Statistical Analysis

Broadly speaking the purpose of these analyses was to estimate the size of association between ethnicity and mental health in adolescence and examine the roles of socioeconomic factors, family adversity and deviant peer affiliation as covariates. The following statistical analyses were conducted using the Statistical Package for the Social Sciences 20.0 (IBM SPSS, 2011). The statistical analyses involved three stages:

The first stage was to compute the unadjusted associations between Māori ethnicity and each mental health outcome assessed at ages 15, 16 and 18, including; major depression, anxiety disorders, suicidal ideation, conduct disorder, alcohol abuse / dependence, and substance

57 abuse / dependence, as well as the combined outcomes of internalising disorders (consisting of major depression, anxiety disorders and suicidal ideation) and externalising disorders (including conduct disorder, alcohol abuse / dependence and substance abuse / dependence) and any disorder (including major depression, anxiety disorders, suicidal ideation, conduct disorder, alcohol abuse / dependence, and substance abuse / dependence) . The bivariate analyses involved chi square tests to ascertain the prevalence rates of disorder at each age in the two populations (Māori and non-Māori). In addition to this, the population-averaged percentages for each mental health outcome across the study period (ages 15, 16 and 18) were calculated for both Māori and non-Māori. The population averaged percentage across the study period was estimated for each ethnicity by adding the number of cases for the chosen ethnicity over the entire study period (including ages 15, 16 and 18) and dividing this by the total number of respondents over the entire study period for the chosen ethnicity. This number was then multiplied by 100 to give the population averaged percentage.

A Generalised Estimating Equation (GEE) (Li, 2006; Liang & Zeger, 1986; Zeger & Liang, 1986) was then fitted to the repeated measures data. The GEE approach pooled the repeated measures on each outcome at ages 15, 16 and 18 years to produce an estimate of the

population averaged effect for ethnicity on each outcome.

This stage of the analysis used a repeated measures GEE model. This analysis:

i. Tested the significance of the association between ethnicity and the mental health outcomes;

ii. Estimated the strength of association using risk ratio estimates, with odds ratios (OR) also calculated (using standard 95% confidence intervals).

The models fitted took the general form of Logit (Yit) = B0 + B1x1 + Ui

Where Yit is the log odds of each disorder (major depression, anxiety, suicidal ideation, conduct disorder, alcohol abuse / dependence and illicit substance abuse / dependence); B0 is the intercept term; B1 is the measure of ethnicity and Ui is the individual-specific error term. The parameter of B1 was then transformed to obtain estimates of the odds ratio and 95% Confidence Intervals by taking eB. Please note that the GEE models discussed above assume an absence of interaction between age and the effects of ethnicity, as well as gender and the effects of ethnicity. The GEE models were therefore also extended to include gender and age interactions to ensure that these assumptions were satisfied.

58 Prior to extending the GEE models to include covariate factors, ethnic differences were estimated between the Māori and non-Māori populations in this sample for each factor. These were calculated by fitting independent sample t-tests (for continuous measures) and chi- square tests (for dichotomous measures) to the data. Due to the fact that the variables that utilised t-tests were dichotomous measures and that the number of participants provided a sufficiently large sample size, estimates of Cohen’s d were able to be calculated for the effect size (with a 95% confidence interval) of all covariate factors.

Cohen’s d provides an estimate of effect size and was calculated using the formula:

D = X1 – X2 / (√sp2)

Where X1 was the mean of group 1 (non-Māori), and X2 was the mean of group 2 (Māori), and sp2 was the pooled variance, with the mean of each group and the pooled variance being altered as appropriate for each particular variable.

The next stage of the analysis involved adjusting the associations between ethnicity and mental health outcomes including internalising disorders, externalising disorders, and any disorder. This analysis involved extending the GEE model in stage 1 above to include a series of socio-economic covariates. The model fitted was:

Logit (Yit)=B0+B1X1+ΣBjΖj

Where Yit was the log odds of each disorder (major depression, anxiety, suicidal ideation, conduct disorder, alcohol abuse / dependence and Illicit substance abuse / dependence); B0 was the intercept term; B1 was the measure of ethnicity and ΣBjΖj was the set of socio- economic measures in childhood including socio-economic level, maternal education level, maternal age at birth and single parent status at birth.

The associations between ethnicity and mental health outcomes were then further adjusted to include the omnibus measure of family adversity. The model fitted was:

Logit (Yit)=B0+B1X1+ ΣBjΖj + B2X2

With B2X2 which represents the omnibus measure of family adversity.

59 with a series of discrete childhood adversity measures to compare the effect that each of these sets of measures had on the associations between ethnicity and mental health. The model fitted was:

Logit (Yit)=B0+B1X1 + ΣBjΖj + ΣBkZk

With ΣBkZk representing the discrete measures of childhood adversity

The final step of the analysis involved adjusting the remaining associations between ethnicity and externalising disorders to include measures of deviant peer affiliation. The model fitted was:

Logit (Yit)=B0+B1X1 + ΣBjΖj + ΣBkZk + BqitXit

With BqitXit representing the standardised measure of deviant peer affiliation for individual i at time t (t = 15, 16 and 18 years).