| Title: | Inference About the Standardized Mortality Ratio when Evaluating the Effect of a Screening Program on Survival |
|---|---|
| Description: | Functions to make inference about the standardized mortality ratio (SMR) when evaluating the effect of a screening program. The package is based on methods described in Sasieni (2003) <doi: 10.1097/00001648-200301000-00026> and Talbot et al. (2011) <doi: 10.1002/sim.4334>. |
| Authors: | Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal |
| Maintainer: | Denis Talbot <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.2 |
| Built: | 2025-02-14 06:12:08 UTC |
| Source: | https://github.com/cran/InferenceSMR |
contrib is a function that finds out how much time was contributed for every combination
of the incidence covariates, the survival covariates, and follow up time.
Using these contibutions makes the calculation of the variance of the expected number
of deaths much more efficient than making the calculations on the raw data.
contrib(start_follow, end_follow, incid_cov, surv_cov, follow_up, increment)contrib(start_follow, end_follow, incid_cov, surv_cov, follow_up, increment)
start_follow |
A vector that contains the amount of follow-up time elapsed when this set of covariate values started. |
end_follow |
A vector that contains the amount of follow-up time that will have elapsed when this set of covariate values changes or when follow-up ends. |
incid_cov |
A vector that contains the values of the covariates for incidence. |
surv_cov |
A vector that contains the values of the covariates for survival. |
follow_up |
A vector that contains the total follow-up time for that individual. |
increment |
The value of the time increment that will be used for Sasieni's estimator and variance (a numeric). |
If only time independent covariates are used, then all vectors are of dimension n = sample size.
Otherwise, the function contrib needs an augmented dataset, in which each
person-time corresponds to one row. Each row contains the values of the
time-invariant covariates and the updated values of time-dependent variables.
Therefore, the covariates must have a finite number of values (they must be discrete).
For example, if only the covariate “age” is used for incidence and survival, an individual followed for 3.4 years that was 54.6 years at the begining of the study should be entered as follow:
#start_follow, end_follow, incid_cov, surv_cov, follow_up 0 0.4 54 54 3.4 0.4 1.4 55 55 3.4 1.4 2.4 56 56 3.4 2.4 3.4 57 57 3.4
An example of the code required to do such a thing is provided in the screening dataset help page.
The resulting list is directly usable in functions est.expDeath, var.expDeath and inference.SMR. The list contains the following elements :
contrib |
A matrix giving the total time contributed for every combination of discretized follow-up times, incidence covariates and survival covariates. |
ncov.incid |
The number of covariates for incidence. |
ncov.surv |
The number of covariates for survival. |
increment |
The increment used for discretization of follow-up times. |
Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal.
est.expDeath, var.expDeath, inference.SMR, screening
Estimation of the expected number of deaths in a screening program using the method proposed by Sasieni (2003).
est.expDeath(contribution, incid, cox, fuzz, covnames)est.expDeath(contribution, incid, cox, fuzz, covnames)
contribution |
An object of contributions produced by the function |
incid |
A matrix containing: the incidences, the value of the covariates and the person-years at risk, in that order. It can be obtained with the function |
cox |
An oject of class |
fuzz |
Numerical precision is problematic when it comes to test equality between objects. The option |
covnames |
An alphanumeric vector containing the names of the covariates used to estimate the survival in the cohort of non-participants, that is, the names of the covariates used to obtain the |
Returns the expected number of deaths
A complete example of usage is provided in the help page of the screening dataset.
Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal.
Sasieni P. (2003) On the expected number of cancer deaths during follow-up of an initially cancer-free cohort. Epidemiology, 14, 108-110.
var.expDeath,inference.SMR, screening
#This example uses pre-built objects and shows the simple usage #of the est.expDeath function when those objects already exists. #For an example of how to built those object, refer to the #help page of the screening dataset. data(req.objects); cox.data = req.objects$cox.data; #Remove "#" to run example : #est.expDeath(req.objects$contribution,req.objects$incid,req.objects$cox,fuzz = 0.01, #req.objects$covnames); #[1] 33.44264#This example uses pre-built objects and shows the simple usage #of the est.expDeath function when those objects already exists. #For an example of how to built those object, refer to the #help page of the screening dataset. data(req.objects); cox.data = req.objects$cox.data; #Remove "#" to run example : #est.expDeath(req.objects$contribution,req.objects$incid,req.objects$cox,fuzz = 0.01, #req.objects$covnames); #[1] 33.44264
A function to calculate incidence rates for every combination of age and calendar years.
incidences(age_min, age_max, year_min, year_max, follow_up, start_age, start_year, case)incidences(age_min, age_max, year_min, year_max, follow_up, start_age, start_year, case)
age_min |
The age at which incidences should begin to be calculated. |
age_max |
The age at which incidences should stop to be calculated. |
year_min |
The calendar year at which indicidences should begin to be calculated. |
year_max |
The calendar year at which incidences should stop to be calculated. |
follow_up |
A vector of dimension |
start_age |
A vector of dimension |
start_year |
A vector of dimension |
case |
A vector of dimension |
This function can be used to obtain incidences for the functions est.expDeath, var.expDeath and inference.SMR. A complete example of usage is provided in the help page of the screening dataset.
A matrix whose first column is the number of person-years at risk, the second column is the calendar years, the third column is the ages and the fourth column is the incidence rates.
Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal.
est.expDeath, var.expDeath, inference.SMR, screening
This function estimates the expected number of deaths, its variance, the SMR and confidence intervals about the SMR.
inference.SMR(obs.death, normal = "log-smr", alpha = 0.05, contribution, incid, cox, fuzz = 0.01, Poisson = FALSE, covnames)inference.SMR(obs.death, normal = "log-smr", alpha = 0.05, contribution, incid, cox, fuzz = 0.01, Poisson = FALSE, covnames)
obs.death |
The observed number of deaths for the people participating in the screening program. A numeric value. |
normal |
Indicates at which level should the normality assumption be made, either at the SMR level, at the log-SMR level or at the root-SMR level. A character vector containing one or many of the following elements “smr”, “log-smr” and “root-smr”. |
alpha |
The nominal error rate of the confidence intervals. A numeric value between 0 and 1, e.g. 0.05 to obtain a 95 |
contribution |
An object of contributions produced by the function |
incid |
A matrix containing: the incidences, the value of the covariates and the person-years at risk, in that order. It can be obtained with the function |
cox |
An oject of class |
fuzz |
Numerical precision is problematic when it comes to test equality between objects. The option |
Poisson |
Indicates whether the incidences' variance should be estimated with a Poisson distribution (TRUE) or a binomial distribution (FALSE). The default is FALSE. |
covnames |
An alphanumeric vector containing the names of the covariates used to estimate the survival in the cohort of non-participants, that is, the names of the covariates used to obtain the |
The inference.SMR function estimates the expected number of deaths as in Sasieni (2003), estimates the variance of the expected number of deaths and builds confidence intervals as in Talbot et al. (2011). As suggested in the latter, the variance of the observed number of deaths is estimated by the observed number of deaths.
expected |
The expected number of deaths |
obs.death |
The observed number of deaths |
variance |
The variance of the expected number of deaths |
smr |
The standardized mortality ratio |
smr.var |
The variance of the SMR. Only returned if “smr” was given in the |
smr.ci |
A 1- |
logSMR.var |
The variance of the natural logarithm of the SMR. Only returned if “log-smr” was given in the |
logSMR.ci |
A 1- |
rootSMR.var |
The variance of the square root of the SMR. Only returned if “root-smr” was given in the |
rootSMR.ci |
A 1- |
A complete example of usage is provided in the help page of the screening dataset.
Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal.
Sasieni P. (2003) On the expected number of cancer deaths during follow-up of an initially cancer-free cohort. Epidemiology, 14, 108-110.
Talbot, D., Duchesne, T., Brisson, J., Vandal, N. (2011) Variance estimation and confidence intervals for the standardized mortality ratio with application to the assessment of a cancer screening program, Statistics in Medicine, 30, 3024-3037.
est.expDeath, var.expDeath, screening
#This example uses pre-built objects and shows the simple usage #of the est.expDeath function when those objects already exist. #For an example of how to build those objects, refer to the #help page of the screening dataset. #Estimating the variance can be very long even in this small sample example, e.g. a few hours. #Remove "#" to run example : #data(req.objects); #cox.data = req.objects$cox.data; #results = inference.SMR(obs.death = sum(screening$deathSCN), # normal = c("smr", "log-smr", "root-smr"), # alpha = 0.05, req.objects$contribution, req.objects$incid, # cox = req.objects$cox, fuzz = 0.01, Poisson = TRUE, req.objects$covnames); #******** INFERENCE ABOUT THE SMR ********* # #Observed = 18 Expected = 33.44264 #Obs.var. = 18 Exp.var. = 39.38153 #SMR = 0.5382351 # # 95 % Confidence intervals with normality assumption at : # #The SMR level : ( 0.2204119 0.8560583 ) # #The log-SMR level : ( 0.2982118 0.9714471 ) # #The root-SMR level : ( 0.2673299 0.9029762 ) #results # #$expected #[1] 33.44264 # #$obs.death #[1] 18 # #$variance # 2 #[1,] 39.38153 # #$smr #[1] 0.5400112 # #$smr.var # 2 #[1,] 0.02629511 # #$smr.ci #[1] 0.2204119 0.8560583 # #$logSMR.var # 2 #[1,] 0.09076763 # #$logSMR.ci #[1] 0.2982118 0.9714471 # #$rootSMR.var # 2 #[1,] 0.01221358 # #$rootSMR.ci #[1] 0.2673299 0.9029762#This example uses pre-built objects and shows the simple usage #of the est.expDeath function when those objects already exist. #For an example of how to build those objects, refer to the #help page of the screening dataset. #Estimating the variance can be very long even in this small sample example, e.g. a few hours. #Remove "#" to run example : #data(req.objects); #cox.data = req.objects$cox.data; #results = inference.SMR(obs.death = sum(screening$deathSCN), # normal = c("smr", "log-smr", "root-smr"), # alpha = 0.05, req.objects$contribution, req.objects$incid, # cox = req.objects$cox, fuzz = 0.01, Poisson = TRUE, req.objects$covnames); #******** INFERENCE ABOUT THE SMR ********* # #Observed = 18 Expected = 33.44264 #Obs.var. = 18 Exp.var. = 39.38153 #SMR = 0.5382351 # # 95 % Confidence intervals with normality assumption at : # #The SMR level : ( 0.2204119 0.8560583 ) # #The log-SMR level : ( 0.2982118 0.9714471 ) # #The root-SMR level : ( 0.2673299 0.9029762 ) #results # #$expected #[1] 33.44264 # #$obs.death #[1] 18 # #$variance # 2 #[1,] 39.38153 # #$smr #[1] 0.5400112 # #$smr.var # 2 #[1,] 0.02629511 # #$smr.ci #[1] 0.2204119 0.8560583 # #$logSMR.var # 2 #[1,] 0.09076763 # #$logSMR.ci #[1] 0.2982118 0.9714471 # #$rootSMR.var # 2 #[1,] 0.01221358 # #$rootSMR.ci #[1] 0.2673299 0.9029762
This dataset contains a simulated population of size 10,000. The population was simulated as described in Talbot et al (2011).
data(screening)data(screening)
A data frame with 10000 observations on the following 12 variables.
yearSCNYear at which the person would become a participant in the screening program
ageSCNAge at which the person would become a participant in the screening program
yearONSYear at which the disease onset would happen for a non-participant
deathBCIndicator variable that has a value of 1 if the non-participant dies from the screened disease, 0 otherwise.
ageFLAge at which the person is eligible to the screening program for the first time
yearFLYear at which the person is eligible to the screening program for the first time
followONSFollow-up time for a non-participant after the disease onset
followSCNFollow-up time as participant in the screening program
participIndicator variable that has a value of 1 if the individual eventually became a participant in the screening program, 0 otherwise
OnsetIndicator variable that has a value of 1 if the disease onset happens while the person is a non-participant
endYear at which the follow-up ends
deathSCNIndicator variable that has a value of 1 if the participants dies from the screened disease, 0 otherwise.
Note that even though there are no missing values in the dataset, some events do not occur. For example, if yearsSCN has a greater value than end, then the inidividual never becomes a participant.
require(survival); #load survival package; data(screening); head(screening); #Data to be used in the example; NB = nrow(screening); #Sample size #Be careful with R round function. If it was used to obtain discrete value, then #fuzz option should be used for expected and expected variance i=1:NB yearSCN<-screening[i,1]; #Year at which the woman started participating ageSCN<-screening[i,2]; #Age at which the woman started participating yearONS<-screening[i,3]; #Year of breast cancer diagnosis deathBC<-screening[i,4]; #Death by breast cancer indicator for non-participating woman. ageFL<-screening[i,5]; #Age at which the woman became eligible yearFL<-screening[i,6]; #Year at which the woman became eligible followONS<-screening[i,7]; #Follow-up time after disease onset for a non-participant followSCN<-screening[i,8]; #Follow-up time as a participant in the screening program particip<-screening[i,9]; #Indicator that the woman participated into the screening #program at some point Onset<-screening[i,10]; #Indicator that the non-participating woman got breast cancer end<-screening[i,11]; #year of eligibility end. deathSCN<-screening[i,12]; #Death by breast cancer indicator for participating woman. nb_onset=length(Onset[Onset==1]); #Number of women with breast cancer #Objects that will containt covariates for the Cox model year<-numeric(nb_onset); age1<-numeric(nb_onset); age2<-numeric(nb_onset); age3<-numeric(nb_onset); age4<-numeric(nb_onset); ti<-numeric(nb_onset); year[yearONS[Onset==1] <= 3] = 1; #Indicator that diagnosis happened before year 3 year[yearONS[Onset==1] > 3] = 0; #Indicator that diagnosis happened before year 3 age1[ageSCN[Onset==1] < 55] = 1; #Indicator that age at diagnosis is smaller than 55 age1[ageSCN[Onset==1] >= 55] = 0; #Indicator that age at diagnosis is smaller than 55 age2[ageSCN[Onset==1] >= 55 & ageSCN[Onset==1] < 60] = 1; #... >= 55 and < 60 age2[ageSCN[Onset==1] < 55 | ageSCN[Onset==1] >= 60] = 0; #... >= 55 and < 60 age3[ageSCN[Onset==1] >= 60 & ageSCN[Onset==1] < 65] = 1; #... >= 60 and < 65 age3[ageSCN[Onset==1] < 60 | ageSCN[Onset==1] >= 65] = 0; #... >= 60 and < 65 age4[ageSCN[Onset==1] >= 65 & ageSCN[Onset==1] < 70] = 1; #... >= 65 and < 70 age4[ageSCN[Onset==1] < 65 | ageSCN[Onset==1] >= 70] = 0; #... >= 65 and < 70 cox.data = data.frame(followONS = followONS[Onset == 1], deathBC = deathBC[Onset == 1], year, age1, age2, age3, age4); x<-coxph(Surv(time = followONS, event = deathBC, type = 'right')~ year + age1 + age2 + age3 + age4, data = cox.data, method="breslow",control=coxph.control(iter.max=100)) #Creating a matrix with many more lines than what will be used new_data<-matrix(0,nrow=12*sum(particip),ncol=10); #Creating a matrix containing data in a new form. #Each line contains stable covariates, so that a #given individual might be divided on many lines. #For example, if only the covariate age is used for incidence and survival, #an individual followed for 3.4 years that was 54.6 years at the begining #of the study should be entered as follow: #start_follow, end_follow, incid_cov, surv_cov, follow_up #0 0.4 54 54 3.4 #0.4 1.4 55 55 3.4 #1.4 2.4 56 56 3.4 #2.4 3.4 57 57 3.4 r=1 for(i in seq(1,length(ageFL))[particip==1]) { X = followSCN[i]; dep_t = yearSCN[i]; age_t = ageSCN[i]; while(dep_t - yearSCN[i] < X) { Y = min(floor(age_t) + 1 - age_t, floor(dep_t) + 1 - dep_t); if(dep_t - yearSCN[i] + Y >= X) { new_data[r,]<-c(floor(age_t), floor(dep_t), age_t < 55, (age_t >= 55 && age_t < 60), (age_t >= 60 && age_t < 65), (age_t >=65 && age_t <70), dep_t < 3, dep_t - yearSCN[i], X, followSCN[i]); } else { new_data[r,]<-c(floor(age_t), floor(dep_t), age_t < 55, (age_t >= 55 && age_t < 60), (age_t >= 60 && age_t < 65), (age_t >=65 && age_t <70), dep_t < 3, dep_t - yearSCN[i], dep_t - yearSCN[i] + Y, followSCN[i]); } dep_t = dep_t + Y; age_t = age_t + Y; r = r + 1; } } new_data<-new_data[new_data[,1]!=0,]; new_data[1:10,]; #Calculate incidences with incidences function: #follow up time as non-participant: follow_up = apply(cbind(end - yearFL,yearONS - yearFL,yearSCN - yearFL),1,min); incid = incidences(50,75,0,5,follow_up,ageFL,yearFL,Onset); #Calculate contributions with contrib function: start_follow = new_data[,8]; end_follow = new_data[,9]; incid_cov = new_data[,c(2,1)]; surv_cov = data.frame(new_data[,c(7,3,4,5,6)]); follow_up = new_data[,10]; increment = 0.5; #Remove following "#" to run example : #contribution = contrib(start_follow, end_follow, incid_cov, surv_cov, #follow_up, increment); #est.expDeath(contribution,incid,x,fuzz = 0.01, #covnames = c("year", "age1", "age2", "age3", "age4")); #Estimating the variance can be very long even in this small sample example, e.g. a few hours. #Remove the "#" to run example: #var.expDeath(contribution,incid,x,fuzz = 0.01, #covnames = c("year", "age1", "age2", "age3", "age4")); #Estimating the variance can be very long even in this small sample example, e.g. a few hours. #Remove the "#" to run example: #results = inference.SMR(obs.death = sum(deathSCN), normal = c("smr", "log-smr", "root-smr"), # alpha = 0.05, contribution, incid, cox = x, fuzz = 0.01, Poisson = TRUE, # covnames = c("annees", "age1", "age2", "age3", "age4")); #******** INFERENCE ABOUT THE SMR ********* # #Observed = 18 Expected = 33.44264 #Obs.var. = 18 Exp.var. = 39.38153 #SMR = 0.5382351 # # 95 % Confidence intervals with normality assumption at : # #The SMR level : ( 0.2204119 0.8560583 ) # #The log-SMR level : ( 0.2982118 0.9714471 ) # #The root-SMR level : ( 0.2673299 0.9029762 ) #results # #$expected #[1] 33.44264 # #$obs.death #[1] 18 # #$variance # 2 #[1,] 39.38153 # #$smr #[1] 0.5400112 # #$smr.var # 2 #[1,] 0.02629511 # #$smr.ci #[1] 0.2204119 0.8560583 # #$logSMR.var # 2 #[1,] 0.09076763 # #$logSMR.ci #[1] 0.2982118 0.9714471 # #$rootSMR.var # 2 #[1,] 0.01221358 # #$rootSMR.ci #[1] 0.2673299 0.9029762require(survival); #load survival package; data(screening); head(screening); #Data to be used in the example; NB = nrow(screening); #Sample size #Be careful with R round function. If it was used to obtain discrete value, then #fuzz option should be used for expected and expected variance i=1:NB yearSCN<-screening[i,1]; #Year at which the woman started participating ageSCN<-screening[i,2]; #Age at which the woman started participating yearONS<-screening[i,3]; #Year of breast cancer diagnosis deathBC<-screening[i,4]; #Death by breast cancer indicator for non-participating woman. ageFL<-screening[i,5]; #Age at which the woman became eligible yearFL<-screening[i,6]; #Year at which the woman became eligible followONS<-screening[i,7]; #Follow-up time after disease onset for a non-participant followSCN<-screening[i,8]; #Follow-up time as a participant in the screening program particip<-screening[i,9]; #Indicator that the woman participated into the screening #program at some point Onset<-screening[i,10]; #Indicator that the non-participating woman got breast cancer end<-screening[i,11]; #year of eligibility end. deathSCN<-screening[i,12]; #Death by breast cancer indicator for participating woman. nb_onset=length(Onset[Onset==1]); #Number of women with breast cancer #Objects that will containt covariates for the Cox model year<-numeric(nb_onset); age1<-numeric(nb_onset); age2<-numeric(nb_onset); age3<-numeric(nb_onset); age4<-numeric(nb_onset); ti<-numeric(nb_onset); year[yearONS[Onset==1] <= 3] = 1; #Indicator that diagnosis happened before year 3 year[yearONS[Onset==1] > 3] = 0; #Indicator that diagnosis happened before year 3 age1[ageSCN[Onset==1] < 55] = 1; #Indicator that age at diagnosis is smaller than 55 age1[ageSCN[Onset==1] >= 55] = 0; #Indicator that age at diagnosis is smaller than 55 age2[ageSCN[Onset==1] >= 55 & ageSCN[Onset==1] < 60] = 1; #... >= 55 and < 60 age2[ageSCN[Onset==1] < 55 | ageSCN[Onset==1] >= 60] = 0; #... >= 55 and < 60 age3[ageSCN[Onset==1] >= 60 & ageSCN[Onset==1] < 65] = 1; #... >= 60 and < 65 age3[ageSCN[Onset==1] < 60 | ageSCN[Onset==1] >= 65] = 0; #... >= 60 and < 65 age4[ageSCN[Onset==1] >= 65 & ageSCN[Onset==1] < 70] = 1; #... >= 65 and < 70 age4[ageSCN[Onset==1] < 65 | ageSCN[Onset==1] >= 70] = 0; #... >= 65 and < 70 cox.data = data.frame(followONS = followONS[Onset == 1], deathBC = deathBC[Onset == 1], year, age1, age2, age3, age4); x<-coxph(Surv(time = followONS, event = deathBC, type = 'right')~ year + age1 + age2 + age3 + age4, data = cox.data, method="breslow",control=coxph.control(iter.max=100)) #Creating a matrix with many more lines than what will be used new_data<-matrix(0,nrow=12*sum(particip),ncol=10); #Creating a matrix containing data in a new form. #Each line contains stable covariates, so that a #given individual might be divided on many lines. #For example, if only the covariate age is used for incidence and survival, #an individual followed for 3.4 years that was 54.6 years at the begining #of the study should be entered as follow: #start_follow, end_follow, incid_cov, surv_cov, follow_up #0 0.4 54 54 3.4 #0.4 1.4 55 55 3.4 #1.4 2.4 56 56 3.4 #2.4 3.4 57 57 3.4 r=1 for(i in seq(1,length(ageFL))[particip==1]) { X = followSCN[i]; dep_t = yearSCN[i]; age_t = ageSCN[i]; while(dep_t - yearSCN[i] < X) { Y = min(floor(age_t) + 1 - age_t, floor(dep_t) + 1 - dep_t); if(dep_t - yearSCN[i] + Y >= X) { new_data[r,]<-c(floor(age_t), floor(dep_t), age_t < 55, (age_t >= 55 && age_t < 60), (age_t >= 60 && age_t < 65), (age_t >=65 && age_t <70), dep_t < 3, dep_t - yearSCN[i], X, followSCN[i]); } else { new_data[r,]<-c(floor(age_t), floor(dep_t), age_t < 55, (age_t >= 55 && age_t < 60), (age_t >= 60 && age_t < 65), (age_t >=65 && age_t <70), dep_t < 3, dep_t - yearSCN[i], dep_t - yearSCN[i] + Y, followSCN[i]); } dep_t = dep_t + Y; age_t = age_t + Y; r = r + 1; } } new_data<-new_data[new_data[,1]!=0,]; new_data[1:10,]; #Calculate incidences with incidences function: #follow up time as non-participant: follow_up = apply(cbind(end - yearFL,yearONS - yearFL,yearSCN - yearFL),1,min); incid = incidences(50,75,0,5,follow_up,ageFL,yearFL,Onset); #Calculate contributions with contrib function: start_follow = new_data[,8]; end_follow = new_data[,9]; incid_cov = new_data[,c(2,1)]; surv_cov = data.frame(new_data[,c(7,3,4,5,6)]); follow_up = new_data[,10]; increment = 0.5; #Remove following "#" to run example : #contribution = contrib(start_follow, end_follow, incid_cov, surv_cov, #follow_up, increment); #est.expDeath(contribution,incid,x,fuzz = 0.01, #covnames = c("year", "age1", "age2", "age3", "age4")); #Estimating the variance can be very long even in this small sample example, e.g. a few hours. #Remove the "#" to run example: #var.expDeath(contribution,incid,x,fuzz = 0.01, #covnames = c("year", "age1", "age2", "age3", "age4")); #Estimating the variance can be very long even in this small sample example, e.g. a few hours. #Remove the "#" to run example: #results = inference.SMR(obs.death = sum(deathSCN), normal = c("smr", "log-smr", "root-smr"), # alpha = 0.05, contribution, incid, cox = x, fuzz = 0.01, Poisson = TRUE, # covnames = c("annees", "age1", "age2", "age3", "age4")); #******** INFERENCE ABOUT THE SMR ********* # #Observed = 18 Expected = 33.44264 #Obs.var. = 18 Exp.var. = 39.38153 #SMR = 0.5382351 # # 95 % Confidence intervals with normality assumption at : # #The SMR level : ( 0.2204119 0.8560583 ) # #The log-SMR level : ( 0.2982118 0.9714471 ) # #The root-SMR level : ( 0.2673299 0.9029762 ) #results # #$expected #[1] 33.44264 # #$obs.death #[1] 18 # #$variance # 2 #[1,] 39.38153 # #$smr #[1] 0.5400112 # #$smr.var # 2 #[1,] 0.02629511 # #$smr.ci #[1] 0.2204119 0.8560583 # #$logSMR.var # 2 #[1,] 0.09076763 # #$logSMR.ci #[1] 0.2982118 0.9714471 # #$rootSMR.var # 2 #[1,] 0.01221358 # #$rootSMR.ci #[1] 0.2673299 0.9029762
This function estimates the variance of the expected number of deaths when the latter is estimated using Sasieni's method.
var.expDeath(contribution, incid, cox, fuzz, Poisson = FALSE, covnames)var.expDeath(contribution, incid, cox, fuzz, Poisson = FALSE, covnames)
contribution |
An object of contributions produced by the function |
incid |
A matrix containing: the incidences, the value of the covariates and the person-years at risk, in that order. It can be obtained with the function |
cox |
An oject of class |
fuzz |
Numerical precision is problematic when it comes to test equality between objects. The option |
covnames |
An alphanumeric vector containing the names of the covariates used to estimate the survival in the cohort of non-participants, that is, the names of the covariates used to obtain the |
Poisson |
Indicates whether the incidences' variance should be estimated with a Poisson distribution (TRUE) or a binomial distribution (FALSE). The default is FALSE. |
The function returns the variance of the expected number of deaths
A complete example of how to use this function is available in the help page of the screening dataset.
Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal.
Talbot, D., Duchesne, T., Brisson, J., Vandal, N. (2011) Variance estimation and confidence intervals for the standardized mortality ratio with application to the assessment of a cancer screening program, Statistics in Medicine, 30, 3024-3037.
est.expDeath, inference.SMR, screening
#This example uses pre-built objects and shows the simple usage #of the est.expDeath function when those objects already exists. #For an example of how to built those object, refer to the #help page of the screening dataset. #Remove "#" to run example. The function can be quite long (a few hours) to run: #data(req.objects); #cox.data = req.objects$cox.data; #var.expDeath(req.objects$contribution,req.objects$incid,req.objects$cox,fuzz = 0.01, #req.objects$covnames); #[1,] 39.31382#This example uses pre-built objects and shows the simple usage #of the est.expDeath function when those objects already exists. #For an example of how to built those object, refer to the #help page of the screening dataset. #Remove "#" to run example. The function can be quite long (a few hours) to run: #data(req.objects); #cox.data = req.objects$cox.data; #var.expDeath(req.objects$contribution,req.objects$incid,req.objects$cox,fuzz = 0.01, #req.objects$covnames); #[1,] 39.31382