The relative importance of genetics and the environment in causing schizophrenia is still being debated. Although the high proportion of monozygote cotwins of schizophrenia patients who are discordant suggests that there may be a significant environmental contribution to the development of schizophrenia, this discordance is predicted by an accumulative multimutation model of schizophrenia onset constructed here implying a genetic origin of schizophrenia. In this model, schizophrenics are viewed as having been born with the genetic susceptibility to develop schizophrenia. As susceptible gene carriers age, they randomly accumulate the necessary mutations to cause schizophrenia, the last needed mutation coinciding with disease onset. The mutation model predicts that the concordance rate in monozygote twin studies will monotonically increase with age, theoretically approaching 100% given sufficient longevity. In dizygote cotwins of schizophrenia patients, the model predicts that at least 71% of cotwins are incapable of developing schizophrenia even though every cotwin and their schizophrenic twin shared a similar early environment. The multimutation model is shown to fit all of the monozygote and dizygote concordance rate data of the principle classical twin studies completed before 1970 considered in this paper. Thus, the genetic hypothesis of schizophrenia can be tested by bringing these studies up to date.
Schizophrenia is a brain disease characterized by delusions, hallucinations, and behavioral and functional disturbances. Once the disease develops, most patients’ functioning is seriously impaired. Discovering its cause and cure remain some of the biggest challenges to modern medicine and neuroscience. A fundamental debate on the etiology of schizophrenia is the relative importance of genetics and environmental factors in causing the disease. A consistently higher concordance rate of schizophrenia in monozygotic twins than in dizygotic twins supports the genetic hypothesis. By contrast, external environmental factors are thought to contribute to the development of schizophrenia because a significant proportion of monozygotic twins are discordant. However, this inference from this fact is challenged by the mutation model to be developed in this paper.
The high rate of discordance in monozygotic twins (around 50%) is typically credited to environmental factors [
A common misconception in the literature is the mistaken belief that if genes were 100% responsible for schizophrenia, then “when one identical twin had schizophrenia, there would be 100% chance that that the other twin would have it as well.” Perhaps the best way to demonstrate the fallacy of this argument is to consider the physics of radioactive nuclear decay.
For example, all uranium-238 nuclei are naturally radioactive and decay in multiple steps ending in the stable nucleus lead-206. Despite the fact that uranium-238 nuclei are completely indistinguishable from each other and are considered to be identical particles, about half of a sample of pure U-238 nuclei remains exactly as it was 4.5 billion years ago, while the other half has decayed into lead-206. In physics, each of these decays, or the lack thereof, is considered a random event, having nothing to do with external triggers, and is entirely dictated by the internal physics of the nucleus [
According to the World Health Organization (WHO), schizophrenia occurs in all the countries of the world with a prevalence rate that is very narrowly proscribed (within a factor of about two between the highest and lowest sites). While there is much local evidence of environmental triggers for increasing prevalence in specific regions and times, a meta-analysis of 188 schizophrenia studies, producing a total of 1,721 prevalence estimates drawn from 46 countries, led to the conclusions that the lifetime prevalence rate was around 0.72% worldwide and there was no significant prevalence difference between males and females or between urban, rural, and mixed sites [
The fact that some monozygote twins susceptible to developing schizophrenia remain discordant at a certain age does not necessarily mean that external environmental factors contribute to the development of the disease. Analogous to a chain of radioactive nuclear decays, a genetically driven random mutation model is constructed here that is shown to successfully fit disparate schizophrenia age-of-onset data from both general population and twin studies.
In this section, the age-of-onset schizophrenia prevalence function that will be used to fit singleton and twin study data will be derived from a novel multimutation model (MMM). A relatively simple model for the development of schizophrenia assumes that the brain of every person susceptible to the developing this disease must chronically undergo a series of characteristic changes or mutations, numbering
Consider a random sample of a risk population all born in the same year with the susceptibility to develop schizophrenia later in life. The size of the sample population will be denoted by
Now, suppose a total of
The
The fraction of the risk population that develops schizophrenia between the ages of
The best fits to schizophrenia data occurred if
The values of the parameters in the prevalence function in (
If the set of
Unlike point or lifetime prevalence, true age-of-onset prevalence rate in a given population is difficult to ascertain for schizophrenia because the definition of “onset” does not have a common consensus in many cases of insidious onset or prolonged prodromal cases. A relatively objective estimate for age-of-onset is first hospitalization for psychotic break, especially in the earlier era where hospitalization was still widely available and considered a standard of care for the first psychotic episodes in schizophrenia patients. Therefore, we used the schizophrenia age-at-first admission incidence rate data for USA hospitals by Kramer et al. (see Table 3.4 in [
The male and female cumulative incidence data as a function of age curves (i.e., the original data in [
Values of model parameters for the independent mutation model fits to USA schizophrenia first hospital admissions data (males M, females F, and males + females, M + F).
Cohort | Number of parameters in model |
|
|
|
|
chisq error in (years)−2 |
---|---|---|---|---|---|---|
USA males | 3 | 10 | 0.08172 | 0.00137 |
|
|
USA males | 4 | 16 | 0.11653 | 0.028465 | 0.0015737 |
|
USA females | 4 | 16 | 0.09859 | 0.035728 | 0.0016428 |
|
USA males + females | 4 | 16 | 0.10757 | 0.029959 | 0.0016363 |
|
USAMF4P. Four-parameter independent mutation model fit to Kramer male and female USA schizophrenia first hospital admission cumulative incidence rate per 100,000 data.
Using the values of the parameters
Plots of model susceptible incidence rates
The 3-parameter model fit to the USA male data also yields a credible fit but with a modest increase in fit error as seen in Table
In this section, the schizophrenia MMM constructed in Section
In our model of schizophrenia susceptibility, all members of both subcohorts are born with the susceptibility to develop the disease; thus, it is predicted that all monozygote cotwins will eventually develop schizophrenia if they can live long enough.
When one twin (the index twin) in each pair has developed the disease, the other twin will be referred to as the cotwin in this paper. Our model posits that in monozygote twin pairs, the cotwin has the same susceptibility to develop schizophrenia as the index twin. Consider a
The probability that any member of subcohort 1 will be found [will not to be found] to have schizophrenia by age
It is important to note that subcohort concordance as defined above, for example, is not the same as pairwise concordance as usually used in the literature. Here, if a member of subcohort 1 and a member of subcohort 2 are chosen at random at age
For monozygote (MZ) twins, subcohorts 1 and 2 are genetically identical so that
When a susceptible monozygote twin pair in the
In schizophrenia twin studies, the birth cohort consists of only the concordant and discordant twin cases since, to date, it remains difficult to determine susceptibility to schizophrenia unless the disease is emerging (as in some prodrome cases) or actually develops. Thus, referring back to the results in (
Notice that the monozygote concordance rate
For the dizygotic twin cases, the formal results in (
In the same way, the fraction
Solving (
The values of the monozygote and dizygote concordance fractions
Using the singleton USA male plus female multimutation model, the probability curves for identical twin concordance, discordance, and no-schizophrenia defined in (
Plots of concordance probability
What twin studies actually measure is the
The average monozygote and dizygote concordance rates from representative samples of schizophrenia twin studies from around the world are summarized in Table
Concordance rate table. Uncorrected concordance rates in schizophrenia twin studies from around the world and modeling results from fits to these data. Only significant studies published before 1970 are included here so that the updates of these studies could definitively test the predictions of the model.
Investigator | Year | Country | MZ pairs concordance | DZ pairs concordance |
|
|
|
---|---|---|---|---|---|---|---|
Rosanoff et al. [ |
1934 | USA | 28/41 = 0.683 | 15/101 = 0.149 | 0.190 | 0.812 | |
Essen-M |
1941 | Sweden | 6/11 = 0.545 | 4/27 = 0.148 | 0.224 | 0.706 | |
Kallmann [ |
1946 | USA | 120/174 = 0.689 | 53/517 = 0.102 | 0.129 | 0.816 | 31.0 y, (1.94) |
Slater [ |
1953 | UK | 24/37 = 0.648 | 10/112 = 0.0892 | 0.116 | 0.787 | |
Inouye [ |
1961 | Japan | 33/55 = 0.600 | 2/17 = 0.117 | 0.163 | 0.750 | |
Harvald and Hauge [ |
1965 | Denmark | 4/9 = 0.444 | 6/62 = 0.0967 | 0.167 | 0.615 | |
Gottesman and Shields [ |
1966 | UK | 10/24 = 0.416 | 3/33 = 0.0909 | 0.165 | 0.588 | 41.0 y, |
Kringlen [ |
1966 | Norway | 19/50 = 0.380 | 13/94 = 0.138 | 0.283 | 0.551 | |
Hoffer and Pollin [ |
1970 | USA | 11/80 = 0.137 | 6/145 = 0.0413 | 0.197 | 0.242 | 43 y, (0.631) |
Let us first consider the Gottesman and Shields data [
We next turn our attention to the Hoffer and Pollin [
As we have seen in Section
Comparison of schizophrenia prevalence functions
As a final example, consider the largest twin study in Table
In the twin data analysis, we introduced the probability that a fraternal cotwin of a schizophrenic will also inherit the susceptibility to develop schizophrenia and denoted it by
Although the monozygote concordance rates of these studies vary widely (from 0.138 to 0.689), the range in the value of
Using the Gottesman and Shields data as a typical example of the results we have obtained, the susceptible prevalence
Plots of Gottesman and Shields prevalence
The model predicts that both the monozygote and dizygote concordance rate curves are monotonically increasing functions of age but saturate at 1 and
We can find only one study that made one follow-up diagnosis of the nonill monozygote cotwins after variable years [
Now, the fraction of dizygotic cotwins that has susceptibility to develop schizophrenia is, by definition,
Although a wide variety of prenatal maternal infections, such as influenza, herpes, polio, rubella, and toxoplasmosis, have been linked to schizophrenia [