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Predicting individual side effects is generally not feasible in current clinical practice, although in the purview of "personalized medicine", mostly as a research goal/topic. For psychotropic medications, this is largely envisaged to work through pharmacogenomics:

In pharmacogenomics, genomic information is used to study individual responses to drugs. When a gene variant is associated with a particular drug response in a patient, there is the potential for making clinical decisions based on genetics by adjusting the dosage or choosing a different drug, for example. Scientists assess gene variants affecting an individual's drug response the same way they assess gene variants associated with diseases: by identifying genetic loci associated with known drug responses, and then testing individuals whose response is unknown. [...] Scientists believe many idiosyncratic effects result from individual variation that is encoded in the genome. Thus, genetic variation in genes for drug-metabolizing enzymes, drug receptors, and drug transporters have been associated with individual variability in the efficacy and toxicity of drugs. Genetics also underlies hypersensitivity reactions in patients who are allergic to certain drugs, such as penicillin, wherein the body mounts a rapid, aggressive immune response that can cause not only a rash, but can also hinder breathing and cause edema to the point of cardiovascular collapse. Predicting serious ADRs [adverse drug reactions] is a priority for pharmacogenomic research. For example, the enzyme CYP2D6, one of a class of drug-metabolizing enzymes found in the liver, breaks down and terminates the action of certain antidepressant, antiarrhythmic, and antipsychotic drugs. Molecular cloning and characterization studies of the gene that codes for this enzyme have described more than 70 variant alleles (Meyer, 2000). These alleles contain one or more point mutations, only some of which affect enzyme activity; however, some of these alleles involve gene deletions and duplications that can lead to increased enzyme activity. Individuals who are homozygous or heterozygous for the wild-type or normal activity enzymes (75%–85% of the population) are called extensive metabolizers; intermediate (10%–15%) or poor (5%–10%) metabolizers are carriers of two alleles that decrease enzyme activity (Ingelman-Sundberg, 1999); and ultrarapid metabolizers (1%–10%) are carriers of duplicated genes. The most common alleles can be detected by DNA chip microarrays, allowing most patients to be assigned to a particular phenotype group. [...] With the completion of the Human Genome Project, anticipation was high that genetic information would radically improve medicine, that side effects would be more predictable, and that patients could be screened for likely drug responses. But thus far, progress has been much slower than what the initial excitement suggested. A great deal of this delay relates to the fact that an individual's response to drugs is multifactorial, resulting from multiple gene and environmental interactions (Haga & Burke, 2004). Scientists also recognize that even as the knowledge base continues to expand, the clinical translation of that knowledge still requires empirical evidence, generated for a particular disease and drug combination, before treatment can be customized to a patient's genotype. Thus, much work remains to be done before personalized medicine can reach its fullest potential.

Last year the FDA has issued a warning against improper/premature use of pharmacogenomics to select antidepressants. An excerpt...

For example, the FDA is aware of genetic tests that claim results can be used to help physicians identify which antidepressant medication would have increased effectiveness or side effects compared to other antidepressant medications. However, the relationship between DNA variations and the effectiveness of antidepressant medication has never been established. The FDA is aware that health care providers may have made inappropriate changes to a patient's medication based on the results from genetic tests that claim to provide information on the personalized dosage or treatment regimens for some antidepressants. [...] There are a limited number of cases for which at least some evidence does exist to support a correlation between a genetic variant and drug levels within the body, and this is described in the labeling of FDA cleared or approved genetic tests and FDA approved medications.

As noted in a review of last year there are now several guidelines trying to put together the available knowledge:

There are multiple guidelines in various stages of development during the past 5 years including those by the Clinical Pharmacogenetics Implementation Consortium (CPIC), a registered service mark of the US Department of Health and Human Services and other authoritative scientific consortia [(e.g., Dutch Pharmacogenetic Working Group (DPWG)] for cytochrome P450 and drug therapy including for psychiatry.

CPIC has a database page roughly ordered by the drug in question, e.g. "CYP2D6, CYP2C19 and Selective Serotonin Reuptake Inhibitors". The DPWG guidelines currently seem to be one large (book-sized) pdf document, not restricted to psychotropic drugs. Various papers, e.g. Lunenburg et al. describe how their methodology (and thus sometimes conclusions) differs from CPIC etc. The latter consortium also publishes journal papers on their individual drug guidelines, e.g. they have one on "Genotypes and Dosing of Tricyclic Antidepressants".