Tests for Linear Trends in Proportions

# Test for trends in proportions, based on scores
score.prop.test <- function(x) {
  colsum <- apply(x,2,sum)
  rowsum <- apply(x,1,sum)
  propcol <- x[1,]/colsum
  frate <- rowsum[1]/sum(rowsum)
  if(ncol(x)%%2 == 0) {
    scores <- seq(2,ncol(x)*2,by=2)-(ncol(x)+1)
  } else {
    scores <- 1:ncol(x)-ceiling(ncol(x)/2)
  }
  scoresMean <- sum(colsum*scores)/sum(colsum)
  Npxx <- sum(colsum*propcol*(scores-scoresMean))
  Nxx2 <- sum(colsum*(scores-scoresMean)^2)
  b <- Npxx/Nxx2
  Vb <- (frate*(1-frate))/Nxx2
  X2 <- (b^2)/Vb
  df <- ifelse(ncol(x) <= 2, 1, ncol(x)-2)
  pvalue <- 1-pchisq(X2,df)
  structure(list("b"=b, "V(b)"=Vb, "X squared"=X2, "df"=df, "p-value"=pvalue))
}

# TEST

# Relationship between nasal carrier rate for Streptococcus pyogenes and size of tonsils.
stcarriers <- matrix(c( 19, 29, 24,
                       497,560,269),
                     ncol=3, byrow=TRUE)

score.prop.test(stcarriers)

# Armitage, P. (1955). Tests for Linear Trends in Proportions and Frequencies.
# Biometrics, Vol. 11, No. 3 (Sep., 1955), pp. 375-386
# URL: http://www.jstor.org/stable/3001775