R/ispline1.R

In SCCS: The Self-Controlled Case Series Method

ispline1 <- function(x, knots1, m) {    # ispline1 is a function that evaluates integral of an I-spline
  
  # x is a vector of values to compute the I-spline at
  # i ith I-spline, k= knots vector, m= order
  # m <- order 4
  # k <-knots (the knots used in computing M-splines of order 5 should be used
  # in computing the I-splines)
  
  dk <- knots1[2]-knots1[1]
  k  <- c(knots1[1]-dk*(4:1), knots1, knots1[length(knots1)]+dk*(1:4))
  k6  <- c(knots1[1]-dk*(5:1), knots1, knots1[length(knots1)]+dk*(1:5))
  
  msplinedesign6 <- dmsplinedesign (x, knots1, 6, deriv=0) # A matrix of order 6 to be used in computing the I-splines (integral of the M-splines of order 5),
  # k6 = knots6 is the set of knots used to compute M-splines of order 6
  
  d <- length(k)-m-1 # number of columuns for the I-sipline matrices
  resu <- matrix(0, length(x), length(k)-m-1)
  for (j in 1:length(x))
    for (i in 1:(length(k)-m-1))
      if (x[j]>k[i+m+1]){
        # resu[j,i] <- 1
        resu[j,i] <- (x[j]-k[i+m+1]) + ((k[i+m+1+1]-k[i+1])/(m+1))*((((k6[i+m+2+1]-k6[i+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+1+1])) + (((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+1+1+1])) + (((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+2+1+1])) + (((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+3+1+1])))
        
        + ((k[i+1+m+1+1]-k[i+1+1])/(m+1))*((((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+1+1+1])) + (((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+2+1+1])) + (((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+3+1+1])))
        + ((k[i+2+m+1+1]-k[i+2+1])/(m+1))*((((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+2+1+1])) + (((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+3+1+1])))
        + ((k[i+3+m+1+1]-k[i+3+1])/(m+1))*((((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*((dmsplinedesign(k[i+m+1], knots1, 6, deriv=0))[1,i+3+1+1])))
      } else if (x[j] < k[i+1]) {
        # resu[j,i]<- 0
        resu[j,i]<- 0
      } else if (x[j]> k[i+1] && x[j]<=k[i+1+1]) {
        # resu[j,i] <- (k[i+m+1]-k[i])*(msplinedesign5[j,i])/(m+1)
        resu[j,i] <- ((k[i+m+1+1]-k[i+1])/(m+1))*((k6[i+m+2+1]-k6[i+1])/(m+2))*(msplinedesign6[j,i+1+1])
      } else if (x[j]>k[i+1+1] && x[j]<=k[i+2+1]) {
        # resu[j,i] <- (k[i+m+1]-k[i])*(msplinedesign5[j,i])/(m+1) + (k[i+1+m+1]-k[i+1])*(msplinedesign5[j,i+1])/(m+1)
        resu[j,i] <- ((k[i+m+1+1]-k[i+1])/(m+1))*((((k6[i+m+2+1]-k6[i+1])/(m+2))*(msplinedesign6[j,i+1+1])) + (((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*(msplinedesign6[j,i+1+1+1]))) + ((k[i+1+m+1+1]-k[i+1+1])/(m+1))*(((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*(msplinedesign6[j,i+1+1+1]))
      } else if (x[j]>k[i+2+1] && x[j] <= k[i+3+1]){
        # resu[j,i] <- (k[i+m+1]-k[i])*(msplinedesign5[j,i])/(m+1) + (k[i+1+m+1]-k[i+1])*(msplinedesign5[j,i+1])/(m+1) + (k[i+2+m+1]-k[i+2])*(msplinedesign5[j,i+2])/(m+1)
        resu[j,i] <- ((k[i+m+1+1]-k[i+1])/(m+1))* ((((k6[i+m+2+1]-k6[i+1])/(m+2))*(msplinedesign6[j,i+1+1])) + (((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*(msplinedesign6[j,i+1+1+1])) + (((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*(msplinedesign6[j,i+2+1+1]))) + ((k[i+1+m+1+1]-k[i+1+1])/(m+1))* ((((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*(msplinedesign6[j,i+1+1+1])) + (((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*(msplinedesign6[j,i+2+1+1]))) + ((k[i+2+m+1+1]-k[i+2+1])/(m+1)) * (((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*(msplinedesign6[j,i+2+1+1]))
        
      } else
        #if (x>=k[i+3] && x < k[i+4])
      {
        # resu[j,i] <- (k[i+m+1]-k[i])*(msplinedesign5[j,i])/(m+1) + (k[i+1+m+1]-k[i+1])*(msplinedesign5[j,i+1])/(m+1) + (k[i+2+m+1]-k[i+2])*(msplinedesign5[j,i+2])/(m+1) + (k[i+3+m+1]-k[i+3])*(msplinedesign5[j,i+3])/(m+1)
        resu[j,i] <- ((k[i+m+1+1]-k[i+1])/(m+1))*((((k6[i+m+2+1]-k6[i+1])/(m+2))*(msplinedesign6[j,i+1+1])) + (((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*(msplinedesign6[j,i+1+1+1])) + (((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*(msplinedesign6[j,i+2+1+1])) + (((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*(msplinedesign6[j,i+3+1+1]))) + ((k[i+1+m+1+1]-k[i+1+1])/(m+1))*((((k6[i+1+m+2+1]-k6[i+1+1])/(m+2))*(msplinedesign6[j,i+1+1+1])) + (((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*(msplinedesign6[j,i+2+1+1])) + (((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*(msplinedesign6[j,i+3+1+1]))) + ((k[i+2+m+1+1]-k[i+2+1])/(m+1))*((((k6[i+2+m+2+1]-k6[i+2+1])/(m+2))*(msplinedesign6[j,i+2+1+1])) + (((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*(msplinedesign6[j,i+3+1+1]))) + ((k[i+3+m+1+1]-k[i+3+1])/(m+1))*(((k6[i+3+m+2+1]-k6[i+3+1])/(m+2))*(msplinedesign6[j,i+3+1+1]))
        
      }
  return(resu[,1:(d-1)])
}