# (K)inetic (O)utlier (D)etection using several methods Identifies and/or removes qPCR runs according to several published methods or own ideas. The univariate measures are based on efficiency or difference in first/second derivative maxima. Multivariate methods are implemented that describe the structure of the curves according to several fixpoints such as first/second derivative maximum, slope at first derivative maximum or plateau fluorescence. These measures are compared with a set of curves using the `mahalanobis` distance with a robust covariance matrix and calculation of statistics by a $\chi^2$ distribution. See 'Details'. ```r KOD(object, method = c("uni1", "uni2", "multi1", "multi2", "multi3"), par = parKOD(), remove = FALSE, verbose = TRUE, plot = TRUE, ...) ``` ## Arguments - `object`: an object of class 'modlist' or 'replist'. - `method`: which method to use for kinetic outlier identification. Method `"uni1"` is default. See 'Details' for all methods. - `par`: parameters for the different `method`s. See `parKOD`. - `remove`: logical. If `TRUE`, outlier runs are removed and the object is updated. If `FALSE`, the individual qPCR runs are tagged as 'outliers' or not. See 'Details'. - `verbose`: logical. If `TRUE`, all calculation steps and results are displayed on the console. - `plot`: logical. If `TRUE`, a multivariate plot is displayed. - `...`: any other parameters to be passed to `sliwin`, `efficiency` or `expfit`. ## Details The following methods for the detection of kinetic outliers areimplemented `uni1`: KOD method according to Bar et al. (2003). Outliers are defined by removing the sample efficiency from the replicate group and testing it against the remaining samples' efficiencies using a Z-test: $$ P = 2 \cdot \left[1 - \Phi\left(\frac{e_i - \mu_{train}}{\sigma_{train}}\right)\right] < 0.05 $$ `uni2`: This method from the package author is more or less a test on sigmoidal structure for the individual curves. It is different in that there is no comparison against other curves from a replicate set. The test is simple: The difference between first and second derivative maxima should be less than 10 cycles: $$ \left(\frac{\partial^3 F(x;a,b,...)}{\partial x^3} = 0\right) - \left(\frac{\partial^2 F(x;a,b...)}{\partial x^2} = 0\right) < 10 $$ Sounds astonishingly simple, but works: Runs are defines as 'outliers' that really failed to amplify, i.e. have no sigmoidal structure or are very shallow. It is the default setting in `modlist`. `multi1`: KOD method according to Tichopad et al. (2010). Assuming two vectors with first and second derivative maxima $t_1$ and $t_2$ from a 4-parameter sigmoidal fit within a window of points around the first derivative maximum, a linear model $t_2 = t_1 \cdot b + a + \tau$ is made. Both $t_1$ and the residuals from the fit $\tau = t_2 - \hat{t_2}$ are Z-transformed: $$ t_1(norm) = \frac{t_1 - \bar{t}_1}{{\sigma_t}_1}, \; {\tau_1}_{norm} = \frac{\tau_1 - \bar{\tau}_1}{{\sigma_\tau}_1} $$ Both $t_1$ and $\tau$ are used for making a robust covariance matrix. The outcome is plugged into a `mahalanobis` distance analysis using the 'adaptive reweighted estimator' from package 'mvoutlier' and p-values for significance of being an 'outlier' are deduced from a $\chi^2$ distribution. If more than two parameters are supplied, `princomp` is used instead. `multi2`: Second KOD method according to Tichopad et al. (2010), mentioned in the paper. Uses the same pipeline as `multi1`, but with the slope at the first derivative maximum and maximum fluorescence as parameters: $$ \frac{\partial F(x;a,b,...)}{\partial x}, F_{max} $$ `multi3`: KOD method according to Sisti et al. (2010). Similar to `multi2`, but uses maximum fluorescence, slope at first derivative maximum and y-value at first derivative maximum as fixpoints: $$ \frac{\partial F(x;a,b,...)}{\partial x}, F\left(\frac{\partial^2 F(x;a,b,...)}{\partial x^2} = 0\right), F_{max} $$ All essential parameters for the methods can be tweaked by `parKOD`. See there and in 'Examples'. ## Returns An object of the same class as in `object` that is 'tagged' in its name (**name**) if it is an outlier and also with an item `$isOutlier` with outlier information (see `is.outlier`). If `remove = TRUE`, the outlier runs are removed (and the fitting updated in case of a 'replist'). ## Author(s) Andrej-Nikolai Spiess ## See Also Function `is.outlier` to get an outlier summary. ## References Kinetic Outlier Detection (KOD) in real-time PCR. Bar T, Stahlberg A, Muszta A & Kubista M. **Nucl Acid Res** (2003), 31 : e105. Quality control for quantitative PCR based on amplification compatibility test. Tichopad A, Bar T, Pecen L, Kitchen RR, Kubista M &, Pfaffl MW. **Methods** (2010), 50 : 308-312. Shape based kinetic outlier detection in real-time PCR. Sisti D, Guescini M, Rocchi MBL, Tibollo P, D'Atri M & Stocchi V. **BMC Bioinformatics** (2010), 11 : 186. ## Examples ```r ## kinetic outliers: ## on a 'modlist', using efficiency from sigmoidal fit ## and alpha = 0.01. ## F7.3 detected as outlier (shallower => low efficiency) ml1 <- modlist(reps, 1, c(2:5, 28), model = l5) res1 <- KOD(ml1, method = "uni1", par = parKOD(eff = "sliwin", alpha = 0.01)) plot(res1) ## Sigmoidal outliers: ## remove runs without sigmoidal structure. ml2 <- modlist(testdat, model = l5) res2 <- KOD(ml2, method = "uni2", remove = TRUE) plot(res2, which = "single") ## Not run: ## Multivariate outliers: ## a few runs are identified. ml3 <- modlist(reps, model = l5) res3 <- KOD(ml3, method = "multi1") ## On a 'replist', several outliers identified. rl3 <- replist(ml3, group = gl(7, 4)) res4 <- KOD(rl3, method = "uni1") ## End(Not run) ```

KOD.rd function