Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
MDEs for main treatment effects:
Our MDEs are conservative in that they assume a sample size of N=3,580, which assumes we are only able to recruit 67% of the intended sample size of N=5,370. We assume an intra-class correlation (ICC) of 0.33 for mental health (as measured by depression score on Geriatric Depression Scale) and 0.21 for functional impairment (as measured by disability score on World Health Organization Disability Assessment Scale). The ICC estimates are based on baseline data from the Tamil Nadu Elderly Panel Survey (2019) when subsetting the sample to elderly women in rural areas. We assume that including baseline covariates and strata fixed effects reduces the residual variance in the outcome measure by 20%, thus decreasing standard errors accordingly.
Given our two cross-randomizations occur at different levels (CBT is randomized across individuals; Group activities are randomized across villages), we include MDEs for both clustered and unclustered regressions. Specifically, we will estimate three different regressions. The first will regress the outcome on an indicator for CBT treatment (along with other covariates), without clustered standard errors. The second will regress the outcome on an indicator for GA treatment (along with other covariates), with clustered standard errors. The third will regress the outcome on indicators for assignment to CBT treatment only, GA treatment only, and both (along with other covariates), with clustered standard errors. The other covariates will be strata fixed effects, surveyor fixed effects, and the value of the outcome measured at baseline. Additionally, in the first regression we will control for GA treatment, and in the second we will control for CBT treatment.
Regression 1. MDE for treatment effect of therapy without clustered standard errors, if running a regression pooling across Group Activities arms is 0.09 SD for both primary outcomes (mental health and functional impairment).
Regression 2. MDE for treatment effect of Group Activities with village-clustered standard errors, if running a regression pooling across CBT arms is 0.18 SD for mental health and 0.16 SD for functional impairment.
Regression 3. MDE for treatment effects of (1) CBT only, (2) Group Activites only, and (3) CBT + Group activities (relative to a control group of elders who do not receive CBT and are in villages without Group Activities) with village-clustered standard errors, if running a regression with the third specification is 0.2 SD for mental health and 0.18 SD for functional impairment.
MDEs for Actigraph-based measurements (sleep and mobility):
Some of our outcomes rely on device-based measurements using Actigraph wearable devices. First, we use Actigraphs to measure sleep (time asleep and efficiency, which is time asleep divided by time in bed). Second, we use Actigraphs to measure step count, which is a measure of mobility. For these outcomes, we only intend to collect data from N=1000 elders from N=358 villages, constituting approximately 20% of our sample. For both sleep and step count, we assume an ICC of 0.26, which is the ICC observed in self-reported sleep hours in wave 1 of the Tamil Nadu Elderly Panel Survey (2022). We will estimate the same specifications for these outcomes as described above, except we will not have baseline measures of these outcomes to include as controls.
Regression 1. MDE for treatment effect of therapy without clustered standard errors, pooling across Group Activities arms is 0.18 SD for both the sleep time and step count outcomes.
Regression 2. MDE for treatment effect of Group Activities with village-clustered standard errors, if running a regression pooling across CBT arms is 0.22 SD for both the sleep time and step count outcomes.
Regression 3. MDE for treatment effects of (1) CBT, (2) Group Activites, and (3) CBT + Group activities (relative to a control group of elders who do not receive CBT and are in villages without Group Activities) with village-clustered standard errors, if running a regression with the third specification is 0.29 SD for both the sleep time and step count outcomes.