Asked by Statistics
What analysis should I use if I am measuring levels of depression, anxiety, and substance use before and after HIV disclosure? Within subjects design. Continuous variables. Data is not normally distributed. Variables may be influencing each other
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Short answer
- If you only have two time points (pre vs post) and just want to test whether each measure changed: use a paired nonparametric test — Wilcoxon signed-rank test for each outcome (report effect sizes).
- If you want to model the three outcomes jointly (they are correlated) or to adjust for covariates/missing data: use a mixed model or GEE on the repeated (within-subject) data — either a multivariate mixed-effects model or separate mixed models with robust SEs. These approaches handle correlated observations and can be made robust to non‑normality (via transformation, alternative families or robust/bootstrapped inference).
- If you want to model how the outcomes influence each other over time: use longitudinal structural equation models (latent change score or cross-lagged panel models) — but these require ≥3 waves (or careful interpretation with 2 waves) and larger samples.
Guidance and practical options
1) Simple pre vs post, each outcome separately (two time points)
- Test: Wilcoxon signed-rank test (paired). Use when the continuous variable is non‑normal and you only need a univariate pre/post comparison.
- Report: median (IQR) pre/post, Wilcoxon statistic, p-value and an effect size (rank-biserial or r).
- R: wilcox.test(x_pre, x_post, paired=TRUE)
2) Repeated-measures modelling that handles correlations and covariates
- Linear mixed-effects model (LMM): outcome ~ time + (1 | subject) (and add covariates). LMMs handle correlated repeated measures and unbalanced/missing data. If residuals are non‑normal consider: transforming the outcome (log, square-root), using robust (sandwich) standard errors, or bootstrap CIs.
- Generalized estimating equations (GEE): use if you care about population-average effects and want robust inference to misspecified correlation structure (geepack in R).
- If outcomes are skewed, consider GLMMs with an appropriate family (e.g., Gamma + log link) or model transformed scores.
3) Joint modelling of multiple correlated outcomes
- Multivariate LMM (joint mixed model): model depression, anxiety and substance use together to account for between-outcome correlations and test overall time effect. This is preferable to doing three separate tests if you want a single multivariate test and to model covariance between outcomes.
- Practical strategies: (a) reshape data to long format and include outcome-type as factor and time*outcome interaction in a mixed model, or (b) use packages that fit multivariate mixed models (e.g., mvtnorm-based approaches, or R packages like brms or MCMCglmm for a Bayesian joint model).
- If you cannot meet parametric assumptions, use robust or bootstrap inference.
4) Modeling reciprocal influences among outcomes (causal/temporal relations)
- If you have ≥3 time points: use cross-lagged panel models or latent change score models in structural equation modeling (lavaan in R, Mplus). These model how one variable at prior time predicts change in another variable later.
- If you have only 2 time points: you can model change scores (post − pre) and regress change in one outcome on baseline values of another (e.g., ΔDepression ~ baseline substance use + baseline depression), but causal claims are limited.
- SEM can incorporate measurement error (if you have multi-item scales) and test mediation.
Other practical points
- Always inspect distributions and residuals; consider transformations if appropriate.
- Correct for multiple testing if running separate tests (e.g., Holm or FDR).
- Use effect sizes and confidence intervals, not just p-values.
- Missing data: mixed models/GEE are more forgiving (assume MAR). Consider multiple imputation if data are not MAR.
- If sample size is small and assumptions are dubious, consider permutation tests or bootstrap CIs for paired differences.
Suggested workflow example
1. Plot pre/post distributions and paired differences for each measure.
2. If only two time points and no need to model interdependence: run Wilcoxon signed-rank for each variable.
3. If modeling jointly/adjusting covariates: fit a mixed model (outcome ~ time + covariates + (1|subject)). If you have 3 outcomes and want a joint test, fit a multivariate mixed model or a long-format mixed model with outcome* time interaction.
4. If interested in reciprocal influences and you have ≥3 waves: specify a cross-lagged SEM or latent change model.
If you tell me:
- how many time points you have,
- sample size,
- whether outcomes are scale scores (and ranges),
- whether you want joint tests or causal directionality,
I can give a tailored analysis plan and example code (R).
- If you only have two time points (pre vs post) and just want to test whether each measure changed: use a paired nonparametric test — Wilcoxon signed-rank test for each outcome (report effect sizes).
- If you want to model the three outcomes jointly (they are correlated) or to adjust for covariates/missing data: use a mixed model or GEE on the repeated (within-subject) data — either a multivariate mixed-effects model or separate mixed models with robust SEs. These approaches handle correlated observations and can be made robust to non‑normality (via transformation, alternative families or robust/bootstrapped inference).
- If you want to model how the outcomes influence each other over time: use longitudinal structural equation models (latent change score or cross-lagged panel models) — but these require ≥3 waves (or careful interpretation with 2 waves) and larger samples.
Guidance and practical options
1) Simple pre vs post, each outcome separately (two time points)
- Test: Wilcoxon signed-rank test (paired). Use when the continuous variable is non‑normal and you only need a univariate pre/post comparison.
- Report: median (IQR) pre/post, Wilcoxon statistic, p-value and an effect size (rank-biserial or r).
- R: wilcox.test(x_pre, x_post, paired=TRUE)
2) Repeated-measures modelling that handles correlations and covariates
- Linear mixed-effects model (LMM): outcome ~ time + (1 | subject) (and add covariates). LMMs handle correlated repeated measures and unbalanced/missing data. If residuals are non‑normal consider: transforming the outcome (log, square-root), using robust (sandwich) standard errors, or bootstrap CIs.
- Generalized estimating equations (GEE): use if you care about population-average effects and want robust inference to misspecified correlation structure (geepack in R).
- If outcomes are skewed, consider GLMMs with an appropriate family (e.g., Gamma + log link) or model transformed scores.
3) Joint modelling of multiple correlated outcomes
- Multivariate LMM (joint mixed model): model depression, anxiety and substance use together to account for between-outcome correlations and test overall time effect. This is preferable to doing three separate tests if you want a single multivariate test and to model covariance between outcomes.
- Practical strategies: (a) reshape data to long format and include outcome-type as factor and time*outcome interaction in a mixed model, or (b) use packages that fit multivariate mixed models (e.g., mvtnorm-based approaches, or R packages like brms or MCMCglmm for a Bayesian joint model).
- If you cannot meet parametric assumptions, use robust or bootstrap inference.
4) Modeling reciprocal influences among outcomes (causal/temporal relations)
- If you have ≥3 time points: use cross-lagged panel models or latent change score models in structural equation modeling (lavaan in R, Mplus). These model how one variable at prior time predicts change in another variable later.
- If you have only 2 time points: you can model change scores (post − pre) and regress change in one outcome on baseline values of another (e.g., ΔDepression ~ baseline substance use + baseline depression), but causal claims are limited.
- SEM can incorporate measurement error (if you have multi-item scales) and test mediation.
Other practical points
- Always inspect distributions and residuals; consider transformations if appropriate.
- Correct for multiple testing if running separate tests (e.g., Holm or FDR).
- Use effect sizes and confidence intervals, not just p-values.
- Missing data: mixed models/GEE are more forgiving (assume MAR). Consider multiple imputation if data are not MAR.
- If sample size is small and assumptions are dubious, consider permutation tests or bootstrap CIs for paired differences.
Suggested workflow example
1. Plot pre/post distributions and paired differences for each measure.
2. If only two time points and no need to model interdependence: run Wilcoxon signed-rank for each variable.
3. If modeling jointly/adjusting covariates: fit a mixed model (outcome ~ time + covariates + (1|subject)). If you have 3 outcomes and want a joint test, fit a multivariate mixed model or a long-format mixed model with outcome* time interaction.
4. If interested in reciprocal influences and you have ≥3 waves: specify a cross-lagged SEM or latent change model.
If you tell me:
- how many time points you have,
- sample size,
- whether outcomes are scale scores (and ranges),
- whether you want joint tests or causal directionality,
I can give a tailored analysis plan and example code (R).
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