Input
The InputTable, lungcancer, contains data from a randomized trial of two treatment regimens for lung cancer used to model survival analysis. There are three categorical predictors and three numerical predictors:
Predictor | Description | Possible Values |
---|---|---|
trt | Treatment plan (categorical) |
|
celltype | Cancerous cell type (categorical) |
|
prior | Whether the patient has undergone prior therapy (categorical) |
|
karno | Karnofsky score assigned by patient (numerical) | [0, 100], where 100 is perfect health and 0 is death |
diagtime | Months from diagnosis to randomization (numerical) | Nonnegative number |
age | Patient age, in years (numerical) | Nonnegative number |
In addition to a column for each predictor, the InputTable has these columns:
Column | Description | Possible Values |
---|---|---|
id | Patient identifier | Positive integer |
status | Censoring status or survival event |
|
time_int | Survival time in months | Nonnegative number |
id | trt | celltype | time_int | status | karno | diagtime | age | prior |
---|---|---|---|---|---|---|---|---|
1 | standard | squamous | 72 | 1 | 60 | 7 | 69 | no |
2 | standard | squamous | 411 | 1 | 70 | 5 | 64 | yes |
3 | standard | squamous | 228 | 1 | 60 | 3 | 38 | no |
4 | standard | squamous | 126 | 1 | 60 | 9 | 63 | yes |
5 | standard | squamous | 118 | 1 | 70 | 11 | 65 | yes |
6 | standard | squamous | 10 | 1 | 20 | 5 | 49 | no |
7 | standard | squamous | 82 | 1 | 40 | 10 | 69 | yes |
8 | standard | squamous | 110 | 1 | 80 | 29 | 68 | no |
9 | standard | squamous | 314 | 1 | 50 | 18 | 43 | no |
10 | standard | squamous | 100 | 0 | 70 | 6 | 70 | no |
... | ... | ... | ... | ... | ... | ... | ... | ... |
SQL Call
SELECT * FROM CoxPH ( ON lungcancer AS InputTable OUT TABLE CoefficientTable (lungcancer_coef) OUT TABLE LinearPredictorTable (lungcancer_lp) USING TargetColumns ('trt', 'celltype', 'karno', 'diagtime', 'age', 'prior') CategoricalColumns ('trt','celltype','prior') TimeIntervalColumn ('time_int') EventColumn ('status') ) AS dt;
Output
Coefficients are estimated at 95% CI. Coefficients of variables karno, squamous, and large celltype are significant.
predictor category coefficient exp_coef std_error z_score p_value significance --------------------- --------- ----------- -------- --------- --------- -------- ---------------------- karno NULL -0.032815 0.967717 0.005508 -5.95802 0.0 *** diagtime NULL 8.1E-5 1.000081 0.009136 0.008901 0.992898 age NULL -0.008706 0.991331 0.0093 -0.93615 0.349196 trt standard 0.0 1.0 0.0 NULL NULL trt test 0.294603 1.342593 0.20755 1.419433 0.155773 celltype adeno 0.0 1.0 0.0 NULL NULL celltype large -0.794775 0.451683 0.302878 -2.624078 0.008688 ** celltype smallcell -0.334506 0.715692 0.275978 -1.212075 0.225483 celltype squamous -1.196066 0.302381 0.300917 -3.974739 7.0E-5 *** prior no 0.0 1.0 0.0 NULL NULL prior yes 0.071594 1.074219 0.232305 0.308187 0.75794 Iteration # NULL 5.0 NULL NULL NULL NULL NULL Convergence NULL NULL NULL NULL NULL NULL yes Likelihood ratio test NULL 62.1039 NULL NULL NULL 0.0 on 8 degree of freedom Wald test NULL 62.3673 NULL NULL NULL 0.0 on 8 degree of freedom Score test NULL 66.7375 NULL NULL NULL 0.0 on 8 degree of freedom
The coefficients are output in the table lungcancer_coef, which is later used for prediction. Because celltype, trt and prior are categorical variables, one of their categories is considered a reference for the other categories; thus trt = standard, celltype = adeno, and prior = no don not show default coefficient values in each column.
SELECT * FROM lungcancer_coef;
id predictor category coefficient exp_coef std_error z_score p_value significance -- --------- --------- --------------------- ------------------- -------------------- ------------------- --------------------- ------------ 6 celltype adeno 0.0 1.0 0.0 NaN NaN 7 celltype large -0.7947747198519008 0.45168297867006735 0.3028777154344899 -2.6240779012472593 0.008688391049300193 ** 4 trt standard 0.0 1.0 0.0 NaN NaN 1 karno NULL -0.03281532619416623 0.967717255116806 0.005507756886462303 -5.958020092503375 2.5531213809770748E-9 *** 2 diagtime NULL 8.132050870746436E-5 1.0000813238153097 0.009136062247771979 0.00890104582281016 0.992898086742232 9 celltype squamous -1.196066374179321 0.3023813305507525 0.3009169944930761 -3.974738536100997 7.045661593763075E-5 *** 10 prior no 0.0 1.0 0.0 NaN NaN 3 age NULL -0.008706474945498829 0.9913313166507652 0.00930029912031481 -0.9361499918299531 0.349195966726048 8 celltype smallcell -0.3345059114259308 0.715691614057431 0.27597778619114416 -1.2120754936205251 0.22548348359761572 11 prior yes 0.0715936019179391 1.0742186949258055 0.23230538406730558 0.30818744130870585 0.7579397080883754 5 trt test 0.29460282149804123 1.3425930036967717 0.20754960360351904 1.4194333132084391 0.15577272598042358
This query returns the following table:
SELECT * FROM lungcancer_lp;
linear_predictor event time_interval ------------------- ----- ------------- -2.980877152089424 1 8 -2.8463872419210983 1 1 -3.257006840737693 1 8 -1.564001681356389 1 13 -2.117355347321969 1 12 -2.054218838259662 1 21 -1.7084899854095867 1 16 -1.624947005974881 1 25 -1.4221870363135072 1 20 -2.9462665286870284 1 25 -2.434789369837646 1 24 -2.442649811965947 1 33 -3.4071856019850353 1 44 -1.8065272956361809 1 49 -3.1102722260025875 1 52 -2.9549730036325275 1 61 -2.0484512112822597 1 52 -2.886352701880789 0 97 -3.7651634735077617 1 72 -3.3599858929260527 1 117 -2.297446672118591 1 80 -3.5271609138650435 1 133 -2.818648125234491 1 92 -2.937273645905877 1 177 -3.013183095954195 1 100 -3.811385585389109 1 260 -3.0601432402647024 1 132 -2.6683655462084883 1 384 -2.7287087995359043 1 144 -3.375114709644063 1 587 -3.316471618690865 1 164 -2.6015691736492057 1 7 -2.8870579190955397 1 216 -1.2699424346183548 1 7 -4.298710491359266 1 283 -2.8178380916784085 1 15 -3.978353399821406 1 411 -1.7110222308341465 1 19 -1.6610798950650794 1 2 -2.8425763656271723 1 27 -2.2785835678485507 1 10 -2.6699318353835886 1 31 -1.3552645753895942 1 18 -2.823220614819555 1 43 -2.8951404973349955 1 22 -2.2137115942293226 1 51 -2.8342764932252105 1 30 -1.8847239276909267 1 59 -3.4363210445728862 1 54 -3.450139582091726 0 83 -3.0370193861803756 1 82 -2.5310485172903783 1 87 -4.410974471254024 1 110 -2.8679895746862467 1 95 -3.418898204826858 1 122 -3.3686819810181166 1 99 -3.959395659462589 1 162 -2.5770263684479797 0 103 -4.287792882930374 0 182 -3.7380938713677208 1 111 -3.1516017880658023 1 242 -3.516783762453739 1 139 -3.702454766498651 1 357 -2.5750431462691723 1 151 -3.5616972880689657 1 991 -2.922722393567932 0 231 -1.951682941267624 1 4 -3.209747337387348 1 314 -1.1142628039753721 1 8 -3.500889234864567 1 553 -1.9203842320696556 1 8 -2.0503896154212327 1 1 -2.626858615890042 1 12 -2.7906627979890093 1 13 -1.8844799661648044 1 20 -1.3140440529068012 1 21 -1.5402360819811227 1 24 -4.201703680382252 0 25 -2.5329144196993636 1 36 -2.1033504598175616 1 25 -0.7384496289941964 1 48 -1.9351993949733006 1 29 -2.860557560516451 1 52 -1.6185130359819047 1 45 -3.26154098159325 1 56 -3.0427429703022666 1 53 -1.5661928658002042 1 80 -2.283526034810728 1 73 -2.7985058367034155 1 84 -3.9937336361923395 1 105 -4.10210453090363 0 100 -2.9559095024448387 1 117 -4.048590221892262 1 112 -2.7792013156024873 1 153 -2.5507339721338984 1 140 -3.905555769218769 1 201 -3.666312258829045 1 156 -3.610205583394069 1 340 -3.7043968401282226 1 200 -2.2388339734516705 1 392 -3.4955880322321278 1 228 -1.3585942469553143 1 3 -2.8044262148432018 1 287 -1.5226604910727102 1 7 -4.411894665650751 1 467 -3.8385618776411796 1 11 -2.1569888069227905 1 10 -2.0327330032017357 1 15 -1.8410289119460175 1 18 -1.752265323100532 1 19 -1.5467567930465507 1 18 -3.3613322859196995 1 31 -3.7461497822435597 1 30 -1.8519265713353317 1 35 -3.8698851343798704 1 42 -1.4593764113618188 1 51 -3.214831245857281 1 54 -2.8866779839156185 1 51 -2.0362578443173707 1 90 -2.392288492922404 1 63 -3.986571951714659 1 118 -3.944356484072399 0 87 -3.6411683808994146 1 126 -2.920920961645429 1 95 -3.182033889501686 1 162 -2.9635981580693187 1 99 -3.1809210711807268 1 186 -3.7504402607706178 1 103 -3.481046559567376 1 250 -3.025899263972221 1 111 -4.394481715759753 1 389 -2.125731119668893 0 123 -4.252423109190747 1 999 -4.269892009987132 1 143 -3.307521182219244 1 231 -3.311226366963812 1 278 -3.6909935833097514 1 378
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