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#print out the results Model 1
fit.weib

Call:
idm(formula01 = formula1 ~ prediabetes + diabetes + sex + smoke + 
    drink, formula02 = formula2 ~ prediabetes + diabetes + sex + 
    smoke + drink, data = feb)

Illness-death regression model using Weibull parametrization 
to estimate the baseline transition intensities.

number of subjects:  1788 
number of events '0 -> 1':  374 
number of events '0 -> 2' or '0 -> 1 -> 2':  479 
number of covariates:  5 5 5 
----
Model converged.
number of iterations:  14 
convergence criteria: parameters= 1e-09 
                    : likelihood= 1e-08 
                    : second derivatives= 1e-12 

                Without covariates With covariates
 log-likelihood          -3847.996       -3767.299

Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
          transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a)        9.25627265       12.71828442        6.91867827
scale (b)        0.01139174        0.01168751        0.01402317


Regression coefficients:

$`transition 0 -> 1`
       Factor    coef SE coef exp(coef)          CI   p-value
1 prediabetes  0.3400  0.1128    1.4050 [1.13;1.75] 0.0025750
2    diabetes  0.5055  0.1510    1.6579 [1.23;2.23] 0.0008149
3         sex  0.1969  0.1477    1.2176 [0.91;1.63] 0.1826221
4       smoke -0.5032  0.1282    0.6046 [0.47;0.78]   < 1e-04
5       drink -0.2868  0.1495    0.7507 [0.56;1.01] 0.0550085

$`transition 0 -> 2`
        Factor    coef SE coef exp(coef)          CI   p-value
6  prediabetes  0.1741  0.1272    1.1902 [0.93;1.53] 0.1711681
7     diabetes  0.3820  0.1679    1.4652 [1.05;2.04] 0.0228810
8          sex -0.1856  0.1586    0.8306 [0.61;1.13] 0.2417547
9        smoke -0.6636  0.1383    0.5150 [0.39;0.68]   < 1e-04
10       drink -0.1121  0.1566    0.8939 [0.66;1.21] 0.4738512

$`transition 1 -> 2`
        Factor    coef SE coef exp(coef)          CI   p-value
11 prediabetes  0.1472  0.1711    1.1586 [0.83;1.62] 0.3895990
12    diabetes  0.1905  0.2151    1.2099 [0.79;1.84] 0.3757779
13         sex -0.7135  0.2105    0.4899 [0.32;0.74] 0.0007024
14       smoke -0.7572  0.1827    0.4690 [0.33;0.67]   < 1e-04
15       drink  0.4168  0.2065    1.5172 [1.01;2.27] 0.0435466

print(summary(fit.weib,digits = 4))

Method: Weibull parametrization 

number of subjects:  1788 
number of events '0-->1':  374 
number of events '0-->2 or 0-->1-->2':  479 
number of covariates:  5 5 5 
observation deleted due to missing:  1 

#print out the results Model 2
fit.weib2

Call:
idm(formula01 = formula1 ~ prediabetes + diabetes + sex + underweight + 
    obese + smoke + drink, formula02 = formula2 ~ prediabetes + 
    diabetes + sex + underweight + obese + smoke + drink, data = feb)

Illness-death regression model using Weibull parametrization 
to estimate the baseline transition intensities.

number of subjects:  1787 
number of events '0 -> 1':  374 
number of events '0 -> 2' or '0 -> 1 -> 2':  479 
number of covariates:  7 7 7 
----
Model converged.
number of iterations:  20 
convergence criteria: parameters= 1.1e-08 
                    : likelihood= 2.7e-08 
                    : second derivatives= 9.4e-14 

                Without covariates With covariates
 log-likelihood          -3847.886       -3762.253

Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
          transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a)        9.29214530       12.73193017        6.90660077
scale (b)        0.01154579        0.01171112        0.01395997


Regression coefficients:

$`transition 0 -> 1`
       Factor    coef SE coef exp(coef)          CI   p-value
1 prediabetes  0.3260  0.1128    1.3854 [1.11;1.73] 0.0038573
2    diabetes  0.5054  0.1509    1.6576 [1.23;2.23] 0.0008088
3         sex  0.1828  0.1484    1.2006 [0.90;1.61] 0.2179094
4 underweight  0.2155  0.2493    1.2405 [0.76;2.02] 0.3873206
5       obese -0.2506  0.1099    0.7783 [0.63;0.97] 0.0225435
6       smoke -0.5050  0.1285    0.6035 [0.47;0.78]   < 1e-04
7       drink -0.2922  0.1495    0.7466 [0.56;1.00] 0.0506860

$`transition 0 -> 2`
        Factor    coef SE coef exp(coef)          CI   p-value
8  prediabetes  0.1615  0.1290    1.1753 [0.91;1.51] 0.2104449
9     diabetes  0.3714  0.1703    1.4498 [1.04;2.02] 0.0291502
10         sex -0.1795  0.1614    0.8357 [0.61;1.15] 0.2662359
11 underweight -0.1379  0.3993    0.8712 [0.40;1.91] 0.7298915
12       obese -0.0851  0.1190    0.9184 [0.73;1.16] 0.4743116
13       smoke -0.6509  0.1404    0.5216 [0.40;0.69]   < 1e-04
14       drink -0.1236  0.1609    0.8838 [0.64;1.21] 0.4425781

$`transition 1 -> 2`
        Factor    coef SE coef exp(coef)          CI   p-value
15 prediabetes  0.1712  0.1716    1.1867 [0.85;1.66] 0.3183304
16    diabetes  0.2387  0.2169    1.2695 [0.83;1.94] 0.2712914
17         sex -0.7306  0.2133    0.4816 [0.32;0.73] 0.0006142
18 underweight  0.5806  0.3190    1.7871 [0.96;3.34] 0.0687775
19       obese  0.0374  0.1789    1.0382 [0.73;1.47] 0.8342068
20       smoke -0.7677  0.1831    0.4641 [0.32;0.66]   < 1e-04
21       drink  0.4322  0.2133    1.5407 [1.01;2.34] 0.0426893

print(summary(fit.weib2,digits = 4))

Method: Weibull parametrization 

number of subjects:  1787 
number of events '0-->1':  374 
number of events '0-->2 or 0-->1-->2':  479 
number of covariates:  7 7 7 
observation deleted due to missing:  1 

#print out the results Model 3
fit.weib3

Call:
idm(formula01 = formula1 ~ prediabetes + diabetes + sex + underweight + 
    obese + smoke + drink + base_hyp + base_tch + base_hdl + 
    base_tg, formula02 = formula2 ~ prediabetes + diabetes + 
    sex + underweight + obese + smoke + drink + base_hyp + base_tch + 
    base_hdl + base_tg, data = feb)

Illness-death regression model using Weibull parametrization 
to estimate the baseline transition intensities.

number of subjects:  1787 
number of events '0 -> 1':  374 
number of events '0 -> 2' or '0 -> 1 -> 2':  479 
number of covariates:  11 11 11 
----
Model converged.
number of iterations:  27 
convergence criteria: parameters= 1.7e-10 
                    : likelihood= 2.7e-07 
                    : second derivatives= 1.2e-06 

                Without covariates With covariates
 log-likelihood          -3847.886       -3751.507

Parameters of the Weibull distributions: 'S(t) = exp(-(b*t)^a)'
          transition 0 -> 1 transition 0 -> 2 transition 1 -> 2
shape (a)        9.26895557        12.8117972        7.08733291
scale (b)        0.01128546         0.0117958        0.01341032


Regression coefficients:

$`transition 0 -> 1`
        Factor    coef SE coef exp(coef)          CI   p-value
1  prediabetes  0.3013  0.1133    1.3516 [1.08;1.69] 0.0078489
2     diabetes  0.5091  0.1516    1.6638 [1.24;2.24] 0.0007835
3          sex  0.2264  0.1520    1.2540 [0.93;1.69] 0.1364213
4  underweight  0.1983  0.2516    1.2193 [0.74;2.00] 0.4305390
5        obese -0.2470  0.1098    0.7812 [0.63;0.97] 0.0244871
6        smoke -0.4940  0.1314    0.6102 [0.47;0.79] 0.0001704
7        drink -0.2826  0.1513    0.7538 [0.56;1.01] 0.0617227
8     base_hyp  0.2915  0.1041    1.3384 [1.09;1.64] 0.0051190
9     base_tch -0.0910  0.1321    0.9130 [0.70;1.18] 0.4909232
10    base_hdl -0.0788  0.1595    0.9242 [0.68;1.26] 0.6212870
11     base_tg  0.1025  0.1156    1.1079 [0.88;1.39] 0.3753372

$`transition 0 -> 2`
        Factor    coef SE coef exp(coef)          CI   p-value
12 prediabetes  0.1746  0.1277    1.1907 [0.93;1.53] 0.1716223
13    diabetes  0.3499  0.1704    1.4189 [1.02;1.98] 0.0400081
14         sex -0.2725  0.1639    0.7615 [0.55;1.05] 0.0964527
15 underweight -0.0427  0.3628    0.9582 [0.47;1.95] 0.9063967
16       obese -0.0924  0.1178    0.9118 [0.72;1.15] 0.4327868
17       smoke -0.6956  0.1400    0.4988 [0.38;0.66]   < 1e-04
18       drink -0.0542  0.1579    0.9473 [0.70;1.29] 0.7315440
19    base_hyp  0.0091  0.1036    1.0091 [0.82;1.24] 0.9301192
20    base_tch  0.0866  0.1417    1.0904 [0.83;1.44] 0.5410335
21    base_hdl -0.3726  0.1847    0.6889 [0.48;0.99] 0.0437044
22     base_tg  0.1881  0.1267    1.2070 [0.94;1.55] 0.1376511

$`transition 1 -> 2`
        Factor    coef SE coef exp(coef)          CI   p-value
23 prediabetes  0.1399  0.1712    1.1502 [0.82;1.61] 0.4135854
24    diabetes  0.1860  0.2165    1.2044 [0.79;1.84] 0.3902579
25         sex -0.6265  0.2227    0.5345 [0.35;0.83] 0.0048984
26 underweight  0.6217  0.3236    1.8620 [0.99;3.51] 0.0547457
27       obese -0.0013  0.1012    0.9987 [0.82;1.22] 0.9894045
28       smoke -0.7184  0.1858    0.4875 [0.34;0.70] 0.0001103
29       drink  0.3015  0.2120    1.3518 [0.89;2.05] 0.1550309
30    base_hyp  0.0602  0.1598    1.0621 [0.78;1.45] 0.7063391
31    base_tch  0.0087  0.2754    1.0088 [0.59;1.73] 0.9746970
32    base_hdl  0.4069  0.2115    1.5021 [0.99;2.27] 0.0543499
33     base_tg  0.2185  0.1724    1.2441 [0.89;1.74] 0.2050491

print(summary(fit.weib3,digits = 4))

Method: Weibull parametrization 

number of subjects:  1787 
number of events '0-->1':  374 
number of events '0-->2 or 0-->1-->2':  479 
number of covariates:  11 11 11 
observation deleted due to missing:  1 

#plot transition intensities
par(mgp=c(4,1,0),mar=c(5,5,5,5))
plot(fit.weib,conf.int = TRUE,lwd = 3,citype = "shadow",xlim = c(65,100),axis2.las=2,axis1.at=seq(65,100,5),xlab = "Age(years)")
plot(fit.weib2,conf.int = TRUE,lwd = 3,citype = "shadow",xlim = c(65,100),axis2.las=2,axis1.at=seq(65,100,5),xlab = "Age(years)")

plot(fit.weib3,conf.int = TRUE,lwd = 3,citype = "shadow",xlim = c(65,100),axis2.las=2,axis1.at=seq(65,100,5),xlab = "Age(years)")
#Predictive probabilities
# Women age 65 with diabetes in obese grps, no smoking and no alc drinking
pred_w10yr<-predict(fit.weib2,s=65,t=75,newdata=data.frame(diabetes=1,prediabetes=0,sex=2,smoke=0, drink=0, underweight=0, obese=1))
pred_prob_w10yr<-as.data.frame(pred_w10yr$transprob)
pred_prob_w10yr

# Men age 65 with diabetes in obese grps, no smoking and no alc drinking
pred_m10yr<-predict(fit.weib2,s=65,t=75,newdata=data.frame(diabetes=1,prediabetes=0,sex=1,smoke=0, drink=0, underweight=0, obese=1))
pred_prob_m10yr<-as.data.frame(pred_m10yr$transprob)
pred_prob_m10yr

#Figure of predictive probabilities

# create sequence of x values from 0 to 10 representing 10 years
x <- seq(0, 10, length.out = 100)
# set the estimate values
estimate <- probsubset$Estimate
# calculate corresponding y values for each estimate
y <- matrix(0, nrow = length(x), ncol = length(estimate))
for (i in 1:length(estimate)) {
  y[,i] <- estimate[i] * (1 - exp(-0.1 * x))
}
# calculate the space between y[i+1] and y[i] as the difference between y[i+1] and the sum of y[i] and y[i+1]
space <- matrix(0, nrow = length(x), ncol = length(estimate))
for (i in 2:length(estimate)) {
  space[,i] <- y[,i] - (y[,1]+y[,i])
}
# plot curves for each estimate
plot(x, y[,1], type = "l", col = "blue", ylim = c(0,1), lwd = 2, main = "Curves for Estimates")
for (i in 2:length(estimate)) {
  lines(x, y[,i], type = "l", col = i, lwd = 2)
}

# add labels and axis
xlabel <- "Years"
ylabel <- "Predictive probabilities"
title <- "Curves for prediction over 10 Years"
axis(1, at = seq(0, 10, by = 2), labels = seq(0, 10, by = 2))
axis(2, at = seq(0, 1, by = 0.2), labels = seq(0, 1, by = 0.2))

title(xlab = xlabel, ylab = ylabel, main = title)
legend("topright", legend = paste0("Estimate ", 1:length(estimate)), col = 1:length(estimate), lwd = 2)

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