We may or may not have achieved the global optimal solution and underlying truth in the above section. Luckily SMASH provides a hands-off thorough grid search without any prior knowledge of the number of subclones, subclone configuration, subclone proportions, proportion of unclassified point mutations, etc. in the following code.
grid_ith = grid_ITH_optim(
my_data = input,
my_purity = sim$purity,
list_eS = eS,
trials = 50,
max_iter = 4e3)
#> cc = 1; kk = 1 **********
#> cc = 2; kk = 1 **********
#> cc = 3; kk = 1 ********** kk = 2 **********
#> cc = 4; kk = 1 ********** kk = 2 ********** kk = 3 **********
#> cc = 5; kk = 1 ********** kk = 2 ********** kk = 3 ********** kk = 4 ********** kk = 5 ********** kk = 6 **********
names(grid_ith)
#> [1] "GRID" "INFER"
# Grid of solutions
grid_ith$GRID
#> cc kk ms entropy LL AIC BIC q unc_q0 alloc pi_eps
#> 1 1 1 2 0.00 -307.41 -618.82 -622.6440 1 1|13 0.78001400
#> 2 2 1 6 0.39 -224.26 -460.52 -471.9921 0.87,0.13 1.588782 1|13;2|20 0.38062121
#> 3 2 1 6 0.69 -246.62 -505.24 -516.7121 0.53,0.47 -0.435362 1|13;2|19 0.41285982
#> 4 2 1 5 0.59 -295.80 -601.60 -611.1601 0.72,0.28 1.218544 1|16;2|34 0.00000000
#> 5 3 1 9 0.98 -142.87 -303.74 -320.9482 0.51,0.36,0.13 1.743127,1.847057 1|13;2|18;3|19 0.00000000
#> 6 3 1 8 0.99 -153.38 -322.76 -338.0562 0.45,0.42,0.13 -2.362137,-0.482741 1|13;2|18;3|19 0.00000000
#> 7 3 1 8 1.02 -161.29 -338.58 -353.8762 0.5,0.32,0.18 -1.018705,0.552578 1|13;2|18;3|19 0.00000000
#> 8 3 1 8 0.87 -245.73 -507.46 -522.7562 0.05,0.47,0.47 -1.813139,-0.40923 1|5;2|8;3|19 0.40978325
#> 9 3 2 9 0.98 -142.87 -303.74 -320.9482 0.38,0.49,0.13 1.047088,1.478796 1|13;2|18;3|19 0.00000000
#> 10 4 1 10 1.21 -139.76 -299.52 -318.6402 0.44,0.09,0.33,0.13 1.836166,1.377129,1.943698 1|13;2|4;3|14;4|19 0.00000000
#> 11 4 1 11 1.15 -154.35 -330.70 -351.7323 0.05,0.45,0.36,0.13 -1.495057,-0.455178,0.98301 1|5;2|8;3|18;4|19 0.09135708
#> 12 4 1 9 0.62 -221.83 -461.66 -478.8682 0.01,0.04,0.81,0.13 -2.448191,-2.178116,0.921208 1|2;2|3;3|9;4|20 0.37729469
#> 13 4 1 10 1.11 -142.74 -305.48 -324.6002 0.04,0.48,0.36,0.13 1.12048,1.767768,1.92637 1|6;2|7;3|18;4|19 0.00000000
#> 14 4 1 11 1.15 -142.09 -306.18 -327.2123 0.05,0.46,0.36,0.13 -1.771242,0.650579,-1.312927 1|5;2|8;3|18;4|19 0.00000000
#> 15 4 1 10 1.14 -141.33 -302.66 -321.7802 0.49,0.05,0.33,0.13 1.658064,1.481153,1.212404 1|13;2|8;3|10;4|19 0.00000000
#> 16 4 2 10 1.10 -142.74 -305.48 -324.6002 0.04,0.35,0.13,0.49 -1.287477,-0.870428,-1.949154 1|6;2|7;3|19;4|18 0.00000000
#> 17 4 2 11 1.14 -142.09 -306.18 -327.2123 0.05,0.33,0.13,0.49 -1.808309,-1.307732,-0.78863 1|5;2|8;3|19;4|18 0.00000000
#> 18 4 2 10 1.21 -142.72 -305.44 -324.5602 0.51,0.22,0.14,0.13 1.987396,1.916164,1.635483 1|13;2|18;3|4;4|15 0.00000000
#> 19 4 2 10 1.21 -142.81 -305.62 -324.7402 0.51,0.23,0.13,0.13 0.620006,-1.596313,-2.235706 1|13;2|18;3|14;4|5 0.00000000
#> 20 4 2 9 0.95 -221.87 -461.74 -478.9482 0.06,0.68,0.13,0.13 -2.835281,0.899629,-2.90326 1|5;2|9;3|15;4|5 0.37687450
#> 21 4 2 9 1.10 -164.37 -346.74 -363.9482 0.03,0.35,0.13,0.48 -1.142864,-2.582756,-0.127506 1|6;2|7;3|19;4|18 0.20601182
#> 22 4 2 11 1.14 -152.52 -327.04 -348.0723 0.05,0.33,0.13,0.49 -1.761158,-0.22231,-2.716538 1|5;2|8;3|19;4|18 0.11454631
#> 23 4 3 10 1.21 -139.76 -299.52 -318.6402 0.31,0.09,0.46,0.13 1.637031,1.659007,1.995268 1|13;2|4;3|14;4|19 0.00000000
#> 24 4 3 10 1.08 -141.33 -302.66 -321.7802 0.03,0.33,0.13,0.51 -2.173503,-1.507991,-1.775524 1|13;2|10;3|19;4|8 0.00000000
#> 25 4 3 10 1.15 -141.33 -302.66 -321.7802 0.36,0.05,0.46,0.13 1.81663,1.661772,1.796831 1|13;2|8;3|10;4|19 0.00000000
#> 26 4 3 10 1.10 -141.33 -302.66 -321.7802 0.03,0.38,0.13,0.46 -2.802917,0.654739,-2.200637 1|13;2|8;3|19;4|10 0.00000000
#> 27 4 3 10 1.27 -142.72 -305.44 -324.5602 0.38,0.35,0.14,0.13 1.804812,1.197795,1.055059 1|13;2|18;3|4;4|15 0.00000000
#> 28 4 3 10 1.02 -142.72 -305.44 -324.5602 0.38,0.01,0.13,0.49 -0.23425,-0.966434,-1.782314 1|13;2|4;3|15;4|18 0.00000000
#> 29 5 1 11 1.26 -141.19 -304.38 -325.4123 0.04,0.45,0.05,0.33,0.13 1.765709,1.420863,1.80696,1.959864 1|6;2|7;3|8;4|10;5|19 0.00000000
#> 30 5 1 11 1.34 -139.64 -301.28 -322.3123 0.04,0.41,0.09,0.33,0.13 1.245093,1.53851,1.243456,1.849004 1|6;2|7;3|4;4|14;5|19 0.00000000
#> 31 5 1 11 1.14 -142.58 -307.16 -328.1923 0.04,0.48,0.35,0.01,0.13 1.477177,1.835859,1.565682,1.570549 1|6;2|7;3|18;4|4;5|15 0.00000000
#> 32 5 1 12 1.38 -139.19 -302.38 -325.3243 0.05,0.39,0.09,0.33,0.13 -0.904063,-2.302741,0.883772,-1.853337 1|5;2|8;3|4;4|14;5|19 0.00000000
#> 33 5 1 11 1.17 -141.17 -304.34 -325.3723 0.49,0.05,0.32,0.01,0.13 0.763207,0.99262,-0.597088,-2.010696 1|13;2|8;3|10;4|4;5|15 0.00000000
#> 34 5 2 11 1.34 -142.58 -307.16 -328.1923 0.04,0.48,0.22,0.14,0.13 1.280233,1.308232,1.98148,1.681647 1|6;2|7;3|18;4|4;5|15 0.00000000
#> 35 5 2 11 1.44 -139.60 -301.20 -322.2323 0.44,0.09,0.19,0.14,0.13 1.927028,1.252031,1.303311,1.658146 1|13;2|4;3|14;4|4;5|15 0.00000000
#> 36 5 3 12 1.43 -141.93 -307.86 -330.8043 0.05,0.33,0.13,0.35,0.14 -0.833174,-1.657431,-1.521311,0.994842 1|5;2|8;3|15;4|18;5|4 0.00000000
#> 37 5 3 11 1.32 -139.64 -301.28 -322.3123 0.04,0.28,0.13,0.09,0.46 -0.971608,-1.117897,-0.977414,-1.624446 1|6;2|7;3|19;4|4;5|14 0.00000000
#> 38 5 3 12 1.35 -139.19 -302.38 -325.3243 0.05,0.26,0.13,0.09,0.46 -2.216888,-0.534829,-0.498728,-1.840551 1|5;2|8;3|19;4|4;5|14 0.00000000
#> 39 5 3 12 1.30 -151.07 -326.14 -349.0843 0.05,0.3,0.13,0.05,0.46 -1.753946,-1.742063,-0.021633,-1.216391 1|5;2|8;3|19;4|9;5|9 0.11171478
#> 40 5 3 12 1.30 -140.69 -305.38 -328.3243 0.05,0.3,0.13,0.05,0.46 -1.472786,-0.668003,-2.66109,0.227856 1|5;2|8;3|19;4|8;5|10 0.00000000
#> 41 5 4 11 1.49 -139.60 -301.20 -322.2323 0.31,0.14,0.09,0.33,0.13 1.52869,1.783527,1.056915,1.953415 1|13;2|4;3|4;4|14;5|15 0.00000000
#> 42 5 4 11 1.42 -141.32 -304.64 -325.6723 0.36,0.13,0.05,0.33,0.13 1.073164,1.166258,1.492443,1.331579 1|13;2|9;3|8;4|10;5|10 0.00000000
#> 43 5 4 11 1.43 -141.17 -304.34 -325.3723 0.35,0.14,0.05,0.33,0.13 1.013462,1.071242,1.233511,1.051077 1|13;2|4;3|8;4|10;5|15 0.00000000
#> 44 5 4 11 1.24 -139.70 -301.40 -322.4323 0.31,0.13,0.09,0.01,0.46 -0.638205,-0.50668,-2.686646,-2.285308 1|13;2|19;3|4;4|4;5|10 0.00000000
#> 45 5 4 11 1.14 -141.17 -304.34 -325.3723 0.03,0.46,0.37,0.01,0.13 1.399218,1.818312,1.365729,1.283677 1|13;2|10;3|8;4|4;5|15 0.00000000
#> 46 5 6 11 1.18 -141.17 -304.34 -325.3723 0.35,0.01,0.05,0.46,0.13 1.196523,1.306683,1.515869,1.692234 1|13;2|4;3|8;4|10;5|15 0.00000000
#> 47 5 6 11 1.38 -141.17 -304.34 -325.3723 0.03,0.33,0.37,0.14,0.13 1.537019,1.888057,1.515215,1.854318 1|13;2|10;3|8;4|4;5|15 0.00000000
#> 48 5 6 11 1.25 -139.60 -301.20 -322.2323 0.31,0.09,0.01,0.13,0.46 -0.705352,0.59871,-2.944075,-0.70181 1|13;2|4;3|4;4|15;5|14 0.00000000
#> 49 5 6 11 1.37 -141.32 -304.64 -325.6723 0.03,0.33,0.38,0.13,0.13 1.21288,1.470929,1.647752,1.398339 1|13;2|10;3|8;4|9;5|10 0.00000000
# Order solution(s) based on BIC (larger BIC correspond to better fits)
gg = grid_ith$GRID
gg = gg[order(-gg$BIC),]
head(gg)
#> cc kk ms entropy LL AIC BIC q unc_q0 alloc pi_eps
#> 10 4 1 10 1.21 -139.76 -299.52 -318.6402 0.44,0.09,0.33,0.13 1.836166,1.377129,1.943698 1|13;2|4;3|14;4|19 0
#> 23 4 3 10 1.21 -139.76 -299.52 -318.6402 0.31,0.09,0.46,0.13 1.637031,1.659007,1.995268 1|13;2|4;3|14;4|19 0
#> 5 3 1 9 0.98 -142.87 -303.74 -320.9482 0.51,0.36,0.13 1.743127,1.847057 1|13;2|18;3|19 0
#> 9 3 2 9 0.98 -142.87 -303.74 -320.9482 0.38,0.49,0.13 1.047088,1.478796 1|13;2|18;3|19 0
#> 15 4 1 10 1.14 -141.33 -302.66 -321.7802 0.49,0.05,0.33,0.13 1.658064,1.481153,1.212404 1|13;2|8;3|10;4|19 0
#> 24 4 3 10 1.08 -141.33 -302.66 -321.7802 0.03,0.33,0.13,0.51 -2.173503,-1.507991,-1.775524 1|13;2|10;3|19;4|8 0
# true cancer proportions
sim$q
#> [1] 0.4028888 0.4643963 0.1327149
# true entropy
-sum(sim$q * log(sim$q))
#> [1] 0.9904886From the grid of solutions (grid_ith$GRID), we can use AIC or BIC to score the model fit per solution. Sometimes the same configuration matrix can lead to multiple solutions. The column definitions are provided.
We can calculate a posterior probability to compare and visualize model fits with the following formula:
where \(IC_s\) corresponds to the \(s\)-th modelâs information criterion. The function logSumExp from package smartr will aid us here.
pp = vis_GRID(GRID = grid_ith$GRID)
print(pp)The above figure provides a landscape of which solutions appear more favorable to others.
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