The present research used data from Building a Knowledge Base on Population Aging in India (BKPAI), a national-level survey conducted in 2011 across seven states of India. The survey was sponsored by the Institute for Social and Economic Change (ISEC), Tata Institute for Social Sciences (TISS), Institute for Economic Growth (IEG), and United Nations Population Fund (UNFPA), New Delhi. The survey gathered information on various socio-economic and health aspects of ageing among those aged 60 years and above. Seven major regionally representative states were selected for the survey with the highest 60+ years population than the national average. This survey was carried out on a representative sample in India's northern, western, eastern, and southern parts following a random sampling process.
The Primary Sampling Unit (PSU) was villages for rural areas and urban wards in urban areas. The sample of 1280 elderly households was fixed for each state. Further details on the sampling procedure, the sample size is available in national and state reports of BKPAI, 2011 (BKPAI, 2012) . For the current study, the effective sample size was 9541 older adults residing in seven states aged 60+ years were selected.
This study utilized three outcome variables, namely ADL (Activity of Daily Living), IADL (Instrumental Activity of Daily Living), and Impairments. ADL was dichotomized from six questions asked to the older adults, given in the supplementary file 1. Activities of daily living (ADL) were categorized on a scale of 0 to 6, wherein a higher score represents higher independence. A detailed methodology on how we formed ADL is given in the supplementary file 1.
Instrumental activities of daily living were categorized into a scale of 0 to 8, wherein a higher score represents higher independence (For detail, see supplementary file 1). A score of 6+ was categorized as 0, representing high IADL, and a score of 5 and less was recoded as 1 representing low IADL . At last, impairment was coded as 0 means “no impairment,” and 1 means “having an impairment” (For detail, see supplementary file 1).
The predictor variables included age (60-69, 70-79 and 80+ years), gender (men and women), education (no education, below five years, 6-10 years and 11+ years), marital status (not in a union and currently in a union), living arrangement (alone, with spouse, with children and others), economic independence (independent, pension and dependent), working status (no, yes and retired), having children (yes and no), self-rated health (good and poor), chronic disease (no and yes), substance use (no and yes), wealth (poorest, poorer, middle, richer, and richest), religion (Hindu, Muslim, Sikh, and others), Caste (Scheduled Caste (SC), Scheduled Tribe (ST), Other Backward Class (OBC) and others), residence (rural and urban) and states (Himachal Pradesh, Punjab, West Bengal, Orrisa, Maharashtra, Kerala, and Tamil Nadu).
Descriptive statistics and bivariate analysis were used to find the preliminary results. Further, multivariate analysis (binary logistic) has been done to fulfill the objectives of the study. The results were presented in an odds ratio (OR) with a 95% confidence interval (CI).
The model is usually put into a more compact form as follows:
Where are the regression coefficient indicating the relative effect of a particular explanatory variable on the outcome. These coefficients change as per the context in the analysis in the study.
Moreover, the wealth quintile was the critical variable to measure the economic status of the household. A household wealth index was calculated in the survey by combining household amenities, assets, and durables and characterizing households in a range varying from the poorest to the richest, corresponding to wealth quintiles ranging from the lowest to the highest.
The study used wealth score (continuous variable) for decomposition analysis. For calculating the Concentration Index (CI), the study used the wealth quintile, divided into five equal sizes of the population.
The concentration index was calculated for ADL, IADL, and impairments. Concentration index represents the magnitude of inequality by measuring the area between the concentration curve and line of equality and is calculated as twice the weighted covariance between the outcome and fractional rank in the wealth distribution divided by the variable mean.
The concentration index can be written as follows:
Where C is the concentration index; Yi is the outcome variable index; R is the fractional rank of individual i in the distribution of socio-economic position; μ is the mean of the outcome variable of the sample, cov and denotes the covariance. The index value lies between -1 to +1.
Further, the study decomposes the concentration index to understand the relative contribution of various socio-economic factors to IADL among older adults. We only decomposed factors for IADL and not for ADL and impairments as the concentration index result for ADL and impairments did not show any observed socio-economic inequality. For decomposing the socio-economic factors, the study used a regression-based decomposition technique proposed by Wagstaff et al. .