

for such analyses, the use and interpretation of the

techniques most commonly encountered in medical litera-

ture and finally, consideration will be given to the strengths

and weaknesses of this technique. This will all be illustrated

with reference to ‘open-access’ examples taken from core

medical journals.

Author: Robert Flynn, PhD, MSc, GradStat, Statistician and

Epidemiologist, Medicines Monitoring Unit, University of Dundee,

Ninewells Hospital & Medical School, Dundee, UK

Correspondence: Robert Flynn, Statistician and Epidemiologist,

Medicines Monitoring Unit, University of Dundee, Ninewells

Hospital & Medical School, Dundee DD1 9SY, UK. Telephone:

+44 01382 383119.

E-mails: [email protected]

� 2012 Blackwell Publishing Ltd

Journal of Clinical Nursing, doi: 10.1111/j.1365-2702.2011.04023.x 1

Background

Survival analysis is widely used in clinical and epidemiolog-

ical research. In randomised clinical trials, it is used to

compare the occurrence of outcomes in patients receiving

different treatments to establish which is the most effective

(Dumville et al. 2009, Severe et al. 2010). Observational

(non-randomised) research also makes extensive use of

survival models, to determine and test the existence of

epidemiological association (Versmissen et al. 2008, de

Oliveira et al. 2010). It is worth noting that although

originally developed for the purposes of analysing clinical

data, survival analysis is increasingly being used to analyse

non-medical data, for example, by the financial services

sector (to assess time to default of bank loans) and in

engineering (for example to assess time to failure of a

component). This article will focus on the use of survival

analysis in healthcare.

Why use survival analysis?

When considering the likelihood of an event in a cohort of

patients, an intuitive approach might be to calculate the risk

of an event occurring by measuring the proportion of patients

suffering a particular event after a fixed time period, for

example, the proportion deceased one year after starting a

given treatment. There are, however, several problems with

this simple approach. Some subjects will be known to be alive

after one year, others will be known to be deceased, but a

certain proportion will be ‘lost’ to follow-up, their where-

abouts unknown, perhaps because they have moved house or

emigrated (as discussed later, these are referred to as censored

observations). Because the status of these patients is

unknown, then cannot be included in the one-year analysis,

even though they may have been followed for several weeks

or months. Another issue is that patients who die after

one week will have an equal weighting in the analysis as

those dying after 51 weeks, whereas a patient dying after

53 weeks will not be included in the count of deceased

patients in the one-year analysis. Additionally, the realities of

clinical research are that patients tend to be followed-up for

different periods of time: some patients who are enroled in

the early stages of a study can be easily followed for longer

periods. In the above example of a one-year mortality study,

some patients could have been followed-up for three years;

however, when calculating the one-year mortality rate, the

final two years of follow-up would be ignored. Other

patients, however, may be recruited at the end of a study

and might only be followed-up for a short period, say

six months. These patients would have to be excluded from

the analysis as they would not have sufficient follow-up.

What is needed is a form of analysis that takes into account

these different follow-up times. This is what survival analysis

does.

Structure of survival data

Outcome data

Survival analysis is used when considering the occurrence in a

population of a binary (or dichotomous) outcome: that is,

one that may be either present or absent. This binary

outcome is often death, hence the label ‘survival analysis’;

however, it could also be any event like the onset of acute

illness (such as myocardial infarction or stroke) or chronic

illness (such as onset of diabetes). This is sometimes referred

to as the dependent variable.

Censoring

This important concept relates to subjects who form part of a

cohort but who never suffer the event of interest. This could

be because a patient is ‘lost to follow-up’ (leaves the

population prior to the end of a study), because the study is

completed before the patient suffers the event of interest, or

because the patient suffers another event which stops them

from suffering the principal event of interest (for example,

being hospitalised for infection in a study with hospitalisation

for myocardial infarction as the outcome). Although none of

these subjects suffer the event of interest, the fact that they

contribute time without suffering an event is vitally impor-

tant.

For all the method of survival analysis described in this

article, there is an import assumption that the censoring is

non-informative. That is, censoring is not related to the

probability of an event occurring. This could occur, for

example, if patients left the study population shortly before

dying.

Explanatory variables

Typically two or more different groups of subjects are

considered with the survival experience compared between

these different categories. These two groups could be patients

exposed to different medicines (placebo vs. active), but could

also include other prognostically important factors such as

age or sex. These may also be referred to as predictors or

independent variables. As will be seen, observational studies

in particular tend to include data of a large number of such

variables. It is generally the case that attention is focused on

R Flynn


2 Journal of Clinical Nursing

one explanatory variable in particular with the others being

referred to as covariates.

Survival time

The final next key piece of information is the follow-up time.

This is the interval – usually in days, months or years –

between the start of follow-up for that subject until the

occurrence of the event of interest or until censored. A

summary of commonly used terms and definitions used in

survival analysis is shown in Table 1.

Survival analysis techniques

As will be seen, the output of survival analysis can take the

form of life tables, survival curves, formal hypothesis tests

and measures of relative risk. The use, implementation and

interpretation of these will be discussed in the following

sections.

Simple survival techniques

One of the most widely used techniques is that developed by

Kaplan and Meier (1958). This remains in wide use in

randomised controlled trials but also has a more limited role

to play in observational research. It is a simple technique that

considers at different points the number of patients remaining

in the cohort and the cumulative number of events that have

occurred up to that point. As an example, consider the

hypothetical data shown in Table 2. This shows data on nine

patients enroled in a study in 2006 and 2007 and followed-up

until the end of 2009, with a patient identifier, the dates

between which they were follow, the duration of follow-up

and the outcome (death or censored). These same data are

presented in Fig. 1. Panel a shows these data as timelines,

with an ‘X’ showing deaths and ‘O’ showing censored

observations. By considering the duration of follow-up from

the same baseline (Fig. 1 panel b) and by then putting the

timelines in the order of their duration (Fig. 1 panel c), it

starts to become clear how a survival curve might be

Table 1 Terms and definitions commonly encountered in survival analysis and referred to in this article

Randomised Controlled Trials (RCT) – a clinical trial whereby study subjects (typically patients) are randomly assigned to receive different

interventions, for example, treatment or placebo.

Observational (non-randomised) research – a clinical study where no intervention is instigated by those undertaking the research. The inves-

tigators instead observe exposures and outcomes in groups of patient and draw conclusion from these. Such research may take one of several

recognised study types, for example, cohort study, case-control study or ecological study.

Epidemiological association – a measured relationship between two factors that may or may not be the result of a causal association. Such

associations are often identified in observational studies.

Censoring – This occurs in subjects who are included in the follow-up for a study but who never suffer the event of interest. This may occur if a

patient is lost to follow-up, if the study finishes before the event has occurred, or if the patient suffers another event which excludes them from

follow-up.

Explanatory variables (predictors or independent variables) – prognostically important factors that may be measured for subsequent analyses.

Generally, the focus is on one explanatory variable in particular (for example, exposure to a specific medicine) with the other variables being

referred to as covariates (such as age, sex, exposure to other medicines).

Survival time – the interval (measured in days, months or years) between start of follow-up and the occurrence of the event of interest or until

censored. Also referred to as follow-up time.

Life table – a summary table used to describe the survival experience of population. These are seldom used as where there are a large number of

events or a comparison is made between groups, the table rapidly becomes lengthy and complex.

Survival curves – A curve that shows the proportion of the population ‘surviving’ at successive points in time. This may include two or more

discrete groups that can easily be compared. The Kaplan–Meier survival plot usually compares two groups in a univariate analysis.

Log-rank test – a non-parametric hypothesis test that compares survival curves to see whether any difference that exist is likely to have arisen by

chance.

Confounding variable – a variable that can cause the outcome of interest and which is associated with the principal variable of interest. This can

cause misleading epidemiological associations between independent variables and outcomes.

Cox Proportional Hazard Model – a multivariate proportional hazards survival model that assumes that the impact of variables on the hazard

rate remains constant over time and is multiplicative. This technique is widely used in medical literature, in particular in observational studies.

Hazard Ratio (HR) – a type of relative risk derived from a Cox model. When comparing against a reference group (i.e. a placebo medicine) an

HR > 1 indicates increase risk of an event whilst an HR < 1 indicates reduced risk.

Parametric/non-parametric/semi-parametric survival models – these terms describe the assumptions made in the various survival analysis

methods. The simplest methods are the non- parametric techniques which made no assumption about the underlying distribution (or shape) of

hazard function (e.g. Kaplan–Meier method). Parametric survival models make assumptions about the impact of variables on outcomes and the

shape of the hazard function – at present these are not widely encountered in medical literature. Semi-parametric techniques include the Cox

model and make assumptions about the impact of variables on outcomes but not the shape of the hazard function.

Original article Survival analysis


Journal of Clinical Nursing 3

constructed. The final Kaplan–Meier survival curve (shown in

panel d) is actually derived from the life table shown

in Table 3. This life table shows the survival function – that

is, the probability that an individual will survive until the

given time – which is recalculated as the cumulative

probability of survival since baseline, based on the number

of surviving patients at each point an event occurs.

Although as shown in Table 3 the life table is easy to

comprehend, in studies where there are large numbers of

patients or outcomes, or where there are different groups of

patients being compared, the life table rapidly becomes too

large and unwieldy to be easily interpreted. For this reason,

the Kaplan–Meier survival plot is more commonly used. This

is simply a plot of the survival function against time (Fig. 1

panel d). Where two (or more) groups are involved, these are

displayed as two (or more) separate curves on the same axes.

The nearer the origin the curve is (i.e. the lower it is), the

worse the survival experience is for that group. The approach

Figure 1 Pictorial representation of survival data. panel (a) shows the raw data as timelines as it would be collected in a clinical study, panel (b)

shows the same timelines but all originating at the same baseline, panel (c) shows these ordered by duration of follow-up and panel (d) shows a

survival curve generated using the Kaplan–Meier methodology.

Table 2 Structure of a typical data set for survival analysis

Subject Start of follow-up End of follow-up

Duration

of follow-up (months) Outcome

6 January 2006 4 June 2008 28Æ9 Death

2 28 April 2006 19 November 2006 6Æ7 Censored

3 23 November 2006 2 April 2007 4Æ3 Death

4 6 February 2007 21 December 2009 34Æ5 Censored

5 6 January 2006 21 December 2009 47Æ5 Censored

6 20 December 2006 21 April 2008 16Æ0 Death

7 23 July 2006 30 December 2006 5Æ3 Death

8 31 March 2007 22 August 2008 16Æ8 Death

9 28 March 2006 19 October 2009 42Æ7 Death

R Flynn



of Kaplan and Meier is often referred to as non-parametric as

it makes no assumptions about the underlying distribution of

the data and makes no attempt to describe this numerically.

Whilst it may be clear that there is a difference between two

lines on a Kaplan–Meier survival plot, it might not be clear

whether such differences have arisen by chance or whether

there is actually a meaningful underlying difference. Several

statistics exist that formally test whether there is a statistically

significant difference between two (or more) survival curves.

The most commonly applied of these is the log-rank test. Where

this takes a p-value of <0Æ05 then this would be considered a

statistically significant difference. Other tests do exist but are

not widely used in medical literature.

A good example is seen in a study published by Severe et al.

(2010). This randomised study compared early vs. standar-

dised antiretroviral therapy in HIV infected patients in Haiti.

In two separate survival plots considering time until death

and time until development of tuberculosis, the survival curve

for the standard therapy group is below that of the early

intervention group in each. For both of these, the log-rank

test gave a small p-value (0Æ001 and 0Æ01 respectively)

indicating that these are both statistically significant findings.

The authors concluded that the early intervention approach

resulted in better outcomes.

In another randomised study by Dumville et al. (2009), the

investigators studied the impact of larval therapy (maggots)

on leg ulcers to see whether there was an impact on time-

to-healing and time-to-debridement of the ulcer. In this case,

the time being modelled is that until the onset of a beneficial

outcome (healing of the wound), so the plots are inverted. In

the case of time-to-healing, the two survival curves run more

or less concurrently and there seems to be no difference

between the two treatment groups – this suspicion that there

is no difference in time-to-healing is confirmed by the log-

rank test that has non-significant p-value of 0Æ331. For the

time-to-debridement of the wound, the larvae curve is

substantially higher than the control group indicating a

shorter time until debridement of the wound, a finding that –

with a log-rank test p<0Æ001 – is highly significant.

Whilst this technique is easy to use and interpret, it has its

limitations. Although differences between groups can be seen

and their statistical significance tested, no estimate of the

actual effect size is quantified. In addition where there are

imbalances between groups, as will very likely occur in non-

randomised observational studies, the findings will be prone

to confounding and bias. This cannot be adjusted for with

such a simple analysis. The next section will deal with

multivariate techniques that can address these issues.

Multivariate analysis

Multivariate survival models are widely used in medical

literature with examples of both randomised and observa-

tional studies (Versmissen et al. 2008, Dumville et al. 2009,

de Oliveira et al. 2010, Severe et al. 2010). In randomised

controlled trials, such methodologies can be used where there

is a desire to quantify the size of relative differences between

groups (Severe et al. 2010), where there is the existence of

strong prognostic indicators that could be biasing the results

(Dumville et al. 2009), or where there is a desire to quantify

the impact of other prognostic indicators (Dumville et al.

2009). However, it is in non-randomised observational

studies – where the nature of the data means there are likely

to be confounding variables – that multivariate survival

analyses have had the biggest impact.

The most widely used technique is the Cox Proportional

Hazard Model, developed by Sir David Cox, in a paper which

has become one of the most widely cited (and perhaps least

read) papers with almost 25,000 citations currently recorded

by ISI Web of knowledge (Cox 1972). This technique works

by modelling the hazard function. This is most easily

interpreted as a subject’s risk of suffering the event of interest

at any given time during the follow-up. The model makes no

assumptions about the underlying shape of the hazard, and

no attempt is made to parameterise or describe this numer-

ically. However, it is assumed that the impact of the variables

included is proportional and this part of the model is

parameterised. For this reason, this technique is sometimes

referred to as a semi-parametric approach.

An important consideration is whether there are sufficient

events in the cohort for the study to be valid. Where there are

a large number of covariates included in an analysis, it is

important to check that the analysis is not underpowered.

Typically, it is thought that there should be approximately 10

events per covariate for an analysis to be valid, although there

Table 3 Life table representation of the data from Table 1

Time (months) Number Events

Proportion surviving

until end of period

Cumulative

proportion

surviving

4Æ3 9 1 1 � 1/9 = 0Æ889 0Æ889

5Æ3 8 1 1 � 1/8 = 0Æ875 0Æ778

6Æ7* 7 0 1 � 0/7 = 1Æ000 0Æ778

16Æ0 6 1 1 � 1/6 = 0Æ833 0Æ648

16Æ8 5 1 1 � 1/5 = 0Æ800 0Æ519

28Æ9 4 1 1 � 1/4 = 0Æ750 0Æ389

34Æ5* 3 0 1 � 0/3 = 1Æ000 0Æ389

42Æ7 2 1 1 � 1/2 = 0Æ500 0Æ194

47Æ5* 1 0 1 � 0/1 = 1Æ000 0Æ194

*Censored observations.




is some suggestion that this could be relaxed (Vittinghoff &

McCulloch 2007).

Assumption of proportional hazards

The assumption of proportional hazards is of key impor-

tance, and there are some implications that should be

considered. If the subjects are divided up into four groups

based on their age, it is assumed that the relative impact on

outcome on going from age group 1 to age group 2 would be

the same as going from age group 3 to age group 4. This

assumption can easily be tested by plotting ‘log-minus-log’

plots, something that should always be performed and

reported when using this analysis. It also assumes that the

impact of combined variables is multiplicative, for example,

if men are at double the risk of an adverse event and if

patients with diabetes are also at double the risk, then male

patients with diabetes would have a quadrupled risk overall.

This assumption can easily be tested by modelling interaction

terms, which could – if found to be significant – allow male

patients with diabetes to have a disproportionately high or

low risk. There is also an implicit assumption of a constant

hazard function. This means that it is assumed the instanta-

neous risk of an event remains constant throughout the

duration of follow-up and that the relative difference between

categories also remains constant. Again this assumption can

easily be tested either by plotting log-minus-log plots or by

modelling interactions with time and should always be

reported.

Interpretation of the Cox model

The output from the Cox model is the Hazard Ratio (HR)

which is interpreted in the same way as other relative risks

(see example discussed below). Where the HR is >1, this

indicates there is an increased risk of an event associated with

that variable. Where the HR is below 1, this indicates a

reduced risk. The associated 95% confidence interval (CI)

gives an indication of the statistical uncertainty of the HR

estimate: where these cross 1, this indicates that there is no

statistically significant difference. The Cox model also allows

the plotting of ‘adjusted’ Kaplan–Meier survival curves which

allow the comparison of curves that are balanced for the

other variables in the model.

In the randomised study considering the impact on wound

healing of larval therapy (Dumville et al. 2009), the authors

used a multivariate Cox model to investigate whether any

relationship between the treatment and known prognostic

indicators had an impact on time-to-healing and time-

to-debridement. For both outcomes, this produced results in

line with the unadjusted analysis: a non-significant HRs of

1Æ13 (95% CI 0Æ76–1Æ68) for time-to-healing and a significant

2Æ31 (95% CI 1Æ65–3Æ24) for time-to-debridement of wound.

The advantage here is that the Cox model adjusts for the

impact of other covariates and provides an effect size (a 2Æ3

times increased ‘risk’ of early debridement of the ulcer),

something the Kaplan–Meier approach would not provide.

An observational study using data from a Scotland-wide

health survey looked to see whether there was an association

between frequency of toothbrushing and incidence of car-

diovascular disease, seeking to confirm a biologically plau-

sible association that had previously been observed elsewhere

(de Oliveira et al. 2010). In an observational study like this,

there is a strong likelihood of confounding, particularly

relating to socioeconomic status and health behaviour – this

would mean that any association observed between worse

oral hygiene and cardiovascular outcomes might be because

subjects with lower socioeconomic status were less likely to

brush their teeth regularly and more likely to suffer cardio-

vascular events because of other associated unhealthy behav-

iour. To adjust for this, the authors used a multivariate Cox

model that adjusted for other prognostic indicators including

socioeconomic status. The results show that, for a simple

model which took into account only age and sex, there is a

strong association between cardiovascular disease and tooth-

bushing twice daily vs. less than once daily: HR 2Æ3 (95% CI

1Æ8–3Æ1). However, when a more complex Cox model was

used that incorporated socioeconomic status as a variable, the

relationship remained but was weaker with a HR of 1Æ7 (95%

CI 1Æ3–2Æ3). This implies that the association between

toothbrushing and cardiovascular outcomes is partly con-

founded by socioeconomic status, but that an association

remains after this is taken into account.

Figure 2 shows an example of Kaplan–Meier survival

curves. In this study, the authors were attempting to establish

whether there was an association between thyroid-stimulat-

ing hormone (TSH) serum concentration and cardiovascular

morbidity and mortality in patient receiving long-term

thyroxine (Flynn et al. 2010). In this case, the TSH is an

indicator of whether the patient is being over or undertreated

with thyroxine – ‘high’ TSH indicating undertreatment,

‘normal’ TSH indicating appropriate treatment control and

‘low’ and ‘suppressed’ indicating overtreatment. The survival

curves shown were ‘adjusted’, that is, they were derived from

a Cox model so that the four groups were balanced for the

various covariates included in the analysis (see Fig. 2 for

details). They show increased risk of cardiovascular events

for patients with a high and suppressed TSH compared with a

normal (p < 0Æ0001 for both), but no difference between

patients with normal and low TSH (p = 0Æ084).

R Flynn



Time-dependent variables

Extensions and alternatives to the Cox proportional hazards

model are sometimes encountered in medical research. Data

from both clinical trials and observational studies sometimes

use the Cox model with a ‘time-dependent variable’ or ‘time

varying covariate’. This allows for the fact that during

follow-up, patients may spend some periods of time both

exposed and not exposed to the variable of interest. For

example, in an observational study considering the efficacy of

statins in familial hypercholesterolemia (Versmissen et al.

2008), the authors were aware that during a total of

16,792 years of follow-up amongst the 1950 individuals,

patients were likely to spend some periods of time taking

statins and other periods not taking statins. To allow for this

in their analysis, they entered statins as a time-dependent

variable so that events that occurred whilst exposed were

considered separately to events that occurred whilst not

exposed. In this situation, the resulting HR is interpreted the

same way as for any other Cox model (i.e. where the HR is

<1, then the effect is protective and if it is greater, the effect

is associated with greater harm). In the study mentioned

above, it was concluded that use of statins had a HR of 0Æ18,

indicating an 82% reduction in the rate of coronary heart

disease associated with statin use.

It is worth noting that where a time-dependent variable is

used, it is not possible to plot survival curves: survival curves

are based on fixed categories of patients that are usually

defined at baseline – however, where a time-dependent

variable is used, patients may be switching between catego-

ries during follow-up.

Parametric survival models

Another extension of the techniques discussed above is the

use of fully parametric survival models such as the acceler-

ated failure time models. Here, assumptions are made about

both the impact of the variables considered and the shape of

the underlying survival function (i.e. the shape of the survival

curve). These assumptions allow stronger inferences to be

made and these have several implications. Whereas the Cox

proportional hazards approach models the impact of vari-

ables on the hazard function, parametric analyses typically

model the impact of variables directly on survival time. This

means the interpretation of the model differs from the Cox

model with the output relating directly to the duration of

survival, thus allowing an inference to be made about the

actual time until the event. This also means that for a given

set of variables, it is possible to calculate what would be the

‘mean’ survival time. In many ways, this might be easier to

interpret, especially for patients who may struggle with the

concept of relative risks. Another implication is that risk

estimates are calculated that typically have narrower CIs

implying a reduced level of statistical uncertainty; however, it

should be remembered that the assumptions made might lead

to a less stable or inaccurate representation of the data. A

further advantage of these parametric models is that it is

possible to incorporate non-constant hazard functions.

Whereas the Cox model has the assumption that the risk of

an event remains constant with time, the Weibull parametric

model allows the inclusion of a risk that, in time, may either

increase (e.g. increasing risk of cardiovascular disease) or

decrease (e.g. risk of death following a road traffic accident).

A model commonly encountered is that which assumes an

exponential function – this is essentially a constant hazard

function and should in many respects yield conclusions

similar to that from the Cox model. Other advantages of

these models are briefly, but clearly discussed by May et al.

(2003). Here, it is shown that by making basic assumptions,

it is possible to build a more useful model that allows an

estimate of survival functions to be made where very few or

no events occur. This paper also shows how parametric

methods give narrower CI limits.

Despite the advantage of such models, they remain

relatively uncommon in medical literature, perhaps because

of the problem of easily interpreting models where risk is

changing throughout the course of the study or perhaps

because of the ubiquitous nature of the Cox models which is

so well established and widely used. Readers wishing to

Figure 2 Adjusted survival curve derived from a Cox model showing

time to cardiovascular admission or death (adjusted for age, sex,

history of hyperthyroidism, history of cardiovascular disease, socio-

economic status and diabetic status). There were increased events for

patients with a high thyroid-stimulating hormone (TSH)

(p < 0Æ0001) and those with a suppressed TSH (p < 0Æ0001) com-

pared with a normal TSH, but no difference between normal and low

TSH (p < 0Æ084) (Flynn et al. 2010). Copyright 2010, The Endo-

crine Society.




explore these parametric survival models are directed to the

bibliography for further reading.

Strengths

There are some advantages in using survival analysis

techniques. As stated above, they enable a very efficient

use of data where there are varying durations of follow-up

(as is often the case with clinical data); to use any other

form of analysis where there is a dichotomous outcome

would represent a waste of potentially valuable informa-

tion.

The widespread use of survival analyses, especially

involving Kaplan–Meier survival curves and the Cox pro-

portional hazards models means that these methodologies

are widely understood and that there is good knowledge on

how to interpret them. Another advantage is the ability to

adjust for potentially confounding variables which has

resulted in the Cox model being commonly used in obser-

vational studies.

Weaknesses

The limitations of survival analysis stem from the nature of

the methodology and the assumptions involved when using

them. Survival analysis cannot be used where there is a

continuous outcome measure, for example, blood pressure or

serum creatinine concentration. Another potential issue is

with attrition of the cohort, and it should always be made

clear how many patients survive to the end of follow-up.

Although studies will have plenty of subjects in the early

stages of follow-up, by the final stage, towards the end there

might be very few subjects involved with the result that the

survival curve might be subject to a considerable degree of

statistical uncertainty – ideally, the actual number of patients

still exposed should be made clear under the x-axis of a

Kaplan–Meier survival plot, as in the case by Severe et al.

(2010).

The assumptions that are so important in underpinning the

model may often be violated or inadequately checked. In

particular, the assumption that there is a constant hazard

function is often not true, something that is especially likely

over a protracted time period. Where such a situation arises,

another type of model should be considered, for example, the

Weibull survival model, although interpretation will not be as

straightforward. As with other statistical modelling tech-

niques, where a continuous variable is included as a potential

predictor, there is an implicit assumption of linearity, so that

the difference in risk in individuals between ages 20–30 years

will be the same as the difference between 75 and 85 years.

Although this might often be a reasonable assumption, there

will obviously be occasions where this assumption is not

valid. In such cases, it might be more appropriate to

categorise the continuous variables (for example, expressing

age in groups). Alternatively, a continuous variable could be

fitted as a fraction polynomial which allows for the nonlinear

modelling of continuous variables (Sauerbrei et al. 1999);

however, this again can be hard to explain and interpret. The

ease and speed with which modern statistical software can

produce such a model means it is very easy for errors to be

unintentionally introduced!

Conclusion

In summary, survival analysis techniques are valuable and

widely used tools when analysing data that have a binary (or

dichotomous) outcome in subjects with uneven follow-up

time. These techniques are easy to use and are readily

interpreted by readers without the need for detailed under-

standing of statistical methods (see Table 1 for a list of

commonly encountered terminology). Although easy and

widespread, there are several challenges, assumptions and

difficulties that may be encountered and these should always

be reported by investigators and carefully considered by

readers. A variety of more advanced techniques can be

employed to enhance the analyses. Although not yet widely

employed, it seems like that these techniques will become

increasingly widespread over the coming years.

Relevance to clinical practice

Survival analysis is widely encountered in clinical literature

for describing both observational research as well as rando-

mised controlled trials. It is important that readers can

understand and critically evaluate the use of this technique.

Contributions

Study design: RF; data collection and analysis: RF and

manuscript preparation: RF.

Conflict of interest

The author has no conflicts of interest to declare.

R Flynn



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