# Different results in Cox model and negative binomial?

I am confused about a problem in my research. Can anyone give me some advices ? I used a Negative binomial ( in MASS package) to examine the effects of 3 covariates on dependent variable ( number of living buds) . Then, I used Cox proportional hazard model to examine the effects of these 3 covariates on survival of this count data. Personally, I think that the 3 covariates should have same effects ( negative or positive) in 2 models. However, the results of 2 models were not consistent. I mean that the effects of 3 covariates on number of living trees and survival of tree were different in 2 models. Are there something wrong ? Or my thinking is wrong?

I'm not sure I understand your experiment entirely. You mention counts of buds that you model with negative binomial regression model, but what is the event that you use in the cox regression model? You can't model a count in a cox regression, if I'm not mistaken.

Principally, you're correct that the covariates should have similar effects. However, this assumes that the covariates are measured at baseline or that they are measured later, but not subject to change. If you have a covariate that might change with time, and you measure it after baseline, you can get results that are difficult to interpret and that can sometimes be surprising. The cox proportional hazards also assumes that the hazards are proportional across the covariates. If this assumption is violated, you may also get these kinds of strange results.

Data in the negative binomial model:

stumpID sprouts DBH  stump_length  slope
2       7       18   70            25.9
6       3       34.7 63            30.9
8       38      23.1 70            21.9
33      60      22   71.3          32.4
38      4       27.1 73.4          35
44      4       35.2 80            31.1


Data in Cox model:

sproutID time1 time2 status stump_diameter stump_length slope
1        35    37    1      23.14          70           21.88
2        35    37    1      23.14          70           21.88
3        35    37    1      23.14          70           21.88
146      21    41    0      26.36          47           24.63
147      21    41    0      26.36          47           24.63
148      25    27    1      26.36          47           24.63
152      23    25    1      26.36          47           24.63

• Thank you @JonB for your reply. I observed the number of buds for different time periods in a year, every month ( count death buds and new buds). For negative binomial model, I only used number of living buds data at the end of survey. For cox model, my data don't violate assumptions of proportionality and linearity . And 3 covariates are time-independent (not change over time). More detail, I could not detect ant effects of 3 covariates on number of living buds at the time point in end of survey, but the these 3 covariates had effects on survival of buds. I am so confused about the results. Commented Oct 13, 2015 at 11:04
• Can you update your question with a sample of your dataset?
– JonB
Commented Oct 13, 2015 at 11:10
• Hi@JonB. Thank you for your reply.This is a sample of data in negative binomial model: stumpID sprouts DBH stump length slope 2 7 18 70 25.9 6 3 34.7 63 30.9 8 38 23.1 70 21.9 33 60 22 71.3 32.4 38 4 27.1 73.4 35 44 4 35.2 80 31.1 And this is data in Cox model: sproutID time 1 time 2 status stump diameter stump length slope 1 35 37 1 23.14 70 21.88 2 35 37 1 23.14 70 21.88 3 35 37 1 23.14 70 21.88 146 21 41 0 26.36 47 24.63 147 21 41 0 26.36 47 24.63 148 25 27 1 26.36 47 24.63 152 23 25 1 26.36 47 24.63 Commented Oct 14, 2015 at 4:50
• Ok. I was hoping that you could update your question with a table of your data, but perhaps you can't due to low reputation? Anyway, it seems you have two times per row in the cox model. Are there time-dependent covariates? What does the "status" variable indicate?
– JonB
Commented Oct 14, 2015 at 6:40
• Thank you @JonB. In cox model, the "time.1" is the entry time, the "time.2" is censoring time or time when event occurred. The "status" variable indicates the death of sprouts. The 3 covariates : stump.diameter, stump length and slope are constant over time. I am afraid of that my problem coming from sample size. Commented Oct 14, 2015 at 7:10

Did you observe and note the entry date of every single bud in your sample from the time it was brand new? Because you're measuring a lifetime, and if you include older buds, you end up measuring less than a lifetime in those specific cases, which biases your results.