# Cox Proportional Hazard models for more than 2 treatments and covariates

I am trying to figure out how to properly interpret the results of this cox proportional hazard model, represented by a forest plot.

I have looked into a lot of references, but almost all of them have only two groups: a treatment and a control. I found another example with four groups but it didn't use covariates. I can post the data set if desired but here is a little info about it: I have several plant species planted with three treatments, a drought, water and control. I have measured several traits, but averaged them by treatment and applied to all species within that treatment to act as a covariate because I only was able to take data from right censored plants. I standardized variables using a linear transformation: (x-mean(x))/std(x) and I did so because the scale in units was so different (e.g. 0.002 vs 250) to not over emphasize certain values of beta.

A little more about the data: Individuals were planted 3 years ago by another person - I started working on the project last year and took trait data. Because of that I was only able to take data from plants that are still alive at the latest census. I have three treatments: control, water, shelter (n= 5 each). In plots there are 7-9 plants of each species planted. I took traits from surviving individuals in each plot. I averaged the values for all individuals per species by treatment. I then used these mean trait values for alive AND dead individuals (e.g. mean traits for alive ARCA-water, ARCA-shelter, ARCA-control applied respectively to alive and dead ARCA-water, ARCA-shelter and ARCA-control plants)

Note - Prior to running the cox regression, I generated a Pearson's correlation matrix [species x trait] to reduce colinerarity in the model (removed correlated covariates).

The treatment effect is easiest to understand: Plants in the shelter treatment are 49.7% less likely to experience an event compared to the control group and the water treatment is 57.8% less likely to experience an event (death) compared to the control group. However when it gets to the covariates I start to become unsure.

For example it seems an increase in st.Area decreases the hazard by 32% or a increase in st.Growth_Rate increase hazard by 389%. But how does this relate to treatments? Are the covariants significance comparing to the control or absolute values?

In another example (https://www.students4bestevidence.net/tutorial-read-forest-plot/) they say going to the right favors the control and going to the left of the null axis favors the treatment, but I also have two treatments. Does this mean I have to separate them?

Here is the summary output:

Call:
coxph(formula = Surv(Time, Event, type = c("right")) ~ Treatment +
st.Area + st.Growth_Rate + st.SLA + st.VLA + st.LV + st.PD10 +
st.PD50 + st.VLAVar, data = YLRMeans)

n= 410, number of events= 282
(805 observations deleted due to missingness)

coef exp(coef) se(coef)      z Pr(>|z|)
Treatmentshelter -0.69871   0.49722  0.20960 -3.334 0.000857 ***
Treatmentwatered -0.54834   0.57791  0.21674 -2.530 0.011407 *
st.Area          -1.12896   0.32337  0.53930 -2.093 0.036315 *
st.Growth_Rate    1.35953   3.89435  0.46551  2.921 0.003494 **
st.SLA           -3.59592   0.02744  1.75451 -2.050 0.040410 *
st.VLA            1.15986   3.18949  0.70606  1.643 0.100438
st.LV             1.46487   4.32700  0.65011  2.253 0.024243 *
st.PD10          -0.28738   0.75023  0.23904 -1.202 0.229264
st.PD50           1.15713   3.18078  0.42920  2.696 0.007018 **
st.VLAVar        -2.22733   0.10782  0.99551 -2.237 0.025262 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

exp(coef) exp(-coef) lower .95 upper .95
Treatmentshelter   0.49722     2.0112 0.3297163    0.7498
Treatmentwatered   0.57791     1.7304 0.3778938    0.8838
st.Area            0.32337     3.0924 0.1123694    0.9306
st.Growth_Rate     3.89435     0.2568 1.5638495    9.6979
st.SLA             0.02744    36.4494 0.0008808    0.8546
st.VLA             3.18949     0.3135 0.7993304   12.7267
st.LV              4.32700     0.2311 1.2100663   15.4726
st.PD10            0.75023     1.3329 0.4695960    1.1986
st.PD50            3.18078     0.3144 1.3715060    7.3768
st.VLAVar          0.10782     9.2751 0.0153215    0.7587

Concordance= 0.667  (se = 0.028 )
Rsquare= 0.154   (max possible= 1 )
Likelihood ratio test= 68.53  on 10 df,   p=8.509e-11
Wald test            = 53.01  on 10 df,   p=7.415e-08
Score (logrank) test = 60.14  on 10 df,   p=3.404e-09


• Welcome to the site. What do you mean by "but averaged them by treatment and applied to all species within that treatment to act as a covariate because I only was able to take data from right censored plants." – Peter Flom Oct 6 '18 at 16:36
• individuals were planted 3 years ago by another person - I started working on the project last year and took trait data. Because of that I was only able to take data from plants that are still alive at the latest census. I have three treatments: control, water, shelter (n= 5 each). In plots there are 7-9 plants of each species planted. I took traits from surviving individuals in each plot. I averaged the values for all individuals per species by treatment. I then used these mean trait values for alive AND dead plants (e.g. mean traits for alive ARCA-water, ARCA-shelter applied to dead plants) – Justin Luong Oct 6 '18 at 16:48

• Peter thanks, for example then, would I have to test coxph(survivalobject~Treatment+st.SLA+st.LV+st.SLA:Treatment+st.LV:Treatment is that right – Justin Luong Oct 6 '18 at 17:24