But were your cells killed by the drug or they remained alive? And which method did you use to evaluate apoptosis? Do you measure true apoptosis or cell death in general? Indeed, since apoptosis is a programmed strictly regulated process, it requires that the cell is otherwise intact, functional and that possess sufficient energetic substrates. Thus, it is usually expected that high very toxic concentration of cytotoxics can induce a massive "physical" damage to most cell components including cell membranes leading to membrane leakage and death by necrosis. However, it will depend upon the the kind of substance you employ and the presumed mechanism by which it induces apoptosis.  Theoretically, it could be possible that your drug at high concentrations inhibits some specific molecules and process needed to apoptosis induction.

There are divers processes mediating cell death.  It is likely  that at high drug concentrations  other death mechanisms such as necrosis and increased autophagy are more prevalent than apoptosis.

We may have to consider the interaction properties of ligand as well (Intra).

All the suggestions above are very important. I would just add its better to do a time course and a dose response and follow the course of the drug causing cell death and the types of cell death processes that occur with time and dose. Also, its always important to include a control that causes apoptosis , such as may be Fas. When one follows the course then it will be obvious at what dose or time maximum apoptosis takes place and what follows after that. 

Hope this will be of help.

Many drugs can have a dual effect depending on a dose. A wide range dose response curve should be helpful

Apoptosis is a time dependent process. If the cell die in a short time triggered by other death mechanism, Apoptosis would not happen.  

But were your cells killed by the drug or they remained alive? And which method did you use to evaluate apoptosis? Do you measure true apoptosis or cell death in general? Indeed, since apoptosis is a programmed strictly regulated process, it requires that the cell is otherwise intact, functional and that possess sufficient energetic substrates. Thus, it is usually expected that high very toxic concentration of cytotoxics can induce a massive "physical" damage to most cell components including cell membranes leading to membrane leakage and death by necrosis. However, it will depend upon the the kind of substance you employ and the presumed mechanism by which it induces apoptosis.  Theoretically, it could be possible that your drug at high concentrations inhibits some specific molecules and process needed to apoptosis induction.

Apoptosis is an energy-demanding process. At higher concentrations, your drug will be less specific and (although it's tough to say without knowing target and concentrations) would speculate that necrosis will predominate due to a shut-down of translation and decreased ATP concentrations in the cell. See Pierluigi Nicotera's work on ATP/apoptosis/necrosis.

How is your dose response curve?

Do you have other endpoint besides apoptosis assessment?

On a general toxicological viewpoint, qualitatively, apoptosis may or may not be adverse whereas necrosis - without time for the cell to set forth the apoptosis program upon injurious stimuli - is always adverse...

A discussed by previous respondents, it may be that the drug has a pharmacological and/or deleterious effect whereby at high doses there is more necrosis than apoptosis whereas at low dose, mainly apoptosis is witnessed...

Hope it helps