To determine the best-fit model, BIC values, classification quality, and utility of the latent class were examined. The BIC statistics were 3184.64 for the one-class model, 3097.95 for the two-class, 3109.25 for the three-class, 3104.50 for the four-class, 3118.45 for the five-class, and 3130.55 for the six-class solutions. BIC values for a single class or more than four were quite large and not further considered. The average estimated posterior probabilities, conditional on the class assignment for the two, three, and four-class solutions, revealed that the classification errors were similar and reasonably low. Therefore, based on the first two considerations, two, three, and four-class models were considered as optimal models for the data.
Because of an insufficient number of cases in two classes of the four-class model, this model was not considered further. Although the BIC value was slightly better for the two-class solution than the three-class solution, the three-class model was chosen because it most accurately reflected the number of classes found on visual inspection of all of the trajectory data. Moreover, individual class membership could be achieved with good confidence based on the average difference between likelihoods across pairs of comparisons. Specifically, each individual had a likelihood estimated for each of the three classes. Inspection of these likelihoods revealed that placement of a given subject in either of the two most extreme classes (e.g., disparity between likelihoods was greatest), resulted in a mean difference across all subjects of .85 ± .015. Even in the case where placement in either of two classes was more ambiguous (the smallest likelihood difference between any two classes for a given individual) when averaged across all subjects also gave reasonably large values (.71 ± .03), indicating that placement in a specific class could be done with minimal ambiguity for each individual.
illustrates the three estimated developmental curves of P300 amplitude for the three-class solution: high intercept P3b—flat trajectory (Class 1), representing 26% of the participants; high intercept P3b—downward trajectory (Class 2), which included 54% of the subjects; and low intercept P3b—flat trajectory (Class 3), which represented only 20% of the children/adolescents studied. The mean ages and gender distribution for each class can be seen in .
Figure 2 Estimated growth curves are illustrated for the three-class solution that provided the best fit to the visual P3b amplitude data analyzed obtained at the five annual assessments. Actual data are plotted for each curve. Note that 2 years separated waves (more ...)
Means (SE) of Age (Years) by Gender and Class Membership
K-SADS diagnoses were obtained at approximately yearly intervals during the child–adolescent developmental period for which ERP was recorded. Among the 85 children and adolescents for whom P300 trajectories were classified, 37 reached an average age of 15.6 ± 2.1 years without having received a child or adolescent diagnosis (the age at the last interview). Analysis of the concurrent relationship between P3b Class membership and K-SADS diagnosis was based on only the first five waves of available data.
The individuals followed into young adulthood were 20.1 ± 1.3 years of age at the time of their CIDI interview. The majority of the 35 cases (66%) did not meet criteria for having had a psychiatric illness within the past year; however, among the young adults receiving a diagnosis, the majority (76.9%) had a substance use disorder. The high rate of substance use disorders probably reflects the familial risk for alcohol dependence that the high-risk members of this cohort have. (Among the nine individuals with a substance use disorder, only two came from control families.)
Risk Status and Class Membership
As may be seen in , an approximately even proportion of high- and low-risk children, both boys and girls, were found in Class 1 and 2, whereas high-risk children outnumbered low-risk children by more than 2 to 1 in Class 3, although not significantly (χ2 = 3.75, df = 2, ns). The proportion of children classified as having one of the three patterns were, for Class 1, 2, and 3, respectively, as follows: high-risk: 26.5%, 46.9%, and 26.5%; low-risk: 25.0%, 63.9%, and 11.1%).
Percentage of Children Classified by Trajectory Pattern and Risk Group Status
Gender and Trajectory Patterns
displays the observed frequencies of cases by gender, familial risk, and the presence of a child/adolescent lifetime diagnosis for each class. Although there was no evidence that the proportion of individuals classified into the three trajectory patterns differed by gender only (χ2
= 1.47, df
= 2, ns
), the interaction of risk and gender was further tested, based on previous findings (Hill et al 1999c
Risk Status, Gender and Class Membership
Analysis by risk within each gender altered the results dramatically. The proportion of high- and low-risk boys in each of the classes differed significantly. More high-risk than low-risk boys fell in Class 3 (z
= 2.06, p
= .04), whereas fewer high-risk boys were in Class 1 (z
= −2.12, p
= .03). These findings are consistent with previous results showing significantly different growth curves for P300 amplitude when high- and low-risk male subjects were compared (Hill et al 1999c
). Fewer high-risk than low-risk girls were found in Class 2 (z
= −2.59, p
The pattern of visual P3b amplitude across the child–adolescent developmental period studied was significantly related to the presence of childhood diagnosis (χ2
= 9.23, df
= 2, p
= .01). The proportion of children with a diagnosis, followed by those without in the three classes were as follows: Class 1: 20.9% and 31.0%; Class 2: 46.5% and 61.9%; Class 3: 32.6% and 7.1%, respectively. There were significantly more children and adolescents who had any lifetime disorder in Class 3 (z
= 3.10, p
= .002) compared with individuals who had no diagnosis. Previous reports have suggested that the presence of externalizing psychopathology (conduct disorder symptoms) is responsible for lower amplitude P3b in childhood and adolescence (Bauer and Hesselbrock 1999
). Because of the small number of individuals in pattern 3, we could not determine if membership in this group was specifically associated with externalizing disorders or more generally associated with presence of a diagnosis; however, it may be noted that among the children in group 3 with a diagnosis, 23.5% had an externalizing disorder, 29.4% had an internalizing disorder, and 29.5% of the children had both an internalizing and an externalizing disorder. Therefore, it appears that this pattern is not associated with any particular type of psychopathology.
Risk and Childhood Diagnosis
Significant trajectory differences were seen when risk status was combined with the presence or absence of lifetime psychopathology (χ2 = 21.31, df = 6, p = .002). Accordingly, Class 3 contained more male and female high-risk children with any diagnosis by lifetime history than low-risk control subjects with any diagnosis (z = 3.27, p = .001). In addition, analysis within Class 3 showed that significantly more high-risk children with any lifetime diagnosis were included in this class than high-risk children with no diagnosis (z = 4.85, p < .001).
Risk, Childhood Diagnosis, and Gender
Membership in the three classes was found to differ by risk status, the presence of any childhood diagnosis, and gender (χ2 = 35.12, df = 14, p = .001). The presence of a childhood diagnosis altered the likelihood of fitting a particular trajectory class even among control individuals. Comparing low-risk boys without a diagnosis to high-risk boys with a diagnosis, a significant difference was found (z = 2.80, p = .005). High-risk girls with one or more childhood diagnoses had P3b trajectories typical of the Class 3 pattern more often than did high-risk girls without a diagnosis (z = 2.58, p = .01). For high-risk boys, the presence of a lifetime diagnosis increased the likelihood that the high-risk boys would have a Class 3 pattern in comparison to high-risk boys without a diagnosis (z = 4.13, p < .001).
Level of Risk, Age of Onset to Develop Childhood Diagnoses and Class Membership
Age of onset to begin regular drinking has been shown to be related to the likelihood that an individual will develop alcohol dependence (Grant and Dawson 1997
). High-risk offspring have an earlier onset to begin drinking than do low-risk control subjects (Hill et al 2000
). The amplitude of P300 appears to be related to substance abuse outcome at 8-year follow-up (Hill et al 1995c
). High-risk children also have a greater likelihood of having a psychiatric disorder (Hill et al 1999a
). Therefore, data were analyzed to determine if membership in specific P300 trajectory categories would be related to age of onset to develop psychopathology. Knowing that a child or adolescent is at higher risk for developing psychiatric disorders in childhood, adolescence, or adulthood based on their familial and genetic loading is a useful prediction; however, it was hypothesized that those at highest risk might be identified by relating childhood diagnoses to the developmental P300 patterns identified. Accordingly, a survival analysis was performed using the earliest age of onset of any diagnosis based on the presence of a K-SADS diagnosis (e.g., depression, anxiety disorders, attention-deficit/hyperactivity disorder, oppositional defiant disorder, conduct disorder). These diagnoses were obtained prospectively at approximately yearly intervals allowing for relatively precise ages of onset. Comparison of high-risk children in Class 1 and 2 versus those in Class 3 revealed a significant difference (Tarone-Ware statistic = 4.76, df
= 1, p
= .03). Clearly, those having a Class 3 pattern not only were more likely to have a diagnosis but also developed a disorder earlier than those having either a Class 1 or 2 pattern. illustrates the differing survival curves of high-risk individuals in Class 3 versus those in Classes 1 and 2.
Figure 3 Survival curves for the age of onset at first childhood diagnosis among high-risk for alcoholism offspring. Membership in Class 3 P3b developmental trajectory pattern increases the likelihood that a child with a familial/genetic risk for alcohol dependence (more ...)
Young Adult Diagnosis and Class Membership
An analysis was performed contrasting young adults with any diagnosis with those without a diagnosis. A 2 × 3 chi square revealed a significant overall effect (χ2 = 6.65, df = 2, p = .04). Also, within Class 3 significantly more young adults with a diagnosis were found than those without (z = 3.30, p = .001).