Keywords:
Expected Survival;
Epidemiologic Methods; Follow-
up Studies; Life Tables; One-
sample log-rank test;
Standardized Mortality Ratio;
Survival Analysis
Corresponding author:
Adelino F. Leite-Moreira
amoreira@med.up.pt
Confict of interest:
The authors declare no confict
of interests.
First published: 22JUN2021
EXTENDED ABSTRACT
© 2020 The Authors. This is an open access article distributed under CC BY license, whis license allows reusers
to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given
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Open Access
Publication
J. Stat. Health Decis. 2021;3(1):52-53 | https://doi.org/10.34624/jshd.v3i1.24853 52
A16 Comparing one sample’s observed survival with the
expected in the general population or in specifc high-
risk subgroups
Raquel Moreira
1
, Francisca A. Saraiva
1
, Rui J. Cerqueira
1,2
, Ana F. Ferreira
1
, Mário J.
Amorim
1,2
, António S. Barros
1
, Paulo Pinho
2
, André P. Lourenço
1,3
, Adelino F. Leite-Moreira
1,2
1
Cardiovascular Research and Development Center, Department of Surgery and Physiology, Faculty of Medicine of the University of Porto, Porto, Portugal;
2
Department of Cardiothoracic Surgery, Centro Hospitalar Universitário São João, Porto, Portugal;
3
Department of Anesthesiology, Centro Hospitalar Universitário São João, Porto, Portugal
Introduction
There are doubts if a certain therapy is safe in some diseases. End-stage renal disease (ESRD) is an
example for which patient’s life expectancy is reduced. The high rate of comorbidities and therapy adjust-
ments has been a major concern. Whether these patients would beneft from an invasive procedure needs to
be evaluated since their fragile clinical status may result in reduced survival, regardless of the intervention.
The knowledge about which/when would the outcomes of high-risk patients be observed is of utmost relev-
ance, using previous studies or registries.
The most frequently reported method to compare the observed patient’s survival with the expected in
the general population uses life tables and a one-sample log-rank test (1, 2). However, life tables available
in each country limit the analysis to comparisons with the general population. It is diffcult to extrapolate
about the impact of an intervention in specifc patients, e.g. ESRD, to a population with the same disease but
with no intervention, since there are no adequate registries in those subgroups. To surpass this caveat, we
considered the paper from Guyot et al. who depicted the process of digitising Kaplan-Meier (KM) curves
to extract survival statistics (3).
The aim of this study was to explore two methods of comparing the observed survival of our ESRD
patients submitted to coronary artery bypass grafting (CABG) with (i) the expected survival in the general
population, age and sex-matched; and (ii) the expected survival in a haemodialysis (HD) population not
submitted to CABG.
Methods
Single-centre retrospective study including consecutive HD patients submitted to CABG. To compare
the observed survival of the sample with the expected in general population we used the one-sample log-
rank test, available at http://biostatistics.mgh.harvard.edu/biostatistics/resources.html as an excel spread-
sheet with a supplement (4). Data from the observed sample, (age at operation, gender, race and follow-up
(FUP) time) were introduced. To determine the time-to-event in the general population, the annual death
rate for each age during the FUP time, adjusted for age, gender and race, obtained through https://
www.ine.pt/ was inserted. The survival rate in the sample at each year after diagnosis results from
dividing the sum of N survival rates at each time by the number of patients .The
expected number of deaths is calculated by cumulative death rates at last FUP for all patients and for each
year after diagnosis: .This expected number of deaths (E) results from adding the
cumulative death rate at the last age of FUP (t
i
) over the sample size . The software cal-
culates the expected survival for a similar subject in the population and a standardized mortality ratio
(SMR).
Using GetData Graph Digitizer 2.26 (http://getdata-graph-digitizer.com/), we imported and digitised
the curve from Almeida et al. (5) reporting the survival of Portuguese HD patients; and the KM curve from
our sample. A delineation of each curve was done and two ASCII (text) fles, were exported. An event table
was built considering the number of patients at risk provided for each year. These fles were imported by an
R script to read the number at risk at each time point and calculate approximations of number of censored
on each interval, i; adjusting the total number at risk and number of events within each i according to KM
estimates from curves. It obtains individual patient data (time, event and group). Finally, the coxph formula
to estimate hazard ratio (HR) and confdence intervals through Cox proportional hazard regression was
applied.