Bioequivalence and Bioavailability Forum • lag-times of profiles and cor()

lag-times of profiles and cor() [🇷 for BE/BA]

posted by Helmut – Vienna, Austria, 2024-04-04 11:39 (459 d 11:10 ago) – Posting: # 23933
Views: 10,094

Hi ElMaestro,

❝ It all relates to SaToWIB and the functions that compare two concentration vectors…

A word of caution: If you have lag-times, a simple correlation of concentrations might be small even if profiles are very similar. Generate a profile (for simplicity with equally spaced sampling times) and shift the second one. Try this one:

t <- seq(0, 24, 0.5) lag <- 2 c1 <- exp(-log(2) / 4 * t) - exp(-log(2) / 1 * t) # no lag-time c2 <- exp(-log(2) / 4 * (t - lag)) - exp(-log(2) / 1 * (t - lag)) # lag-time c2[c2 < 0] <- NA plot(t, c1, type = "l", ylab = "c", las = 1) lines(t, c2) data <- data.frame(t = t, c1 = c1, c2 = c2) m1 <- lm(c2 ~ c1, data = data) m2 <- lm(c2 ~ c1 * t, data = data) res <- data.frame(model = c("Pearson", "simple", "nested"), r.sq = c(cor(data$c2, data$c1, use = "complete.obs"), summary(m1)$r.squared, summary(m2)$r.squared), r.sq.adj = c(NA, summary(m1)$adj.r.squared, summary(m2)$adj.r.squared)) # shift c2 by the estimated lag-time c3 <- c2[tail(which(c2 == 0), 1):length(c2)] c3 <- c(c3, rep(NA, length(c1) - length(c3))) ski <- paste("correlation of shifted profiles =", cor(c3, c1, use = "complete.obs"), "\n") print(res, row.names = FALSE); cat(ski) model r.sq r.sq.adj Pearson 0.8059089 NA simple 0.6494891 0.6413377 nested 0.9711260 0.9690133 correlation of shifted profiles = 1

Only in the nested model (taking time into account) we see that profiles are highly correlated.
If you are courageous, estimate the lag-time and shift the profile(s). Of course, this works only with equally spaced intervals, which we never have. Hence, I would opt for the nested model.

# visualize why the simple model is crap plot(c1, c2, ylab = "c2, c3", las = 1, col = "blue") abline(coef(m1), col = "blue") # out of competition points(c1, c3, col = "red") abline(lm(c3 ~ c1), col = "red")

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Complete thread:

The order function ElMaestro 2024-03-24 17:07 [🇷 for BE/BA]
- The order function ElMaestro 2024-03-24 20:31
  - The order function Helmut 2024-03-24 21:12
  - The order function d_labes 2024-03-26 19:58
    - The order function ElMaestro 2024-03-27 08:43
      - The sort function Helmut 2024-04-02 10:51
        
        The sort function ElMaestro 2024-04-02 22:44
        
        lag-times of profiles and cor()Helmut 2024-04-04 09:39
        
        Roaster VII/VIII, Bandana Castor, and Effiou ElMaestro 2024-04-04 12:30
        
        Nomen est omen Helmut 2024-04-04 13:04
        
        Nomen est omen ElMaestro 2024-04-04 13:50
        
        Nomen est omen Ohlbe 2024-04-04 14:52
        
        Nomen est omen ElMaestro 2024-04-04 16:16
        
        Nomen est omen nobody 2024-04-10 09:21
        
        Nomen est omen Ohlbe 2024-04-10 09:34
        
        Nomen est omen nobody 2024-04-10 10:21
        
        Source ElMaestro 2024-04-11 10:50
        
        Source nobody 2024-04-12 11:46
        
        Inquiry Ohlbe 2024-04-12 18:23
        
        Inquiry nobody 2024-04-15 09:54