The typical relation is SR=I (current) /P(Power)

But the parameters depends on the other factors.

You can check the below link.

https://www.lumerical.com/support/whitepaper/optoelectronic_modeling_photosensitive_devices.html

Just to expand upon the answer given by Sujoy, spectral response gives the ratio between

the current generated by a typical optoelectronic device  at a given wavelength of the spectrum and

the power incident on the device at that particular wavelength

SR=i(λ)/P(λ). 

It could be related to the external quantum efficiency (EQE) of a device which is given by 

EQE=(No. of Electrons collected)/(No. of photons incident on the device) at a given wavelength of the spectrum per unit time

EQE=(i/q)/(P/Ephoton) where i/q gives the no. of electrons collected and P/Ephoton gives the number of photons incident on the device.

SR=EQE*q/Ephoton

When you say "higher power density", this could be done or happen by three possible ways (depending upon how you are increasing the power density):

1. Increasing the flux density(No of photons incident per unit time) at a given wavelength. 

2. Keeping the flux density   constant while increasing the energy of the incident photons (changing the source). In other words decreasing the wavelength(Eg. red to blue end) of the source used while maintaining constant incident flux density.

3. Combination of both the above.

For materials with inherent gain (For example: materials which exhibit multiple exciton generation/impact ionization), ideally, increasing incident light power density by following point 2 above will result in a higher spectral response. However, if light power density is increased by following point 1 above, it won't result in an increase in spectral response (in the ratio it get cancelled out).

For materials like graphene, (which exhibits absence of any gain mechanism that can generate multiple charge carriers from one incident photon http://www.nature.com/nnano/journal/v7/n6/full/nnano.2012.60.html ), ideally, none of the above points should cause an increase in spectral response when the power density is increased.

Hope that helps. However, having said that, as a "statement of disclaimer", I should state that nature is good at showing outlandish interesting behaviour. So if you observe something different than above, I think it is really an interesting phenomenon to explore further in view of the above points and worth systematic study and reporting to the scientific community.

Thanks for answers.

p(f) = [8pi h (v/f)^3]/[exp(-Eg/KT) -1]

I= p(f) v

Where

I=light intensity

v= velocity of light within the laser

p(f) = spectral density

p(f) = Phf

Where P = photon density

h = Plank's constant

f= frequency

Therefore

I = Phfv. (W/m^2)