# Multivariate semi-parametric Cox proportional hazard

**URL:** https://discourse.pymc.io/t/multivariate-semi-parametric-cox-proportional-hazard/9827
**Category:** v5
**Tags:** modeling
**Created:** [July 6, 2022, 7:23am UTC](https://discourse.pymc.io/t/multivariate-semi-parametric-cox-proportional-hazard/9827 "2022-07-06T07:23:07Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![PeePeeJay](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/peepeejay/32/5347_2.png) [@PeePeeJay](https://discourse.pymc.io/u/PeePeeJay)
#### Post date: [July 6, 2022, 7:23am UTC](https://discourse.pymc.io/t/multivariate-semi-parametric-cox-proportional-hazard/9827/1 "2022-07-06T07:23:07Z")

</div>

Hello PyMC3 World!

I just started using PyMC3 and thus have to excuse for my very beginners questions in advance.

I am trying to use a semi-parametric Cox Regression model for survival analysis as described in this post by @AustinRochford :

[https://docs.pymc.io/en/v3/pymc-examples/examples/survival\_analysis/survival\_analysis.html](https://docs.pymc.io/en/v3/pymc-examples/examples/survival_analysis/survival_analysis.html)

In order to perform multivariate analysis I was trying to use the shape parameter for `beta` to assign all regression coefficients in a single stochastic variable. The model looks something like this:

```auto
covariates = [covariate1, covariate2]  

with pm.Model(coords=coords) as model:
      lambda0 = pm.Gamma("lambda0", 0.01, 0.01, dims="intervals")

      beta = pm.Normal("beta", 0, sigma=1000, shape=len(covariates))

      exponent = pm.math.dot(data[covariates].to_numpy(dtype=float), beta)

      lambda_ = pm.Deterministic("lambda_",
                                 T.outer(T.exp(exponent), lambda0))
      
      mu = pm.Deterministic("mu", exposure * lambda_)

      obs = pm.Poisson("obs", mu, observed=death)

```

wehre `data` is a pandas dataframe which holds the survival time as well as the covariate values in its columns.

After sampling I expected a `beta` from the posterior of shape `(2,)` with two regression coefficients for each covariate under inspection.  
It turns out that both `beta` values are equal which is not what I expected.

I think there must be something wrong in the `exponent` evaluation but I can’t find a good solution besides splitting `beta` into two separate variables like `beta0` and `beta1` which is not the way I want to implement it since there are more covariates which I want to consider in the future.

Thanks in advance and again sorry for such a newbie question.

Best,  
Paul