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11. Cox regression introduction

# 11. Cox regression introduction -...

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!"#\$%&’\$’(\$ *+, -./"(&0 !"#1.%23 444 562"78 9:++ ;7"<.2\$"%3 #= >&\$?"78%#7 !&[email protected]&2& -(A7"8?%B C?DED !4F5G *+, 562"78 9:++ !D -(A7"8?% 4HGIFE;JG4FH GF JFK ILMIL554FH NFI JLH5FILE 5;IO4OPQ EPGP F;GQ4HL M.7.2&0 N#21 #= %?. J#R I.82.\$\$"#7 -#/.0 J#.S(".7% 47%.262.%&’#7 J#7T/.7(. 47%.2<&0\$ &7/ U36#%?.\$"\$ G.\$%\$ LR&160.\$V F7. @"7&23 <&2"&@0. F7. (#7’7W#W\$ 0"7.&2 <&2"&@0. F7. X82#W6./Y0"7.&2Z <&2"&@0. F7. \$.% #= /W113 <&2"&@0.\$ G[# @"7&23 <&2"&@0.\$ F7. @"7&23 &7/ #7. (#7’7W#W\$ 0"7.&2 <&2"&@0. 5%2&’T./ J#R -#/.0 \9] !4F5G *+, 562"78 9:++ !D -(A7"8?%

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JFK ILMIL554FH -FELQ !4F5G *+, 562"78 9:++ !D -(A7"8?% \9^ CIFCFIG4FHPQ UP_PIE5 -FELQ !4F5G *+, 562"78 9:++ !D -(A7"8?% \9‘
LKP-CQL !4F5G *+, 562"78 9:++ !D -(A7"8?% \,: LKP-CQL Proportional Hazards t ! (t) Parallel Log Hazards t log ! (t) !4F5G *+, 562"78 9:++ !D -(A7"8?% \,+

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ILQPG4FH5U4C GF 5;IO4OPQ N;HJG4FH !4F5G *+, 562"78 9:++ !D -(A7"8?% \,9 C4JG;IL 0.0 0.4 0.8 Hazard Function t ! (t) 0.0 0.4 0.8 Survival function t S(t) 0.0 0.4 0.8 Density function t f(t) !4F5G *+, 562"78 9:++ !D -(A7"8?% \,,
L5G4-PGL5 PHE JFHN4ELHJL 4HGLIOPQ5 !4F5G *+, 562"78 9:++ !D -(A7"8?% \,\ UaCFGUL545 GL5G5 As before, three tests of H 0 : β = 0 are possible: 1. Wald test: ˆ β se ( ˆ β ) 2. (Partial) Likelihood ratio test 3. Score test: ( logrank test) !4F5G *+, 562"78 9:++ !D -(A7"8?% \,*

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4H 5GPGP !4F5G *+, 562"78 9:++ !D -(A7"8?% \,b . sts test treat failure _d: censor analysis time _t: time Log-rank test for equality of survivor functions | Events Events treat | observed expected ------+------------------------- 1 | 64 64.50 2 | 64 63.50 ------+------------------------- Total | 128 128.00 chi2(1) = 0.01 Pr>chi2 = 0.9277 4H 5GPGP !4F5G *+, 562"78 9:++ !D -(A7"8?% \,] . stcox treat failure _d: censor analysis time _t: time Iteration 0: log likelihood = -505.88396 Iteration 1: log likelihood = -505.87987 Iteration 2: log likelihood = -505.87987 Refining estimates: Iteration 0: log likelihood = -505.87987 Cox regression -- Breslow method for ties No. of subjects = 137 Number of obs = 137 No. of failures = 128 Time at risk = 16663 LR chi2(1) = 0.01 Log likelihood = -505.87987 Prob > chi2 = 0.9280 ------------------------------------------------------------------------------ _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- treat | 1.016462 .1836255 0.09 0.928 .7133788 1.448312 ------------------------------------------------------------------------------
5LJFHE LKP-CQL !4F5G *+, 562"78 9:++ !D -(A7"8?% \,^ JFHG4H;F;5 Q4HLPI K Proportional Hazards t ! ( t ) exp( " x) 0.5 1.0 1.5 2.0 Parallel Log Hazards t log ! ( t ) exp( " x) 0.5 1.0 1.5 2.0 !4F5G *+, 562"78 9:++ !D -(A7"8?% \,‘

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4H 5GPGP !4F5G *+, 562"78 9:++ !D -(A7"8?% \\: . stcox status failure _d: censor analysis time _t: time Iteration 0: log likelihood = -505.88396 Iteration 1: log likelihood = -485.31167 Iteration 2: log likelihood = -485.07085 Refining estimates: Iteration 0: log likelihood = -485.07085 Cox regression -- Breslow method for ties No. of subjects = 137 Number of obs = 137 No. of failures = 128 Time at risk = 16663 LR chi2(1) = 41.63 Log likelihood = -485.07085 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- status | .9673035 .0049074 -6.55 0.000 .9577329 .9769698 ------------------------------------------------------------------------------ 4H 5GPGP !4F5G *+, 562"78 9:++ !D -(A7"8?% \\+ . lincom 10* status ( 1) 10*status = 0 ------------------------------------------------------------------------------ _t | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -.3324294 .0507327 -6.55 0.000 -.4318637 -.232995 ------------------------------------------------------------------------------ . lincom 10*status, eform ( 1) 10*status = 0 ------------------------------------------------------------------------------ _t | exp(b) Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | .7171793 .0363845 -6.55 0.000 .6492979 .7921575 ------------------------------------------------------------------------------
5-FFGU !P5LQ4HL UP_PIE L5G4-PGL 0 .005 .01 Smoothed hazard function 0 200 400 600 800 1000 analysis time Cox proportional hazards regression !4F5G *+, 562"78 9:++ !D -(A7"8?% \\9 stcurve, hazard 5-FFGU !P5LQ4HL UP_PIE L5G4-PGL 0 .002 .004 .006 .008 Smoothed hazard function 0 200 400 600 800 1000 analysis time Cox proportional hazards regression !4F5G *+, 562"78 9:++ !D -(A7"8?% \\, stcurve, hazard width(100)

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JFHG4H;F;5 Q4HLPI Proportional Hazards t !
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11. Cox regression introduction -...

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