Relative survival, AER and SMR based on French death rates

Description

Relative survival, AER and SMR based on French death rates

Author(s)

Jean-Philippe Jais and Hugo Varet

Absolute Excess Risk (AER)

Description

Computes the AER, its confidence interval and its associated p-value

Usage

AER(
  futime,
  status,
  age,
  sex,
  entry_date,
  PY.stand = 10000,
  ratetable = survexp.fr::survexp.fr,
  alpha = 0.05
)

Arguments

Details

The Absolute Excess Risk (AER) is defined as:

AER = O-E

where O is the observed number of deaths and E is the expected number based on the patients'characteristics (sex, age and entry date in the study). This function uses an additive Poisson model to compute the AER.

Value

A list containing the AER with the corresponding number of person-years (PY.stand argument), its confidence interval, its p-value, the observed number of deaths, the expected number of deaths and the observed number of person-years

Author(s)

Jean-Philippe Jais and Hugo Varet

References

N. Breslow and N. Day, Statistical methods in cancer research, Volume II - The design and analysis of cohort studies, World Health Organization, 1987

P. Dickman, A. Sloggett, M. Hills and T. Hakulinen, Regression models for relative survival, Statistics in Medicine, 2004

C. Elie, Y. De Rycke, J.-P. Jais and P. Landais, Appraising relative and excess mortality in population-based studies of chronic diseases such as end-stage renal disease, Clinical Epidemiology, 2011

Examples

attach(data.example)
AER(futime, status, age, sex, entry_date)

Log-Rank test between an observed and an expected survival curve

Description

Log-Rank test between an observed and an expected survival curve

Usage

LR(futime, status, age, sex, entry_date, ratetable = survexp.fr::survexp.fr)

Arguments

Details

The Log-Rank is calculated as:

LR = (O-E)^2/E

where O is the observed number of deaths and E is the expected number based on the patients' characteristics (sex, age and entry date in the study). It follows a Khi-2 distribution with one degree of freedom, which allows to compute its p-value.

Value

A list containing the observed number of deaths, the expected number of deaths, the Log-Rank statistic and its p-value

Author(s)

Hugo Varet

References

R. Peto and J. Peto, Asymptotically Efficient Rank Invariant Test Procedures, Journal of the Royal Statistical Society, 1972

Examples

attach(data.example)
LR(futime, status, age, sex, entry_date)

Standardized Mortality Ratio (SMR)

Description

Computes the SMR, its confidence interval and its associated p-value

Usage

SMR(
  futime,
  status,
  age,
  sex,
  entry_date,
  ratetable = survexp.fr::survexp.fr,
  alpha = 0.05
)

Arguments

Details

The SMR is estimated using two different methods.

The classic method is:

SMR = O/E

where O is the observed number of deaths and E is the expected number based on the patients' characteristics (sex, age and entry date in the study).

The SMR is also estimated performing a Poisson model where O is the dependant variable and E is an offset.

Value

A list containing the observed number of deaths, the expected number of deaths, the "classic" SMR (with its confidence interval and its p-value) and the SMR calculated by a Poisson model (with its confidence interval and its p-value)

Author(s)

Jean-Philippe Jais and Hugo Varet

References

N. Breslow and N. Day, Statistical methods in cancer research, Volume II - The design and analysis of cohort studies, World Health Organization, 1987

Examples

attach(data.example)
SMR(futime, status, age, sex, entry_date)

Example data to illustrate the functions

Description

Example data to illustrate the functions

Format

A data frame with 200 observations on the following 5 variables.

sex

"male" or "female"

age

age in days

entry_date

entry date in the study

status

status at follow-up time: 0 if alive, 1 if dead

futime

follow-up time in days

French data for the expected survival and person years functions

Description

French data for the expected survival and person years functions

Details

Death rates are available from 1977 to 2022 for males and females aged from 0 to 99

Source

https://www.ined.fr/fichier/s_rubrique/193/fr_t68_2022.fr.xlsx

References

Institut national d'études démographiques

Observed Kaplan-Meier, expected and relative survival curves

Description

Displays the observed Kaplan-Meier, expected and relative survival curves

Usage

survexp_plot(
  futime,
  status,
  age,
  sex,
  entry_date,
  ratetable = survexp.fr::survexp.fr,
  main = "Observed and expected survival",
  xlab = "Time (years)",
  ylab = "Survival",
  col.km = "black",
  lwd.km = 2,
  lty.km = 1,
  conf.int.km = TRUE,
  col.exp = "blue",
  lwd.exp = 2,
  lty.exp = 1,
  main.rel = "Relative survival",
  ylab.rel = "Relative survival",
  col.rel = "black",
  lwd.rel = 2,
  lty.rel = 1,
  times = seq(0, max(futime, na.rm = TRUE)/365.241, length = 6)[-1],
  alpha = 0.05,
  xscale = 365.241,
  ...
)

Arguments

Details

This function displays the observed and expected survivals, and the relative survival which is defined as:

r(t) = exp(-exp(\beta) \times t)

where exp(\beta) is the excess risk by time unit estimated by an additive Poisson model.

Value

A matrix containing the values of relative survivals and their confidence intervals for each time of times

Author(s)

Hugo Varet

References

M. Pohar and J. Stare, Making relative survival analysis relatively easy, Computers in Biology and Medicine, 2007

M. Pohar and J. Stare, Relative survival analysis in R, Computers Methods and Programs in Biomedicine, 2006

Examples

attach(data.example)
survexp_plot(futime, status, age, sex, entry_date)