Supplemental Material: Detailed Methods

Supplemental Material: Detailed Methods

Actor-Partner Interdependence Models in a Multilevel Modeling Framework

Actor-Partner Interdependence Models (APIM) allow for the analysis of dyadic data by accounting for interdependence between the dyad members. Failing to account for non-independence can result in biased variances and inference errors (1). In the APIM framework, the “actor” is an individual and the “partner” is the other member of the dyad. Thus, in this study actor effects describe the association between the individual’s psychosocial factors at time 1 on their own depression risk at time 2. Partner effects refer to the association between an individual’s psychosocial factors at time 1 and their partner’s risk of depression at time 2. There are two sources of variation in APIM: between-dyads (how the mean scores differ between couples) and within-dyads (how the scores differ between members of the dyad).

In this study, the APIM were implemented using multilevel modeling. In this context, the dyad can be thought of as a group with two members. For the purposes of this study we used two levels: the individual (lower level), who is nested within the dyad (upper level). The data are reciprocal: all relevant data were available on both members of each dyad. The variables were coded on the individual-level (e.g., age) or the dyad-level (e.g. number of children in the household). As the dyads consisted of husband/wife pairs, they were distinguishable on both their gender and their disease status. We used disease status as the distinguishing variable as disease status is theoretically meaningful for the research question. We conducted nomothetic analyses for this study, meaning that we examined the associations across dyads.

The structure of the data follows the standard dyadic design; each person is linked to one other person in the dataset. The data were organized in a pairwise structure. Each record includes both Time 2 and Time 1 (lagged) psychosocial variables. Each individual represents a record in the dataset, with a variable noting dyad membership (a dyad identifier unique to each couple). Each record also includes key information about the individual’s partner, namely their scores on the psychosocial measures as well as key sociodemographic information.

In order to assess non-independence, correlations and partial correlations (adjusting for gender) between survivors and their spouses were calculated; kappas were used for categorical variables (depression). The results showed partial correlations ranging from 0.26 to 0.45, suggesting moderate non-independence and supporting the use of dyadic models.

We used a two-intercept model, allowing the intercepts for survivors and spouses to be estimated separately (“noint” command in PROC GLIMMIX). In dyadic models, we can only allow for one random variable, as there must be more level-1 units (individuals) per level-2 units (dyads) than random variables. Therefore, only the distinguishing variable (disease status) was included as a random variable in order to allow for random intercepts. The interaction between the distinguishing variable (disease status) and both actor and partner psychosocial factors was included to allow the slope for survivors to differ from the slope for spouses. Disease status was also interacted with age and with depression at Time 1 (for models looking at distress, mental health-related quality of life [HRQoL], or physical HRQoL), as the association between these factors and depression risk may differ for survivors and spouses. The final models also controlled for gender, race/ethnicity, health insurance coverage, % federal poverty level, number of children in the household, presence of health conditions, limitations in activities of daily living or instrumental activities of daily living, cancer type, survivor treatment status, and depression at T1 (not included in the model equations below for brevity).

Cross-lagged APIM were used to estimate the following equations for dyad i:

Y1ti = c1i + a1iX1,t-1,i + p12X2,t-1,i + … + e1ti

Y2ti = c2i + a2iX2,t-1,i + p21X1,t-1,i + … + e2ti

where Y1ti refers to the survivor’s log odds of depression at Time 2, Y2ti refers to spouses’ log odds of depression at Time 2, X1,t-1,i refers to survivors’ psychosocial factors (depression, distress, mental HRQoL, or physical HRQoL, depending on the model) at Time 1, and X2,t-1,i refers to spouses’ psychological factors at Time 1. The ellipse (“…”) refers to the other individual- and dyad-level sociodemographic and health covariates included in the analyses. e1ti and e2ti are error terms. This model predicts the survivors’ actor effects (a1i), the spouses’ actor effects (a2i), the partner effect from the survivor to the spouse (p12), and the partner effect from the spouse to the survivor (p21), as well as the intercept for survivors (c1i) and spouses (c2i). As stated earlier, c1i and c2i were included as random effects.

Showing this in traditional MLM equations:

Depressionij ~ Binomial(1, πij)

logit(πij) = β0jC_Survivor + β1jC_Spouse + β2jX1_Survivor + β3jX1_Spouse + β4jX2_Survivor + β5jX2_Spouse

β0j = β0 + u0j

β1j = β1 + u1j

One key advantage of using multilevel modes is that all the data can be used, even if scores are missing at random for some dyad members (2). However, we only used full dyads in the final analyses in order to simplify the methods and interpretation for the readers. When dyads missing a member were not dropped, the results were substantively unchanged from those presented in the manuscript.

REFERENCES

1. Kenny DA, Kashy DA, Bolger N. Data analysis in social psychology. The handbook of social psychology. 1998;1:233-65.

2. Kenny DA, Kashy DA, Cook WL. Dyadic data analysis: Guilford Press; 2006.