This dataset contains a simulated population of size 10,000. The population was simulated as described in Talbot et al (2011).

1 |

A data frame with 10000 observations on the following 12 variables.

`yearSCN`

Year at which the person would become a participant in the screening program

`ageSCN`

Age at which the person would become a participant in the screening program

`yearONS`

Year at which the disease onset would happen for a non-participant

`deathBC`

Indicator variable that has a value of 1 if the non-participant dies from the screened disease, 0 otherwise.

`ageFL`

Age at which the person is eligible to the screening program for the first time

`yearFL`

Year at which the person is eligible to the screening program for the first time

`followONS`

Follow-up time for a non-participant after the disease onset

`followSCN`

Follow-up time as participant in the screening program

`particip`

Indicator variable that has a value of 1 if the individual eventually became a participant in the screening program, 0 otherwise

`Onset`

Indicator variable that has a value of 1 if the disease onset happens while the person is a non-participant

`end`

Year at which the follow-up ends

`deathSCN`

Indicator 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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 | ```
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 0.9029762
``` |

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