Post-hoc power analysis: a conceptually valid approach for power based on observed study data

Power analysis is a key component of planning prospective studies such as clinical trials. However, some journals in biomedical and psychosocial sciences request power analysis for data already collected and analysed before accepting manuscripts for publication. Many have raised concerns about the conceptual basis for such post-hoc power analyses. More recently, Zhang et al showed by using simulation studies that such power analyses do not indicate true power for detecting statistical significance since post-hoc power estimates vary in the range of practical interests and can be very different from the true power. On the other hand, journals’ request for information about the reliability of statistical findings in a manuscript due to small sample sizes is justified since the sample size plays an important role in the reproducibility of statistical findings. The problem is the wording of the journals' request, as the current power analysis paradigm is not designed to address journals’ concerns about the reliability of the statistical findings. In this paper, we propose an alternate formulation of power analysis to provide a conceptually valid approach to the journals’ wrongly worded but practically significant concern.

Liver Stiffness on Magnetic Resonance Elastography and the MEFIB Index and Liver-Related Outcomes in Nonalcoholic Fatty Liver Disease: A Systematic Review and Meta-Analysis of Individual Participants

BACKGROUND & AIMS

Magnetic resonance elastography (MRE) is an accurate biomarker of liver fibrosis; however, limited data characterize its association with clinical outcomes. We conducted an individual participant data pooled meta-analysis on patients with nonalcoholic fatty liver disease to evaluate the association between liver stiffness on MRE and liver-related outcomes.

METHODS

A systematic search identified 6 cohorts of adults with nonalcoholic fatty liver disease who underwent a baseline MRE and were followed for hepatic decompensation, hepatocellular carcinoma, and death. Cox and logistic regression were used to assess the association between liver stiffness on MRE and liver-related outcomes, including a composite primary outcome defined as varices needing treatment, ascites, and hepatic encephalopathy.

RESULTS

This individual participant data pooled meta-analysis included 2018 patients (53% women) with a mean (± standard deviation) age of 57.8 (±14) years and MRE at baseline of 4.15 (±2.19) kPa, respectively. Among 1707 patients with available longitudinal data with a median (interquartile range) of 3 (4.2) years of follow-up, the hazard ratio for the primary outcome for MRE of 5 to 8 kPa was 11.0 (95% confidence interval [CI]: 7.03-17.1, P < .001) and for ≥ 8 kPa was 15.9 (95% CI: 9.32-27.2, P < .001), compared with those with MRE <5 kPa. The MEFIB index (defined as positive when MRE ≥3.3 kPa and Fibrosis-4 ≥1.6) had a robust association with the primary outcome with a hazard ratio of 20.6 (95% CI: 10.4-40.8, P < .001) and a negative MEFIB had a high negative predictive value for the primary outcome, 99.1% at 5 years. The 3-year risk of incident hepatocellular carcinoma was 0.35% for MRE <5 kPa, 5.25% for 5 to 8 kPa, and 5.66% for MRE ≥8 kPa, respectively.

CONCLUSION

Liver stiffness assessed by MRE is associated with liver-related events, and the combination of MRE and Fibrosis-4 has excellent negative predictive value for hepatic decompensation. These data have important implications for clinical practice.

The Relationship Between Loneliness and Positive Affect in Older Adults

OBJECTIVE

To establish whether positive affect (PA) is uniquely associated with loneliness and other social functioning variables beyond negative affect (NA) among older adults.

METHODS

Four hundred and twenty-eight participants (aged 60+ years old, 82% White, and 48% female) were recruited using random digit-dialing and completed scales for loneliness (UCLA Loneliness Scale), companionship (PROMIS scale), satisfaction with discretionary social activities (PROMIS scale), PA (Center for Epidemiologic Studies [CES] Happiness Scale), and NA (CES-Depression scale and Brief Symptom Inventory-Anxiety Subscale).

RESULTS

Multiple linear regression models found PA to be a significant predictor of lower loneliness where the effect of PA on loneliness is dependent on the level of NA; a large effect size at the mean level of NA, which becomes attenuated when NA increases. Although the direction of effect of PA on loneliness will change for NA > 5.10, which is 5 standard deviations away from 0, based on the model estimates, the percent of subjects with this large NA levels is practically 0. Thus, higher PA is associated with lower loneliness, however this effect is attenuated for larger NA. Similarly, multiple linear regression models found that companionship was associated with PA and NA where the effect of PA is dependent on the level of NA; a medium effect size at the mean level of NA, which becomes attenuated when NA increases. As in the case of loneliness, the direction of effect of PA on companionship will change for NA > 3.52, which is 3.5 standard deviation away from 0, based on the model estimates, but the percent of subjects with this large NA levels is practically 0. Thus, higher PA is associated with increased companionship, aand this effect is attenuated with greater NA. Satisfaction with social activities was associated with PA only (medium effect size).

CONCLUSION

Results suggest PA appears to be uniquely associated with social functioning among older adults. These findings support the potential for treatments that target PA to decrease loneliness among older adults, or vice versa.