genspline.RdGenerates spline basis matrices for fitting to dose-response function
genspline(
x,
spline = "bs",
df = 1,
knots = NULL,
degree = 3,
max.dose = max(x),
boundaries = NULL
)A numeric vector indicating all time points available in the dataset
Indicates the type of spline function. Can be either a
natural cubic spline ("ns"), or B-spline ("bs").
degrees of freedom. One can supply df rather than
knots; ns() then chooses df - 1 - intercept knots at
suitably chosen quantiles of x (which will ignore missing
values). The default, df = NULL, sets the number of
inner knots as length(knots).
Indicates the number/location of internal knots. If a single whole number >=1 is given
it indicates the number of equally-spaced internal knots. Otherwise (a vector, or a non-integer value)
the values are treated as the quantile locations of the knots as a proportion of the maximum dose in the
dataset. For example, if the maximum dose in the dataset is 100mg/d for a particular agent, knots=c(0.1,0.5)
would indicate knots should be fitted at 10mg/d and 50mg/d.
a positive integer giving the degree of the polynomial from which the spline function is composed
(e.g. degree=3 represents a cubic spline).
A number indicating the maximum dose between which to calculate the spline function.
A positive numeric vector of length 2 that represents the doses at which to anchor the B-spline or natural
cubic spline basis matrix. This allows data to extend beyond the boundary knots, or for the basis parameters to not depend on x.
The default (boundaries=NULL) is the range of x.
A spline basis matrix with number of rows equal to length(x) and the number of columns equal to the number
of coefficients in the spline.
x <- 0:100
genspline(x)
#> Warning: 'df' was too small; have used 3
#> 1 2 3
#> 0 0.000000 0.000000 0.000000
#> 1 0.029403 0.000297 0.000001
#> 2 0.057624 0.001176 0.000008
#> 3 0.084681 0.002619 0.000027
#> 4 0.110592 0.004608 0.000064
#> 5 0.135375 0.007125 0.000125
#> 6 0.159048 0.010152 0.000216
#> 7 0.181629 0.013671 0.000343
#> 8 0.203136 0.017664 0.000512
#> 9 0.223587 0.022113 0.000729
#> 10 0.243000 0.027000 0.001000
#> 11 0.261393 0.032307 0.001331
#> 12 0.278784 0.038016 0.001728
#> 13 0.295191 0.044109 0.002197
#> 14 0.310632 0.050568 0.002744
#> 15 0.325125 0.057375 0.003375
#> 16 0.338688 0.064512 0.004096
#> 17 0.351339 0.071961 0.004913
#> 18 0.363096 0.079704 0.005832
#> 19 0.373977 0.087723 0.006859
#> 20 0.384000 0.096000 0.008000
#> 21 0.393183 0.104517 0.009261
#> 22 0.401544 0.113256 0.010648
#> 23 0.409101 0.122199 0.012167
#> 24 0.415872 0.131328 0.013824
#> 25 0.421875 0.140625 0.015625
#> 26 0.427128 0.150072 0.017576
#> 27 0.431649 0.159651 0.019683
#> 28 0.435456 0.169344 0.021952
#> 29 0.438567 0.179133 0.024389
#> 30 0.441000 0.189000 0.027000
#> 31 0.442773 0.198927 0.029791
#> 32 0.443904 0.208896 0.032768
#> 33 0.444411 0.218889 0.035937
#> 34 0.444312 0.228888 0.039304
#> 35 0.443625 0.238875 0.042875
#> 36 0.442368 0.248832 0.046656
#> 37 0.440559 0.258741 0.050653
#> 38 0.438216 0.268584 0.054872
#> 39 0.435357 0.278343 0.059319
#> 40 0.432000 0.288000 0.064000
#> 41 0.428163 0.297537 0.068921
#> 42 0.423864 0.306936 0.074088
#> 43 0.419121 0.316179 0.079507
#> 44 0.413952 0.325248 0.085184
#> 45 0.408375 0.334125 0.091125
#> 46 0.402408 0.342792 0.097336
#> 47 0.396069 0.351231 0.103823
#> 48 0.389376 0.359424 0.110592
#> 49 0.382347 0.367353 0.117649
#> 50 0.375000 0.375000 0.125000
#> 51 0.367353 0.382347 0.132651
#> 52 0.359424 0.389376 0.140608
#> 53 0.351231 0.396069 0.148877
#> 54 0.342792 0.402408 0.157464
#> 55 0.334125 0.408375 0.166375
#> 56 0.325248 0.413952 0.175616
#> 57 0.316179 0.419121 0.185193
#> 58 0.306936 0.423864 0.195112
#> 59 0.297537 0.428163 0.205379
#> 60 0.288000 0.432000 0.216000
#> 61 0.278343 0.435357 0.226981
#> 62 0.268584 0.438216 0.238328
#> 63 0.258741 0.440559 0.250047
#> 64 0.248832 0.442368 0.262144
#> 65 0.238875 0.443625 0.274625
#> 66 0.228888 0.444312 0.287496
#> 67 0.218889 0.444411 0.300763
#> 68 0.208896 0.443904 0.314432
#> 69 0.198927 0.442773 0.328509
#> 70 0.189000 0.441000 0.343000
#> 71 0.179133 0.438567 0.357911
#> 72 0.169344 0.435456 0.373248
#> 73 0.159651 0.431649 0.389017
#> 74 0.150072 0.427128 0.405224
#> 75 0.140625 0.421875 0.421875
#> 76 0.131328 0.415872 0.438976
#> 77 0.122199 0.409101 0.456533
#> 78 0.113256 0.401544 0.474552
#> 79 0.104517 0.393183 0.493039
#> 80 0.096000 0.384000 0.512000
#> 81 0.087723 0.373977 0.531441
#> 82 0.079704 0.363096 0.551368
#> 83 0.071961 0.351339 0.571787
#> 84 0.064512 0.338688 0.592704
#> 85 0.057375 0.325125 0.614125
#> 86 0.050568 0.310632 0.636056
#> 87 0.044109 0.295191 0.658503
#> 88 0.038016 0.278784 0.681472
#> 89 0.032307 0.261393 0.704969
#> 90 0.027000 0.243000 0.729000
#> 91 0.022113 0.223587 0.753571
#> 92 0.017664 0.203136 0.778688
#> 93 0.013671 0.181629 0.804357
#> 94 0.010152 0.159048 0.830584
#> 95 0.007125 0.135375 0.857375
#> 96 0.004608 0.110592 0.884736
#> 97 0.002619 0.084681 0.912673
#> 98 0.001176 0.057624 0.941192
#> 99 0.000297 0.029403 0.970299
#> 100 0.000000 0.000000 1.000000
# Generate a quadratic B-spline with 1 equally spaced internal knot
genspline(x, spline="bs", df=2, degree=2)
#> 1 2
#> 0 0.0000 0.0000
#> 1 0.0198 0.0001
#> 2 0.0392 0.0004
#> 3 0.0582 0.0009
#> 4 0.0768 0.0016
#> 5 0.0950 0.0025
#> 6 0.1128 0.0036
#> 7 0.1302 0.0049
#> 8 0.1472 0.0064
#> 9 0.1638 0.0081
#> 10 0.1800 0.0100
#> 11 0.1958 0.0121
#> 12 0.2112 0.0144
#> 13 0.2262 0.0169
#> 14 0.2408 0.0196
#> 15 0.2550 0.0225
#> 16 0.2688 0.0256
#> 17 0.2822 0.0289
#> 18 0.2952 0.0324
#> 19 0.3078 0.0361
#> 20 0.3200 0.0400
#> 21 0.3318 0.0441
#> 22 0.3432 0.0484
#> 23 0.3542 0.0529
#> 24 0.3648 0.0576
#> 25 0.3750 0.0625
#> 26 0.3848 0.0676
#> 27 0.3942 0.0729
#> 28 0.4032 0.0784
#> 29 0.4118 0.0841
#> 30 0.4200 0.0900
#> 31 0.4278 0.0961
#> 32 0.4352 0.1024
#> 33 0.4422 0.1089
#> 34 0.4488 0.1156
#> 35 0.4550 0.1225
#> 36 0.4608 0.1296
#> 37 0.4662 0.1369
#> 38 0.4712 0.1444
#> 39 0.4758 0.1521
#> 40 0.4800 0.1600
#> 41 0.4838 0.1681
#> 42 0.4872 0.1764
#> 43 0.4902 0.1849
#> 44 0.4928 0.1936
#> 45 0.4950 0.2025
#> 46 0.4968 0.2116
#> 47 0.4982 0.2209
#> 48 0.4992 0.2304
#> 49 0.4998 0.2401
#> 50 0.5000 0.2500
#> 51 0.4998 0.2601
#> 52 0.4992 0.2704
#> 53 0.4982 0.2809
#> 54 0.4968 0.2916
#> 55 0.4950 0.3025
#> 56 0.4928 0.3136
#> 57 0.4902 0.3249
#> 58 0.4872 0.3364
#> 59 0.4838 0.3481
#> 60 0.4800 0.3600
#> 61 0.4758 0.3721
#> 62 0.4712 0.3844
#> 63 0.4662 0.3969
#> 64 0.4608 0.4096
#> 65 0.4550 0.4225
#> 66 0.4488 0.4356
#> 67 0.4422 0.4489
#> 68 0.4352 0.4624
#> 69 0.4278 0.4761
#> 70 0.4200 0.4900
#> 71 0.4118 0.5041
#> 72 0.4032 0.5184
#> 73 0.3942 0.5329
#> 74 0.3848 0.5476
#> 75 0.3750 0.5625
#> 76 0.3648 0.5776
#> 77 0.3542 0.5929
#> 78 0.3432 0.6084
#> 79 0.3318 0.6241
#> 80 0.3200 0.6400
#> 81 0.3078 0.6561
#> 82 0.2952 0.6724
#> 83 0.2822 0.6889
#> 84 0.2688 0.7056
#> 85 0.2550 0.7225
#> 86 0.2408 0.7396
#> 87 0.2262 0.7569
#> 88 0.2112 0.7744
#> 89 0.1958 0.7921
#> 90 0.1800 0.8100
#> 91 0.1638 0.8281
#> 92 0.1472 0.8464
#> 93 0.1302 0.8649
#> 94 0.1128 0.8836
#> 95 0.0950 0.9025
#> 96 0.0768 0.9216
#> 97 0.0582 0.9409
#> 98 0.0392 0.9604
#> 99 0.0198 0.9801
#> 100 0.0000 1.0000
# Generate a natural cubic spline with 3 knots at selected quantiles
genspline(x, spline="ns", knots=c(0.1, 0.5, 0.7))
#> 1 2 3 4
#> 0 0.000000e+00 0.000000000 0.00000000 0.000000000
#> 1 2.857143e-05 -0.014927620 0.03980699 -0.024879367
#> 2 2.285714e-04 -0.029744212 0.07931790 -0.049573687
#> 3 7.714286e-04 -0.044338747 0.11823666 -0.073897912
#> 4 1.828571e-03 -0.058600197 0.15626719 -0.097666996
#> 5 3.571429e-03 -0.072417534 0.19311342 -0.120695890
#> 6 6.171429e-03 -0.085679729 0.22847928 -0.142799548
#> 7 9.800000e-03 -0.098275754 0.26206868 -0.163792923
#> 8 1.462857e-02 -0.110094580 0.29358555 -0.183490967
#> 9 2.082857e-02 -0.121025179 0.32273381 -0.201708632
#> 10 2.857143e-02 -0.130956524 0.34921740 -0.218260873
#> 11 3.798228e-02 -0.139798290 0.37280779 -0.233004866
#> 12 4.900106e-02 -0.147542979 0.39354671 -0.245966693
#> 13 6.152143e-02 -0.154203797 0.41154346 -0.257214661
#> 14 7.543704e-02 -0.159793949 0.42690732 -0.266817076
#> 15 9.064153e-02 -0.164326642 0.43974759 -0.274842244
#> 16 1.070286e-01 -0.167815083 0.45017355 -0.281358472
#> 17 1.244918e-01 -0.170272477 0.45829451 -0.286434066
#> 18 1.429249e-01 -0.171712030 0.46421973 -0.290137334
#> 19 1.622214e-01 -0.172146949 0.46805853 -0.292536581
#> 20 1.822751e-01 -0.171590439 0.46992018 -0.293700114
#> 21 2.029796e-01 -0.170055707 0.46991398 -0.293696240
#> 22 2.242286e-01 -0.167555959 0.46814922 -0.292593265
#> 23 2.459156e-01 -0.164104401 0.46473519 -0.290459496
#> 24 2.679344e-01 -0.159714240 0.45978118 -0.287363239
#> 25 2.901786e-01 -0.154398680 0.45339648 -0.283372800
#> 26 3.125418e-01 -0.148170929 0.44569038 -0.278556487
#> 27 3.349177e-01 -0.141044193 0.43677217 -0.272982605
#> 28 3.572000e-01 -0.133031677 0.42675114 -0.266719462
#> 29 3.792823e-01 -0.124146589 0.41573658 -0.259835364
#> 30 4.010582e-01 -0.114402133 0.40383779 -0.252398616
#> 31 4.224214e-01 -0.103811516 0.39116404 -0.244477527
#> 32 4.432656e-01 -0.092387945 0.37782464 -0.236140402
#> 33 4.634844e-01 -0.080144625 0.36392888 -0.227455548
#> 34 4.829714e-01 -0.067094763 0.34958603 -0.218491271
#> 35 5.016204e-01 -0.053251564 0.33490541 -0.209315878
#> 36 5.193249e-01 -0.038628235 0.31999628 -0.199997676
#> 37 5.359786e-01 -0.023237982 0.30496795 -0.190604970
#> 38 5.514751e-01 -0.007094011 0.28992971 -0.181206068
#> 39 5.657082e-01 0.009790471 0.27499084 -0.171869276
#> 40 5.785714e-01 0.027402259 0.26026064 -0.162662901
#> 41 5.899585e-01 0.045728147 0.24584840 -0.153655248
#> 42 5.997630e-01 0.064754928 0.23186340 -0.144914626
#> 43 6.078786e-01 0.084469397 0.21841494 -0.136509339
#> 44 6.141989e-01 0.104858346 0.20561231 -0.128507695
#> 45 6.186177e-01 0.125908571 0.19356480 -0.120978000
#> 46 6.210286e-01 0.147606864 0.18238170 -0.113988560
#> 47 6.213251e-01 0.169940020 0.17217229 -0.107607683
#> 48 6.194011e-01 0.192894832 0.16304588 -0.101903675
#> 49 6.151500e-01 0.216458095 0.15511175 -0.096944841
#> 50 6.084656e-01 0.240616602 0.14847918 -0.092799490
#> 51 5.992915e-01 0.265331143 0.14322683 -0.089504269
#> 52 5.877714e-01 0.290458483 0.13931071 -0.086969195
#> 53 5.740989e-01 0.315829385 0.13665621 -0.085072629
#> 54 5.584677e-01 0.341274612 0.13518869 -0.083692931
#> 55 5.410714e-01 0.366624925 0.13483353 -0.082708458
#> 56 5.221037e-01 0.391711086 0.13551612 -0.081997572
#> 57 5.017582e-01 0.416363858 0.13716181 -0.081438631
#> 58 4.802286e-01 0.440414002 0.13969599 -0.080909996
#> 59 4.577085e-01 0.463692281 0.14304404 -0.080290025
#> 60 4.343915e-01 0.486029456 0.14713133 -0.079457079
#> 61 4.104714e-01 0.507256290 0.15188323 -0.078289517
#> 62 3.861418e-01 0.527203544 0.15722512 -0.076665698
#> 63 3.615963e-01 0.545701981 0.16308237 -0.074463982
#> 64 3.370286e-01 0.562582363 0.16938037 -0.071562729
#> 65 3.126323e-01 0.577675451 0.17604448 -0.067840298
#> 66 2.886011e-01 0.590812008 0.18300008 -0.063175049
#> 67 2.651286e-01 0.601822795 0.19017255 -0.057445341
#> 68 2.424085e-01 0.610538576 0.19748725 -0.050529534
#> 69 2.206344e-01 0.616790111 0.20486958 -0.042305988
#> 70 2.000000e-01 0.620408163 0.21224490 -0.032653061
#> 71 1.806593e-01 0.621267271 0.21955147 -0.021478005
#> 72 1.626074e-01 0.619417082 0.22677914 -0.008803628
#> 73 1.458000e-01 0.614951020 0.23393061 0.005318367
#> 74 1.301926e-01 0.607962509 0.24100862 0.020836281
#> 75 1.157407e-01 0.598544974 0.24801587 0.037698413
#> 76 1.024000e-01 0.586791837 0.25495510 0.055853061
#> 77 9.012593e-02 0.572796523 0.26182902 0.075248526
#> 78 7.887407e-02 0.556652457 0.26864036 0.095833107
#> 79 6.860000e-02 0.538453061 0.27539184 0.117555102
#> 80 5.925926e-02 0.518291761 0.28208617 0.140362812
#> 81 5.080741e-02 0.496261980 0.28872608 0.164204535
#> 82 4.320000e-02 0.472457143 0.29531429 0.189028571
#> 83 3.639259e-02 0.446970673 0.30185351 0.214783220
#> 84 3.034074e-02 0.419895994 0.30834649 0.241416780
#> 85 2.500000e-02 0.391326531 0.31479592 0.268877551
#> 86 2.032593e-02 0.361355707 0.32120454 0.297113832
#> 87 1.627407e-02 0.330076946 0.32757506 0.326073923
#> 88 1.280000e-02 0.297583673 0.33391020 0.355706122
#> 89 9.859259e-03 0.263969312 0.34021270 0.385958730
#> 90 7.407407e-03 0.229327286 0.34648526 0.416780045
#> 91 5.400000e-03 0.193751020 0.35273061 0.448118367
#> 92 3.792593e-03 0.157333938 0.35895147 0.479921995
#> 93 2.540741e-03 0.120169463 0.36515057 0.512139229
#> 94 1.600000e-03 0.082351020 0.37133061 0.544718367
#> 95 9.259259e-04 0.043972033 0.37749433 0.577607710
#> 96 4.740741e-04 0.005125926 0.38364444 0.610755556
#> 97 2.000000e-04 -0.034093878 0.38978367 0.644110204
#> 98 5.925926e-05 -0.073593953 0.39591474 0.677619955
#> 99 7.407407e-06 -0.113280877 0.40204036 0.711233107
#> 100 0.000000e+00 -0.153061224 0.40816327 0.744897959
# Generate a piecewise linear spline with 2 equally spaced knots
genspline(x, spline="bs", degree=1, df=3)
#> 1 2 3
#> 0 0.00 0.00 0.00
#> 1 0.03 0.00 0.00
#> 2 0.06 0.00 0.00
#> 3 0.09 0.00 0.00
#> 4 0.12 0.00 0.00
#> 5 0.15 0.00 0.00
#> 6 0.18 0.00 0.00
#> 7 0.21 0.00 0.00
#> 8 0.24 0.00 0.00
#> 9 0.27 0.00 0.00
#> 10 0.30 0.00 0.00
#> 11 0.33 0.00 0.00
#> 12 0.36 0.00 0.00
#> 13 0.39 0.00 0.00
#> 14 0.42 0.00 0.00
#> 15 0.45 0.00 0.00
#> 16 0.48 0.00 0.00
#> 17 0.51 0.00 0.00
#> 18 0.54 0.00 0.00
#> 19 0.57 0.00 0.00
#> 20 0.60 0.00 0.00
#> 21 0.63 0.00 0.00
#> 22 0.66 0.00 0.00
#> 23 0.69 0.00 0.00
#> 24 0.72 0.00 0.00
#> 25 0.75 0.00 0.00
#> 26 0.78 0.00 0.00
#> 27 0.81 0.00 0.00
#> 28 0.84 0.00 0.00
#> 29 0.87 0.00 0.00
#> 30 0.90 0.00 0.00
#> 31 0.93 0.00 0.00
#> 32 0.96 0.00 0.00
#> 33 0.99 0.00 0.00
#> 34 0.98 0.02 0.00
#> 35 0.95 0.05 0.00
#> 36 0.92 0.08 0.00
#> 37 0.89 0.11 0.00
#> 38 0.86 0.14 0.00
#> 39 0.83 0.17 0.00
#> 40 0.80 0.20 0.00
#> 41 0.77 0.23 0.00
#> 42 0.74 0.26 0.00
#> 43 0.71 0.29 0.00
#> 44 0.68 0.32 0.00
#> 45 0.65 0.35 0.00
#> 46 0.62 0.38 0.00
#> 47 0.59 0.41 0.00
#> 48 0.56 0.44 0.00
#> 49 0.53 0.47 0.00
#> 50 0.50 0.50 0.00
#> 51 0.47 0.53 0.00
#> 52 0.44 0.56 0.00
#> 53 0.41 0.59 0.00
#> 54 0.38 0.62 0.00
#> 55 0.35 0.65 0.00
#> 56 0.32 0.68 0.00
#> 57 0.29 0.71 0.00
#> 58 0.26 0.74 0.00
#> 59 0.23 0.77 0.00
#> 60 0.20 0.80 0.00
#> 61 0.17 0.83 0.00
#> 62 0.14 0.86 0.00
#> 63 0.11 0.89 0.00
#> 64 0.08 0.92 0.00
#> 65 0.05 0.95 0.00
#> 66 0.02 0.98 0.00
#> 67 0.00 0.99 0.01
#> 68 0.00 0.96 0.04
#> 69 0.00 0.93 0.07
#> 70 0.00 0.90 0.10
#> 71 0.00 0.87 0.13
#> 72 0.00 0.84 0.16
#> 73 0.00 0.81 0.19
#> 74 0.00 0.78 0.22
#> 75 0.00 0.75 0.25
#> 76 0.00 0.72 0.28
#> 77 0.00 0.69 0.31
#> 78 0.00 0.66 0.34
#> 79 0.00 0.63 0.37
#> 80 0.00 0.60 0.40
#> 81 0.00 0.57 0.43
#> 82 0.00 0.54 0.46
#> 83 0.00 0.51 0.49
#> 84 0.00 0.48 0.52
#> 85 0.00 0.45 0.55
#> 86 0.00 0.42 0.58
#> 87 0.00 0.39 0.61
#> 88 0.00 0.36 0.64
#> 89 0.00 0.33 0.67
#> 90 0.00 0.30 0.70
#> 91 0.00 0.27 0.73
#> 92 0.00 0.24 0.76
#> 93 0.00 0.21 0.79
#> 94 0.00 0.18 0.82
#> 95 0.00 0.15 0.85
#> 96 0.00 0.12 0.88
#> 97 0.00 0.09 0.91
#> 98 0.00 0.06 0.94
#> 99 0.00 0.03 0.97
#> 100 0.00 0.00 1.00