genspline.RdGenerates spline basis matrices for fitting to dose-response function
genspline(
x,
spline = "bs",
knots = 1,
degree = 1,
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 piecewise linear spline ("ls"),
natural cubic spline ("ns"), or B-spline ("bs").
The number/location of internal knots. If a single integer is given it indicates the number of knots (they will
be equally spaced across the range of doses for each agent). If a numeric vector is given it indicates the quantiles 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, 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)
#> 1 2
#> 0 0.00 0.00
#> 1 0.02 0.00
#> 2 0.04 0.00
#> 3 0.06 0.00
#> 4 0.08 0.00
#> 5 0.10 0.00
#> 6 0.12 0.00
#> 7 0.14 0.00
#> 8 0.16 0.00
#> 9 0.18 0.00
#> 10 0.20 0.00
#> 11 0.22 0.00
#> 12 0.24 0.00
#> 13 0.26 0.00
#> 14 0.28 0.00
#> 15 0.30 0.00
#> 16 0.32 0.00
#> 17 0.34 0.00
#> 18 0.36 0.00
#> 19 0.38 0.00
#> 20 0.40 0.00
#> 21 0.42 0.00
#> 22 0.44 0.00
#> 23 0.46 0.00
#> 24 0.48 0.00
#> 25 0.50 0.00
#> 26 0.52 0.00
#> 27 0.54 0.00
#> 28 0.56 0.00
#> 29 0.58 0.00
#> 30 0.60 0.00
#> 31 0.62 0.00
#> 32 0.64 0.00
#> 33 0.66 0.00
#> 34 0.68 0.00
#> 35 0.70 0.00
#> 36 0.72 0.00
#> 37 0.74 0.00
#> 38 0.76 0.00
#> 39 0.78 0.00
#> 40 0.80 0.00
#> 41 0.82 0.00
#> 42 0.84 0.00
#> 43 0.86 0.00
#> 44 0.88 0.00
#> 45 0.90 0.00
#> 46 0.92 0.00
#> 47 0.94 0.00
#> 48 0.96 0.00
#> 49 0.98 0.00
#> 50 1.00 0.00
#> 51 0.98 0.02
#> 52 0.96 0.04
#> 53 0.94 0.06
#> 54 0.92 0.08
#> 55 0.90 0.10
#> 56 0.88 0.12
#> 57 0.86 0.14
#> 58 0.84 0.16
#> 59 0.82 0.18
#> 60 0.80 0.20
#> 61 0.78 0.22
#> 62 0.76 0.24
#> 63 0.74 0.26
#> 64 0.72 0.28
#> 65 0.70 0.30
#> 66 0.68 0.32
#> 67 0.66 0.34
#> 68 0.64 0.36
#> 69 0.62 0.38
#> 70 0.60 0.40
#> 71 0.58 0.42
#> 72 0.56 0.44
#> 73 0.54 0.46
#> 74 0.52 0.48
#> 75 0.50 0.50
#> 76 0.48 0.52
#> 77 0.46 0.54
#> 78 0.44 0.56
#> 79 0.42 0.58
#> 80 0.40 0.60
#> 81 0.38 0.62
#> 82 0.36 0.64
#> 83 0.34 0.66
#> 84 0.32 0.68
#> 85 0.30 0.70
#> 86 0.28 0.72
#> 87 0.26 0.74
#> 88 0.24 0.76
#> 89 0.22 0.78
#> 90 0.20 0.80
#> 91 0.18 0.82
#> 92 0.16 0.84
#> 93 0.14 0.86
#> 94 0.12 0.88
#> 95 0.10 0.90
#> 96 0.08 0.92
#> 97 0.06 0.94
#> 98 0.04 0.96
#> 99 0.02 0.98
#> 100 0.00 1.00
# Generate a quadratic B-spline with 1 equally spaced internal knot
genspline(x, spline="bs", knots=2, degree=2)
#> 1 2 3 4
#> 0 0.00000 0.00000 0.00000 0.0000
#> 1 0.05865 0.00045 0.00000 0.0000
#> 2 0.11460 0.00180 0.00000 0.0000
#> 3 0.16785 0.00405 0.00000 0.0000
#> 4 0.21840 0.00720 0.00000 0.0000
#> 5 0.26625 0.01125 0.00000 0.0000
#> 6 0.31140 0.01620 0.00000 0.0000
#> 7 0.35385 0.02205 0.00000 0.0000
#> 8 0.39360 0.02880 0.00000 0.0000
#> 9 0.43065 0.03645 0.00000 0.0000
#> 10 0.46500 0.04500 0.00000 0.0000
#> 11 0.49665 0.05445 0.00000 0.0000
#> 12 0.52560 0.06480 0.00000 0.0000
#> 13 0.55185 0.07605 0.00000 0.0000
#> 14 0.57540 0.08820 0.00000 0.0000
#> 15 0.59625 0.10125 0.00000 0.0000
#> 16 0.61440 0.11520 0.00000 0.0000
#> 17 0.62985 0.13005 0.00000 0.0000
#> 18 0.64260 0.14580 0.00000 0.0000
#> 19 0.65265 0.16245 0.00000 0.0000
#> 20 0.66000 0.18000 0.00000 0.0000
#> 21 0.66465 0.19845 0.00000 0.0000
#> 22 0.66660 0.21780 0.00000 0.0000
#> 23 0.66585 0.23805 0.00000 0.0000
#> 24 0.66240 0.25920 0.00000 0.0000
#> 25 0.65625 0.28125 0.00000 0.0000
#> 26 0.64740 0.30420 0.00000 0.0000
#> 27 0.63585 0.32805 0.00000 0.0000
#> 28 0.62160 0.35280 0.00000 0.0000
#> 29 0.60465 0.37845 0.00000 0.0000
#> 30 0.58500 0.40500 0.00000 0.0000
#> 31 0.56265 0.43245 0.00000 0.0000
#> 32 0.53760 0.46080 0.00000 0.0000
#> 33 0.50985 0.49005 0.00000 0.0000
#> 34 0.48020 0.51960 0.00020 0.0000
#> 35 0.45125 0.54750 0.00125 0.0000
#> 36 0.42320 0.57360 0.00320 0.0000
#> 37 0.39605 0.59790 0.00605 0.0000
#> 38 0.36980 0.62040 0.00980 0.0000
#> 39 0.34445 0.64110 0.01445 0.0000
#> 40 0.32000 0.66000 0.02000 0.0000
#> 41 0.29645 0.67710 0.02645 0.0000
#> 42 0.27380 0.69240 0.03380 0.0000
#> 43 0.25205 0.70590 0.04205 0.0000
#> 44 0.23120 0.71760 0.05120 0.0000
#> 45 0.21125 0.72750 0.06125 0.0000
#> 46 0.19220 0.73560 0.07220 0.0000
#> 47 0.17405 0.74190 0.08405 0.0000
#> 48 0.15680 0.74640 0.09680 0.0000
#> 49 0.14045 0.74910 0.11045 0.0000
#> 50 0.12500 0.75000 0.12500 0.0000
#> 51 0.11045 0.74910 0.14045 0.0000
#> 52 0.09680 0.74640 0.15680 0.0000
#> 53 0.08405 0.74190 0.17405 0.0000
#> 54 0.07220 0.73560 0.19220 0.0000
#> 55 0.06125 0.72750 0.21125 0.0000
#> 56 0.05120 0.71760 0.23120 0.0000
#> 57 0.04205 0.70590 0.25205 0.0000
#> 58 0.03380 0.69240 0.27380 0.0000
#> 59 0.02645 0.67710 0.29645 0.0000
#> 60 0.02000 0.66000 0.32000 0.0000
#> 61 0.01445 0.64110 0.34445 0.0000
#> 62 0.00980 0.62040 0.36980 0.0000
#> 63 0.00605 0.59790 0.39605 0.0000
#> 64 0.00320 0.57360 0.42320 0.0000
#> 65 0.00125 0.54750 0.45125 0.0000
#> 66 0.00020 0.51960 0.48020 0.0000
#> 67 0.00000 0.49005 0.50985 0.0001
#> 68 0.00000 0.46080 0.53760 0.0016
#> 69 0.00000 0.43245 0.56265 0.0049
#> 70 0.00000 0.40500 0.58500 0.0100
#> 71 0.00000 0.37845 0.60465 0.0169
#> 72 0.00000 0.35280 0.62160 0.0256
#> 73 0.00000 0.32805 0.63585 0.0361
#> 74 0.00000 0.30420 0.64740 0.0484
#> 75 0.00000 0.28125 0.65625 0.0625
#> 76 0.00000 0.25920 0.66240 0.0784
#> 77 0.00000 0.23805 0.66585 0.0961
#> 78 0.00000 0.21780 0.66660 0.1156
#> 79 0.00000 0.19845 0.66465 0.1369
#> 80 0.00000 0.18000 0.66000 0.1600
#> 81 0.00000 0.16245 0.65265 0.1849
#> 82 0.00000 0.14580 0.64260 0.2116
#> 83 0.00000 0.13005 0.62985 0.2401
#> 84 0.00000 0.11520 0.61440 0.2704
#> 85 0.00000 0.10125 0.59625 0.3025
#> 86 0.00000 0.08820 0.57540 0.3364
#> 87 0.00000 0.07605 0.55185 0.3721
#> 88 0.00000 0.06480 0.52560 0.4096
#> 89 0.00000 0.05445 0.49665 0.4489
#> 90 0.00000 0.04500 0.46500 0.4900
#> 91 0.00000 0.03645 0.43065 0.5329
#> 92 0.00000 0.02880 0.39360 0.5776
#> 93 0.00000 0.02205 0.35385 0.6241
#> 94 0.00000 0.01620 0.31140 0.6724
#> 95 0.00000 0.01125 0.26625 0.7225
#> 96 0.00000 0.00720 0.21840 0.7744
#> 97 0.00000 0.00405 0.16785 0.8281
#> 98 0.00000 0.00180 0.11460 0.8836
#> 99 0.00000 0.00045 0.05865 0.9409
#> 100 0.00000 0.00000 0.00000 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 3 equally spaced knots
genspline(x, spline="ls", knots=3)
#> 1 2 3 4
#> 0 0 0 0 0
#> 1 1 0 0 0
#> 2 2 0 0 0
#> 3 3 0 0 0
#> 4 4 0 0 0
#> 5 5 0 0 0
#> 6 6 0 0 0
#> 7 7 0 0 0
#> 8 8 0 0 0
#> 9 9 0 0 0
#> 10 10 0 0 0
#> 11 11 0 0 0
#> 12 12 0 0 0
#> 13 13 0 0 0
#> 14 14 0 0 0
#> 15 15 0 0 0
#> 16 16 0 0 0
#> 17 17 0 0 0
#> 18 18 0 0 0
#> 19 19 0 0 0
#> 20 20 0 0 0
#> 21 21 0 0 0
#> 22 22 0 0 0
#> 23 23 0 0 0
#> 24 24 0 0 0
#> 25 25 0 0 0
#> 26 25 1 0 0
#> 27 25 2 0 0
#> 28 25 3 0 0
#> 29 25 4 0 0
#> 30 25 5 0 0
#> 31 25 6 0 0
#> 32 25 7 0 0
#> 33 25 8 0 0
#> 34 25 9 0 0
#> 35 25 10 0 0
#> 36 25 11 0 0
#> 37 25 12 0 0
#> 38 25 13 0 0
#> 39 25 14 0 0
#> 40 25 15 0 0
#> 41 25 16 0 0
#> 42 25 17 0 0
#> 43 25 18 0 0
#> 44 25 19 0 0
#> 45 25 20 0 0
#> 46 25 21 0 0
#> 47 25 22 0 0
#> 48 25 23 0 0
#> 49 25 24 0 0
#> 50 25 25 0 0
#> 51 25 25 1 0
#> 52 25 25 2 0
#> 53 25 25 3 0
#> 54 25 25 4 0
#> 55 25 25 5 0
#> 56 25 25 6 0
#> 57 25 25 7 0
#> 58 25 25 8 0
#> 59 25 25 9 0
#> 60 25 25 10 0
#> 61 25 25 11 0
#> 62 25 25 12 0
#> 63 25 25 13 0
#> 64 25 25 14 0
#> 65 25 25 15 0
#> 66 25 25 16 0
#> 67 25 25 17 0
#> 68 25 25 18 0
#> 69 25 25 19 0
#> 70 25 25 20 0
#> 71 25 25 21 0
#> 72 25 25 22 0
#> 73 25 25 23 0
#> 74 25 25 24 0
#> 75 25 25 25 0
#> 76 25 25 25 1
#> 77 25 25 25 2
#> 78 25 25 25 3
#> 79 25 25 25 4
#> 80 25 25 25 5
#> 81 25 25 25 6
#> 82 25 25 25 7
#> 83 25 25 25 8
#> 84 25 25 25 9
#> 85 25 25 25 10
#> 86 25 25 25 11
#> 87 25 25 25 12
#> 88 25 25 25 13
#> 89 25 25 25 14
#> 90 25 25 25 15
#> 91 25 25 25 16
#> 92 25 25 25 17
#> 93 25 25 25 18
#> 94 25 25 25 19
#> 95 25 25 25 20
#> 96 25 25 25 21
#> 97 25 25 25 22
#> 98 25 25 25 23
#> 99 25 25 25 24
#> 100 25 25 25 25