Could owning a cat as a child be related to mental illness later in life?
Toxoplasmosis is a disease transmitted primarily through contact with cat
feces, and has recently been linked with schizophrenia and other mental
illnesses. Also, people infected with Toxoplasmosis tend to like cats more and
are 2.5 times more likely to get in a car accident, due to delayed reaction
times. The CDC estimates that about \(22.5 \%\) of Americans are infected with
Toxoplasmosis (most have no symptoms), and this prevalence can be as high as
\(95 \%\) in other parts of the world. A study \(^{37}\) randomly selected 262
people registered with the National Alliance for the Mentally Ill (NAMI),
almost all of whom had schizophrenia, and for each person selected, chose two
people from families without mental illness who were the same age, sex, and
socioeconomic status as the person selected from NAMI. Each participant was
asked whether or not they owned a cat as a child. The results showed that 136
of the 262 people in the mentally ill group had owned a cat, while 220 of the
522 people in the not mentally ill group had owned a cat.
(a) This is known as a case-control study, where cases are selected as people
with a specific disease or trait, and controls are chosen to be people without
the disease or trait being studied.
Both cases and controls are then asked about some variable from their past
being studied as a potential risk factor. This is particularly useful for
studying rare diseases (such as schizophrenia), because the design ensures a
sufficient sample size of people with the disease. Can casecontrol studies
such as this be used to infer a causal relationship between the hypothesized
risk factor (e.g., cat ownership) and the disease (e.g., schizophrenia)? Why
or why not?
(b) In case-control studies, controls are usually chosen to be similar to the
cases. For example, in this study each control was chosen to be the same age,
sex, and socioeconomic status as the corresponding case. Why choose controls
who are similar to the cases?
(c) For this study, calculate the relevant difference in proportions;
proportion of cases (those with schizophrenia) who owned a cat as a child
minus proportion of controls (no mental illness) who owned a cat as a child.
(d) For testing the hypothesis that the proportion of cat owners is higher in
the schizophrenic group than the control group, use technology to generate a
randomization distribution and calculate the p-value.
(e) Do you think this provides evidence that there is an association between
owning a cat as a child and developing schizophrenia? \(^{38}\) Why or why not?
