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Table 2 Parameters of the sample size calculation: expected effect sizes

From: Supporting adolescent girls to stay in school, reduce child marriage and reduce entry into sex work as HIV risk prevention in north Karnataka, India: protocol for a cluster randomised controlled trial

Parameter

Derivation

Harmonic mean cluster size

Based on an enumeration carried out in the 225 high schools located in 121 villages by KHPT. Approximately 15 SC/ST girls are available at each school. Therefore, over the two years, we have assumed a mean of 30 girls per cluster.

Refusal/loss to follow-up

Refusal and loss to follow-up are expected to be low, approximately 5-10% (14 girls per cluster per year - > 28 at endline)

Between cluster variation (k)

The between cluster variation in the outcomes is not known. Therefore, we have reported sample sizes for 0.15, 0.2, and 0.25.

Control arm proportions

 

Proportion transitioning 7-8th (actualized in terms of the proportion dropping out between 7th and 8th)

We calculate cluster numbers for a range of drop-out proportions, from 9% (the State level drop-out proportion among SC/ST girls) to 17% (the dropout rate among all girls in Bijapur district [36]. These are conservative estimates.

Proportion completing 10th (actualized in terms of the proportion dropping out between 7th and 10th)

30-40% of girls drop out before standard 10 [36].

Proportion married before age 15

The district Level Household Surveys (DLHS-2007-08) collected data on age at marriage and has a reasonable sample size in each district. About 21% of women aged 18–25 married before the age of 15 years. A higher percent of SC/ST women were married compared to others (25.9% vs. 19.3%)1. Therefore the proportion is likely to be around 25%

Proportion sexual intercourse before age 15

Data from IBBA surveys among FSWs conducted in Belgaum district found 44.7% of FSWs reported their first sex was before the age of 15 years2. Given 25.9% of SC/ST women married before the age of 15 years, the proportion who had their first sex before 15 years will be a number above this, but within 44.7%. The Polling Booth Surveys conducted in the rural areas of these districts in 2011 found that 8% of unmarried females (15–24 years) had ever had sex, whereas 5.3% of married females (15–24 years) had sex before marriage in Bijapur district3. Therefore the proportion who had sex before 15 years is likely to be a number above 30%.

Effect (risk ratio)

 

Proportion transitioning 7-8th

We have reported a range of Risk Ratio minimum detectable effect sizes of 30-40%. This is considered to be the most likely of the outcomes to be influenced by the intervention

Proportion completing 10th

We have reported a range of Risk Ratio minimum detectable effect sizes of 20-25%. The lower effect size compared to outcome 1 reflects the likelihood that this will be harder to influence, as the barriers to staying in school increase over time

Proportion married before age 15

The intervention will target marriage directly through school and home based interventions. We aim to decrease the proportion married before 15 by 25-30%.

Proportion sexual intercourse before age 15

The intervention will target sexual debut directly through school and home based interventions. We aim to decrease the proportion married before 15 by 25-30%.

Type 1 error

We have set this at the 5% level

Power

We have set this at the 80% level

  1. 1Unpublished, District Level Household and Facility Survey (DLHS-3) data, 2007–8, Government of India. 2Unpublished female sex worker, integrated behavioural biological assessment (IBBA) survey data, Belgaum District, 2010, Karnataka Health Promotion Trust. 3Unpublished general population, polling booth survey data (PBS), 2011, Karnataka Health Promotion Trust.