Redundancy analysis of covariates in a Cox model using flexible parametric additive models

data analysis
1

Hi there,
I want to analyze possible redundancies in a dataset that will be used to fit a Cox PH model.
As I am performing the analysis with R I chose redun() function available in HMisc package. As it is stated in RDocumentation, it “Uses flexible parametric additive models (see areg and its use of regression splines), or alternatively to run a regular regression after replacing continuous variables with ranks, to determine how well each variable can be predicted from the remaining variables. Variables are dropped in a stepwise fashion, removing the most predictable variable at each step. The remaining variables are used to predict. The process continues until no variable still in the list of predictors can be predicted with an R2 or adjusted R2 of at least r2 or until dropping the variable with the highest R2 (adjusted or ordinary) would cause a variable that was dropped earlier to no longer be predicted at least at the r2 level from the now smaller list of predictors.”

When I perform the analysis the output I get is that 3 of the covariates are redundant, and the result is very plausible and logical, but I would like to know which of the other variables contained in the dataset are those that explain more these redundant covariates.

This would be of great help because of these reasons:
1.- To better justify the removal of these covariates.
2.- To know which covariates may be removed in later analyses without losing the information of the detected redundant variables.

I have an idea of fitting areg() models with the redundant variable as Y and all other covariates as X but I don’t know in which way I can evaluate how much each X contribute in the explanation of Y.

Thank you so much for your help!
Marc

2

Can you elaborate on this sentence to establish the goal in detail?

3

Hi professor Harrell, thank you so much for your response.

My field of research is not related to medicine, I work in reliability of machinery and more precisely in centrifugal pumps of the Oil & Gas industry.

In my case study I have 25 covariates (some are categorical and others are continuous). The output of redun() function indicates that 3 of them are redundant, so I understand that these 3 covariates may be removed because they can be predicted from the other 22 available covariates.

My goal is to know how the other covariates predict these 3 redundant ones and to determine which of them ‘predict’ each one. (I assume that not all covariates predict these redundant 3). In few words: To know which covariates are the most important to predict each redundant covariate.

E.g. covariate relative density could be predicted by temperature, vapour pressure and fluid but I believe that could not be predicted by the manufacturer of a pump or by the flow or discharge pressure. And the output I get from redun() is that relative density is redundant but I don’t know which specific covariates predicts it.

Thank you for your help!
Marc

4

I just added some code to help. Until a new Hmisc comes up run two commands to bring in the new code:

source('https://raw.githubusercontent.com/harrelfe/Hmisc/master/R/redun.s')
source('https://raw.githubusercontent.com/harrelfe/Hmisc/master/R/r2describe.r')

Then save the result of redun in an object and run r2describe(that object$scores).

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5

Many thanks for your help professor Harrell, I have already tested it and it is exactly what I needed.

Very best regards for sharing!
Marc

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6

Thanks for motivating me to add this which I think helps people decode the redundancies.

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7

Hi again professor Harrell, I have rechecked the new feature and I am not sure if it works well or not.

This is the output of redun():

image

And R2 scores of each variable do not atch with the reduced information given by the output summary of redun() function.

e.g. FLUID2 in the previous summary shows a R2 prediction 0.087 and in the r2$scores a R2=0.892 is shown. Something similar happen to the other covariates.

r2describe(r2$scores)

Strongest Predictors of Each Variable With Cumulative R^2

FLUID2
REL.DENSITY (0.757) + DIN.VISCOSITY (0.861) + VAPOR.P (0.872) + TIP.SPEED (0.879) + YEAR (0.883) +DISCH.PRESS (0.885) + POWER (0.888) +NPSH.MARGIN (0.891) + EFFICIENCY (0.892) + LUBE (0.892)

SDT
LUBE (0.127) + TEMP (0.187) + DISCH.PRESS (0.21) + DIN.VISCOSITY (0.237) + BOTTOM (0.26) + SEAL.ARRGT(0.276) + TYPE3 (0.295) + FLOW.RATIO (0.309) + VIBRATIONS (0.318) + RATIO.DIAMETER (0.322)

TYPE3
DOUBLE.SUCTION (0.667) + POWER (0.732) + TIP.SPEED (0.78) + STABLE (0.801) + LUBE (0.811) + VAPOR.P (0.821)+ RATIO.DIAMETER (0.826) + YEAR (0.829) + SDT (0.831) + TEMP (0.834)

TEMP
BOTTOM (0.086) + POWER (0.133) + VAPOR.P (0.164) + LUBE (0.181) + SDT (0.205) + SEAL.ARRGT (0.219) + TYPE3(0.237) + FLOW.RATIO (0.25) + STABLE (0.253) + SEAL.TYPE2 (0.256)

DISCH.PRESS
TIP.SPEED (0.324) + VAPOR.P (0.373) + LUBE (0.401) + FLUID2 (0.425) + NPSH.MARGIN (0.45) + POWER (0.467) +EFFICIENCY (0.519) + RPM (0.558) + STABLE (0.574) + REL.DENSITY (0.587)

YEAR
VIBRATIONS (0.201) + NPSH.MARGIN (0.285) + SEAL.TYPE2 (0.318) + TIP.SPEED (0.334) + REL.DENSITY (0.363) +SEAL.ARRGT (0.374) + TYPE3 (0.39) + RPM (0.398) + STABLE (0.404) + SDT (0.41)

DOUBLE.SUCTION
TYPE3 (0.667) + TIP.SPEED (0.679) + DISCH.PRESS (0.696) + POWER (0.705) + STABLE (0.709) + RATIO.DIAMETER(0.712) + VIBRATIONS (0.715) + VAPOR.P (0.717) + EFFICIENCY (0.718) + LUBE (0.719)

RPM
TIP.SPEED (0.226) + POWER (0.429) + SEAL.ARRGT (0.508) + DISCH.PRESS (0.546) + STABLE (0.585) + VAPOR.P(0.605) + LUBE (0.618) + TYPE3 (0.626) + EFFICIENCY (0.631) + YEAR (0.635)

POWER
EFFICIENCY (0.472) + TIP.SPEED (0.699) + TYPE3 (0.789) + DISCH.PRESS (0.805) + VAPOR.P (0.826) + VIBRATIONS(0.836) + RPM (0.846) + DOUBLE.SUCTION (0.851) + STABLE (0.855) + REL.DENSITY (0.858)

VIBRATIONS
POWER (0.324) + YEAR (0.424) + TIP.SPEED (0.466) + DISCH.PRESS (0.477) + SDT (0.491) + DOUBLE.SUCTION(0.495) + NPSH.MARGIN (0.499) + LUBE (0.502) + SEAL.ARRGT (0.505) + FLUID2 (0.506)

SEAL.ARRGT
SEAL.TYPE2 (0.269) + RPM (0.398) + NPSH.MARGIN (0.416) +RATIO.DIAMETER (0.436) + TEMP (0.451) + STABLE(0.462) + EFFICIENCY (0.486) + TIP.SPEED (0.5) + SDT (0.511) + LUBE (0.517)

SEAL.TYPE2
SEAL.ARRGT (0.269) + REL.DENSITY (0.382) + EFFICIENCY (0.442) + YEAR (0.455) + NPSH.MARGIN (0.469) + RATIO.DIAMETER (0.479) + STABLE (0.487) + VAPOR.P (0.492) + VIBRATIONS (0.495) + FLOW.RATIO (0.497)

BOTTOM
TEMP (0.086) + NPSH.MARGIN (0.109) + SDT (0.126) + DISCH.PRESS (0.134) + DIN.VISCOSITY (0.143) + REL.DENSITY (0.154) + TIP.SPEED (0.164) + VAPOR.P (0.168) + LUBE (0.171) + EFFICIENCY (0.175)

FLOW.RATIO
VAPOR.P (0.036) + TEMP (0.05) + TYPE3 (0.06) + SDT (0.075) + YEAR (0.081) + DOUBLE.SUCTION (0.084) + POWER(0.087) + STABLE (0.091) + SEAL.ARRGT (0.094) + SEAL.TYPE2 (0.099)

NPSH.MARGIN
VAPOR.P (0.122) + YEAR (0.201) + DISCH.PRESS (0.224) + BOTTOM (0.233) + SEAL.ARRGT (0.241) + SEAL.TYPE2(0.26) + SDT (0.263) + TEMP (0.266) + RATIO.DIAMETER (0.268) + TIP.SPEED (0.27)

REL.DENSITY
FLUID2 (0.757) + DIN.VISCOSITY (0.904) + VAPOR.P (0.921) + YEAR (0.926) + SEAL.TYPE2 (0.927) + NPSH.MARGIN(0.928) + SDT (0.928) + POWER (0.929) + EFFICIENCY (0.93) + DISCH.PRESS (0.932)

DIN.VISCOSITY
VAPOR.P (0.416) + REL.DENSITY (0.473) + FLUID2 (0.643) + TYPE3 (0.668) + SDT (0.679) + YEAR (0.685) + LUBE(0.691) + BOTTOM (0.694) + POWER (0.695) + RATIO.DIAMETER (0.696)

VAPOR.P
REL.DENSITY (0.419) + FLUID2 (0.549) + DISCH.PRESS (0.562) + NPSH.MARGIN (0.577) + DIN.VISCOSITY (0.591) +RPM (0.601) + POWER (0.61) + TEMP (0.618) + TYPE3 (0.624) + STABLE (0.631)

TIP.SPEED
DISCH.PRESS (0.324) + FLUID2 (0.458) + STABLE (0.542) + RPM (0.579) + POWER (0.641) + EFFICIENCY (0.706) +LUBE (0.718) + VIBRATIONS (0.724) + YEAR (0.737) + DOUBLE.SUCTION (0.744)

RATIO.DIAMETER
RPM (0.073) + DISCH.PRESS (0.094) + SEAL.ARRGT (0.12) + TYPE3 (0.133) + DOUBLE.SUCTION (0.139) + POWER(0.145) + STABLE (0.161) + SEAL.TYPE2 (0.168) + EFFICIENCY (0.174) + SDT (0.178)

EFFICIENCY
POWER (0.472) + TIP.SPEED (0.619) + STABLE (0.668) + RPM (0.696) + REL.DENSITY (0.711) + DISCH.PRESS(0.727) + SEAL.ARRGT (0.732) + SEAL.TYPE2 (0.736) + RATIO.DIAMETER (0.739) + SDT (0.741)

STABLE
TIP.SPEED (0.211) + EFFICIENCY (0.328) + RPM (0.446) + SEAL.ARRGT (0.48) + TYPE3 (0.516) + RATIO.DIAMETER(0.529) + YEAR (0.541) + SEAL.TYPE2 (0.548) + DOUBLE.SUCTION (0.552) + POWER (0.556)

LUBE
TYPE3 (0.197) + RPM (0.304) + SDT (0.331) + SEAL.ARRGT (0.346) + VIBRATIONS (0.353) + TEMP (0.358) + FLUID2(0.362) + TIP.SPEED (0.365) + POWER (0.37) + EFFICIENCY (0.375)

What are your thoughts about this issue?

Thank you!
Marc

8

It does look like a bug. The results are not supposed to match exactly because the R^2 summary uses the last solved-for transformation of each variable, and the regular redun output uses the current transformation. If you can create a simple example using simulated data that fails I can debug. Start by seeing if the example in the redun help file fails for the R^2 summary.

9

Hi,
I’ve tested the function and seems to work well with the examples of redun help file.

I think that maybe there was a misunderstanding in my interpretation of the results, because I’ve experienced this issue with categorical covariates, and I did not see this sentence that is shown in the output of``redun` function:

(For categorical variables the minimum R^2 for any sufficiently
frequent dummy variable is displayed)

So it has sense that for FLUID2 (categorical covariate) the summary shows a R2 prediction 0.087 and in the r2$scores a R2=0.892 is shown, because it only considers one of the dummy variable predictability.

Does this explanation make sense to you?

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10

Yes and you might also see if the allcat option does anything good for you.

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11

Dear all,
Is there an optimal (or widely approved) threshold for the r2 cutoff in the redundancy analysis?
Thanks a lot
Marco

12

No; it’s all relative. What is redundant enough with a large sample size might not be treated as redundant with a smaller one.

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