Since the principal objective is to determine whether there are age-varying effects of the predictive variables, survival analysis using standard Cox proportional hazards models in which effects are age invariant is not appropriate. In addition, such models cannot account for differential effects on survival which are the result of unmeasured heterogeneity in the sample. DTSA provides an alternative model which avoids these problems and which can be implemented with logistic regression methods. By dividing subjects into groups based upon age of onset, a single logistic regression model can be applied to estimate the probability of those at risk in each age group of becoming alcohol dependent as a function of the predictive variables . The functional form of the model can be set to determine age-specific effects and/or age-independent effects, and use age-invariant and/or age-dependent covariates. A weighted model was employed to enable the use of all members of multi-member families . The output of a DTSA calculation is the same as the output from a logistic regression calculation. Each DTSA model had the following structure: the outcomes, or dependent variables were either alcohol dependence or regular alcohol use. Regular alcohol use was defined as consumption at least once a month for 6 or more consecutive months. In all cases four distinct age ranges were used: under 16, 16 and 17, 18 and 19, over 19. These age groups were determined by the fact that ages of onset were whole numbers of years, that the numbers of those who became alcohol dependent be about the same in each group, and that there be at least 50 subjects in each group who became alcohol dependent to provide a reasonable degree of statistical reliability in the calculations. The same age grouping was used for regular alcohol use for comparative purposes.
The covariates were a genotype from a CHRM2 SNP, ERO power from one of the leads, family type , number of parents who smoke, gender,cannabis grow equipment and scores on principal components 1 and 2 derived from the stratification analysis of the sample genome . The CHRM2 SNPs analyzed here, rs978437, rs7800170, rs1824024, rs2061174, and rs2350786 include the three most significant of those for alcohol dependence with comorbid drug dependence in Dick et al.as well as two others that appear to be in a range of significance indicated by that table. From preliminary statistical screening of the genotypic distributions in the sample, a recessive model was employed which contrasted major allele homozygotes with those who were not. The electrophysiological phenotypes used in the analysis were found to be significant in previous studies ; these studies showed reduced amplitudes in alcoholics and in those offspring at high risk. The number of parents who smoke were selected in part because the Kaplan–Meier curves with different values showed considerable variation for a discussion of the effects of parental smoking on adolescent behavior.DTSA results were calculated for the entire sample. Our fourth item for investigation, whether the influence of these SNPs would be greater in a behaviorally defined sub-sample comprising a putatively more genetically vulnerable group was suggested by the results of Dick et al.and King and Chassin . Given the prevalence of various substance abuse categories in the sample and the number of subjects in each category who become alcohol dependent during the age range of the study, the broad criterion of the use of an illicit drug regardless of age of onset or frequency of use was employed to define the more genetically vulnerable group. This sub-sample will be called the ‘‘illicit drug use’’ sub-sample. Unlike the definition of illicit drug use in Dick et al. , this definition does not categorize regular use of cannabis as illicit drug use. Since more than half the sample are characterized as regular users of cannabis at some time during the age range of the study , regular use of cannabis can not be considered a practice that violates norms of age related behavior or involves enhanced risk taking, and thus not an element of ‘‘externalizing psychopathology’’.
We note that 90 % of cannabis dependent subjects who are also alcohol dependent are included in the sub-sample, so although our criterion does not span regular cannabis use we are probably picking up those more genetically vulnerable cannabis dependent subjects and thus paralleling the group used in Dick et al. . For the regular alcohol use outcome, there were a sufficient number of illicit drug non-users who became regular users of alcohol to provide a sub-sample to contrast with the illicit drug use sub-sample. Since about 75 % of the alcohol dependent subjects were members of the illicit drug use sub-sample, there were too few alcohol dependent subjects with no illicit drug use to provide a contrasting sub-sample. However some inferences about the significance of illicit drug use for the onset of alcohol dependence can be drawn from the differences between the DTSA results for the entire sample and the results for the illicit drug use sub-sample. Since regular alcohol use is a necessary condition of alcohol dependence, it could not be used as a covariate in the DTSA calculation of the onset of alcohol dependence. In order to investigate the duration of the transition from regular alcohol use to alcohol dependence as a function of the age of onset of alcohol dependence, the third item for investigation, logistic regression analyses of the onset of alcohol dependence as the outcome in each of the age ranges, restricted to the sample of those who are regular users of alcohol within that age range, were carried out. All covariates used in the DTSA calculations were used with duration of drinking as an additional covariate.Although those who become alcohol dependent are removed from the sample at each age range, this is not a survival analysis method because new regular users of alcohol are added to the sample at each age range. However, the results of these tests can be compared to the DTSA results for the illicit drug use sub-sample to examine the effect of including all alcohol dependent subjects in the sample, as opposed to a restricted sub-sample as found in the illicit drug use sub-sample.
In order to investigate the duration of the transition from regular alcohol use to alcohol dependence as a function of the age of onset of regular alcohol use,vertical grow system both Fisher’s exact test and the Cochran-Armitage trend test were applied to the distribution in each of the first three age ranges of the proportion of those who became alcohol dependent in the same or subsequent age range for those who became regular users of alcohol in that age range.We investigated whether there were age-related trends in the genotypic distributions which underlie the results of the DTSA for the SNP covariates and the rapidity of the transition from regular alcohol use to alcohol dependence. Two separate Cochran-Armitage trend tests were carried out on genotypic distributions of the SNPs of the illicit drug use sub-sample. Given the use of the recessive genetic model in the DTSA tests, subjects in the illicit drug use sub-sample were divided into two genotypic groups, those who had two copies of the major allele and those who did not. The first trend test was of the genotypic distribution of those who became alcohol dependent as a function of age of onset of alcohol dependence, comparing those who had two copies of the major allele with those who did not. The null hypothesis is that the relative effect of having a particular genotype does not vary linearly between ages of onset; that is, that the ratio of different genotypes of those who become alcohol dependent does not display a linear trend between ages of onset.To test whether there was trend in the genotypic distributions as a function of the rapidity of the transition from regular alcohol use to alcohol dependence, a second trend test was carried out. This test was of the genotypic distribution of those who began regular alcohol use in the youngest age range and became alcohol dependent at any age as a function of age of onset of alcohol dependence, comparing those who had two copies of the major allele with those who did not. The null hypothesis is that the ratio of different genotypes of those who become alcohol dependent does not show a trend between different time spans from the onset of regular alcohol use to the onset of alcohol dependence. We restricted our analysis to those who became regular alcohol users in the youngest age range in order to obtain results for those who might take a relatively long time to develop alcohol dependence.A question of interest is whether regular consumption of alcohol affected ERO values in our sample. To examine this the residuals from the non-parametric age regression of the log transformed ERO data were used in an ANCOVA. Subjects were divided into three groups: non-drinkers , drinkers from community families , and drinkers from COGA families.
The continuous covariate was the difference between the age at test and the age at onset of drinking. In order to include the non-drinkers in this test, the difference values for them were taken from normally distributed random numbers with the same mean and variance as the difference values for the drinkers. To further characterize the illicit drug sub-sample, we determined whether ERO values differed between the illicit drug sub-sample and its complement in the entire sample. A two sample t test was used for this purpose.The prevalence of alcohol use and dependence in the sample being studied is shown in Table 1 in a form relevant to DTSA. In DTSA, for each outcome, those who have the possibility of suffering the outcome in each age range are the at-risk group. The at-risk group in the youngest age range is the entire sample. In each succeeding age range those who have suffered the outcome previously or for whom no information for that age range is available are removed from the at-risk group. Consequently the at-risk group diminishes in size in each successive age range. Because more subjects become regular users of alcohol than become alcohol dependent in each age range, the at risk group for alcohol dependence is increasingly larger than the at-risk group for regular alcohol use in each subsequent age range. The illicit drug use sub-sample is also characterized in the table.For each of the five SNPs an analysis was run with the ERO measure taken from each of the three leads, as described in ‘‘Electrophysiology’’ section for a total of fifteen models. An examination of the logistic regression results showed that for each SNP, the beta coefficients had little difference when different leads were used; similarly, for each ERO measure the beta coefficients had little difference when different SNPs used. The same was true of coefficients for the clinical variables. We conclude that the effect of each covariate is essentially independent of the effect of any of the others. Thus results from SNPs, electrophysiological variables, and other variables can be reported seriatim without any distortion. Applying the Nyholt correction derived from the LD matrix, we obtain 3.2 effective SNPs. The independence of the covariates also implies that the effective number of tests is no more than the number of age ranges times the sum of the effective number of SNPs and electrophysiological variables in each sample group. Considering that the overall pattern of results is of primary interest, not only the positive results, and that no consensus exists for the most appropriate way to handle the analysis of correlated phenotypes and correlated SNPs in these circumstances, we do not enter any corrections for multiple testing. Table 2 provides all significant results for the youngest and oldest age ranges.In all cases, risk increased with lower ERO values. For the onset of regular alcohol use in the entire sample, ERO values were only significant for the group with earliest ages of onset, under 16 years of age. For the onset of regular alcohol use in the illicit drug use sub-sample, ERO values were significant for the earliest ages of onset, and weakly significant in the oldest age range, over 19 years of age.