Intergenerational Transmission of Psychiatric Conditions and Psychiatric, Behavioral, and Psychosocial Outcomes in Offspring

Key Points Question Is the intergenerational transmission of psychiatric conditions attributable to broader psychopathology comorbidity or to specific conditions? Findings In this cohort study including 2 947 703 participants, children whose parents scored 1 SD above the mean on the general psychopathology factor had a statistically significant 8% to 40% higher odds of 31 different outcomes. The specific psychopathology factors were primarily associated with within-spectrum and related offspring outcomes. Meaning Because the intergenerational transmission of psychiatric conditions appeared largely attributable to a parental general psychopathology factor, mental health care professionals might benefit from taking the total number of parental psychiatric conditions into account when estimating patient prognosis.


eTable 1. Description of Registries and Variables Extracted
Register Description Variables Total Population Register Established in 1968 and includes demographic information (e.g., sex, age, place of birth) for the entire Swedish population. 1 Individual identification number, birthyear

Multi-Generation Register
Links all index persons born in Sweden since 1932 and alive in 1960 to their biological parent. 2 Individual identification number

Prescribed Drug Register
Established in 2005 and contains all dispensed prescribed pharmaceuticals. 5escription of medication

National Crime Register
Comprises all registered criminal convictions of those aged 15 and older (the age of criminal responsibility) since 1973. 6urt convictions of violent crimes

National School Register
Includes averaged junior high final grades (age 15) and (in)eligibility for high school since 1988.

Cause of Death Register
Records all deaths in Sweden since 1952 and provides information on causes of death according to ICD. 7 Death by suicide, death by accidents Longitudinal Integration Database for Health Insurance and Market Studies Information from the labor market and educational and social sectors for all individuals registered in Sweden over 16 years of age since 1990. 8cial welfare recipiency, unemployment, parental educational level Conscription Register Includes measures of general cognitive ability for 18-year-old males in stanine format (a nine-point scale with a mean of 5 and a standard deviation of 2   These appendices address an issue with second-order models, namely, that they lack one degree of freedom when estimating associations between a latent measurement model and exposures/outcomes.Specifically, because second-order models estimate x factors, they can only estimate x associations with outcomes.Second-order models, however, generate x+1 factors, such that they lack one degree of freedom when estimating associations with exposures/outcomes.One approach to circumvent this issue is to only estimate x associations with the exposures/outcomes.For example, one could constrain one specific factor to have zero residual and therefore it would have no association with the exposures/outcomes.Alternatively, one could constrain two associations to equality such that one only estimates x associations with the exposures/outcomes (this might be defensible if two specific factors capture similar constructs).Yet another approach is to use a Direct Schmid-Leiman (DSL) rotation, which simply re-distributes the x associations into x+1 associations.We used the first approach in the second-order CFA model and the latter approach in the second-order EFA model.

Applying a Direct Schmid-Leiman rotation manually within an ESEM framework: Matrix algebra
To circumvent the issue with second-order EFA model lacking one degree of freedom when estimating associations with outcomes, we applied a DSL rotation within an Exploratory Structural Equation Modeling (ESEM) framework.
This DSL rotation approximates a so-called second-order hierarchical factor model, which has previously been identified in three steps.First, a set of lower-order factors are extracted (e.g., based on EFA).Second, a higher-order factor is in turn extracted based on the correlations among the lower-order factors, such that the lower-order factors are decomposed into a part that is explained by the higher-order factor and a residual part that is not.Third, the second-order model is converted into a hierarchical model by computing the associations between the higher-order and the residual parts of the lower-order factors, and the observed indicators.
In contrast to prior hierarchical factor models, the DSL rotation achieves this three-step process with a single rotation.The higherorder factor is usually labeled a general factor, and the residual lower-order factors are usually labeled specific factors.
The software Mplus (https://www.statmodel.com/)contains various rotations that can be used within an ESEM framework.However, it does not (yet) include the DSL rotation.Below we outline the basic ESEM equations as applied to the lambda (factor loading pattern) and beta (regressions between factors and exposures/outcomes) matrices and the rotation of beta matrix, which might be helpful to review before reading the practical steps of how to apply this rotation manually below.To simplify the estimation, Mplus treats all outcomes as latent variables (that are perfectly indicated by their observed counter-part).Therefore, we applied the rotation to the beta matrix containing the regression of the (latent) outcome onto the latent measurement model.

ESEM equations:
x is the indicator (parental exposures), η is the latent factor (offspring outcomes were also treated as latent factor in Mplus), z is the covariate variable (i.e., offspring birth year, the highest parental educational level), Λx is the factor loading matrix, B is the beta matrix of the latent factor on the latent factor (also offspring outcomes), K is the beta matrix of the covariate on the outcomes, τx and α are intercepts, δ and ζ are the error terms.H is the rotation matrix, B* is the rotated beta matrix.

Applying a second-order CFA measurement model
To circumvent the issue with second-order CFA model lacking one degree of freedom when estimating associations with exposures/outcomes, we constrained one specific factor to have zero residual and therefore it would have no association with the exposures/outcomes.This method has already been applied in a recently published study 1 .When the higher order loadings were freely estimated, the internalizing factor was near-perfect loaded on the general factor (loading 0.965).So, we constrained the specific internalizing factor to have zero residual and no association with specific internalizing factor was estimated.Same as second-order EFA model, we fixed the factor loadings to the second-order CFA without outcomes.Below is the Mplus script.
Step 1: Derive the factor loadings to the CFA without outcomes

eFigure 2 . 3 .
Associations Between General and Specific Psychopathology Factors in Parents and Offspring Outcomes Note: a Sample sizes varied for high school ineligibility (1 546 888 individuals), low school grade (2 398 752 individuals), social welfare recipiency and unemployment (2 497 731 individuals), low cognitive ability (156 239 individuals) depending on outcome missing information.b Odds ratios do not meet criteria for false discovery rate statistical significance c only for male.Abbreviations: ADHD = Attention-Deficit/Hyperactivity Disorder, ASD = autism spectrum disorder, PTSD = post-traumatic stress disorder, OCD = obsessive-compulsive disorder, ODD = oppositional defiant disorder.Bivariate Parent-Offspring Correlations Decomposed Into General Versus Specific Psychopathology Factor Contributions Note: Different colors represent the estimated correlation that can be attributed to the latent factor.Abbreviations: BPD = bipolar disorder, SCZ = schizophrenia, SCZAF = schizoaffective disorder, ANX = anxiety, DEP = depression, OCD = obsessive-compulsive disorder, PTSD = post-traumatic stress disorder, ALC = M et al.JAMA Network Open.alcohol-related disorders, DRG = drug-related disorders, VC = violent crimes, ADHD = Attention-Deficit/Hyperactivity Disorder, ASD = autism spectrum disorder, ODD = oppositional defiant disorder.

eFigure 4 .
Proportion of Variance in the Outcomes Explained by Latent General and Specific Factors Note: Abbreviations: ADHD= Attention-Deficit/Hyperactivity Disorder, ASD= autism spectrum disorder, PTSD= post-traumatic stress disorder, OCD= obsessivecompulsive disorder, ODD= oppositional defiant disorder.*: only for male.eAppendix.Matrix Algebra, R, and Mplus Supplementary Code 1. Applying a Direct Schmid-Leiman rotation manually within an ESEM framework: Matrix algebra 2. Applying a Direct Schmid-Leiman rotation manually within an ESEM framework: Mplus-and R-code 3. Applying a second-order CFA measurement model

Exposure/outcome ICD 08 (1969-1986) ICD 09 (1987-1996) ICD 10 (1997-) ATC code
).The ICD/ATC Code, Classified Convictions for Violent Crimes, and the Cut-Off Age for Each Exposure and Outcome Factor Loadings for Hierarchical Models of Different Sensitivity Analyses An Exploratory Structural Equation Modeling Framework Note: All other arrows among parental exposures, parental latent factor, and offspring outcomes were omitted for visualization.Offspring outcomes were listed as clusters.1) λ11* β11 is the bivariate correlation between parental bipolar disorder and offspring psychotic outcomes (e.g.offspring bipolar disorder) that could be attributable to general psychopathology factor.2) β11 2 /( β11 2 + β12 2 + β13 2 + β14 2 ) is the proportion of variance in offspring psychotic outcomes (e.g.offspring bipolar disorder) that could be explained by the general psychopathology factor.Abbreviations: OCD = obsessive-compulsive disorder, PTSD = post-traumatic stress disorder © 2023 Zhou M et al.JAMA Network Open.eTable 2. © 2023 Zhou M et al.JAMA Network Open.eTable 4. Note: Sensitivity1a: a second-order CFA model; Sensitivity1b: a bifactor EFA model; Sensitivity2a: a second-order EFA model based on six parental diagnoses; Sensitivity2b: a second-order CFA model based on six parental diagnoses; Sensitivity3: a second-order EFA model, limited individuals whose parents were diagnosed before childbirth.eFigure 1.