There is a problem in DataCamp about computing the probability of winning an NBA series. Cavs and the Warriors are playing a seven game championship series. The first to win four games wins the series. They each have a 50-50 chance of winning each game. If the Cavs lose the first game, what is the probability that they win the series?
Here is how DataCamp computed the probability using Monte Carlo simulation:
B <- 10000
set.seed(1)
results<-replicate(B,{x<-sample(0:1,6,replace=T) # 0 when game is lost and 1 when won.
sum(x)>=4})
mean(results)
Here is a different way they computed the probability using simple code:
# Assign a variable 'n' as the number of remaining games.
n<-6
# Assign a variable `outcomes` as a vector of possible game outcomes: 0 indicates a loss and 1 a win for the Cavs.
outcomes<-c(0,1)
# Assign a variable `l` to a list of all possible outcomes in all remaining games. Use the `rep` function on `list(outcomes)` to create list of length `n`.
l<-rep(list(outcomes),n)
# Create a data frame named 'possibilities' that contains all combinations of possible outcomes for the remaining games.
possibilities<-expand.grid(l) # My comment: note how this produces 64 combinations.
# Create a vector named 'results' that indicates whether each row in the data frame 'possibilities' contains enough wins for the Cavs to win the series.
rowSums(possibilities)
results<-rowSums(possibilities)>=4
# Calculate the proportion of 'results' in which the Cavs win the series.
mean(results)
Question/Problem:
They both produce approximately the same probability of winning the series ~ 0.34. However, there seems to be a flaw in the the concept and the code design. For example, the code (sampling six times) allows for combinations such as the following:
G2 G3 G4 G5 G6 G7 rowSums
0 0 0 0 0 0 0 # Series over after G4 (Cavs lose). No need for game G5-G7.
0 0 0 0 1 0 1 # Series over after G4 (Cavs lose). Double counting!
0 0 0 0 0 1 1 # Double counting!
...
1 1 1 1 0 0 4 # No need for game G6 and G7.
1 1 1 1 0 1 5 # Double counting! This is the same as 1,1,1,1,0,0.
0 1 1 1 1 1 5 # No need for game G7.
1 1 1 1 1 1 6 # Series over after G5 (Cavs win). Double counting!
> rowSums(possibilities)
[1] 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 4 3 4 4 5 1 2 2 3 2 3 3 4 2 3 3 4 3 4 4 5 2 3 3 4 3 4 4 5 3 4 4 5 4 5 5 6
As you can see, these are never possible. After winning the first four of the remaining six games, no more games should be played. Similarly, after losing the first three games of the remaining six games, no more games should be played. So these combinations shouldn't be included in the computation of the probability of winning the series. There is double counting for some of the combinations.
Here is what I did to omit some of the combinations that are not possible in real life.
outcomes<-c(0,1)
l<-rep(list(outcomes),6)
possibilities<-expand.grid(l)
possibilities<-possibilities %>% mutate(rowsums=rowSums(possibilities)) %>% filter(rowsums<=4)
But then I am not able to omit the other unnecessary combinations. For example, I want to remove two of these three: (a) 1,0,0,0,0,0 (b) 1,0,0,0,0,1 (c) 1,0,0,0,1,1. This is because no more games will be played after losing three times in a row. And they are basically double counting.
There are too many conditions for me to be able to filter them individually. There has to be a more efficient and intuitive way to do this. Can someone provide me with some hints on how to solve this whole mess?
Here is a way:
library(dplyr)
outcomes<-c(0,1)
l<-rep(list(outcomes),6)
possibilities<-expand.grid(l)
possibilities %>%
mutate(rowsums=rowSums(cur_data()),
anti_sum = rowSums(!cur_data())) %>%
filter(rowsums<=4, anti_sum <= 3)
We use the fact that r can coerce into a logical where 0 will be false. See sum(!0) as a short example.
I’m in the process of cleaning some longitudinal data and I have several missing cases. I am trying to use an imputation that incorporates observations before and after the missing case. I’m wondering how I can go about addressing the issues detailed below.
I’ve been trying to break the problem apart into smaller, more manageable operations and objects, however, the solutions I keep coming to force me to use conditional formatting based on rows immediately above and below the a missing value and, quite frankly, I’m at a bit of a loss as to how to do this. I would love a little guidance if you think you know of a good technique I can use, experiment with, or if you know of any good search terms I can use when looking up a solution.
The details are below:
#Fake dataset creation
id <- c(1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4)
time <-c(0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6)
ss <- c(1,3,2,3,NA,0,0,2,4,0,NA,0,0,0,4,1,2,4,2,3,NA,2,1,0,NA,NA,0,0)
mydat <- data.frame(id, time, ss)
*Bold characters represent changes from the dataset above
The goal here is to find a way to get the mean of the value before (3) and after (0) the NA value for ID #1 (variable ss) so that the data look like this: 1,3,2,3,1.5,0,0,
ID# 2 (variable ss) should look like this: 2,4,0,0,0,0,0
ID #3 (variable ss) should use a last observation carried forward approach, so it would need to look like this: 4,1,2,4,2,3,3
ID #4 (variable ss) has two consecutive NA values and should not be changed. It will be flagged for a different analysis later in my project. So, it should look like this: 2,1,0,NA,NA,0,0 (no change).
I use a package, smwrBase, the syntax for only filling in 1 missing value is below, but doesn't address id.
smwrBase::fillMissing(ss, max.fill=1)
The zoo package might be more standard, same issue though.
zoo::na.approx(ss, maxgap=1)
Below is an approach that accounts for the variable id. Current interpolation approaches dont like to fill in the last value, so i added a manual if stmt for that. A bit brute force as there might be a tapply approach out there.
> id <- c(1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4)
> time <-c(0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6)
> ss <- c(1,3,2,3,NA,0,0,2,4,0,NA,0,0,0,4,1,2,4,2,3,NA,2,1,0,NA,NA,0,0)
> mydat <- data.frame(id, time, ss, ss2=NA_real_)
> for (i in unique(id)) {
+ # interpolate for gaps
+ mydat$ss2[mydat$id==i] <- zoo::na.approx(ss[mydat$id==i], maxgap=1, na.rm=FALSE)
+ # extension for gap as last value
+ if(is.na(mydat$ss2[mydat$id==i][length(mydat$ss2[mydat$id==i])])) {
+ mydat$ss2[mydat$id==i][length(mydat$ss2[mydat$id==i])] <-
+ mydat$ss2[mydat$id==i][length(mydat$ss2[mydat$id==i])-1]
+ }
+ }
> mydat
id time ss ss2
1 1 0 1 1.0
2 1 1 3 3.0
3 1 2 2 2.0
4 1 3 3 3.0
5 1 4 NA 1.5
6 1 5 0 0.0
7 1 6 0 0.0
8 2 0 2 2.0
9 2 1 4 4.0
10 2 2 0 0.0
11 2 3 NA 0.0
12 2 4 0 0.0
13 2 5 0 0.0
14 2 6 0 0.0
15 3 0 4 4.0
16 3 1 1 1.0
17 3 2 2 2.0
18 3 3 4 4.0
19 3 4 2 2.0
20 3 5 3 3.0
21 3 6 NA 3.0
22 4 0 2 2.0
23 4 1 1 1.0
24 4 2 0 0.0
25 4 3 NA NA
26 4 4 NA NA
27 4 5 0 0.0
28 4 6 0 0.0
The interpolated value in id=1 is 1.5 (avg of 3 and 0), id=2 is 0 (avg of 0 and 0, and id=3 is 3 (the value preceding since it there is no following value).
I´m obviously a novice in writing R-code.
I have tried multiple solutions to my problem from stackoverflow but I'm still stuck.
My dataset is carcinoid, patients with a small bowel cancer, with multiple variables.
i would like to know how different variables are distributed
carcinoid$met_any - with metastatic disease 1=yes, 2=no(computed variable)
carcinoid$liver_mets_y_n - liver metastases 1=yes, 2=no
carcinoid$regional_lymph_nodes_y_n - regional lymph nodes 1=yes, 2=no
peritoneal_carcinosis_y_n - peritoneal carcinosis 1=yes, 2=no
i have tried this solution which is close to my wanted result
ddply(carcinoid, .(carcinoid$met_any), summarize,
livermetastases=sum(carcinoid$liver_mets_y_n=="1"),
regionalmets=sum(carcinoid$regional_lymph_nodes_y_n=="1"),
pc=sum(carcinoid$peritoneal_carcinosis_y_n=="1"))
with the result being:
carcinoid$met_any livermetastases regionalmets pc
1 1 21 46 7
2 2 21 46 7
Now, i expected the row with 2(=no metastases), to be empty. i would also like the rows in the column carcinoid$met_any to give the number of patients.
If someone could help me it would be very much appreciated!
John
Edit
My dataset, although the column numbers are: 1, 43,28,31,33
1=yes2=no
case_nr met_any liver_mets_y_n regional_lymph_nodes_y_n pc
1 1 1 1 2
2 1 2 1 2
3 2 2 2 2
4 1 2 1 1
5 1 2 1 1
desired output - I want to count the numbers of 1:s and 2:s, if it works, all 1:s should end up in the met_any=1 row
nr liver_mets regional_lymph_nodes pc
met_any=1 4 1 4 2
met_any=2 1 4 1 3
EDIT
Although i probably was very unclear in my question, with your help i could make the table i needed!
setDT(carcinoid)[,lapply(.SD,table),.SDcols=c(43,28,31,33,17)]
gives
met_any lymph_nod liver_met paraortal extrahep
1: 50 46 21 6 15
2: 111 115 140 151 146
i am very grateful! #mtoto provided the solution
John
Based on your example data, this data.table approach works:
library(data.table)
setDT(df)[,lapply(.SD,table),.SDcols=c(2:5)]
# met_any liver_mets_y_n regional_lymph_nodes_y_n pc
# 1: 4 1 4 2
# 2: 1 4 1 3