Direct effect
Create two expanded datasets so that hazards given A=1 can be
computed for all subjects (even those with A=0), and viceversa (everyone
has A = 0). In an RCT this is not necessary, could stratify models above
and this step by treatment arm.
Data set construction where A = 1
treated <- baseline[rep(1:n,each=length(cutTimes)),] #One row for each interval k+1 for k=0,...,K
treated$dtime <- rep(cutTimes,n)
treated$rx <-1
- Data set construction where A = 0
# Make analogous dataset for placebo
placebo <- baseline[rep(1:n,each=length(cutTimes)),] #One row for each time
placebo$dtime <- rep(cutTimes,n)
placebo$rx <- 0
- Estimate conditional discrete hazards (cause specific for each cause
of death/competing event conditioned for event and hazard of competing
event) for each subject in each time interval in both cloned
datasets
treated$hazardP <- predict(plrFitP, newdata = treated, type = 'response')
treated$hazardO <- 0
treated$s <- (1-treated$hazardP) * (1-treated$hazardO)
placebo$hazardP <- predict(plrFitP, newdata = placebo, type = 'response')
placebo$hazardO <- 0
placebo$s <- (1-placebo$hazardP) * (1-placebo$hazardO)
- Glimpse of “treated” data:
treated %>%
filter(patno %in% c(489)) %>% select(
patno, dtime, rx, hazardP, hazardO, s
) %>% slice(1:5, 55:59) %>% knitr::kable()
8478 |
489 |
0 |
1 |
0.0231061 |
0 |
0.9768939 |
8478.1 |
489 |
1 |
1 |
0.0234620 |
0 |
0.9765380 |
8478.2 |
489 |
2 |
1 |
0.0238175 |
0 |
0.9761825 |
8478.3 |
489 |
3 |
1 |
0.0241730 |
0 |
0.9758270 |
8478.4 |
489 |
4 |
1 |
0.0245289 |
0 |
0.9754711 |
8478.54 |
489 |
54 |
1 |
0.0658483 |
0 |
0.9341517 |
8478.55 |
489 |
55 |
1 |
0.0681584 |
0 |
0.9318416 |
8478.56 |
489 |
56 |
1 |
0.0706130 |
0 |
0.9293870 |
8478.57 |
489 |
57 |
1 |
0.0732226 |
0 |
0.9267774 |
8478.58 |
489 |
58 |
1 |
0.0759986 |
0 |
0.9240014 |
- Glimpse of “placebo” data:
placebo %>%
filter(patno %in% c(489)) %>% select(
patno, dtime, rx, hazardP, hazardO, s
) %>% slice(1:5, 55:59) %>% knitr::kable()
8478 |
489 |
0 |
0 |
0.0458879 |
0 |
0.9541121 |
8478.1 |
489 |
1 |
0 |
0.0431460 |
0 |
0.9568540 |
8478.2 |
489 |
2 |
0 |
0.0409669 |
0 |
0.9590331 |
8478.3 |
489 |
3 |
0 |
0.0392643 |
0 |
0.9607357 |
8478.4 |
489 |
4 |
0 |
0.0379704 |
0 |
0.9620296 |
8478.54 |
489 |
54 |
0 |
0.0142297 |
0 |
0.9857703 |
8478.55 |
489 |
55 |
0 |
0.0113442 |
0 |
0.9886558 |
8478.56 |
489 |
56 |
0 |
0.0088875 |
0 |
0.9911125 |
8478.57 |
489 |
57 |
0 |
0.0068390 |
0 |
0.9931610 |
8478.58 |
489 |
58 |
0 |
0.0051668 |
0 |
0.9948332 |
We will implement the following estimator, wrapped as the function
calculateCumInc
from the utility_functions
script available in this repository.
calculateCumInc <-
function(inputData,
timepts = cutTimes,
competing = FALSE) {
cumulativeIncidence <-
matrix(NA, ncol = length(unique(inputData$patno)), nrow = length(cutTimes))
# Insert the event probabilities at the first time interval:
cumulativeIncidence[1,] <-
inputData[inputData$dtime == 0,]$hazardP * inputData[inputData$dtime ==
0,]$hazardO
# Create a matrix compatible with 'cumulativeIncidence' with survival probabilities at each time
survivalProb <-
t(aggregate(s ~ patno, data = inputData, FUN = cumprod)$s) #split the long data into subsets per subject
for (i in 2:length(cutTimes)) {
subInputDataP <-
inputData[inputData$dtime == (i - 1),]$hazardP #OBS: dtime starts at 0
subInputDataO <-
(1 - inputData[inputData$dtime == (i - 1),]$hazardO) #OBS: dtime starts at 0
if (!competing)
cumulativeIncidence[i,] <-
subInputDataO * subInputDataP * survivalProb[(i - 1),] # OBS: survivalProb entry i is time point i-1
else
cumulativeIncidence[i,] <-
(1 - subInputDataO) * survivalProb[(i - 1),]
}
meanCumulativeIncidence <-
rowMeans(apply(cumulativeIncidence, MARGIN = 2, cumsum)) #rowMeans(cumulativeIncidence)
return(meanCumulativeIncidence)
}
cumIncTreated <- calculateCumInc(treated)#a=1
cumIncPlacebo <- calculateCumInc(placebo)#a=0
cumIncTreated_de_60 <- cumIncTreated[length(cutTimes)]
cumIncPlacebo_de_60 <- cumIncPlacebo[length(cutTimes)]
de_rr <- cumIncTreated_de_60 / cumIncPlacebo_de_60
de_rd <- cumIncTreated_de_60 - cumIncPlacebo_de_60
results_de <- data.frame(cumIncTreated_de_60, cumIncPlacebo_de_60, de_rr, de_rd)
knitr::kable(round(results_de, 2))
Total effect
- We are going to use the same code as in the previous section, except
that in this case instead of fixing the hazard of other causes to death
as 0, we are going to calculate hazards for this outcome using predicted
values from the
plrfit0
model and recalculate the survival
probability, given death
treated$hazardO <- predict(plrFitO, newdata = treated, type = 'response')
treated$s <- (1-treated$hazardP) * (1-treated$hazardO)
placebo$hazardO <- predict(plrFitO, newdata = placebo, type = 'response')
placebo$s <- (1-placebo$hazardP) * (1-placebo$hazardO)
- Glimpse of “treated” data:
treated %>%
filter(patno %in% c(489)) %>% select(
patno, dtime, rx, hazardP, hazardO, s
) %>% slice(1:5, 55:59) %>% knitr::kable()
8478 |
489 |
0 |
1 |
0.0231061 |
0.0759711 |
0.9026781 |
8478.1 |
489 |
1 |
1 |
0.0234620 |
0.0747473 |
0.9035444 |
8478.2 |
489 |
2 |
1 |
0.0238175 |
0.0735928 |
0.9043425 |
8478.3 |
489 |
3 |
1 |
0.0241730 |
0.0725053 |
0.9050744 |
8478.4 |
489 |
4 |
1 |
0.0245289 |
0.0714825 |
0.9057420 |
8478.54 |
489 |
54 |
1 |
0.0658483 |
0.0853839 |
0.8543902 |
8478.55 |
489 |
55 |
1 |
0.0681584 |
0.0871989 |
0.8505860 |
8478.56 |
489 |
56 |
1 |
0.0706130 |
0.0891097 |
0.8465696 |
8478.57 |
489 |
57 |
1 |
0.0732226 |
0.0911205 |
0.8423290 |
8478.58 |
489 |
58 |
1 |
0.0759986 |
0.0932355 |
0.8378517 |
- Glimpse of “placebo” data:
placebo %>%
filter(patno %in% c(489)) %>% select(
patno, dtime, rx, hazardP, hazardO, s
) %>% slice(1:5, 55:59) %>% knitr::kable()
8478 |
489 |
0 |
0 |
0.0458879 |
0.0614893 |
0.8954444 |
8478.1 |
489 |
1 |
0 |
0.0431460 |
0.0604835 |
0.8989802 |
8478.2 |
489 |
2 |
0 |
0.0409669 |
0.0595351 |
0.9019369 |
8478.3 |
489 |
3 |
0 |
0.0392643 |
0.0586422 |
0.9043961 |
8478.4 |
489 |
4 |
0 |
0.0379704 |
0.0578028 |
0.9064217 |
8478.54 |
489 |
54 |
0 |
0.0142297 |
0.0692422 |
0.9175134 |
8478.55 |
489 |
55 |
0 |
0.0113442 |
0.0707406 |
0.9187176 |
8478.56 |
489 |
56 |
0 |
0.0088875 |
0.0723194 |
0.9194359 |
8478.57 |
489 |
57 |
0 |
0.0068390 |
0.0739820 |
0.9196849 |
8478.58 |
489 |
58 |
0 |
0.0051668 |
0.0757324 |
0.9194921 |
- Calculate risks and corresponding treatment effects (RR/RD) by end
of follow-up using parametric g-formula
cumIncTreated_te <- calculateCumInc(treated)#a=1
cumIncPlacebo_te <- calculateCumInc(placebo)#a=0
cumIncTreated_te_60 <- cumIncTreated_te[length(cutTimes)]
cumIncPlacebo_te_60 <- cumIncPlacebo_te[length(cutTimes)]
te_rr <- cumIncTreated_te_60 / cumIncPlacebo_te_60
te_rd <- cumIncTreated_te_60 - cumIncPlacebo_te_60
results_te <- data.frame(cumIncTreated_te_60, cumIncPlacebo_te_60, te_rr, te_rd)
knitr::kable(round(results_te, 2))
Separable effects
Following equation (9) from Stensrud
et al. Journal of the American Statistical Association. 2020
To this matter, we will use the long format data set prepared before:
longProstRed
.
- Make one extra copy of the exposure
rx
, named
Orx
, to be used in the hazard of death due to other
causes.
longProstRed$Orx <- longProstRed$rx
- Fit conditional pooled logistic regression models
plrFitP <-
glm(
prostateDeath ~ rx*(dtime + I(dtime ^ 2)+ I(dtime ^ 3)) + normalAct + ageCat + hx + hgBinary,
data = longProstRed,
family = binomial()
)
plrFitO <-
glm(
otherDeath ~ Orx * (dtime + I(dtime ^ 2) + I(dtime ^ 3)) + normalAct + ageCat + hx + hgBinary,
data = longProstRed,
family = binomial()
)
Create three copies of the data:
- Data set construction where Ay and Ad = 1
treated <-
baseline[rep(1:n, each = length(cutTimes)), ] #One row for each time
treated$dtime <- rep(cutTimes, n)
treated$rx <- 1
treated$Orx <- 1
- Dataset construction where Ay and Ad = 1
placebo <-
baseline[rep(1:n, each = length(cutTimes)), ] #One row for each time
placebo$dtime <- rep(cutTimes, n)
placebo$rx <- 0
placebo$Orx <- 0
- Dataset construction where Ay = 1, Ad = 0
treatAy <-
baseline[rep(1:n, each = length(cutTimes)), ]
treatAy$dtime <- rep(cutTimes, n)
treatAy$rx <- 1
treatAy$Orx <- 0
- Calculate hazards for each time interval in the three cloned data
sets
## For Ay = 1 and Ad = 1
treated$hazardP <-
predict(plrFitP, newdata = treated, type = 'response')
treated$hazardO <-
predict(plrFitO, newdata = treated, type = 'response')
treated$s <- (1 - treated$hazardP) * (1 - treated$hazardO)
## For Ay = 0, Ad = 0
placebo$hazardP <-
predict(plrFitP, newdata = placebo, type = 'response')
placebo$hazardO <-
predict(plrFitO, newdata = placebo, type = 'response')
placebo$s <- (1 - placebo$hazardP) * (1 - placebo$hazardO)
## For Ay = 1, Ad = 0
treatAy$hazardP <-
predict(plrFitP, newdata = treatAy, type = 'response')
treatAy$hazardO <-
predict(plrFitO, newdata = treatAy, type = 'response')
treatAy$s <- (1 - treatAy$hazardP) * (1 - treatAy$hazardO)
- Glimpse of “treated” data:
treated %>%
filter(patno %in% c(489)) %>% select(
patno, dtime, rx, Orx, hazardP, hazardO, s
) %>% slice(1:5, 55:59) %>% knitr::kable()
8478 |
489 |
0 |
1 |
1 |
0.0231061 |
0.1215098 |
0.8581917 |
8478.1 |
489 |
1 |
1 |
1 |
0.0234620 |
0.1070610 |
0.8719889 |
8478.2 |
489 |
2 |
1 |
1 |
0.0238175 |
0.0951232 |
0.8833249 |
8478.3 |
489 |
3 |
1 |
1 |
0.0241730 |
0.0852474 |
0.8926403 |
8478.4 |
489 |
4 |
1 |
1 |
0.0245289 |
0.0770658 |
0.9002956 |
8478.54 |
489 |
54 |
1 |
1 |
0.0658483 |
0.0763298 |
0.8628481 |
8478.55 |
489 |
55 |
1 |
1 |
0.0681584 |
0.0726713 |
0.8641235 |
8478.56 |
489 |
56 |
1 |
1 |
0.0706130 |
0.0686332 |
0.8656002 |
8478.57 |
489 |
57 |
1 |
1 |
0.0732226 |
0.0642719 |
0.8672116 |
8478.58 |
489 |
58 |
1 |
1 |
0.0759986 |
0.0596529 |
0.8688820 |
- Glimpse of “placebo” data:
placebo %>%
filter(patno %in% c(489)) %>% select(
patno, dtime, rx, Orx, hazardP, hazardO, s
) %>% slice(1:5, 55:59) %>% knitr::kable()
8478 |
489 |
0 |
0 |
0 |
0.0458879 |
0.0509117 |
0.9055366 |
8478.1 |
489 |
1 |
0 |
0 |
0.0431460 |
0.0501587 |
0.9088594 |
8478.2 |
489 |
2 |
0 |
0 |
0.0409669 |
0.0495393 |
0.9115233 |
8478.3 |
489 |
3 |
0 |
0 |
0.0392643 |
0.0490433 |
0.9136181 |
8478.4 |
489 |
4 |
0 |
0 |
0.0379704 |
0.0486621 |
0.9152153 |
8478.54 |
489 |
54 |
0 |
0 |
0.0142297 |
0.0488282 |
0.9376369 |
8478.55 |
489 |
55 |
0 |
0 |
0.0113442 |
0.0468247 |
0.9423623 |
8478.56 |
489 |
56 |
0 |
0 |
0.0088875 |
0.0447376 |
0.9467726 |
8478.57 |
489 |
57 |
0 |
0 |
0.0068390 |
0.0425801 |
0.9508721 |
8478.58 |
489 |
58 |
0 |
0 |
0.0051668 |
0.0403663 |
0.9546755 |
- Glimpse of “treatAy” data:
treatAy %>%
filter(patno %in% c(489)) %>% select(
patno, dtime, rx, Orx, hazardP, hazardO, s
) %>% slice(1:5, 55:59) %>% knitr::kable()
8478 |
489 |
0 |
1 |
0 |
0.0231061 |
0.0509117 |
0.9271586 |
8478.1 |
489 |
1 |
1 |
0 |
0.0234620 |
0.0501587 |
0.9275561 |
8478.2 |
489 |
2 |
1 |
0 |
0.0238175 |
0.0495393 |
0.9278231 |
8478.3 |
489 |
3 |
1 |
0 |
0.0241730 |
0.0490433 |
0.9279692 |
8478.4 |
489 |
4 |
1 |
0 |
0.0245289 |
0.0486621 |
0.9280027 |
8478.54 |
489 |
54 |
1 |
0 |
0.0658483 |
0.0488282 |
0.8885387 |
8478.55 |
489 |
55 |
1 |
0 |
0.0681584 |
0.0468247 |
0.8882084 |
8478.56 |
489 |
56 |
1 |
0 |
0.0706130 |
0.0447376 |
0.8878085 |
8478.57 |
489 |
57 |
1 |
0 |
0.0732226 |
0.0425801 |
0.8873151 |
8478.58 |
489 |
58 |
1 |
0 |
0.0759986 |
0.0403663 |
0.8867029 |
- Calculate cumulative incidence
cumIncTreated <- calculateCumInc(treated)
cumIncTreatAy <- calculateCumInc(treatAy)
cumIncPlacebo <- calculateCumInc(placebo)
estimatesFullData <-
data.frame(cumIncTreated, cumIncTreatAy, cumIncPlacebo)
knitr::kable(round(estimatesFullData[36,], 2))
- Cumulative incidence curves
plot(cutTimes, cumIncTreated, type = "s",
ylim = c(0, 1), ylab = "Risk",
xlab = "Months",
lty = 1, lwd = 1, xlim = c(0, 52))
lines(cutTimes, cumIncPlacebo, type = "s",
col = 2, ylim = c(0, 1), lwd = 1)
lines(cutTimes, cumIncTreatAy, type = "s",
col = 3, ylim = c(0, 1), lwd = 1)
legend(x = 0, y = 1,
c("(Ay=1,Ad=1)", "(Ay=1,Ad=0)", "(Ay=0,Ad=0)"),
bty = "n", col = c(1, 3, 2),
lty = c(1, 1, 1), cex = 1, pt.cex = 1, lwd = 1)
![](data:image/png;base64,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)