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Overview of bigPLScox

Frédéric Bertrand

2025-11-06

Introduction

The goal of bigPLScox is to provide Partial Least Squares (PLS) variants of the Cox proportional hazards model that scale to high-dimensional survival settings. The package implements several algorithms tailored for large-scale problems, including sparse, grouped, and deviance-residual-based approaches. It integrates with the bigmemory ecosystem so that data stored on disk can be analysed without exhausting RAM.

This vignette gives a quick tour of the core workflows. It highlights how to prepare data, fit a model, assess model quality, and explore advanced extensions. The complementary vignette “Getting started with bigPLScox” offers a more hands-on tutorial, while “Benchmarking bigPLScox” focuses on performance comparisons.

Package highlights

Generalised PLS Cox regression via coxgpls() with support for grouped predictors.
Sparse and structured-sparse extensions through coxsgpls() and coxspls_sgpls().
Deviance-residual estimators such as coxgplsDR() for increased robustness.
Cross-validation helpers (cv.coxgpls(), cv.coxsgpls(), …) to select the number of latent components.
Big-memory interfaces (big_pls_cox(), big_pls_cox_gd()) designed for file-backed matrices stored with bigmemory.

Available algorithms

The following modeling functions are provided:

coxgpls() for generalized PLS Cox regression.
coxsgpls() and coxspls_sgpls() for sparse and structured sparse extensions.
coxgplsDR() and coxsgplsDR() for deviance-residual-based estimation.
cv.coxgpls() and related cv.* helpers for component selection.

For stochastic gradient descent on large data the package includes big_pls_cox() and big_pls_cox_gd().

Loading an example dataset

The package ships with a small allelotyping dataset that we use throughout this vignette. The data include censoring indicators alongside a large set of predictors.

library(bigPLScox)

data(micro.censure)
data(Xmicro.censure_compl_imp)

train_idx <- seq_len(80)
Y_train <- micro.censure$survyear[train_idx]
C_train <- micro.censure$DC[train_idx]
X_train <- Xmicro.censure_compl_imp[train_idx, -40]

Fitting a PLS-Cox model

coxgpls() provides a matrix interface that mirrors survival::coxph() but adds latent components to stabilise estimation in high dimensions.

fit <- coxgpls(
  X_train,
  Y_train,
  C_train,
  ncomp = 6,
  ind.block.x = c(3, 10, 15)
)
fit
#> Call:
#> coxph(formula = YCsurv ~ ., data = tt_gpls)
#> 
#>          coef exp(coef) se(coef)      z       p
#> dim.1 -0.6003    0.5486   0.2197 -2.733 0.00628
#> dim.2 -0.6876    0.5028   0.2816 -2.442 0.01460
#> dim.3 -0.4922    0.6113   0.2498 -1.971 0.04877
#> dim.4  0.2393    1.2703   0.2861  0.836 0.40292
#> dim.5 -0.3689    0.6915   0.2200 -1.677 0.09359
#> dim.6  0.1570    1.1700   0.2763  0.568 0.56979
#> 
#> Likelihood ratio test=23.99  on 6 df, p=0.0005249
#> n= 80, number of events= 17

The summary includes convergence diagnostics, latent component information, and predicted linear predictors that can be used for risk stratification.

Model assessment

Cross-validation helps decide how many components should be retained. The cv.coxgpls() helper accepts either a matrix or a list containing x, time, and status elements.

set.seed(123)
cv_res <- cv.coxgpls(
  list(x = X_train, time = Y_train, status = C_train),
  nt = 10,
  ind.block.x = c(3, 10, 15)
)
#> CV Fold 1
#> CV Fold 2
#> CV Fold 3
#> CV Fold 4
#> CV Fold 5

cv_res
#> $nt
#> [1] 10
#> 
#> $cv.error10
#>  [1] 0.5000000 0.6013049 0.5183694 0.4226056 0.3860331 0.4071207 0.4252845
#>  [8] 0.4001223 0.4464093 0.4526887 0.4695600
#> 
#> $cv.se10
#>  [1] 0.00000000 0.03487588 0.06866706 0.07717020 0.07373734 0.07084802
#>  [7] 0.07707939 0.07247893 0.07317843 0.06341118 0.06252387
#> 
#> $folds
#> $folds$`1`
#>  [1] 31 42 69 75 72 12 66 27 71 55 58 49 11 30 37 22
#> 
#> $folds$`2`
#>  [1] 79 50 57 68 17 15 64 74 34 13 80 76 61  2 24 35
#> 
#> $folds$`3`
#>  [1] 51 43  9 62 73 32 41 78 29 18  6 16 44 59 33 48
#> 
#> $folds$`4`
#>  [1] 14 77 26 19 39 65 10 56  5  1 21 20 46 60  3 47
#> 
#> $folds$`5`
#>  [1] 67 25  7 36 53 45 23 38  8 40 54 28 52  4 70 63
#> 
#> 
#> $lambda.min10
#> [1] 1
#> 
#> $lambda.1se10
#> [1] 0

The resulting object may be plotted to visualise the cross-validated deviance or to apply one-standard-error rules when choosing the number of components.

Alternative estimators

Deviance-residual-based estimators provide increased robustness by iteratively updating residuals. Sparse variants enable feature selection in extremely high-dimensional designs.

dr_fit <- coxgplsDR(
  X_train,
  Y_train,
  C_train,
  ncomp = 6,
  ind.block.x = c(3, 10, 15)
)
dr_fit
#> Call:
#> coxph(formula = YCsurv ~ ., data = tt_gplsDR)
#> 
#>          coef exp(coef) se(coef)     z        p
#> dim.1 0.92699   2.52690  0.23301 3.978 6.94e-05
#> dim.2 0.85445   2.35008  0.27352 3.124  0.00178
#> dim.3 0.56308   1.75607  0.29847 1.887  0.05922
#> dim.4 0.49242   1.63627  0.32344 1.522  0.12789
#> dim.5 0.18706   1.20569  0.38769 0.482  0.62946
#> dim.6 0.08581   1.08960  0.31517 0.272  0.78541
#> 
#> Likelihood ratio test=51.46  on 6 df, p=2.39e-09
#> n= 80, number of events= 17

Additional sparse estimators can be invoked via coxsgpls() and coxspls_sgpls() by providing keepX or penalty arguments that control the number of active predictors per component.

Working with big data

For extremely large problems, stochastic gradient descent routines operate on memory-mapped matrices created with bigmemory. The helper below converts a standard matrix to a big.matrix and runs a small example.

X_big <- bigmemory::as.big.matrix(X_train)
big_fit <- big_pls_cox(
  X_big,
  time = Y_train,
  status = C_train,
  ncomp = 6
)
big_fit
#> $scores
#>              [,1]        [,2]        [,3]        [,4]        [,5]         [,6]
#>  [1,] -1.67104396 -1.31172970 -0.72053662  0.83758976  0.91523072  2.160972278
#>  [2,]  0.56500329 -2.40102720  1.39614422 -1.87960603 -0.09136061 -0.140687791
#>  [3,]  1.40616746 -0.69684421 -0.56989372 -0.01622647  0.68615313  0.063343145
#>  [4,]  0.58059459  0.14365512 -0.61241544 -2.57730299 -2.32512426 -1.229253581
#>  [5,]  1.42739124  0.02170243 -1.32960235  0.37746910 -1.98097619  1.172392190
#>  [6,] -1.16078731 -0.29961777 -0.22980325  0.21542915 -1.95714711 -1.283204950
#>  [7,] -1.23408322  1.33664160 -1.13549725 -0.12484523  0.20378409  1.580074806
#>  [8,]  2.94332576  0.70819715 -1.98537686 -0.15638169  0.44251820  2.001849745
#>  [9,]  0.02095444 -1.59587258 -0.68434695 -0.95788332  1.90956368 -0.964636074
#> [10,]  0.44524202 -0.96282654  2.47845180 -1.20488166 -1.04036886  1.367535052
#> [11,]  1.08512904  2.24438250 -0.38213400  0.99903346  0.58525310  3.015329777
#> [12,] -2.18125464  1.91284717 -0.28489813  1.73065024 -0.35121927 -0.198850021
#> [13,]  1.07471369 -1.43046906  0.44396702  0.85898313  1.12045349 -0.252855432
#> [14,] -1.61754215  0.88498067  0.30785096  0.77080467  0.73804337  0.443605286
#> [15,]  0.51720528 -0.94643073 -0.62399871  0.33306055  1.83769338 -0.871459432
#> [16,]  1.10085291 -1.78211236 -0.88393696  0.75099254 -0.78588660  1.584139906
#> [17,] -1.83313725 -0.43256798  0.30572026 -1.12545641 -0.19026054 -0.933739972
#> [18,] -1.94290640 -1.00042674 -0.54259313 -1.51321193 -0.16046741  1.346004692
#> [19,]  0.75005248  1.97644125 -0.63694082 -1.29752973  1.82426107 -2.266834083
#> [20,] -2.09144564  1.30983114 -0.77015689  0.30595855  1.02851410  0.391115096
#> [21,] -1.06832948 -1.79812101  1.31156771  0.23309168 -1.16799488  1.820129278
#> [22,] -0.72732728 -1.34943171  0.55404315  2.58015129  1.06548427  0.746357538
#> [23,]  0.68659962 -1.36226471  1.24958039 -0.21141390  1.32707245 -0.001936979
#> [24,]  0.64051825  0.86972749 -1.21949736  0.48197056 -1.15268954 -0.015782803
#> [25,] -3.16258865 -0.50120469 -1.44150348  1.16691956  0.34950903  0.095722045
#> [26,] -2.02253736  1.32415711  0.43825053 -0.91636530 -0.70489654 -0.110385401
#> [27,]  2.39611609  0.43308037  1.09930800  0.38042152 -0.38837697 -1.625543025
#> [28,]  1.79414318 -0.68043226 -2.08114620  0.53616832 -0.28912628 -2.437613030
#> [29,] -0.69653042  0.66341885  1.19836212 -0.87214101 -0.25326952 -3.355545199
#> [30,] -1.97105992  0.41749686  0.14848010 -1.64840958 -3.00195750 -0.439326986
#> [31,]  1.44730927 -0.03883362  1.96930809  2.91946177  1.09629507 -0.299438344
#> [32,] -1.87035902 -1.29281036  0.97050183  1.05646189 -0.41798590  1.262166994
#> [33,] -1.56262929 -1.61071056  1.91396985  0.68380944  1.16192551 -1.371079842
#> [34,] -0.30070481  1.89420490 -0.86002360 -0.93884533  2.11317196 -0.498123661
#> [35,]  1.94052729 -0.12396776 -0.50982180  2.64135497 -0.80210456 -0.757224864
#> [36,] -0.27646381  0.69498270 -0.70971117 -0.33712477  1.13985912 -0.200776009
#> [37,]  1.95839370  2.61494070  0.99400283  0.92655149 -1.80758389 -0.791362282
#> [38,] -1.19623313  1.71199889  1.69254301  1.51103508 -0.13841204 -0.954233914
#> [39,] -2.14893811 -0.42781160  0.79385084  0.40756776 -0.54150003  0.400999382
#> [40,]  0.47443255 -0.71831580  0.04438998  3.25520128  0.12572674 -0.760080990
#> [41,]  0.01038579  1.22634502  1.69247318 -0.01357900 -0.27652801 -1.539936107
#> [42,]  1.79481463 -0.92793623 -1.04005922  0.44122807  0.92921845  2.020257084
#> [43,] -2.01813391  1.06926582  2.30854724  1.73407299 -0.49604293  0.597531041
#> [44,] -0.40610435 -1.69036910  1.94673689  2.01313682 -0.98945192 -1.842766686
#> [45,] -1.15159486  0.79189839 -0.43274270 -1.99462095  1.05097661 -0.579690469
#> [46,]  0.12679724  0.57320104 -1.17330366  1.05916075 -2.70102967  1.830534303
#> [47,] -0.51382960 -1.52544274 -1.65552499 -1.58066193 -1.18635866 -0.005129010
#> [48,]  0.87538342 -1.20599642 -0.27385427 -3.14261822 -2.99232392 -1.194081029
#> [49,]  1.70751237 -0.42660178  0.97017036  1.51612272 -0.49242951  2.238275129
#> [50,] -0.08983474  0.13372715 -0.67666662 -2.00065278  1.06804125  2.219072130
#> [51,] -0.44112040  0.59609280  0.20012549 -2.31915979 -0.22759828 -0.640216836
#> [52,]  2.78002915 -4.25608264  0.29160756  0.16571098 -0.08539776 -0.540835490
#> [53,]  0.62370168 -1.02971836  0.21047586  0.52677910  1.36208648 -2.326641364
#> [54,]  1.99451623  2.01299517  3.85797376 -1.38049960 -1.40722400  0.810774141
#> [55,]  2.73032710  0.42244879  1.67364450 -0.93013251  0.11375487  0.605049105
#> [56,] -1.65794714 -0.52989444 -0.04189889 -0.05063020 -0.09582023  0.332710012
#> [57,] -2.73704777 -0.56825143 -0.24354962 -0.24131501  1.55048560  0.957924363
#> [58,] -0.10959685  1.30286539  2.42567336 -0.82654421 -0.01075101  0.851975320
#> [59,] -1.26087244  3.27637407  0.35929857  1.05281586 -1.43407403  1.173687550
#> [60,] -1.52206614  1.79489975 -0.33082720  0.99602740  1.11155205  0.196947147
#> [61,]  1.35452147  2.46037709 -0.25138125 -1.66482557  0.37463116 -0.745510708
#> [62,]  0.93541981 -0.61964456  2.09574208 -0.05569470  1.82573513  0.255991522
#> [63,]  4.36545770  0.51237927 -2.18648599  2.12424731 -0.01624430 -2.054853673
#> [64,]  0.49976873 -3.43013449 -0.78198124 -1.24522704 -1.16820750 -0.557866407
#> [65,]  2.28093675 -0.19441383  1.01226064 -3.36957600  1.56043016  1.711617208
#> [66,] -0.23703633  0.67594918 -0.28487533 -0.25598604  2.47218024  0.771870212
#> [67,] -2.44029420 -0.98292416 -2.52154120 -1.32320586 -0.36697728 -0.098037461
#> [68,]  0.08767379 -0.24619106 -2.59998415  0.14731033  0.72843686  1.170331755
#> [69,]  1.67254999  1.49937783  0.08055612 -1.75509908  1.36965516  1.595438530
#> [70,] -1.10331590 -0.15710217 -0.59222334 -0.12483345  0.24811213 -0.181938060
#> [71,]  0.19819077  1.00960968  0.71408507  1.55744834 -3.07028981 -0.333454103
#> [72,]  0.98924592  3.30582333 -1.91566026  0.02073128  1.26816027 -1.808580236
#> [73,]  1.22390387 -0.70875958  2.12356215 -0.92751738  1.52488173  0.675741852
#> [74,] -1.02295544 -0.25866087 -0.64929914 -1.83986540 -2.05540629 -0.472837941
#> [75,]  1.64172219 -1.02784392 -0.91509096  0.45459816  0.79625449  0.324813994
#> [76,]  1.81086382  0.57846179 -2.20079914  1.23378170 -2.75895200  1.521891073
#> [77,] -1.06735490 -0.29839478  0.26243399 -0.15851068  1.69887749 -1.157902139
#> [78,] -0.77628937 -0.39154284 -1.92516641  0.86589909  0.09701506 -1.663331304
#> [79,] -1.21317256  1.26811946 -0.32650975 -0.28146744  0.82285640 -1.278680182
#> [80,] -2.45392584 -2.43316354 -0.30239945  1.39063959 -0.26403844 -0.531906810
#> 
#> $loadings
#>               [,1]         [,2]          [,3]         [,4]         [,5]
#>  [1,] -0.007907408  0.270526866 -0.1346712581  0.104027296 -0.126418953
#>  [2,] -0.054350954  0.114923658 -0.0181967641  0.055624084  0.147862732
#>  [3,] -0.064944236  0.166166291  0.1379580022 -0.272085595 -0.019622197
#>  [4,]  0.288963709  0.285763351  0.0447231266 -0.101896305 -0.089373970
#>  [5,] -0.010044191  0.305929506 -0.0009855362 -0.056007642 -0.024672587
#>  [6,] -0.025766375  0.269265072 -0.1225929663 -0.112212757 -0.303260480
#>  [7,] -0.123173378  0.323683296 -0.2606000263  0.211544752  0.034075860
#>  [8,] -0.198349136  0.221068688 -0.3568604653 -0.029350155 -0.136964627
#>  [9,] -0.084633840  0.127479767 -0.1875663683  0.165442284 -0.019979445
#> [10,]  0.166891755  0.151028319 -0.3098019805  0.142754582  0.097009827
#> [11,] -0.177695228 -0.004899100  0.0753697185 -0.154844568  0.218082027
#> [12,] -0.340662705 -0.027886330 -0.0459786749 -0.009847259  0.138068558
#> [13,]  0.056267272  0.259969757  0.1625712917  0.346074069 -0.372989323
#> [14,] -0.208673053  0.245709780 -0.0495597170 -0.251617875  0.313946761
#> [15,]  0.194331074  0.138882645 -0.2437843179 -0.059446437 -0.025929835
#> [16,] -0.248947154 -0.001222654 -0.1216218398  0.110444351 -0.407289398
#> [17,] -0.099005530  0.049072511 -0.0882831462  0.322808106 -0.248102781
#> [18,] -0.105172423  0.119320545  0.0988777535 -0.130283728 -0.106904843
#> [19,] -0.149709844 -0.089084891 -0.0949332008  0.143896146 -0.081850240
#> [20,] -0.028460398 -0.003786869  0.2237221447  0.231194460  0.208863334
#> [21,]  0.070620393  0.194364490 -0.3188777229 -0.162544961  0.141954627
#> [22,] -0.054039914  0.284461778  0.0016323577  0.011418776  0.092962813
#> [23,] -0.296679452  0.219477782 -0.2099858872 -0.052896946 -0.096501018
#> [24,] -0.108014508  0.142823533  0.0323119931  0.004078892  0.062701021
#> [25,] -0.013135682 -0.096537482  0.4518069771  0.257880475 -0.118500275
#> [26,] -0.272241045  0.218515950  0.0783360106  0.187862046  0.003219405
#> [27,]  0.049764074  0.244447856  0.0327620341  0.042175147 -0.129663416
#> [28,] -0.139704253  0.047021417 -0.2203429528  0.435558684 -0.194206651
#> [29,] -0.026552492  0.334921688 -0.1487928122  0.108209934  0.299974166
#> [30,] -0.095756877  0.188706122  0.2879865577  0.031370531 -0.337816403
#> [31,] -0.286327893  0.016984916 -0.0035272670  0.104699186  0.288976162
#> [32,] -0.241861131  0.208778175 -0.0022639029  0.075523620 -0.258075127
#> [33,] -0.168318826  0.040560476 -0.0144626390  0.289249740  0.097696346
#> [34,]  0.036900098 -0.235417402  0.0176137173  0.070599690  0.119878672
#> [35,]  0.055731568  0.171898143 -0.0469189059 -0.184313250  0.017995954
#> [36,]  0.061006304 -0.255681493 -0.0962174410  0.238018538 -0.111571263
#> [37,]  0.200358213  0.055925165 -0.3570718374  0.119349191  0.331869201
#> [38,]  0.383916827 -0.040313802 -0.2055934428  0.206349543  0.097574273
#> [39,]  0.334018148 -0.178990539 -0.1786034771  0.167838017 -0.168236076
#>                [,6]
#>  [1,] -0.0049321154
#>  [2,] -0.3667098942
#>  [3,]  0.0830748871
#>  [4,]  0.0136962645
#>  [5,]  0.1582704751
#>  [6,] -0.1296597068
#>  [7,]  0.1099498946
#>  [8,]  0.0597092961
#>  [9,] -0.0555225440
#> [10,]  0.1067432490
#> [11,] -0.0376990447
#> [12,] -0.2649881493
#> [13,]  0.0002202799
#> [14,] -0.0270200862
#> [15,]  0.1911387534
#> [16,]  0.1287637590
#> [17,] -0.1407074857
#> [18,]  0.1540956062
#> [19,]  0.3096533745
#> [20,] -0.2737300615
#> [21,] -0.0529224406
#> [22,]  0.2489194502
#> [23,]  0.0884256988
#> [24,] -0.0140912439
#> [25,]  0.0044153702
#> [26,] -0.0247163277
#> [27,] -0.0398773617
#> [28,]  0.3059863737
#> [29,] -0.1474950314
#> [30,] -0.0498461608
#> [31,] -0.3479733126
#> [32,]  0.2886978056
#> [33,] -0.1241452725
#> [34,]  0.2945319290
#> [35,] -0.3082694573
#> [36,] -0.2825422619
#> [37,] -0.0534942102
#> [38,]  0.0045059335
#> [39,]  0.1130271900
#> 
#> $weights
#>               [,1]         [,2]         [,3]         [,4]          [,5]
#>  [1,]  0.052215879  0.240419308 -0.161908752  0.024740216 -0.2111604497
#>  [2,] -0.034827909  0.084474856 -0.173922160  0.067864937 -0.1175210182
#>  [3,] -0.001391453  0.141335334  0.154065251 -0.224649019  0.0089002370
#>  [4,]  0.269622725  0.313179816 -0.037979386 -0.054736782 -0.0012735403
#>  [5,]  0.027378727  0.211060958  0.007106119  0.071613945 -0.1542108542
#>  [6,] -0.002555356  0.099603511 -0.178109475 -0.187903009 -0.2954068622
#>  [7,] -0.116609767  0.181948312 -0.091708642  0.187746575  0.1348122575
#>  [8,] -0.199633821 -0.070587422 -0.459236466 -0.003164958 -0.1282159006
#>  [9,] -0.149144225 -0.050383249 -0.146224130  0.187872439  0.0326676473
#> [10,]  0.101522309  0.137118268 -0.246453561  0.093856356  0.0142865523
#> [11,] -0.189760666  0.026011039  0.053665156 -0.137372414  0.2331523845
#> [12,] -0.276556703  0.065526328 -0.067606740  0.057921765  0.1478701776
#> [13,]  0.218056618  0.280310383  0.065577276  0.231986307 -0.2279127641
#> [14,] -0.151591107  0.117880080 -0.112208565 -0.242467908  0.2201492887
#> [15,]  0.195864430  0.189164526 -0.185165309 -0.026577860  0.1077735435
#> [16,] -0.257267985 -0.042343842 -0.073419847  0.045830324 -0.2249531996
#> [17,] -0.148346511  0.020431183 -0.143372621  0.046835578 -0.3366421512
#> [18,] -0.084111601  0.053355845  0.094413706 -0.227346273 -0.0567815343
#> [19,] -0.195725609 -0.010192432 -0.019555057  0.118765157  0.0686796085
#> [20,]  0.007935439 -0.035123813  0.176232317  0.217041233 -0.0173703772
#> [21,]  0.056749548  0.140405020 -0.181444012 -0.108024779  0.0780527249
#> [22,]  0.013721499  0.193867288 -0.050439336  0.072322950  0.1762406678
#> [23,] -0.216454579  0.067135799 -0.177081772  0.015522853 -0.0345302368
#> [24,] -0.097751534  0.079034635  0.023245750  0.146139763  0.0076540950
#> [25,]  0.002239107  0.009120856  0.440139152  0.164461637 -0.1230349122
#> [26,] -0.081356991  0.257305767  0.140494374  0.136831602  0.0555499048
#> [27,]  0.173124225  0.196695428 -0.028694998  0.030037514 -0.0267072869
#> [28,] -0.073427432  0.078668734 -0.047100811  0.352253902 -0.0570259242
#> [29,]  0.050438770  0.209972241 -0.155411864  0.068260790  0.1590282865
#> [30,]  0.009624597  0.136710186  0.155944665 -0.024523385 -0.4211525788
#> [31,] -0.294404574  0.115712071  0.054534578  0.193810422  0.1746227806
#> [32,] -0.155982776  0.100292492  0.041414692 -0.030958106 -0.1892936819
#> [33,] -0.069622279  0.136210412 -0.001628406  0.296639360  0.0556256063
#> [34,]  0.015047130 -0.126879646  0.095115710  0.077653748  0.0529430847
#> [35,]  0.210646938  0.090614166 -0.054018010 -0.267620344  0.0007203354
#> [36,]  0.050204885 -0.235970969 -0.029264420  0.205742962 -0.1602293133
#> [37,]  0.187580708  0.035035882 -0.127899924  0.140120255  0.2123884365
#> [38,]  0.382605577 -0.160444754 -0.059080333  0.284081768  0.1337327840
#> [39,]  0.180538911 -0.415369848 -0.300875022  0.086247873 -0.1001053218
#>               [,6]
#>  [1,] -0.029665386
#>  [2,] -0.430577447
#>  [3,]  0.162026460
#>  [4,]  0.047873822
#>  [5,] -0.031603106
#>  [6,] -0.005719541
#>  [7,]  0.234496364
#>  [8,]  0.060561520
#>  [9,] -0.038825188
#> [10,]  0.036902990
#> [11,]  0.006304792
#> [12,] -0.164474372
#> [13,] -0.029147353
#> [14,] -0.052668936
#> [15,]  0.236984837
#> [16,]  0.219672387
#> [17,] -0.131679559
#> [18,]  0.122756935
#> [19,]  0.245419135
#> [20,] -0.217703853
#> [21,] -0.117210298
#> [22,]  0.095201600
#> [23,]  0.127892607
#> [24,]  0.072265151
#> [25,] -0.041220612
#> [26,]  0.102400260
#> [27,]  0.071365384
#> [28,]  0.239776939
#> [29,] -0.144274171
#> [30,]  0.019200216
#> [31,] -0.317604921
#> [32,]  0.173622871
#> [33,] -0.124328637
#> [34,]  0.213372600
#> [35,] -0.227915458
#> [36,] -0.187689566
#> [37,] -0.070876063
#> [38,]  0.120492759
#> [39,]  0.091659035
#> 
#> $center
#>  [1]  0.52500  0.45000  0.47500  0.60000  0.53750  0.47500  0.52500  0.47500
#>  [9]  0.37500  0.50000  0.46250  0.51250  0.46250  0.40000  0.43750  0.48750
#> [17]  0.45000  0.51250  0.51250  0.51250  0.45000  0.55000  0.42500  0.42500
#> [25]  0.47500  0.46250  0.52500  0.51250  0.48750  0.40000  0.57500  0.48750
#> [33]  0.41250  0.70000 64.23634  1.77500  2.51250  0.55000  0.25000
#> 
#> $scale
#>  [1]  0.5025253  0.5006325  0.5025253  0.4929888  0.5017375  0.5025253
#>  [7]  0.5025253  0.5025253  0.4871774  0.5031546  0.5017375  0.5029973
#> [13]  0.5017375  0.4929888  0.4992082  0.5029973  0.5006325  0.5029973
#> [19]  0.5029973  0.5029973  0.5006325  0.5006325  0.4974619  0.4974619
#> [25]  0.5025253  0.5017375  0.5025253  0.5029973  0.5029973  0.4929888
#> [31]  0.4974619  0.5029973  0.4953901  0.4611488 13.5030422  0.7458747
#> [37]  0.8999824  0.7778581  0.4357447
#> 
#> $cox_fit
#> $cox_fit$coefficients
#> [1] 5.004052 2.746088 2.826956 3.123682 2.212297 1.836690
#> 
#> $cox_fit$var
#>           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]
#> [1,] 1.8176427 1.0007947 1.0270697 1.1557178 0.8273513 0.6773313
#> [2,] 1.0007947 0.6200044 0.5764073 0.6590198 0.4650547 0.3822643
#> [3,] 1.0270697 0.5764073 0.6412628 0.6891091 0.4976229 0.3878208
#> [4,] 1.1557178 0.6590198 0.6891091 0.8165358 0.5775589 0.4726054
#> [5,] 0.8273513 0.4650547 0.4976229 0.5775589 0.4824611 0.3348504
#> [6,] 0.6773313 0.3822643 0.3878208 0.4726054 0.3348504 0.3287053
#> 
#> $cox_fit$loglik
#> [1] -56.43995 -13.11777
#> 
#> $cox_fit$score
#> [1] 47.66948
#> 
#> $cox_fit$iter
#> [1] 8
#> 
#> $cox_fit$linear.predictors
#>  [1]  -5.39087955  -6.15109660   5.09550487 -13.88375547   2.39351618
#>  [6] -13.29476930  -2.75192032  15.22802654  -6.75150764   3.03694859
#> [11]  20.46668210  -2.20388522   7.40235358   0.06153643   1.73042067
#> [16]   1.63285788 -15.14819858 -16.61315366   3.19944499  -5.09653794
#> [21]  -5.08886457   6.00858147   5.49932139   1.07251252 -16.68306316
#> [26]  -9.87033333  13.63075463  -2.21580410  -7.72364593 -20.89429368
#> [31]  23.69774455  -5.47242729  -4.64364378   2.09307288  13.01430218
#> [36]  -0.38140506  17.23261789   6.16118530  -8.87236032   9.57734124
#> [41]   4.72160666  10.63749894   4.78039144  -0.45588309  -9.78156407
#> [46]  -0.41319153 -19.01181143 -18.33508937  17.87312742  -1.80604943
#> [51]  -8.92843325   2.38355006   1.27385539  20.47855089  18.01160999
#> [56]  -9.62908763 -11.50954928   8.84579672   5.97522735   2.30930801
#> [61]   7.08300227  13.23913535  19.89632332 -16.62795366   9.81202643
#> [66]   5.95200818 -27.16404514  -3.36617391  13.19271845  -7.80186252
#> [71]   3.24305062   8.16133664  11.89873024 -18.82754928   6.58394537
#> [76]   4.97416410  -4.28205147 -10.53776977  -4.91879100 -17.03328838
#> 
#> $cox_fit$residuals
#>             1             2             3             4             5 
#> -2.744308e-02 -1.781275e-09 -1.504830e-08 -1.243296e-15 -1.760046e-01 
#>             6             7             8             9            10 
#> -5.402201e-15 -2.047726e-10  1.600869e-01 -9.771827e-10 -9.588986e-10 
#>            11            12            13            14            15 
#>  5.583397e-01 -1.017192e-11 -5.262802e-06 -1.051131e-01 -2.596300e-10 
#>            16            17            18            19            20 
#> -2.354962e-10 -2.204648e-13 -1.956207e-16  6.059654e-01 -6.046914e-04 
#>            21            22            23            24            25 
#> -1.855479e-10 -2.322817e-07 -7.847668e-07 -4.696986e-02 -5.617846e-09 
#>            26            27            28            29            30 
#> -2.377997e-15 -2.501978e-02 -3.282543e-09 -1.419315e-12 -7.767146e-20 
#>            31            32            33            34            35 
#> -8.044200e-01 -8.592934e-10 -8.042840e-09 -2.514877e-04  1.856192e-01 
#>            36            37            38            39            40 
#> -1.097466e-02  8.261257e-02 -3.961750e-04 -6.450978e-15  5.523967e-01 
#>            41            42            43            44            45 
#> -5.169046e-09 -8.523020e-03 -1.586027e-07 -1.018698e-02 -2.598743e-15 
#>            46            47            48            49            50 
#> -3.069642e-03 -5.472771e-10 -3.278640e-16 -1.856164e-01  1.075299e-02 
#>            51            52            53            54            55 
#> -1.014002e-08 -7.175306e-02 -4.758185e-09 -4.216039e-02  9.969438e-01 
#>            56            57            58            59            60 
#> -5.498683e-11 -9.917412e-07 -3.195386e-07 -8.049978e-05 -1.617904e-01 
#>            61            62            63            64            65 
#> -6.801896e-07  5.303204e-01 -4.037155e-01 -1.927468e-16 -3.961013e-01 
#>            66            67            68            69            70 
#> -1.769160e-08 -4.800948e-20 -7.061154e-09 -9.098569e-01 -6.572449e-06 
#>            71            72            73            74            75 
#> -4.115968e-01 -2.056243e-01 -4.426646e-03 -1.361713e-15 -2.321597e-06 
#>            76            77            78            79            80 
#>  3.289011e-01 -2.220045e-04 -7.980437e-13 -6.108218e-09 -1.205199e-15 
#> 
#> $cox_fit$means
#> [1] -3.747003e-16 -3.080869e-16 -4.024558e-17  3.635980e-16  1.804112e-17
#> [6]  1.942890e-16
#> 
#> $cox_fit$method
#> [1] "efron"
#> 
#> $cox_fit$class
#> [1] "coxph"
#> 
#> 
#> $keepX
#> [1] 0 0 0 0 0 0
#> 
#> $time
#>  [1] 6.1342466 2.0383562 0.8328767 1.1205479 3.9917808 1.4164384 1.3205479
#>  [8] 1.6712329 2.0547945 0.4520548 0.9150685 0.8794521 1.2356164 5.6712329
#> [15] 0.5013699 0.7506849 2.0164384 1.2794521 3.5452055 4.8493151 1.5890411
#> [22] 0.9150685 1.3287671 4.1123288 4.7589041 0.5945205 1.5780822 1.5780822
#> [29] 1.3506849 0.8602740 0.7753425 1.8109589 2.3452055 2.5178082 2.4356164
#> [36] 4.2246575 1.4246575 2.1972603 0.6054795 2.5013699 0.7150685 1.7260274
#> [43] 1.1315068 3.9013699 0.6164384 3.4191781 5.4219178 1.6054795 1.2849315
#> [50] 5.9260274 2.7726027 4.7041096 1.0849315 1.0246575 0.1835616 2.0958904
#> [57] 5.3369863 0.6410959 1.7726027 4.6821918 0.9260274 1.9397260 1.1890411
#> [64] 1.3260274 2.6575342 0.7561644 1.5972603 1.9150685 2.4493151 4.3726027
#> [71] 3.6876712 2.9753425 1.6000000 1.8410959 1.1890411 3.3397260 3.6958904
#> [78] 1.4712329 2.2712329 1.6630137
#> 
#> $status
#>  [1] 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0
#> [39] 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1
#> [77] 0 0 0 0
#> 
#> attr(,"class")
#> [1] "big_pls_cox"

The big_pls_cox_gd() function exposes a gradient-descent variant that is often preferred for streaming workloads. Both functions can be combined with foreach::foreach() for multi-core execution.