I have a dataset containing the number of infants born per gestational week.

I am trying to determine the median gestational age of delivery based on the frequency of infants born for this particular year

For example:

and onwards, until 41 weeks. The distribution is (not surprisingly) left skewed

I also calculated cumulative frequencies using

data$cumulative_freq = cumsum(data$num_infants_born) 

Do I use the cumulative_freq column to calculate the median number of infants born that corresponds to a gestational week? Using

median(medianGA2001a$cumulative_freq)

gives me an unexpected number.

I am expecting the median GA to be around 35 weeks, based on the distribution

CodePudding user response：

If I understood your question correctly you're going to want to do something like this:

# Your gestational data:
gestational_data <- data.frame(GA_weeks = c(20:26),
                               num_infants_born = c(16,22,34,45,60,67,94))

# See the apply() documentation by running 
# ?apply

apply(gestational_data,
      1,
      function(x){
        rep(x[1],x[2])
      }) |>
  unlist()|>
  median()

CodePudding user response：

What you want is a weighted median. You first want the weeks as numeric, which you get using gsub if not yet available

dat$GA_num <- as.numeric(gsub('\\D', '', dat$GA))

Then, use weightedMedian from the matrixStats package with the number of infants as weights.

matrixStats::weightedMedian(dat$GA_num, w=dat$num_infants_born)
# [1] 24.34646

Note, that there are several definitions of the weighted mean. For a comprehensive discussion, see this answer.

Data:

dat <- structure(list(GA = c("20 weeks", "21 weeks", "22 weeks", "23 weeks", 
"24 weeks", "25 weeks", "26 weeks"), num_infants_born = c(16L, 
22L, 34L, 45L, 60L, 67L, 94L)), class = "data.frame", row.names = c(NA, 
-7L))