glow500: GLOW500 data
In aplore3: Datasets from Hosmer, Lemeshow and Sturdivant, "Applied Logistic Regression" (3rd Ed., 2013)
Description
Usage
Format
Source
Examples
Description
glow500 dataset.
Usage
1
Format
A data.frame with 500 rows and 15 variables:
- sub_id
Identification Code (1 - n)
- site_id
Study Site (1 - 6)
- phy_id
Physician ID code (128 unique codes)
- priorfrac
History of Prior Fracture (1: No, 2: Yes)
- age
Age at Enrollment (Years)
- weight
Weight at enrollment (Kilograms)
- height
Height at enrollment (Centimeters)
- bmi
Body Mass Index (Kg/m^2)
- premeno
Menopause before age 45 (1: No, 2: Yes)
- momfrac
Mother had hip fracture (1: No, 2: Yes)
- armassist
Arms are needed to stand from a chair (1: No, 2: Yes)
- smoke
Former or current smoker (1: No, 2: Yes)
- raterisk
Self-reported risk of fracture (1: Less than others of
the same age, 2: Same as others of the same age, 3: Greater than others
of the same age)
- fracscore
Fracture Risk Score (Composite Risk Score)
- fracture
Any fracture in first year (1: No, 2: Yes)
Source
Hosmer, D.W., Lemeshow, S. and Sturdivant, R.X. (2013) Applied
Logistic Regression, 3rd ed., New York: Wiley
Examples
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head(glow500, n = 10)
summary(glow500)
## Table 2.2 p. 39
summary(mod2.2 <- glm(fracture ~ age + weight + priorfrac +
premeno + raterisk,
family = binomial,
data = glow500))
## Table 2.3 p. 40
summary(mod2.3 <- update(mod2.2, . ~ . - weight - premeno))
## Table 2.4 p. 44
vcov(mod2.3)
## Table 3.6 p. 58
contrasts(glow500$raterisk)
## Contrasts: Table 3.8 and 3.9 p. 60
contrasts(glow500$raterisk) <- matrix(c(-1,-1,1,0,0,1), byrow= TRUE, ncol = 2)
summary(mod3.9 <- glm(fracture ~ raterisk, family = binomial,
data = glow500))
# cleaning modified dataset ...
rm(glow500)
## Table 5.1 pg 160 - Hosmer-Lemeshow test (with vcdExtra package)
mod4.16 <- glm(fracture ~ age * priorfrac + height + momfrac * armassist +
I(as.integer(raterisk) == 3) ,
family = binomial,
data = glow500)
library(vcdExtra)
summary(HLtest(mod4.16))
## Table 5.3 p. 171 - Classification table
glow500$pred4.16 <- predict(mod4.16, type = "response")
with(glow500, addmargins(table( pred4.16 > 0.5, fracture)))
## Sensitivy, specificity, ROC (using pROC)
library(pROC)
## Figure 5.3 p. 177 - ROC curve (using pROC package)
print(roc4.16 <- roc(fracture ~ pred4.16, data = glow500))
plot(roc4.16, main = "Figure 5.3 p. 177")
## Table 5.8 p. 175
vars <- c("thresholds","sensitivities","specificities")
tab5.8 <- data.frame(roc4.16[vars])
## Now, for printing/comparison purposes, steps below in order to find
## threshold values most similar to those in the table
findIndex <- function(x, y) which.min( (x-y)^2 )
cutPoints <- seq(0.05, 0.75, by = 0.05)
tableIndex <- mapply(findIndex, y = cutPoints,
MoreArgs = list(x = roc4.16$thresholds))
## And finally, let's print a reasonable approximation of table 5.8
writeLines("\nTable 5.8 p. 175\n")
tab5.8[tableIndex, ]
## Figure 5.1 p. 175
plot(specificities ~ thresholds, xlim = c(0, 1), type = "l",
xlab = "Probabilty cutoff", ylab = "Sensitivity/specificity",
ylim = c(0, 1), data = tab5.8, main = "Figure 5.1 p. 175")
with(tab5.8, lines(thresholds, sensitivities, col = "red"))
legend(x = 0.75, y = 0.55, legend = c("Sensitivity", "Specificity"),
lty = 1, col = c("red","black"))
abline(h = c(0, 1), col = "grey80", lty = "dotted")
Example output
sub_id site_id phy_id priorfrac age weight height bmi premeno momfrac
1 1 1 14 No 62 70.3 158 28.16055 No No
2 2 4 284 No 65 87.1 160 34.02344 No No
3 3 6 305 Yes 88 50.8 157 20.60936 No Yes
4 4 6 309 No 82 62.1 160 24.25781 No No
5 5 1 37 No 61 68.0 152 29.43213 No No
6 6 5 299 Yes 67 68.0 161 26.23356 No No
7 7 5 302 No 84 50.8 150 22.57778 No No
8 8 1 36 Yes 82 40.8 153 17.42919 No No
9 9 1 8 Yes 86 62.6 156 25.72321 No No
10 10 4 282 No 58 63.5 166 23.04398 No No
armassist smoke raterisk fracscore fracture
1 No No Same 1 No
2 No No Same 2 No
3 Yes No Less 11 No
4 No No Less 5 No
5 No No Same 1 No
6 No Yes Same 4 No
7 No No Less 6 No
8 No No Same 7 No
9 No No Same 7 No
10 No No Less 0 No
sub_id site_id phy_id priorfrac age
Min. : 1.0 Min. :1.000 Min. : 1.00 No :374 Min. :55.00
1st Qu.:125.8 1st Qu.:2.000 1st Qu.: 57.75 Yes:126 1st Qu.:61.00
Median :250.5 Median :3.000 Median :182.50 Median :67.00
Mean :250.5 Mean :3.436 Mean :178.55 Mean :68.56
3rd Qu.:375.2 3rd Qu.:5.000 3rd Qu.:298.00 3rd Qu.:76.00
Max. :500.0 Max. :6.000 Max. :325.00 Max. :90.00
weight height bmi premeno momfrac armassist
Min. : 39.90 Min. :134.0 Min. :14.88 No :403 No :435 No :312
1st Qu.: 59.90 1st Qu.:157.0 1st Qu.:23.27 Yes: 97 Yes: 65 Yes:188
Median : 68.00 Median :161.5 Median :26.42
Mean : 71.82 Mean :161.4 Mean :27.55
3rd Qu.: 81.30 3rd Qu.:165.0 3rd Qu.:30.79
Max. :127.00 Max. :199.0 Max. :49.08
smoke raterisk fracscore fracture
No :465 Less :167 Min. : 0.000 No :375
Yes: 35 Same :186 1st Qu.: 2.000 Yes:125
Greater:147 Median : 3.000
Mean : 3.698
3rd Qu.: 5.000
Max. :11.000
Call:
glm(formula = fracture ~ age + weight + priorfrac + premeno +
raterisk, family = binomial, data = glow500)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.42250 -0.74873 -0.59711 -0.06046 2.28830
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.605794 1.220668 -4.592 4.38e-06 ***
age 0.050142 0.013417 3.737 0.000186 ***
weight 0.004080 0.006926 0.589 0.555803
priorfracYes 0.679457 0.242384 2.803 0.005059 **
premenoYes 0.186958 0.276710 0.676 0.499266
rateriskSame 0.534493 0.275858 1.938 0.052676 .
rateriskGreater 0.874123 0.289157 3.023 0.002503 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 562.34 on 499 degrees of freedom
Residual deviance: 518.08 on 493 degrees of freedom
AIC: 532.08
Number of Fisher Scoring iterations: 4
Call:
glm(formula = fracture ~ age + priorfrac + raterisk, family = binomial,
data = glow500)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.42693 -0.73132 -0.60772 -0.07484 2.23819
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -4.99060 0.90270 -5.529 3.23e-08 ***
age 0.04591 0.01244 3.690 0.000224 ***
priorfracYes 0.70023 0.24116 2.904 0.003689 **
rateriskSame 0.54856 0.27501 1.995 0.046075 *
rateriskGreater 0.86576 0.28621 3.025 0.002487 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 562.34 on 499 degrees of freedom
Residual deviance: 518.90 on 495 degrees of freedom
AIC: 528.9
Number of Fisher Scoring iterations: 4
(Intercept) age priorfracYes rateriskSame
(Intercept) 0.81486728 -0.0108886686 0.0445010519 -0.0603876325
age -0.01088867 0.0001547891 -0.0008344776 0.0002239259
priorfracYes 0.04450105 -0.0008344776 0.0581588491 -0.0031271822
rateriskSame -0.06038763 0.0002239259 -0.0031271822 0.0756289050
rateriskGreater -0.08055123 0.0005370070 -0.0118441110 0.0462406814
rateriskGreater
(Intercept) -0.080551235
age 0.000537007
priorfracYes -0.011844111
rateriskSame 0.046240681
rateriskGreater 0.081913370
Same Greater
Less 0 0
Same 1 0
Greater 0 1
Call:
glm(formula = fracture ~ raterisk, family = binomial, data = glow500)
Deviance Residuals:
Min 1Q Median 3Q Max
-0.9005 -0.7726 -0.6058 -0.0838 1.8899
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.1172 0.1062 -10.514 < 2e-16 ***
raterisk1 0.0611 0.1437 0.425 0.67067
raterisk2 0.4240 0.1466 2.892 0.00383 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 562.34 on 499 degrees of freedom
Residual deviance: 550.58 on 497 degrees of freedom
AIC: 556.58
Number of Fisher Scoring iterations: 4
Loading required package: vcd
Loading required package: MASS
Loading required package: grid
Loading required package: colorspace
Loading required package: gnm
Partition for Hosmer and Lemeshow Goodness-of-Fit Test
cut total obs exp chi
1 [0.0209,0.0847] 50 47 46.68709 0.04579536
2 (0.0847,0.111] 50 46 45.13980 0.12803215
3 (0.111,0.141] 50 43 43.72511 -0.10965679
4 (0.141,0.176] 51 40 42.92385 -0.44627785
5 (0.176,0.208] 49 42 39.60399 0.38073192
6 (0.208,0.249] 50 37 38.60188 -0.25782525
7 (0.249,0.322] 50 41 35.73499 0.88075020
8 (0.322,0.388] 50 31 32.37786 -0.24214783
9 (0.388,0.482] 50 25 28.18856 -0.60056317
10 (0.482,0.747] 50 23 22.01688 0.20952147
Hosmer and Lemeshow Goodness-of-Fit Test
Call:
glm(formula = fracture ~ age * priorfrac + height + momfrac *
armassist + I(as.integer(raterisk) == 3), family = binomial,
data = glow500)
ChiSquare df P_value
6.391925 8 0.6034186
fracture
No Yes Sum
FALSE 356 103 459
TRUE 19 22 41
Sum 375 125 500
Type 'citation("pROC")' for a citation.
Attaching package: 'pROC'
The following object is masked from 'package:colorspace':
coords
The following objects are masked from 'package:stats':
cov, smooth, var
Call:
roc.formula(formula = fracture ~ pred4.16, data = glow500)
Data: pred4.16 in 375 controls (fracture No) < 125 cases (fracture Yes).
Area under the curve: 0.7286
Table 5.8 p. 175
thresholds sensitivities specificities
6 0.05006609 1.000 0.0160000
64 0.09986050 0.952 0.1973333
136 0.15020771 0.848 0.3840000
201 0.20022684 0.768 0.5520000
263 0.24951185 0.640 0.6826667
294 0.30000935 0.624 0.7653333
335 0.34960972 0.488 0.8293333
366 0.40031190 0.392 0.8800000
393 0.44967455 0.296 0.9226667
417 0.50009629 0.176 0.9493333
434 0.54891768 0.096 0.9680000
447 0.59548830 0.032 0.9813333
453 0.65647052 0.024 0.9946667
456 0.70450302 0.000 0.9946667
457 0.74119791 0.000 0.9973333
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Description Usage Format Source Examples
Description
glow500 dataset.
Usage
1 |
Format
A data.frame with 500 rows and 15 variables:
- sub_id
Identification Code (1 - n)
- site_id
Study Site (1 - 6)
- phy_id
Physician ID code (128 unique codes)
- priorfrac
History of Prior Fracture (1: No, 2: Yes)
- age
Age at Enrollment (Years)
- weight
Weight at enrollment (Kilograms)
- height
Height at enrollment (Centimeters)
- bmi
Body Mass Index (Kg/m^2)
- premeno
Menopause before age 45 (1: No, 2: Yes)
- momfrac
Mother had hip fracture (1: No, 2: Yes)
- armassist
Arms are needed to stand from a chair (1: No, 2: Yes)
- smoke
Former or current smoker (1: No, 2: Yes)
- raterisk
Self-reported risk of fracture (1: Less than others of the same age, 2: Same as others of the same age, 3: Greater than others of the same age)
- fracscore
Fracture Risk Score (Composite Risk Score)
- fracture
Any fracture in first year (1: No, 2: Yes)
Source
Hosmer, D.W., Lemeshow, S. and Sturdivant, R.X. (2013) Applied Logistic Regression, 3rd ed., New York: Wiley
Examples
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 | head(glow500, n = 10)
summary(glow500)
## Table 2.2 p. 39
summary(mod2.2 <- glm(fracture ~ age + weight + priorfrac +
premeno + raterisk,
family = binomial,
data = glow500))
## Table 2.3 p. 40
summary(mod2.3 <- update(mod2.2, . ~ . - weight - premeno))
## Table 2.4 p. 44
vcov(mod2.3)
## Table 3.6 p. 58
contrasts(glow500$raterisk)
## Contrasts: Table 3.8 and 3.9 p. 60
contrasts(glow500$raterisk) <- matrix(c(-1,-1,1,0,0,1), byrow= TRUE, ncol = 2)
summary(mod3.9 <- glm(fracture ~ raterisk, family = binomial,
data = glow500))
# cleaning modified dataset ...
rm(glow500)
## Table 5.1 pg 160 - Hosmer-Lemeshow test (with vcdExtra package)
mod4.16 <- glm(fracture ~ age * priorfrac + height + momfrac * armassist +
I(as.integer(raterisk) == 3) ,
family = binomial,
data = glow500)
library(vcdExtra)
summary(HLtest(mod4.16))
## Table 5.3 p. 171 - Classification table
glow500$pred4.16 <- predict(mod4.16, type = "response")
with(glow500, addmargins(table( pred4.16 > 0.5, fracture)))
## Sensitivy, specificity, ROC (using pROC)
library(pROC)
## Figure 5.3 p. 177 - ROC curve (using pROC package)
print(roc4.16 <- roc(fracture ~ pred4.16, data = glow500))
plot(roc4.16, main = "Figure 5.3 p. 177")
## Table 5.8 p. 175
vars <- c("thresholds","sensitivities","specificities")
tab5.8 <- data.frame(roc4.16[vars])
## Now, for printing/comparison purposes, steps below in order to find
## threshold values most similar to those in the table
findIndex <- function(x, y) which.min( (x-y)^2 )
cutPoints <- seq(0.05, 0.75, by = 0.05)
tableIndex <- mapply(findIndex, y = cutPoints,
MoreArgs = list(x = roc4.16$thresholds))
## And finally, let's print a reasonable approximation of table 5.8
writeLines("\nTable 5.8 p. 175\n")
tab5.8[tableIndex, ]
## Figure 5.1 p. 175
plot(specificities ~ thresholds, xlim = c(0, 1), type = "l",
xlab = "Probabilty cutoff", ylab = "Sensitivity/specificity",
ylim = c(0, 1), data = tab5.8, main = "Figure 5.1 p. 175")
with(tab5.8, lines(thresholds, sensitivities, col = "red"))
legend(x = 0.75, y = 0.55, legend = c("Sensitivity", "Specificity"),
lty = 1, col = c("red","black"))
abline(h = c(0, 1), col = "grey80", lty = "dotted")
|
Example output
sub_id site_id phy_id priorfrac age weight height bmi premeno momfrac
1 1 1 14 No 62 70.3 158 28.16055 No No
2 2 4 284 No 65 87.1 160 34.02344 No No
3 3 6 305 Yes 88 50.8 157 20.60936 No Yes
4 4 6 309 No 82 62.1 160 24.25781 No No
5 5 1 37 No 61 68.0 152 29.43213 No No
6 6 5 299 Yes 67 68.0 161 26.23356 No No
7 7 5 302 No 84 50.8 150 22.57778 No No
8 8 1 36 Yes 82 40.8 153 17.42919 No No
9 9 1 8 Yes 86 62.6 156 25.72321 No No
10 10 4 282 No 58 63.5 166 23.04398 No No
armassist smoke raterisk fracscore fracture
1 No No Same 1 No
2 No No Same 2 No
3 Yes No Less 11 No
4 No No Less 5 No
5 No No Same 1 No
6 No Yes Same 4 No
7 No No Less 6 No
8 No No Same 7 No
9 No No Same 7 No
10 No No Less 0 No
sub_id site_id phy_id priorfrac age
Min. : 1.0 Min. :1.000 Min. : 1.00 No :374 Min. :55.00
1st Qu.:125.8 1st Qu.:2.000 1st Qu.: 57.75 Yes:126 1st Qu.:61.00
Median :250.5 Median :3.000 Median :182.50 Median :67.00
Mean :250.5 Mean :3.436 Mean :178.55 Mean :68.56
3rd Qu.:375.2 3rd Qu.:5.000 3rd Qu.:298.00 3rd Qu.:76.00
Max. :500.0 Max. :6.000 Max. :325.00 Max. :90.00
weight height bmi premeno momfrac armassist
Min. : 39.90 Min. :134.0 Min. :14.88 No :403 No :435 No :312
1st Qu.: 59.90 1st Qu.:157.0 1st Qu.:23.27 Yes: 97 Yes: 65 Yes:188
Median : 68.00 Median :161.5 Median :26.42
Mean : 71.82 Mean :161.4 Mean :27.55
3rd Qu.: 81.30 3rd Qu.:165.0 3rd Qu.:30.79
Max. :127.00 Max. :199.0 Max. :49.08
smoke raterisk fracscore fracture
No :465 Less :167 Min. : 0.000 No :375
Yes: 35 Same :186 1st Qu.: 2.000 Yes:125
Greater:147 Median : 3.000
Mean : 3.698
3rd Qu.: 5.000
Max. :11.000
Call:
glm(formula = fracture ~ age + weight + priorfrac + premeno +
raterisk, family = binomial, data = glow500)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.42250 -0.74873 -0.59711 -0.06046 2.28830
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.605794 1.220668 -4.592 4.38e-06 ***
age 0.050142 0.013417 3.737 0.000186 ***
weight 0.004080 0.006926 0.589 0.555803
priorfracYes 0.679457 0.242384 2.803 0.005059 **
premenoYes 0.186958 0.276710 0.676 0.499266
rateriskSame 0.534493 0.275858 1.938 0.052676 .
rateriskGreater 0.874123 0.289157 3.023 0.002503 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 562.34 on 499 degrees of freedom
Residual deviance: 518.08 on 493 degrees of freedom
AIC: 532.08
Number of Fisher Scoring iterations: 4
Call:
glm(formula = fracture ~ age + priorfrac + raterisk, family = binomial,
data = glow500)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.42693 -0.73132 -0.60772 -0.07484 2.23819
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -4.99060 0.90270 -5.529 3.23e-08 ***
age 0.04591 0.01244 3.690 0.000224 ***
priorfracYes 0.70023 0.24116 2.904 0.003689 **
rateriskSame 0.54856 0.27501 1.995 0.046075 *
rateriskGreater 0.86576 0.28621 3.025 0.002487 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 562.34 on 499 degrees of freedom
Residual deviance: 518.90 on 495 degrees of freedom
AIC: 528.9
Number of Fisher Scoring iterations: 4
(Intercept) age priorfracYes rateriskSame
(Intercept) 0.81486728 -0.0108886686 0.0445010519 -0.0603876325
age -0.01088867 0.0001547891 -0.0008344776 0.0002239259
priorfracYes 0.04450105 -0.0008344776 0.0581588491 -0.0031271822
rateriskSame -0.06038763 0.0002239259 -0.0031271822 0.0756289050
rateriskGreater -0.08055123 0.0005370070 -0.0118441110 0.0462406814
rateriskGreater
(Intercept) -0.080551235
age 0.000537007
priorfracYes -0.011844111
rateriskSame 0.046240681
rateriskGreater 0.081913370
Same Greater
Less 0 0
Same 1 0
Greater 0 1
Call:
glm(formula = fracture ~ raterisk, family = binomial, data = glow500)
Deviance Residuals:
Min 1Q Median 3Q Max
-0.9005 -0.7726 -0.6058 -0.0838 1.8899
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.1172 0.1062 -10.514 < 2e-16 ***
raterisk1 0.0611 0.1437 0.425 0.67067
raterisk2 0.4240 0.1466 2.892 0.00383 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 562.34 on 499 degrees of freedom
Residual deviance: 550.58 on 497 degrees of freedom
AIC: 556.58
Number of Fisher Scoring iterations: 4
Loading required package: vcd
Loading required package: MASS
Loading required package: grid
Loading required package: colorspace
Loading required package: gnm
Partition for Hosmer and Lemeshow Goodness-of-Fit Test
cut total obs exp chi
1 [0.0209,0.0847] 50 47 46.68709 0.04579536
2 (0.0847,0.111] 50 46 45.13980 0.12803215
3 (0.111,0.141] 50 43 43.72511 -0.10965679
4 (0.141,0.176] 51 40 42.92385 -0.44627785
5 (0.176,0.208] 49 42 39.60399 0.38073192
6 (0.208,0.249] 50 37 38.60188 -0.25782525
7 (0.249,0.322] 50 41 35.73499 0.88075020
8 (0.322,0.388] 50 31 32.37786 -0.24214783
9 (0.388,0.482] 50 25 28.18856 -0.60056317
10 (0.482,0.747] 50 23 22.01688 0.20952147
Hosmer and Lemeshow Goodness-of-Fit Test
Call:
glm(formula = fracture ~ age * priorfrac + height + momfrac *
armassist + I(as.integer(raterisk) == 3), family = binomial,
data = glow500)
ChiSquare df P_value
6.391925 8 0.6034186
fracture
No Yes Sum
FALSE 356 103 459
TRUE 19 22 41
Sum 375 125 500
Type 'citation("pROC")' for a citation.
Attaching package: 'pROC'
The following object is masked from 'package:colorspace':
coords
The following objects are masked from 'package:stats':
cov, smooth, var
Call:
roc.formula(formula = fracture ~ pred4.16, data = glow500)
Data: pred4.16 in 375 controls (fracture No) < 125 cases (fracture Yes).
Area under the curve: 0.7286
Table 5.8 p. 175
thresholds sensitivities specificities
6 0.05006609 1.000 0.0160000
64 0.09986050 0.952 0.1973333
136 0.15020771 0.848 0.3840000
201 0.20022684 0.768 0.5520000
263 0.24951185 0.640 0.6826667
294 0.30000935 0.624 0.7653333
335 0.34960972 0.488 0.8293333
366 0.40031190 0.392 0.8800000
393 0.44967455 0.296 0.9226667
417 0.50009629 0.176 0.9493333
434 0.54891768 0.096 0.9680000
447 0.59548830 0.032 0.9813333
453 0.65647052 0.024 0.9946667
456 0.70450302 0.000 0.9946667
457 0.74119791 0.000 0.9973333
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