I am using R survival package for survival analysis against gene expression.
fit<-coxph(Surv(time,censor) ~ expression)
However, I got some very high coefficients, such 12 and consequently very high hazard ratio exp(12) = 162754.8. The pvalue is < 0.01.
How to interpret such high coefficient?
selected data:
time censor Expression
Data-78-7159 1221.0 0.0 0.0
Data-78-7158 179.0 1.0 0.0
Data-64-1679 1686.0 0.0 0.0
Data-64-1678 1189.0 0.0 0.0
Data-64-1677 628.0 1.0 0.0
Data-64-1676 1728.0 0.0 0.0
Data-78-7156 976.0 1.0 0.0
Data-78-7150 666.0 1.0 0.0
Data-78-7153 760.0 0.0 0.0
Data-78-7152 1202.0 0.0 0.0
Data-MP-A4TF 336.0 1.0 0.0
Data-MP-A4TD 307.0 1.0 0.0
Data-L9-A443 116.0 0.0 0.0
Data-MP-A4TA 950.0 1.0 0.0
Data-MP-A4TK 582.0 1.0 0.0
Data-MP-A4TJ 339.0 1.0 0.0
Data-MP-A4TI 429.0 1.0 0.0
Data-MP-A4TH 446.0 0.0 0.0
Data-J2-8194 724.0 0.0 0.0
Data-J2-8192 154.0 0.0 0.0
Data-NJ-A4YP 50.0 0.0 0.0
Data-78-7155 1171.0 1.0 0.0
Data-78-7154 593.0 1.0 0.0
Data-67-3771 610.0 0.0 0.0
Data-67-3770 31.0 0.0 0.0
Data-67-3773 427.0 0.0 0.0
Data-67-3772 573.0 0.0 0.0
Data-67-3774 385.0 0.0 0.0
Data-78-7633 994.0 0.0 0.0
Data-05-4382 607.0 0.0 0.0
Data-MP-A4T7 167.0 1.0 0.0
Data-MP-A4T6 1790.0 1.0 0.0
Data-MP-A4T4 2617.0 1.0 0.0
Data-55-6987 1170.0 0.0 0.0
Data-MP-A4T9 1265.0 1.0 0.0
Data-MP-A4T8 161.0 1.0 0.0
Data-55-7727 34.0 0.0 0.0
Data-55-7726 39.0 0.0 0.0
Data-55-7725 39.0 0.0 0.0
Data-55-7724 705.0 0.0 0.0
Data-97-8175 551.0 0.0 0.0
Data-44-5643 417.0 0.0 0.0
Data-44-5644 498.0 0.0 0.0
Data-44-5645 383.0 0.0 0.0
Data-97-8174 164.0 1.0 0.0
Data-97-A4LX 614.0 0.0 0.0
Data-99-8028 1118.0 0.0 0.0
Data-49-6767 677.0 0.0 0.0
Data-49-6761 354.0 0.0 0.0
Data-38-A44F 133.0 0.0 0.0
Data-53-7813 424.0 0.0 0.0
Data-64-5781 1202.0 0.0 0.0
Data-50-5939 460.0 1.0 0.0
Data-50-5936 257.0 1.0 0.0
Data-50-5935 653.0 1.0 0.0
Data-50-5933 2393.0 1.0 0.0
Data-50-5932 1235.0 1.0 0.0
Data-50-5931 434.0 1.0 0.0
Data-50-5930 282.0 1.0 0.0
Data-69-7979 89.0 0.0 0.0
Data-69-7978 70.0 0.0 0.0
Data-97-A4M7 629.0 0.0 0.0
Data-97-A4M6 568.0 0.0 0.0
Data-97-A4M1 601.0 0.0 0.0
Data-97-A4M0 652.0 0.0 0.0
Data-97-A4M3 540.0 0.0 0.0
Data-97-A4M2 624.0 0.0 0.0
Data-69-7973 230.0 0.0 0.0
Data-69-7974 184.0 0.0 0.0
Data-55-8089 100.0 0.0 0.0
Data-55-8087 462.0 0.0 0.0
Data-55-8085 904.0 0.0 0.0062940859132
Data-75-5122 0.0
Data-75-5125 0.0
Data-75-5126 0.0
Data-50-5068 1499.0 1.0 0.0
Data-44-8120 260.0 0.0 0.0
Data-50-5066 944.0 0.0 0.0
Data-80-5607 0.0
Data-50-5072 250.0 1.0 0.0
Data-50-6673 22.0 1.0 0.0217563988823
Data-55-7573 4.0 0.0 0.0
Data-55-7570 6.0 0.0 0.0
Data-55-7576 40.0 0.0 0.0
Data-55-7574 95.0 0.0 0.0
Data-95-7043 2.0 0.0 0.0
Data-38-4628 1492.0 1.0 0.0
Data-73-4668 467.0 0.0 0.0
Data-38-4626 2595.0 0.0 0.0
Data-38-4627 1147.0 1.0 0.0
Data-38-4625 2973.0 0.0 0.0
Data-73-4662 912.0 0.0 0.0
Data-05-4244 0.0
Data-78-7166 258.0 1.0 0.0
Data-78-7167 2681.0 1.0 0.0
Data-78-7160 678.0 0.0 0.0
Data-78-7161 215.0 0.0 0.00593650490343
Data-78-7162 3169.0 1.0 0.0
Data-78-7163 6812.0 0.0 0.0
Data-78-8640 6528.0 0.0 0.0
Data-55-8621 515.0 0.0 0.0
Data-55-8620 66.0 0.0 0.0
Data-05-4249 1523.0 0.0 0.0
Data-NJ-A55O 13.0 0.0 0.0
Data-44-2665 400.0 0.0 0.0
Data-NJ-A55A 8.0 0.0 0.0
Data-05-4418 274.0 1.0 0.0
Data-05-4410 0.0
Data-05-4415 91.0 1.0 0.0
Data-05-4417 455.0 0.0 0.0
Data-35-3615 14.0 0.0 0.0
Data-93-A4JP 578.0 0.0 0.0
Data-93-A4JQ 526.0 0.0 0.0
Data-93-A4JN 718.0 0.0 0.0
Data-93-A4JO 33.0 1.0 0.0
Data-NJ-A55R 603.0 0.0 0.0
Data-86-7701 11.0 0.0 0.0
Data-91-6848 224.0 0.0 0.0
Data-91-6847 842.0 0.0 0.0
Data-91-6840 372.0 0.0 0.0
Data-95-7947 40.0 0.0 0.0
Data-95-7944 21.0 0.0 0.0
Data-55-7994 603.0 0.0 0.0
Data-55-7995 5.0 0.0 0.0
Data-75-7027 0.0
Data-75-7025 0.0
Data-95-8494 84.0 0.0 0.0
Data-69-A59K 214.0 0.0 0.0
Data-50-8459 231.0 0.0 0.0
Data-50-8457 779.0 0.0 0.0
Data-86-8359 444.0 1.0 0.0
Data-86-8358 653.0 0.0 0.0
Data-35-4122 225.0 0.0 0.0
Data-35-4123 182.0 0.0 0.0
Data-78-7537 1622.0 1.0 0.0
Data-78-7536 244.0 1.0 0.0
Data-78-7535 949.0 1.0 0.0
Data-L9-A444 6.0 0.0 0.0
Data-91-7771 492.0 0.0 0.0
Data-78-7539 327.0 0.0 0.0
Data-50-5055 785.0 0.0 0.0
Data-38-7271 800.0 1.0 0.0
Data-86-8073 740.0 0.0 0.0
Data-86-8076 489.0 0.0 0.0
Data-86-8074 24.0 0.0 0.0
Data-86-8075 479.0 0.0 0.0
Data-55-8301 44.0 0.0 0.0
Data-55-8302 23.0 0.0 0.0
Data-62-A46P 594.0 1.0 0.0
Data-62-A46R 1725.0 1.0 0.0
Data-62-A46S 1653.0 1.0 0.0
Data-62-A46U 2067.0 0.0 0.0
Data-62-A46V 2199.0 0.0 0.0
Data-62-A46Y 414.0 1.0 0.0
Data-53-A4EZ 280.0 0.0 0.0
Data-91-6849 35.0 0.0 0.0
Data-64-5815 224.0 0.0 0.0
Data-97-7552 1932.0 0.0 0.0
Data-97-7553 1332.0 0.0 0.0
Data-62-A46O 1454.0 1.0 0.0
Data-86-8671 839.0 0.0 0.0
Data-86-8672 19.0 1.0 0.0
Data-86-8673 455.0 0.0 0.0
Data-86-8674 405.0 0.0 0.0
Data-97-8547 657.0 0.0 0.0
Data-55-A48X 689.0 0.0 0.0
Data-55-A48Z 651.0 0.0 0.0
Data-55-7815 54.0 0.0 0.0
Data-91-A4BD 603.0 0.0 0.0
Data-91-A4BC 44.0 0.0 0.0
Data-05-4420 912.0 0.0 0.0
Data-55-6980 67.0 0.0 0.0
Data-05-4422 365.0 0.0 0.0
Data-55-7728 24.0 0.0 0.0
Data-05-4424 913.0 0.0 0.0
Data-05-4425 669.0 0.0 0.0
Data-05-4426 791.0 0.0 0.0
Data-05-4427 791.0 0.0 0.0
Data-44-7659 444.0 0.0 0.0
Data-73-7499 715.0 0.0 0.0
Data-73-7498 1189.0 0.0 0.0
Data-55-6984 760.0 1.0 0.0
Data-55-6985 1233.0 0.0 0.0
Data-05-5423 151.0 0.0 0.0
Data-05-5420 457.0 0.0 0.0
Data-05-5425 882.0 0.0 0.0
Data-75-5147 0.0
Data-75-5146 0.0
Data-05-5429 275.0 1.0 0.0
Data-05-5428 670.0 0.0 0.0
Data-55-5899 87.0 0.0 0.0
Data-53-7624 1043.0 1.0 0.0
Data-53-7626 929.0 1.0 0.0
Data-86-8056 0.0
Data-55-6712 24.0 0.0 0.0
Data-69-7980 382.0 0.0 0.0
Data-99-8032 44.0 0.0 0.0
Data-99-8033 170.0 0.0 0.0
Data-95-7948 133.0 0.0 0.0
Data-J2-A4AE 282.0 0.0 0.0
Data-J2-A4AD 550.0 1.0 0.0
Data-J2-A4AG 500.0 0.0 0.0
Data-55-6968 1293.0 1.0 0.0
Data-55-6969 1239.0 0.0 0.0
Data-62-8402 1498.0 1.0 0.0
Data-80-5611 0.0
Data-78-8662 3361.0 1.0 0.0
Data-78-8660 321.0 1.0 0.0
Data-67-6215 174.0 0.0 0.0
Data-35-5375 264.0 0.0 0.0
Data-67-6217 422.0 0.0 0.0
Data-67-6216 141.0 0.0 0.0
Data-73-4658 1600.0 1.0 0.0
Data-73-4659 711.0 1.0 0.0
Data-71-8520 3.0 0.0 0.0
Data-38-4631 354.0 1.0 0.0
Data-38-4630 1073.0 1.0 0.0
Data-38-4632 1357.0 1.0 0.0
Data-55-8616 48.0 0.0 0.0
Data-44-A4SU 409.0 1.0 0.0
Data-55-8615 15.0 0.0 0.0104928008745
Data-44-A4SS 415.0 0.0 0.0
Data-05-4398 1431.0 0.0 0.00307299364788
Data-05-4250 121.0 1.0 0.0
Data-05-4396 303.0 1.0 0.0
Data-05-4397 731.0 1.0 0.0
Data-05-4395 0.0 1.0 0.0
Data-05-4390 1126.0 0.0 0.0
Data-55-8619 49.0 0.0 0.0
Data-95-A4VP 605.0 0.0 0.0
Data-95-A4VN 553.0 0.0 0.0
Data-55-6979 237.0 1.0 0.0
Data-95-A4VK 121.0 0.0 0.0
Data-55-7914 3.0 0.0 0.0
Data-55-7910 197.0 0.0 0.0
Data-55-7911 21.0 0.0 0.0
Data-55-A4DF 614.0 1.0 0.0
Data-55-A4DG 608.0 0.0 0.0
Data-64-5774 2550.0 0.0 0.0
Data-64-5775 62.0 1.0 0.0
Data-50-5946 686.0 0.0 0.0
Data-64-5778 926.0 0.0 0.0
Data-64-5779 507.0 0.0 0.0
Data-50-5942 883.0 0.0 0.0
Data-50-5941 567.0 0.0 0.0
Data-MP-A4SV 2620.0 1.0 0.0
Data-MP-A4SW 1778.0 1.0 0.0
Data-69-7760 202.0 0.0 0.0
Data-69-7761 186.0 0.0 0.0
Data-69-7763 690.0 0.0 0.0
Data-69-7764 414.0 0.0 0.0
Data-69-7765 165.0 0.0 0.0
Data-MP-A4SY 1501.0 1.0 0.0
Data-91-6830 60.0 0.0 0.0
Data-91-6831 310.0 0.0 0.0
Data-91-6835 79.0 0.0 0.0
Data-91-6836 417.0 0.0 0.0
Data-97-8171 107.0 0.0 0.0
Data-97-8172 182.0 0.0 0.0
Data-75-7031 0.0
Data-75-7030 0.0
Data-97-8177 147.0 0.0 0.0
Data-97-8176 468.0 1.0 0.0
Data-97-8179 15.0 0.0 0.0
Data-49-6745 522.0 0.0 0.0
Data-49-6744 890.0 0.0 0.0
Data-49-6743 369.0 0.0 0.0
Data-49-6742 445.0 0.0 0.0
Data-44-7669 574.0 1.0 0.0
Data-44-7660 325.0 0.0 0.0
Data-44-7661 366.0 0.0 0.0
Data-44-7662 218.0 0.0 0.0
Data-44-7667 557.0 0.0 0.0
Data-44-A47B 287.0 0.0 0.0
Data-44-A47A 466.0 0.0 0.0
Data-44-A47G 351.0 0.0 0.0
Data-49-4486 2318.0 1.0 0.0
Data-49-4487 855.0 1.0 0.0
Data-44-A479 392.0 0.0 0.0
Data-97-7941 22.0 0.0 0.0
Data-49-4488 869.0 1.0 0.0
Data-86-8281 0.0
Data-86-8280 16.0 0.0 0.0
Data-50-8460 829.0 0.0 0.0
Data-44-3918 197.0 0.0 0.0
Data-44-3919 190.0 0.0 0.0
Data-86-A456 405.0 0.0 0.0
Data-50-5045 2174.0 1.0 0.0
Data-50-5044 624.0 1.0 0.0
Data-93-7347 297.0 0.0 0.0
Data-93-7348 127.0 0.0 0.0
Data-50-5049 2146.0 0.0 0.0
Data-55-8508 15.0 0.0 0.0
Data-55-8506 11.0 0.0 0.0
Data-55-8507 8.0 0.0 0.0
Data-55-8505 29.0 0.0 0.0
Data-86-A4D0 116.0 1.0 0.0
Data-44-6148 362.0 0.0 0.0
Data-44-6146 302.0 0.0 0.0
Data-44-6147 441.0 0.0 0.0
Data-44-6145 328.0 0.0 0.0
Data-50-6590 1288.0 1.0 0.00331897756584
Data-50-6591 119.0 1.0 0.0
Data-50-6592 777.0 1.0 0.0
Data-50-6593 336.0 1.0 0.0
Data-50-6594 370.0 1.0 0.0
Data-50-6595 189.0 1.0 0.0
Data-50-6597 1015.0 0.0 0.0
Data-86-7954 0.0
Data-86-7955 508.0 0.0 0.0
Data-78-7220 807.0 1.0 0.0
Data-75-6212 0.0
Data-75-6211 0.0
Data-91-8496 505.0 0.0 0.0
Data-75-6214 0.0
Data-97-7546 964.0 0.0 0.0
Data-86-8669 938.0 0.0 0.0
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Data-55-A493 28.0 0.0 0.0
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Data-55-A491 626.0 0.0 0.0
Data-55-A494 481.0 0.0 0.0
Data-05-4433 730.0 0.0 0.0
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Data-62-A470 1194.0 1.0 0.0
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Data-97-7547 1965.0 0.0 0.0
Data-86-6851 179.0 0.0 0.0
Data-97-A4M5 634.0 0.0 0.0
Data-NJ-A4YI 4.0 1.0 0.0
Data-95-7039 34.0 0.0 0.0
Data-NJ-A4YF 2161.0 0.0 0.0
Data-NJ-A4YQ 886.0 0.0 0.0
Data-44-4112 370.0 0.0 0.0
Data-99-8025 1060.0 0.0 0.0
Data-95-7562 87.0 1.0 0.0
Data-95-7567 163.0 0.0 0.0
Data-55-8614 536.0 0.0 0.0
Data-91-6829 1258.0 1.0 0.0
Data-49-4514 1700.0 0.0 0.0
Data-44-2662 480.0 0.0 0.0
Data-44-2661 446.0 0.0 0.0
Data-91-6828 323.0 0.0 0.0
Data-49-4510 896.0 1.0 0.0
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Data-44-2668 246.0 0.0 0.0
Data-44-3398 253.0 0.0 0.0
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Data-64-1681 1167.0 1.0 0.0
Data-86-A4JF 536.0 0.0 0.0
Data-44-3396 411.0 0.0 0.0
Data-05-4389 1369.0 0.0 0.0
Data-78-7143 4961.0 1.0 0.0
Data-55-6982 995.0 1.0 0.0
Data-55-6983 1826.0 0.0 0.0
Data-78-7146 173.0 1.0 0.0
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Data-78-7145 826.0 1.0 0.0
Data-86-8054 745.0 0.0 0.0
Data-86-8055 124.0 1.0 0.0
Data-78-7148 626.0 1.0 0.0
Data-78-7149 1093.0 0.0 0.0
Data-05-4384 426.0 0.0 0.0
Data-91-8499 36.0 0.0 0.0
Data-78-7542 321.0 1.0 0.0
Data-55-6978 167.0 1.0 0.0
Data-78-7540 881.0 0.0 0.0
Data-55-6975 118.0 1.0 0.0
Data-55-6971 25.0 0.0 0.0
Data-55-6970 464.0 1.0 0.0
Data-55-6972 1475.0 0.0 0.0
Data-55-7907 16.0 0.0 0.0
Data-55-7903 19.0 0.0 0.0
Data-95-8039 27.0 0.0 0.0
Data-38-6178 448.0 0.0 0.0
Data-55-7227 53.0 0.0 0.0
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Data-49-4494 1081.0 1.0 0.0
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Data-62-8397 1289.0 0.0 0.0
Data-05-4430 761.0 0.0 0.0
Data-62-8399 2696.0 0.0 0.0
Data-62-8398 444.0 1.0 0.0
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Data-55-8511 9.0 0.0 0.0
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Data-55-8512 3.0 0.0 0.0
Data-55-6543 2.0 0.0 0.0
Data-78-8648 1209.0 1.0 0.0
Data-73-4675 40.0 0.0 0.0
Data-73-4676 164.0 0.0 0.0
Data-73-4677 38.0 1.0 0.0
Data-73-4670 131.0 0.0 0.0
Data-75-6205 0.0
Data-75-6207 0.0
Data-75-6206 0.0
Data-75-6203 0.0
Data-55-6642 993.0 0.0 0.0
Data-55-7284 121.0 0.0 0.0
Data-38-4629 864.0 1.0 0.0
Data-55-7281 18.0 0.0 0.0
Data-55-7283 35.0 0.0 0.0
Data-73-4666 800.0 0.0 0.0
Data-05-4405 610.0 0.0 0.0
Data-05-4402 244.0 1.0 0.0
Data-05-4403 578.0 0.0 0.0
Data-86-6562 376.0 1.0 0.0
Data-L4-A4E5 578.0 0.0 0.0
Data-L4-A4E6 435.0 0.0 0.0
Data-MP-A5C7 1862.0 0.0 0.0
Data-99-7458 392.0 0.0 0.0
Data-50-5944 764.0 0.0 0.0
Data-86-7713 422.0 0.0 0.0
Data-86-7711 630.0 0.0 0.0
Data-86-7714 625.0 1.0 0.0
Data-50-7109 255.0 0.0 0.0
Data-86-A4P7 415.0 0.0 0.0
Data-86-A4P8 431.0 0.0 0.0
Data-97-7554 775.0 0.0 0.0
Data-MP-A4TC 74.0 1.0 0.0
Data-55-1596 1375.0 0.0 0.0
Data-55-1594 1178.0 0.0 0.0
Data-55-1595 1479.0 0.0 0.0
Data-55-1592 701.0 1.0 0.0
Data-05-5715 62.0 0.0 0.0
Data-55-8299 469.0 1.0 0.0
Data-55-6981 1379.0 1.0 0.0
Data-86-7953 591.0 0.0 0.0
Data-69-8253 100.0 0.0 0.0
Data-69-8255 129.0 0.0 0.0
Data-69-8254 77.0 0.0 0.0
Data-86-8585 35.0 0.0 0.0
Data-44-2659 529.0 0.0 0.0
Data-44-2656 582.0 0.0 0.0
Data-44-2657 400.0 0.0 0.0
Data-44-2655 575.0 0.0 0.0
Data-49-4507 268.0 1.0 0.0
Data-49-4506 999.0 1.0 0.0
Data-49-4505 428.0 1.0 0.0
Data-49-4501 1421.0 1.0 0.0
Data-93-8067 186.0 0.0 0.0
Data-55-8205 33.0 0.0 0.0
Data-55-8204 0.0
Data-55-8207 66.0 0.0 0.0
Data-55-8206 46.0 0.0 0.0
Data-55-8203 547.0 0.0 0.0
Data-55-8208 674.0 0.0 0.0
Best Answer
As you said, say you have an estimated regression coefficient $\beta = 12$ and the maximum value is 0.016. This means that the hazard ratio between an individual with the value 0.016 and an individual with the value 0 is $\exp(0.016 \times 12) = e^{0.192} \approx 1.21 $. What you see probably in the R output as hazard ratio for that coefficient is $e^{12} \approx 16254$ which would be the hazard ratio between a hypothetical individual with the value 1 and an individual with 0.
Thus, the value of the coefficient itself is important as an effect size, but that is relative to the size of the covariate that it relates to (this is the same in linear regression). You can not interpret a hazard ratio (or a regression coefficient) as large or small by itself.
If you want to get smaller numbers (for numerical stability mostly) then depending on your data you can standardize the covariates somehow. For example, you might divide by the maximum value of the covariate in your case, since there are only (small) positive values. In this case, in the example I had in the first paragraph, you would get a regression coefficent of about 0.192 and a hazard ratio of 1.21, which has the interpretation that I mentioned above.