cutpointr is an R package for tidy calculation of “optimal” cutpoints. It supports several methods for calculating cutpoints and includes several metrics that can be maximized or minimized by selecting a cutpoint. Some of these methods are designed to be more robust than the simple empirical optimization of a metric. Additionally, cutpointr can automatically bootstrap the variability of the optimal cutpoints and return out-of-bag estimates of various performance metrics.
You can install cutpointr from CRAN using the menu in RStudio or simply:
For example, the optimal cutpoint for the included data set is 2 when maximizing the sum of sensitivity and specificity.
## age gender dsi suicide ## 1 29 female 1 no ## 2 26 male 0 no ## 3 26 female 0 no ## 4 27 female 0 no ## 5 28 female 0 no ## 6 53 male 2 no
## Assuming the positive class is yes
## Assuming the positive class has higher x values
## Method: maximize_metric ## Predictor: dsi ## Outcome: suicide ## Direction: >= ## ## AUC n n_pos n_neg ## 0.9238 532 36 496 ## ## optimal_cutpoint sum_sens_spec acc sensitivity specificity tp fn fp tn ## 2 1.7518 0.8647 0.8889 0.8629 32 4 68 428 ## ## Predictor summary: ## Data Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD NAs ## Overall 0 0.00 0 0 0.9210526 1 5.00 11 1.852714 0 ## no 0 0.00 0 0 0.6330645 0 4.00 10 1.412225 0 ## yes 0 0.75 4 5 4.8888889 6 9.25 11 2.549821 0
When considering the optimality of a cutpoint, we can only make a judgement based on the sample at hand. Thus, the estimated cutpoint may not be optimal within the population or on unseen data, which is why we sometimes put the “optimal” in quotation marks.
cutpointr makes assumptions about the direction of the dependency between
direction and / or
neg_class are not specified. The same result as above can be achieved by manually defining
direction and the positive / negative classes which is slightly faster, since the classes and direction don’t have to be determined:
opt_cut is a data frame that returns the input data and the ROC curve (and optionally the bootstrap results) in a nested tibble. Methods for summarizing and plotting the data and results are included (e.g.
To inspect the optimization, the function of metric values per cutpoint can be plotted using
plot_metric, if an optimization function was used that returns a metric column in the
roc_curve column. For example, the
minimize_metric functions do so:
Predictions for new data can be made using
##  "no" "no" "yes" "yes" "yes" "yes"
The included methods for calculating cutpoints are:
maximize_metric: Maximize the metric function
minimize_metric: Minimize the metric function
maximize_loess_metric: Maximize the metric function after LOESS smoothing
minimize_loess_metric: Minimize the metric function after LOESS smoothing
maximize_spline_metric: Maximize the metric function after spline smoothing
minimize_spline_metric: Minimize the metric function after spline smoothing
maximize_gam_metric: Maximize the metric function after smoothing via Generalized Additive Models
minimize_gam_metric: Minimize the metric function after smoothing via Generalized Additive Models
maximize_boot_metric: Bootstrap the optimal cutpoint when maximizing a metric
minimize_boot_metric: Bootstrap the optimal cutpoint when minimizing a metric
oc_manual: Specify the cutoff value manually
oc_mean: Use the sample mean as the “optimal” cutpoint
oc_median: Use the sample median as the “optimal” cutpoint
oc_youden_kernel: Maximize the Youden-Index after kernel smoothing the distributions of the two classes
oc_youden_normal: Maximize the Youden-Index parametrically assuming normally distributed data in both classes
The included metrics to be used with the minimization and maximization methods are:
accuracy: Fraction correctly classified
abs_d_sens_spec: The absolute difference of sensitivity and specificity
abs_d_ppv_npv: The absolute difference between positive predictive value (PPV) and negative predictive value (NPV)
roc01: Distance to the point (0,1) on ROC space
cohens_kappa: Cohen’s Kappa
sum_sens_spec: sensitivity + specificity
sum_ppv_npv: The sum of positive predictive value (PPV) and negative predictive value (NPV)
prod_sens_spec: sensitivity * specificity
prod_ppv_npv: The product of positive predictive value (PPV) and negative predictive value (NPV)
youden: Youden- or J-Index = sensitivity + specificity - 1
odds_ratio: (Diagnostic) odds ratio
risk_ratio: risk ratio (relative risk)
p_chisquared: The p-value of a chi-squared test on the confusion matrix
cost_misclassification: The sum of the misclassification cost of false positives and false negatives. Additional arguments: cost_fp, cost_fn
total_utility: The total utility of true / false positives / negatives. Additional arguments: utility_tp, utility_tn, cost_fp, cost_fn
F1_score: The F1-score (2 * TP) / (2 * TP + FP + FN)
metric_constrain: Maximize a selected metric given a minimal value of another selected metric
sens_constrain: Maximize sensitivity given a minimal value of specificity
spec_constrain: Maximize specificity given a minimal value of sensitivity
acc_constrain: Maximize accuracy given a minimal value of sensitivity
Furthermore, the following functions are included which can be used as metric functions but are more useful for plotting purposes, for example in
plot_cutpointr, or for defining new metric functions:
The inputs to the arguments
metric are functions so that user-defined functions can easily be supplied instead of the built-in ones.
Cutpoints can be separately estimated on subgroups that are defined by a third variable,
gender in this case. Additionally, if
boot_runs is larger zero,
cutpointr will carry out the usual cutpoint calculation on the full sample, just as before, and additionally on
boot_runs bootstrap samples. This offers a way of gauging the out-of-sample performance of the cutpoint estimation method. If a subgroup is given, the bootstrapping is carried out separately for every subgroup which is also reflected in the plots and output.
## # A tibble: 1 x 16 ## direction optimal_cutpoint method sum_sens_spec acc sensitivity ## <chr> <dbl> <chr> <dbl> <dbl> <dbl> ## 1 >= 2 maximize_metric 1.75179 0.864662 0.888889 ## specificity AUC pos_class neg_class prevalence outcome predictor ## <dbl> <dbl> <fct> <fct> <dbl> <chr> <chr> ## 1 0.862903 0.923779 yes no 0.0676692 suicide dsi ## data roc_curve boot ## <list> <list> <list> ## 1 <tibble [532 x 2]> <roc_cutpointr [13 x 10]> <tibble [1,000 x 23]>
The returned object has the additional column
boot which is a nested tibble that includes the cutpoints per bootstrap sample along with the metric calculated using the function in
metric and various default metrics. The metrics are suffixed by
_b to indicate in-bag results or
_oob to indicate out-of-bag results:
## [] ## # A tibble: 1,000 x 23 ## optimal_cutpoint AUC_b AUC_oob sum_sens_spec_b sum_sens_spec_o~ acc_b acc_oob ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 2 0.957 0.884 1.80 1.71 0.874 0.842 ## 2 1 0.918 0.935 1.70 1.70 0.752 0.771 ## 3 2 0.920 0.946 1.79 1.73 0.874 0.864 ## 4 2 0.940 0.962 1.82 1.76 0.893 0.851 ## 5 2 0.849 0.96 1.66 1.76 0.848 0.887 ## 6 4 0.926 0.927 1.80 1.51 0.925 0.881 ## 7 2 0.927 0.919 1.74 1.78 0.885 0.862 ## 8 2 0.958 0.882 1.82 1.67 0.863 0.861 ## 9 4 0.911 0.923 1.80 1.53 0.914 0.879 ## 10 1 0.871 0.975 1.62 1.80 0.737 0.820 ## # ... with 990 more rows, and 16 more variables: sensitivity_b <dbl>, ## # sensitivity_oob <dbl>, specificity_b <dbl>, specificity_oob <dbl>, ## # cohens_kappa_b <dbl>, cohens_kappa_oob <dbl>, TP_b <dbl>, FP_b <dbl>, ## # TN_b <int>, FN_b <int>, TP_oob <dbl>, FP_oob <dbl>, TN_oob <int>, ## # FN_oob <int>, roc_curve_b <list>, roc_curve_oob <list>
The summary and plots include additional elements that summarize or display the bootstrap results:
## Method: maximize_metric ## Predictor: dsi ## Outcome: suicide ## Direction: >= ## Nr. of bootstraps: 1000 ## ## AUC n n_pos n_neg ## 0.9238 532 36 496 ## ## optimal_cutpoint sum_sens_spec acc sensitivity specificity tp fn fp tn ## 2 1.7518 0.8647 0.8889 0.8629 32 4 68 428 ## ## Predictor summary: ## Data Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD NAs ## Overall 0 0.00 0 0 0.9210526 1 5.00 11 1.852714 0 ## no 0 0.00 0 0 0.6330645 0 4.00 10 1.412225 0 ## yes 0 0.75 4 5 4.8888889 6 9.25 11 2.549821 0 ## ## Bootstrap summary: ## Variable Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD NAs ## optimal_cutpoint 1.00 1.00 2.00 2.00 2.12 2.00 4.00 4.00 0.72 0 ## AUC_b 0.83 0.88 0.91 0.93 0.92 0.94 0.96 0.98 0.02 0 ## AUC_oob 0.82 0.86 0.90 0.92 0.92 0.95 0.97 1.00 0.03 0 ## sum_sens_spec_b 1.57 1.67 1.72 1.76 1.76 1.80 1.84 1.89 0.05 0 ## sum_sens_spec_oob 1.37 1.56 1.66 1.72 1.71 1.78 1.86 1.90 0.09 0 ## acc_b 0.73 0.77 0.85 0.87 0.86 0.88 0.91 0.94 0.04 0 ## acc_oob 0.72 0.77 0.85 0.86 0.86 0.88 0.90 0.93 0.04 0 ## sensitivity_b 0.72 0.81 0.86 0.90 0.90 0.94 0.98 1.00 0.05 0 ## sensitivity_oob 0.44 0.67 0.80 0.87 0.86 0.93 1.00 1.00 0.10 0 ## specificity_b 0.72 0.76 0.85 0.86 0.86 0.88 0.91 0.94 0.04 0 ## specificity_oob 0.69 0.76 0.84 0.86 0.86 0.88 0.91 0.94 0.04 0 ## cohens_kappa_b 0.16 0.27 0.37 0.42 0.41 0.46 0.52 0.66 0.07 0 ## cohens_kappa_oob 0.15 0.25 0.34 0.39 0.39 0.44 0.51 0.62 0.08 0
doRNG the bootstrapping can be parallelized easily. The doRNG package is being used to make the bootstrap sampling reproducible.
By default, most packages only return the “best” cutpoint and disregard other cutpoints with quite similar performance, even if the performance differences are minuscule. cutpointr makes this process more explicit via the
tol_metric argument. For example, if all cutpoints are of interest that achieve at least an accuracy within
0.05 of the optimally achievable accuracy,
tol_metric can be set to
0.05 and also those cutpoints will be returned.
In the case of the
suicide data and when maximizing the sum of sensitivity and specificity, empirically the cutpoints 2 and 3 lead to quite similar performances. If
tol_metric is set to
0.05, both will be returned.
## ## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats': ## ## filter, lag
## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union
## Assuming the positive class is yes
## Assuming the positive class has higher x values
## Multiple optimal cutpoints found, applying break_ties.
## # A tibble: 2 x 2 ## optimal_cutpoint sum_sens_spec ## <dbl> <dbl> ## 1 2 1.75 ## 2 1 1.70
oc_manual function the optimal cutpoint will not be determined based on, for example, a metric but is instead set manually using the
cutpoint argument. This is useful for supplying and evaluating cutpoints that were found in the literature or in other external sources.
oc_manual function could also be used to set the cutpoint to the sample mean using
cutpoint = mean(data$x). However, this may introduce bias into the bootstrap validation procedure, since the actual mean of the population is not known and thus the mean to be used as the cutpoint should be automatically determined in every resample. To do so, the
oc_median functions can be used.
The arguments to
cutpointr do not need to be enclosed in quotes. This is possible thanks to nonstandard evaluation of the arguments, which are evaluated on
Functions that use nonstandard evaluation are often not suitable for programming with. The use of nonstandard evaluation may lead to scoping problems and subsequent obvious as well as possibly subtle errors. cutpointr uses tidyeval internally and accordingly the same rules as for programming with
dplyr apply. Arguments can be unquoted with
So far - which is the default in
cutpointr - we have considered all unique values of the predictor as possible cutpoints. An alternative could be to use a sequence of equidistant values instead, for example in the case of the
suicide data all integers in \([0, 10]\). However, with very sparse data and small intervals between the candidate cutpoints (i.e. a ‘dense’ sequence like
seq(0, 10, by = 0.01)) this leads to the uninformative evaluation of large ranges of cutpoints that all result in the same metric value. A more elegant alternative, not only for the case of sparse data, that is supported by cutpointr is the use of a mean value of the optimal cutpoint and the next highest (if
direction = ">=") or the next lowest (if
direction = "<=") predictor value in the data. The result is an optimal cutpoint that is equal to the cutpoint that would be obtained using an infinitely dense sequence of candidate cutpoints and is thus usually more efficient computationally.
This behavior can be activated by setting
use_midpoints = TRUE, which is the default. If we use this setting, we obtain an optimal cutpoint of 1.5 for the complete sample on the
suicide data instead of 2 when maximizing the sum of sensitivity and specificity.
Assume the following small data set:
Since the distance of the optimal cutpoint (8) to the next lowest observation (3) is rather large we arrive at a range of possible cutpoints that all maximize the metric. In the case of this kind of sparseness it might for example be desirable to classify a new observation with a predictor value of 4 as belonging to the negative class. If
use_midpoints is set to
TRUE, the mean of the optimal cutpoint and the next lowest observation is returned as the optimal cutpoint, if direction is
>=. The mean of the optimal cutpoint and the next highest observation is returned as the optimal cutpoint, if
direction = "<=".
## Assuming the positive class is pos
## Assuming the positive class has higher x values
A simulation demonstrates more clearly that setting
use_midpoints = TRUE avoids biasing the cutpoints. To simulate the bias of the metric functions, the predictor values of both classes were drawn from normal distributions with constant standard deviations of 10, a constant mean of the negative class of 100 and higher mean values of the positive class that are selected in such a way that optimal Youden-Index values of 0.2, 0.4, 0.6, and 0.8 result in the population. Samples of 9 different sizes were drawn and the cutpoints that maximize the Youden-Index were estimated. The simulation was repeated 10000 times. As can be seen by the mean error,
use_midpoints = TRUE eliminates the bias that is introduced by otherwise selecting the value of an observation as the optimal cutpoint. If
direction = ">=", as in this case, the observation that represents the optimal cutpoint is the highest possible cutpoint that leads to the optimal metric value and thus the biases are positive. The methods
oc_youden_kernel are always unbiased, as they don’t select a cutpoint based on the ROC-curve or the function of metric values per cutpoint.