I perform a multivariate Cox analysis using 'survival' package in R
## Call:
## coxph(formula = S.6m.y ~ CD4.6m + sex_f.y + marriage_f +transmission_f.y + WHO_stage_2f.y + age_atART.y.y, data = data.6m)
##
## n= 850, number of events= 31
## (1129 observations deleted due to missingness)
## exp(coef) exp(-coef) lower .95
## CD4.6m<50 3.128e+01 3.197e-02 3.47903
## CD4.6m50-199 1.682e+00 5.947e-01 0.72677
## sex_f.ymale 4.944e-01 2.023e+00 0.21678
## marriage_fdivorced 3.877e-01 2.580e+00 0.05131
## marriage_funmarried 1.439e+00 6.949e-01 0.42915
## marriage_fwidowed 3.241e-01 3.086e+00 0.04147
## transmission_f.yheterosexual 6.537e+06 1.530e-07 0.00000
## transmission_f.yhomosexual 2.894e+00 3.455e-01 0.00000
## transmission_f.yinjecting_drug_users(IDU) 1.242e+08 8.049e-09 0.00000
## transmission_f.yMother_to_Child 7.183e+00 1.392e-01 0.00000
## transmission_f.yOthers/unknown 3.091e+07 3.235e-08 0.00000
## WHO_stage_2f.ystage III/IV 9.993e-01 1.001e+00 0.43314
## age_atART.y.y 1.000e+00 9.998e-01 1.00015
## upper .95
## CD4.6m<50 281.259
## CD4.6m50-199 3.890
## sex_f.ymale 1.128
## marriage_fdivorced 2.929
## marriage_funmarried 4.826
## marriage_fwidowed 2.533
## transmission_f.yheterosexual Inf
## transmission_f.yhomosexual Inf
## transmission_f.yinjecting_drug_users(IDU) Inf
## transmission_f.yMother_to_Child Inf
## transmission_f.yOthers/unknown Inf
## WHO_stage_2f.ystage III/IV 2.306
## age_atART.y.y 1.000
##
## Concordance= 0.851 (se = 0.059 )
## Rsquare= 0.065 (max possible= 0.348 )
## Likelihood ratio test= 57.32 on 13 df, p=1.572e-07
## Wald test = 31.58 on 13 df, p=0.002771
## Score (logrank) test = 58.62 on 13 df, p=9.253e-08
The variable of interest is 'CD4.6m' (Three categories: CD4.6m200 (reference); CD4.6m<50;and CD4.6m50-199). When I first saw the Hazard Ratio estimations based on this multivariate model: category: 'CD4.6m<50' has an abnormal high HR as 3.128e+01. I say 'abnormal' is because that it is around 1-10 based on previous studies. At this time, I realized 'Inf' upper.95 for covariable of 'transmission'. By excluding it from the model, the output turns out:
## Call:
## coxph(formula = S.6m.y ~ CD4.6m + sex_f.y + marriage_f + WHO_stage_2f.y +
## age_atART.y.y, data = data.6m)
##
## n= 850, number of events= 31
## (1129 observations deleted due to missingness)
##
## exp(coef) exp(-coef) lower .95 upper .95
## CD4.6m<50 10.0054 0.09995 1.27572 78.472
## CD4.6m50-199 1.5063 0.66388 0.66580 3.408
## sex_f.ymale 0.8122 1.23121 0.37294 1.769
## marriage_fdivorced 0.3244 3.08280 0.04326 2.432
## marriage_funmarried 2.4448 0.40903 0.74461 8.027
## marriage_fwidowed 0.3800 2.63156 0.05002 2.887
## WHO_stage_2f.ystage III/IV 0.9757 1.02492 0.42979 2.215
## age_atART.y.y 1.0002 0.99981 1.00011 1.000
##
## Concordance= 0.763 (se = 0.059 )
## Rsquare= 0.032 (max possible= 0.348 )
## Likelihood ratio test= 27.34 on 8 df, p=0.0006182
## Wald test = 28.55 on 8 df, p=0.0003809
## Score (logrank) test = 32.22 on 8 df, p=8.508e-05
Then the hazard ratio for 'CD4.6m<50' become quite 'normal'(what I expected): 10.0054. Based on all of those, it seems that the 'infinite' upper .95 heavily impacts the hazard ratio estimation for my interesting variable(CD4.6m).
Additional information, the categorical variable of 'transmission' is very unbalanced in terms of sample size:
transmission1 6
transmission2 1400
transmission3 42
transmission4 244
transmission5 5
transmission6 282
My first question: Should I remove 'transmission' from my model in my case? Second question: The 'very' unbalanced sample sizes for categorical variable would lead to infinit upper .95 very often?
