# Tests the null hypothesis that the age at the onset of senescence is the same in two groups The function takes as input a log-likelihood function defining a statistical model of the senescence and two datasets. It performs a likelihood ratio test of the null hypothesis that the age at the onset of senescence is the same in the two groups. ```r onset.test(ll, data1, data2, search.range, CI.lvl=0.95, tol=.Machine$double.eps^0.25, warn=FALSE, do.plot=FALSE, plot.file=NULL, grid.len=100) ``` ## Arguments - `ll`: A function computing the log-likelihood of data under a statistical model of the senescence. - `data1`: A data.frame object containing the data for the first group. - `data2`: A data.frame object containing the data for the second group. - `search.range`: The range over which the log-likelihood should be maximized with respect to the age at the onset of senescence. - `CI.lvl`: An optional confidence level to obtain a confidence interval for each onset estimate. No confidence interval is computed if `NA`. Default `0.95`. - `tol`: A tolerance, to be passed to the optimize function. Optional. - `warn`: A logical variable indicating whether the function should issue a warning when the computed likelihood ratio is negative (which may happen for numerical reasons). Optional. - `do.plot`: A logical variable indicating whether the function should produce a plot of the log-likelihood against age at the onset of senescence (with vertical dotted lines indicating the confidence interval if `CI.lvl` is not `NA`). Optional (default `FALSE`). - `plot.file`: If not `NULL` and `do.plot` is `TRUE`, the function makes the plot in a pdf file with name `plot.file`. Optional (default `NULL`). - `grid.len`: Integer value. If `do.plot` is `TRUE`, specifies the number of onset values for which the log-likelihood is evaluated between `search.range[1]` and `search.range[2]`. Optional (default `100`). ## Returns A `list` with elements: - **pv**: A p-value for the tested null hypothesis. - **est.1**: A maximum likelihood estimate for the age at the onset of senescence in the first group. - **est.2**: A maximum likelihood estimate for the age at the onset of senescence in the second group. - **est.joint**: A maximum likelihood estimate for the age at the onset of senescence in the merged groups. - **CI.1**: A confidence interval for the age at the onset of senescence in the first group, with confidence level `CI.lvl` (`NA` if `CI.lvl` is `NA`). - **CI.2**: A confidence interval for the age at the onset of senescence in the second group, with confidence level `CI.lvl` (`NA` if `CI.lvl` is `NA`). - **joint.CI**: A confidence interval for the age at the onset of senescence in the total group, with confidence level `CI.lvl` (`NA` if `CI.lvl` is `NA`). - **lh0**: The log-likelihood maximized under the null hypothesis. - **lh1**: The log-likelihood maximized under the alternative hypothesis. - **llr**: The likelihood ratio statistic. - **cvg.ok**: A logical variable indicating whether the computed likelihood ratio was negative (the returned value is `0` in this case). ## Examples ```r if(requireNamespace("lme4", quietly=TRUE)) { data(RoeDeerMassData) RoeDeerMassData$ID <- factor(RoeDeerMassData$ID) RoeDeerMassData$cohort <- factor(RoeDeerMassData$cohort) dataFCH <- RoeDeerMassData[RoeDeerMassData$sex%in%"F"& RoeDeerMassData$population%in%"CH", ] dataMCH <- RoeDeerMassData[RoeDeerMassData$sex%in%"M"& RoeDeerMassData$population%in%"CH", ] dataFTF <- RoeDeerMassData[RoeDeerMassData$sex%in%"F"& RoeDeerMassData$population%in%"TF", ] dataMTF <- RoeDeerMassData[RoeDeerMassData$sex%in%"M"& RoeDeerMassData$population%in%"TF", ] ## b1: function for piecewise regression (transforms x into 0 before bp) b1 <- function(x, bp) ifelse(x < bp, 0, x - bp) ## Use this function to define the model in which the differential ## onset hypothesis is tested. ll <- function(thr, dataIn){ logLik(lme4::lmer(body.mass ~ b1(age, thr) + age.at.last.capture + last.year.of.capture + (1|ID) + (1|cohort), data=dataIn, REML="FALSE")) } search.range <- c(6,12) # data not available before 6 years old search.range.TF <- search.range.CH <- search.range ## Not run: # if you don't run the example in RStudio, create a new graphic # window with suitable dimensions if(.Platform$GUI!="RStudio") {dev.new(width=15, height=5)} # all graphs are square par(pty="s") # test for Trois Fontaines res.tf <- onset.test(ll, dataFTF, dataMTF, search.range.TF, do.plot=TRUE) if(.Platform$GUI!="RStudio") {dev.new(width=15, height=5)} par(pty="s") # test for Chizé res.ch <- onset.test(ll, dataFCH, dataMCH, search.range.CH, do.plot=TRUE) cat(sprintf("p-value for differential age at onset is %g in Trois Fontaines, %g in Chizé", res.tf$pv, res.ch$pv)) ## End(Not run) # a shorter executable example for Trois Fontaines set.seed(40) shortdataFTF <- dataFTF[sample(1:NROW(dataFTF), 200), ] shortdataMTF <- dataMTF[sample(1:NROW(dataMTF), 100), ] res.tf.short <- onset.test(ll, shortdataFTF, shortdataMTF, search.range.TF, do.plot=FALSE, CI.lvl=NA) } ```

onset.test function