orsf_vi {aorsf} R Documentation

## ORSF variable importance

### Description

Estimate the importance of individual variables using oblique random survival forests.

### Usage

orsf_vi(object, group_factors = TRUE, importance = NULL, oobag_fun = NULL, ...)

orsf_vi_negate(object, group_factors = TRUE, oobag_fun = NULL, ...)

orsf_vi_permute(object, group_factors = TRUE, oobag_fun = NULL, ...)

orsf_vi_anova(object, group_factors = TRUE, ...)


### Arguments

 object (orsf_fit) a trained oblique random survival forest (see orsf). group_factors (logical) if TRUE, the importance of factor variables will be reported overall by aggregating the importance of individual levels of the factor. If FALSE, the importance of individual factor levels will be returned. importance (character) Indicate method for variable importance: 'anova': compute analysis of variance (ANOVA) importance 'negate': compute negation importance 'permute': compute permutation importance oobag_fun (function) to be used for evaluating out-of-bag prediction accuracy after negating coefficients (if importance = 'negate') or permuting the values of a predictor (if importance = 'permute') When oobag_fun = NULL (the default), Harrell's C-statistic (1982) is used to evaluate accuracy. if you use your own oobag_fun note the following: oobag_fun should have two inputs: y_mat and s_vec y_mat is a two column matrix with first column named 'time', second named 'status' s_vec is a numeric vector containing predicted survival probabilities. oobag_fun should return a numeric output of length 1 the same oobag_fun should have been used when you created object so that the initial value of out-of-bag prediction accuracy is consistent with the values that will be computed while variable importance is estimated. For more details, see the out-of-bag vignette. ... Further arguments passed to or from other methods (not currently used).

### Details

When an orsf_fit object is fitted with importance = 'anova', 'negate', or 'permute', the output will have a vector of importance values based on the requested type of importance. However, you may still want to call orsf_vi() on this output if you want to group factor levels into one overall importance value.

orsf_vi() is a general purpose function to extract or compute variable importance estimates from an 'orsf_fit' object (see orsf). orsf_vi_negate(), orsf_vi_permute(), and orsf_vi_anova() are wrappers for orsf_vi(). The way these functions work depends on whether the object they are given already has variable importance estimates in it or not (see examples).

### Value

orsf_vi functions return a named numeric vector.

• Names of the vector are the predictor variables used by object

• Values of the vector are the estimated importance of the given predictor.

The returned vector is sorted from highest to lowest value, with higher values indicating higher importance.

### Variable importance methods

negation importance: Each variable is assessed separately by multiplying the variable's coefficients by -1 and then determining how much the model's performance changes. The worse the model's performance after negating coefficients for a given variable, the more important the variable. This technique is promising b/c it does not require permutation and it emphasizes variables with larger coefficients in linear combinations, but it is also relatively new and hasn't been studied as much as permutation importance. See Jaeger, 2022 for more details on this technique.

permutation importance: Each variable is assessed separately by randomly permuting the variable's values and then determining how much the model's performance changes. The worse the model's performance after permuting the values of a given variable, the more important the variable. This technique is flexible, intuitive, and frequently used. It also has several known limitations

analysis of variance (ANOVA) importance: A p-value is computed for each coefficient in each linear combination of variables in each decision tree. Importance for an individual predictor variable is the proportion of times a p-value for its coefficient is < 0.01. This technique is very efficient computationally, but may not be as effective as permutation or negation in terms of selecting signal over noise variables. See Menze, 2011 for more details on this technique.

### Examples

#### ANOVA importance

The default variable importance technique, ANOVA, is calculated while you fit an ORSF ensemble.

fit <- orsf(pbc_orsf, Surv(time, status) ~ . - id)

fit

## ---------- Oblique random survival forest
##
##      Linear combinations: Accelerated
##           N observations: 276
##                 N events: 111
##                  N trees: 500
##       N predictors total: 17
##    N predictors per node: 5
##  Average leaves per tree: 25
## Min observations in leaf: 5
##       Min events in leaf: 1
##           OOB stat value: 0.84
##            OOB stat type: Harrell's C-statistic
##      Variable importance: anova
##
## -----------------------------------------


ANOVA is the default because it is fast, but it may not be as decisive as the permutation and negation techniques for variable selection.

#### Raw VI values

the ‘raw’ variable importance values can be accessed from the fit object

attr(fit, 'importance_values')

##     edema_1   ascites_1        bili      copper         age     albumin
##  0.41468531  0.34547820  0.27357335  0.19702602  0.17831563  0.17231851
##   edema_0.5     protime        chol       stage       sex_f   spiders_1
##  0.16100917  0.15265823  0.14529486  0.13818084  0.13186813  0.12881052
##         ast    hepato_1    alk.phos        trig    platelet trt_placebo
##  0.12509496  0.11370348  0.10024752  0.09878683  0.08006941  0.06398488


these are ‘raw’ because values for factors have not been aggregated into a single value. Currently there is one value for k-1 levels of a k level factor. For example, you can see edema_1 and edema_0.5 in the importance values above because edema is a factor variable with levels of 0, 0.5, and 1.

#### Collapse VI across factor levels

To get aggregated values across all levels of each factor,

• access the importance element from the orsf fit:

fit\$importance

##    ascites       bili      edema     copper        age    albumin    protime
## 0.34547820 0.27357335 0.26368761 0.19702602 0.17831563 0.17231851 0.15265823
##       chol      stage        sex    spiders        ast     hepato   alk.phos
## 0.14529486 0.13818084 0.13186813 0.12881052 0.12509496 0.11370348 0.10024752
##       trig   platelet        trt
## 0.09878683 0.08006941 0.06398488

• use orsf_vi() with group_factors set to TRUE (the default)

orsf_vi(fit)

##    ascites       bili      edema     copper        age    albumin    protime
## 0.34547820 0.27357335 0.26368761 0.19702602 0.17831563 0.17231851 0.15265823
##       chol      stage        sex    spiders        ast     hepato   alk.phos
## 0.14529486 0.13818084 0.13186813 0.12881052 0.12509496 0.11370348 0.10024752
##       trig   platelet        trt
## 0.09878683 0.08006941 0.06398488


Note that you can make the default returned importance values ungrouped by setting group_factors to FALSE in the orsf_vi functions or the orsf function.

#### Add VI to an ORSF

You can fit an ORSF without VI, then add VI later

fit_no_vi <- orsf(pbc_orsf,
Surv(time, status) ~ . - id,
importance = 'none')

# Note: you can't call orsf_vi_anova() on fit_no_vi because anova
# VI can only be computed while the forest is being grown.

orsf_vi_negate(fit_no_vi)

##          bili        copper           age       protime       albumin
##  0.0717336945  0.0288601792  0.0253698687  0.0110960617  0.0100020838
##          chol       ascites       spiders           ast         stage
##  0.0075015628  0.0060950198  0.0045321942  0.0044280058  0.0025526151
##         edema           sex        hepato      platelet      alk.phos
##  0.0024856369  0.0015628256  0.0004688477  0.0003646593 -0.0007293186
##          trig           trt
## -0.0020316733 -0.0061471140

orsf_vi_permute(fit_no_vi)

##           age          bili        copper       albumin          chol
##  1.109606e-02  1.083559e-02  7.032715e-03  5.157324e-03  4.636383e-03
##       protime       ascites       spiders           ast      platelet
##  4.011252e-03  3.854970e-03  2.396333e-03  1.146072e-03  5.209419e-04
##      alk.phos         edema           sex        hepato          trig
##  2.083767e-04  1.959734e-04  5.209419e-05 -4.688477e-04 -1.719108e-03
##           trt
## -3.698687e-03


#### ORSF and VI all at once

fit an ORSF and compute vi at the same time

fit_permute_vi <- orsf(pbc_orsf,
Surv(time, status) ~ . - id,
importance = 'permute')

# get the vi instantly (i.e., it doesn't need to be computed again)
orsf_vi_permute(fit_permute_vi)

##          bili           age        copper         stage       ascites
##  0.0114086268  0.0094811419  0.0055219837  0.0043238175  0.0032298395
##       albumin        hepato       protime           ast         edema
##  0.0031256512  0.0030214628  0.0029172744  0.0021358616  0.0019051588
##       spiders          chol      alk.phos      platelet           trt
##  0.0017712023  0.0013023547  0.0008335070 -0.0009376954 -0.0016149198
##           sex          trig
## -0.0020837675 -0.0022921442


You can still get negation VI from this fit, but it needs to be computed

orsf_vi_negate(fit_permute_vi)

##          bili        copper           age       protime       albumin
##  0.0773598666  0.0272452594  0.0258387164  0.0115649094  0.0084392582
##           sex          chol           ast       ascites         stage
##  0.0081787872  0.0074494686  0.0060429256  0.0058866431  0.0043238175
##        hepato         edema       spiders      platelet          trig
##  0.0040112523  0.0027684339  0.0026047093  0.0005730360  0.0002083767
##           trt      alk.phos
## -0.0003125651 -0.0016149198


### References

Harrell FE, Califf RM, Pryor DB, Lee KL, Rosati RA. Evaluating the Yield of Medical Tests. JAMA 1982; 247(18):2543-2546. DOI: 10.1001/jama.1982.03320430047030

Breiman L. Random forests. Machine learning 2001 Oct; 45(1):5-32. DOI: 10.1023/A:1010933404324

Menze BH, Kelm BM, Splitthoff DN, Koethe U, Hamprecht FA. On oblique random forests. Joint European Conference on Machine Learning and Knowledge Discovery in Databases 2011 Sep 4; pp. 453-469. DOI: 10.1007/978-3-642-23783-6_29

Jaeger BC, Welden S, Lenoir K, Speiser JL, Segar MW, Pandey A, Pajewski NM. Accelerated and interpretable oblique random survival forests. arXiv e-prints 2022 Aug; arXiv-2208. URL: https://arxiv.org/abs/2208.01129

[Package aorsf version 0.0.7 Index]