Data were drawn from the Avon longitudinal study of parents and children (ALSPAC), an ongoing population-based study designed to investigate the effects of a wide range of influences on the health and development of children. Pregnant women residing in the south-west of England who had an estimated date of delivery between April 1, 1991, and December 31, 1992, were invited to participate. The initial study cohort consisted of 14,062 pregnancies and 13,978 (52 % boys and 48 % girls) singletons/twins still alive at 12 months of age. Compared to the 1991 UK National Census Data, the sample showed a slightly higher proportion of house owner-occupiers, and a smaller proportion of mothers from ethnic minorities . As described in Boyd et al. , children enrolled in ALSPAC were more educated at 16 compared to the national average, were more likely to be white (reflecting the ethnical composition of the area from which the sample was drawn) and less likely to be eligible for free school meals (an indicator of low income in the UK). Ethical approval for the study was obtained from the ALSPAC Law and Ethics Committee and local Research Ethics Committees. Detailed information about ALSPAC is available online (http://www.bris.ac.uk/alspac). Please note that the study website also contains details of all the data that are available through a fully searchable data dictionary (http://www.bristol.ac.uk/alspac/researchers/data-access/data-dictionary/).
Conduct Problem trajectories
The derivation of CP trajectories has been reported previously . Briefly, latent class growth analysis (LCGA) models were applied to six assessments (spanning the age period from 4 to 13 years) of mother-reported CP using the ‘conduct problem’ subscale of the Strengths and Difficulties Questionnaire [16, 17]. The sum-score of each assessment was dichotomized at the standard threshold of scores of 4 or more , yielding six binary indicators for the latent growth classes. The four resulting trajectories were described as low (70.1 %), childhood-limited (CL 12.1 %), adolescent-onset (AO 8.5 %) and early-onset persistent (EOP 9.2 %). Rates quoted are following modal class assignment. Entropy for this model was moderate at 0.689 and the average assignment probabilities under modal class assignment were as follows: low = 0.889, AO = 0.681, CL = 0.718 and EOP = 0.820.
Data for all outcome measures were obtained in computer-assisted interviews during the “Teen Focus 4” (TF4) hands-on assessment clinic held at the ALSPAC premises in Bristol, UK. The median age at attendance was 17 years and 9 months (IQR = 17 years and 7 months to 17 years and 11 months). Alcohol use: Respondents completed the ten-item alcohol use disorders identification test (AUDIT) . We used a cut-off of 16 points and above on the AUDIT scale to indicate harmful use. Smoking: Following positive responses to “having ever smoked” and “having smoked in the last 30 days”, respondents indicated whether they smoked every week. The response to this question was used as binary indicator. Cannabis use: Respondents completed the six item cannabis abuse screen test  asking about cannabis use in the previous 12 months. The sum-score was derived by assigning 1 to the responses “fairly often” and “often” and 0 to the other response options and summing the responses. This scale was then dichotomized to indicate those scoring one or more points. We opted for this cut-off to yield an adequate number of problem users. Illicit drugs: A series of questions was asked about the use of cocaine, amphetamines, inhalants, sedatives, hallucinogens or opioids in the previous 12 months. Respondents were assigned a score of 1 if they had used any of the drugs listed. Self-reported offenses: Items similar to the core offenses in the 2005 Offending, Crime, and Justice Survey (mugging, shoplifting, break and enter, selling drugs, fire setting, selling, buying stolen goods ) were presented to respondents who indicated whether or not they had engaged in these behaviors in the past year. A score of 1 was assigned following a positive response to one or more of the items. Criminal involvement: Respondents indicated whether they had been arrested (in trouble with the police in the last year) or convicted of a criminal offense (on trial in court, got police caution, got court fine, got community service order, received an ASBO (antisocial behavior order) been in a secure unit, been in prison, been in mediation as offender). Respondents were assigned a score of 1 if their response was positive to one or more of the items. Self-harm: An indicator of self-harm in the last year was derived from the following two questions: “Have you ever hurt yourself on purpose in any way (e.g., by taking an overdose of pills, or by cutting yourself)?” If yes, “How many times have you harmed yourself in the last year?” (not in the past year/once/2–5 times/6–10 times/more than 10 times). The response was dichotomized into 0 = not self-harmed in the past year and 1 = self-harmed at least once in the past year. Risky sexual behavior: Respondents were asked how many sexual partners they had had in the last year and were assigned a score of 1 if they reported three or more different partners. Gambling: The problem gambling severity index (PGSI, derived from the longer Canadian Problem Gambling Inventory;  was administered to those who reported engagement in any of 16 types of gambling (e.g., lottery/horse racing/fruit machines) in the past year. For the current analysis, a problem gambler was defined as someone at low, moderate or high risk (e.g., a PGSI score of 1 or more).Footnote 1
Depression and Anxiety: Depression and anxiety were measured using the clinical interview schedule-revised (CIS-R), a self-administered computerized interview which derives diagnoses based on ICD-10 criteria for depression and anxiety disorder (GAD, panic, phobia, social anxiety). The computerized version shows close agreement with the interviewer administered version [22, 23]. A binary variable indicating a primary diagnosis of major depression was taken as the depression outcome measure. A binary variable indicating a primary or secondary diagnosis of anxiety was taken as the anxiety outcome measure.
Models were adjusted for a number of potential confounding factors preceding the CP assessment and previously shown to be associated with CP trajectories : Family characteristics: Socioeconomic status, marital status/cohabitation, maternal education, and age of the mother when first pregnant, drinking during pregnancy (≥2 units per day) and maternal family history of alcohol use, smoking during pregnancy, any maternal contact with the police during child’s first 4 years of life. Birth information: Child birth weight, gestational age, parity and a single indicator for any birth complications (e.g., abruption, preterm rupture, cervical suture). Child characteristics: Language development  and child temperament (activity, adaptability, intensity, and mood subscales  at 24 months postpartum. Child experiences: Maternal depression [26, 27] and anxiety [28, 29] assessed at 32 weeks antenatal and 8 weeks postnatal. Harsh parenting assessed at 24 months and partner emotional and/or physical cruelty to the mother during child’s first 4 years of life. Low emotional and practical support for the mother during child’s first 4 years of life. Indication of child head injury during child’s first 4 years of life. Maternal attitude toward the child (e.g., “I really enjoy this child”) measured at 33 months postpartum.
A ‘three-step’ approach  was chosen for the current analysis. For the first step, LCGA was used within Mplus to derive CP classes as described previously . In the second step, posterior probabilities from the LCGA model were used to assign each respondent to the most-likely class (known as modal class assignment). In the third step, a set of logistic regression models were estimated with the latent class measure as the exposure with outcomes consisting of each of the binary variables described above. This third step incorporated Vermunt’s correction for classification errors (details below). Each regression model was adjusted for the confounders described above. Complete case estimates were compared with those obtained following a multiple imputation routine.
Correcting for classification errors
Estimating the effect of covariates on a latent class measure can bias parameter estimates unless a one-stage model is performed in which covariate effects are estimated at the same time as the latent class measurement . However, Vermunt has described a number of instances in which the one-stage model is not ideal and has proposed a method which uses the classification errors from the original latent class model to adjust for the bias within subsequent regression analyses. This approach is very similar in most respects to the three-step method regularly utilized by LCGA modelers with the difference that uncertainty in the estimation of the latent class measure is incorporated into the final regression model. In Vermunt’s method, the level of agreement between the underlying latent class measure and its predicted (manifested) counterpart forms a set of cell-weights which correct the parameter estimates for the bias mentioned above. This classification-error matrix can be calculated for any 2nd stage class-assignment procedure (e.g., modal class assignment, proportional assignment, random assignment) and furthermore, in the case of modal class assignment, the required matrix can easily be derived from that given in Mplus’ standard output for a latent class model. All regression analyses were carried out in Latent Gold version 126.96.36.19945 .
Attrition analyses and imputation of missing data
The starting sample for this analysis was the 7,218 participants previously assigned to a CP class. Of these, 3,860 (53.5 %) provided information on one or more outcome measures within the TF4 clinic. Unsurprisingly, there was strong evidence (p < 0.001) of an association between modal class and availability of outcome data with 56.0 % of low cases providing follow-up data compared to 50.4 % of CL cases and 45.5 % of both EOP and AO cases. Table 1 depicts further analysis of the relationship between baseline demographics and the availability of CP and outcome data, showing clear evidence of social patterning both in the sample providing data for the longitudinal modeling of CP as well as those who remained part of the study to provide age 18 data. In addition to outcome non-response, not every child included in the LCGA model had complete data on confounders. Preliminary univariable logistic regression models employed listwise deletion resulting in sample ranging from 3,000 to 3,500 cases. Incorporating potential confounders led to a further attenuation of these already depleted sample sizes, hence fully adjusted models will only be shown following missing data imputation.
To address the problem of partial non-response among outcomes and confounders, missing data were imputed by chained equations  using the Stata ice routine  to restore sample size to 7,218 for all analyses. The imputation model contained the CP class assignment, outcomes and confounders described above, as well as several auxiliary variables known to be related to missingness and to key variables in our models. Including auxiliary variables to assist imputation of substantial amounts of missing data reduces bias. 100 datasets were imputed, with 20 cycles of regression switching, and these data exported to Latent Gold which applies the same model to each data set and pools the final results using Rubin’s rules .