Threshold II:

Heritability and the Threshold Model

This exercise applies the principles of heritability to the threshold model. You should do the exercises on heritability before you do this exercise. To understand the Applet, let's begin with a simple example. Set the heritability to .50, the threshold to 1.0, and N (the number of observations) to its maximum value of 5000. Press Submit.

A large number of dots will appear on the screen, and just as in the exercise Heritability I, each dot represents an observation or person. The dots plot the phenotypic value of a person as a function of the genotypic value of the person using the equation

.

Here, P is the phenotypic value, G is the genotypic value, and E is the environmental value for a person. The quantity h is the square root of heritability and e is the square root of environmentability. Because we set heritability to .50, the value of h is the square root of .50 or .7071. Because environmentability is 1.0 - heritability, the value for e also works out to be .7071.

Notice the horizontal red line that crosses the axis where the phenotypic value is 1.0. This line is the threshold. All the dots above this line are affected and all the dots below the line are unaffected.

There are four colors to the dots:

Exercises:

  1. Keep the same values for the heritability, threshold and number of observations. Click on Submit a few times, pausing to observe the scatterplot and examine the dots. Without counting the dots, try to estimate the ratio of genetically vulnerable (blue dots) to environmentally vulnerable (green dots) individual to unfortunates (black dots) who are affected.
  2. Keep heritability at .50 and N at 5000 and change the threshold to 1.96. For this threshold value, 2.5% of the population is affected. (For the threshold of 1.0, 16% of the population would be affected.) Again, click on Submit a few times, pausing to examine the ratio of blue, green, and black dots above the threshold. The ratios have changed, haven't they? Indeed, if you keep entering different values for the threshold, you will soon find that the larger the threshold is (i.e., the rarer the disorder is), the more that unfortunates make up the bulk of affected people.
  3. The heritability of schizophrenia is on the high side for behavioral traits with some estimates in the area of .70. The lifetime risk for someone developing schizophrenia is a bit under 1%. Enter .70 for the heritability and 2.33 for the threshold (this threshold corresponds to a 1% population prevalence). Again, set N to 5000, click Submit several times, and pay attention to the ratio of the colored dots above the threshold. This should give you some appreciation for the implications of the threshold model for a fairly heritable rare disorder (i.e., rare for psychopathology).
  4. If you want to imagine what other disorders may look like according to the threshold model, set the heritability to the moderate range (.30 to .60) and use the threshold values in the table below. Make certain to enter the threshold value and not the prevalence value into the Applet.

Lifetime prevalence for several forms of psychopathology (from the Epidemiological Catchment Area study).

 

 

Women

Men

 

Prevalence

Threshold

Prevalence

Threshold

Depression

10.2

1.27

5.2

1.63

Panic Disorder

2.1

2.03

1.0

2.33

Phobic Disorder

17.4

.94

10.4

1.26

Antisocial Personality

1.0

2.33

4.5

1.70

Alcohol Abuse/Dependence

4.6

1.69

23.8

.71

Drug Abuse/Dependence

4.8

1.66

7.7

1.42