1
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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
Data-86-8668    423.0   0.0 0.0
Data-97-8552    626.0   0.0 0.0
Data-71-6725    61.0    0.0 0.0
Data-55-A493    28.0    0.0 0.0
Data-55-A492    596.0   0.0 0.0
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
Data-05-4432    761.0   0.0 0.0
Data-62-A471    1246.0  0.0 0.0
Data-62-A470    1194.0  1.0 0.0
Data-05-4434    457.0   1.0 0.0
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
Data-44-2666    97.0    1.0 0.0
Data-49-4512    905.0   1.0 0.0
Data-44-2668    246.0   0.0 0.0
Data-44-3398    253.0   0.0 0.0
Data-64-1680    1126.0  0.0 0.0
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
Data-78-7147    586.0   1.0 0.0
Data-55-6986    3261.0  0.0 0.0
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
Data-91-8497    434.0   1.0 0.0
Data-44-6775    370.0   0.0 0.0
Data-44-6774    361.0   0.0 0.0
Data-44-6777    987.0   1.0 0.0
Data-44-6776    1938.0  0.0 0.0
Data-44-6779    500.0   1.0 0.0
Data-44-6778    1110.0  0.0 0.0
Data-83-5908    824.0   0.0 0.0
Data-67-4679            0.0
Data-44-7672    418.0   0.0 0.0
Data-44-7671    535.0   0.0 0.0
Data-44-7670    531.0   0.0 0.0
Data-MN-A4N5    84.0    0.0 0.0
Data-MN-A4N4    1175.0  0.0 0.0
Data-MN-A4N1    827.0   0.0 0.0
Data-49-4490    385.0   1.0 0.0
Data-49-4494    1081.0  1.0 0.0
Data-97-7937    181.0   0.0 0.0
Data-97-7938    18.0    1.0 0.0
Data-50-5051    478.0   1.0 0.0
Data-69-8453    550.0   0.0 0.0
Data-86-8278    476.0   0.0 0.0
Data-86-8279    482.0   0.0 0.0
Data-80-5608            0.0
Data-55-8094    4.0 0.0 0.0
Data-55-8096    719.0   1.0 0.0
Data-55-8097    476.0   0.0 0.0
Data-55-8090    598.0   1.0 0.0
Data-55-8091    600.0   0.0 0.0
Data-55-8092    154.0   1.0 0.0
Data-44-8119    99.0    0.0 0.0
Data-62-A472    910.0   0.0 0.0
Data-44-8117    385.0   0.0 0.0
Data-78-8655    2360.0  0.0 0.0
Data-62-8395    1216.0  0.0 0.0
Data-62-8394    139.0   1.0 0.0
Data-62-8397    1289.0  0.0 0.0
Data-05-4430    761.0   0.0 0.0
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    $\begingroup$ Such values are usually a sign of a data issue. What happens when you look at tabular analyses? Did the only one of your subjects in the stratum with the high coefficient have a very short survival? $\endgroup$
    – DWin
    Commented Apr 4, 2016 at 18:14
  • $\begingroup$ I found the expression values are mostly zeros, with the max value at 0.016. Is this the reason? what should I generally do to avoid this? Is there any related constraints before doing cox ph regression? Thanks. $\endgroup$
    – tsznxyz
    Commented Apr 4, 2016 at 20:25
  • $\begingroup$ I don't think either of your questions can be answered since you have not explained the findings or data with sufficient clarity. $\endgroup$
    – DWin
    Commented Apr 4, 2016 at 20:32
  • $\begingroup$ A hazard ratio of 12 refers to an increase of 1 in your covariate, hence the hazard ratio really depends on the scale of the covariate. That is why it is usually a good idea to standardize continuous covariates in Cox models. Afterwards, you can transform back the hazard ratio to get an effect size. $\endgroup$
    – Theodor
    Commented Apr 4, 2016 at 21:01
  • $\begingroup$ I've added a demo data to better represent the problem. Is there any pre-processing or filters before doing cox ph regression? Thanks. $\endgroup$
    – tsznxyz
    Commented Apr 5, 2016 at 14:29

2 Answers 2

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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.

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I faced a similar issue when I used a log-transformed variable in the coxph model. In my case, taking the original (untransformed) values provided me with a sensible way to interpret the HRs.

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