Study variables and measurement
The outcome variable was time to drop out of a CBHI membership starting from the point at which the households joined the scheme and was measured in years. The event of interest was dropping out of CBHI membership, hence households that dropped out were coded as “1” and otherwise “0”. Membership status at the time of data collection was confirmed based on the information obtained from the membership registration book of the scheme. The predictor variables include age, gender, level of education and marital status of the household head; household size; wealth status; participation in the safety net program; self-rated health status; presence of chronic illness in the household; history of hospitalization; value towards solidarity; perceived risk protection and trust in the scheme. Some of the independent variables have been operationally defined and measured as follows.
Wealth index was generated using the principal component analysis method. The scores for 15 types of assets and utilities were translated into latent factors and a wealth index was calculated based on the first factor that explained most of the variation. Based on the index the study households were categorized into wealth tertile – lower, medium, and higher wealth tertile. Self-rated health status was measured based on a household head’s subjective assessment of the health status of the household and was rated as “excellent, very good, good, fair, or poor”. However, for analysis purposes, it was recategorized into fair, good, and very good, by merging the two extreme response categories that had few frequencies to the next categories.
Value towards solidarity, perceived risk protection, and trust in the scheme are composite variables that were measured on a Likert scale using a 5 - point response format with 1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, and 5 = strongly agree by asking respondents to rate the extent to which they agreed on a set of items designed for each variable. To measure value towards solidarity, a three-item tool was adapted from a previous study conducted in Senegal (26), while a four-item trust measurement scale was adapted based on a previous tool validated and used in Cambodia (27). Perceived risk protection is the perception of insurance members towards the ability of the CBHI scheme to protect subscribers from financial risks. It was measured using three items. An overall index was calculated from a set of items using factor analysis, and a three-level categorical variable labeled as “low, medium, and high” was created for each of the three variables.
Perceived quality of health care was measured on a Likert scale using a 5 - point response format with 1 = strongly disagree to 5 = strongly agree by asking respondents to rate the extent to which they agreed on a set of nine experience questions regarding the health services they received from the nearby health centers contracted by the CBHI scheme. The scores for the nine items were translated into three dimensions, and an overall health care quality index was created based on the first dimension that explained most of the variation. Finally, the health care quality index was categorized into low, medium, and high.
Data collection process
Household-level data were collected from 04 February to 21 March 2021 using a structured interviewer-administered questionnaire by trained data collectors. Data related to membership duration and status of the households was obtained from the membership registration book at each kebele (health post), while information related to socio-demographic characteristics of the household, health status, health care utilization, value towards solidarity, perceived risk protection, trust in the scheme, and perception of respondents towards health care quality were collected at household level in the community. The heads of the households were interviewed at their home or workplace by using the local language, Amharic. The data collectors were guided by the health extension workers to track the sampled households. A mobile data collection platform, Open Data Kit (ODK) was applied to the household survey. The data collectors submitted the completed forms to the ODK aggregator (Kobo) server daily, which helped us to review the daily submissions and facilitate the supervision process.
Before the data collection, the questionnaire was pre-tested on a sample of 84 randomly selected participants in one kebele. As part of the pre-test, a cognitive interview was conducted on selected items using the verbal probe technique among eight respondents to determine whether or not items and response categories were understood and interpreted by the potential respondents as intended. Accordingly, the wording of some items and response options were modified and some items were removed.
Data processing and analysis
The data were analyzed using Stata version 17.0. Exploratory factor analysis was performed to assess the validity of the questionnaires designed to measure value towards solidarity, perceived risk protection, trust in the scheme, and perceived quality of health care. The Bartlett’s test of Sphericity and the Kaiser-Mayer-Olkin’s (KMO) measure of sampling adequacy tests were performed to assess the appropriateness of the data for factor analysis. Items with insignificant loadings (loading below 0.40) and items with a cross-loading were removed from the analysis. The Eigenvalue greater than one decision rule was used to determine the appropriate number of factors to be extracted. The reliability of measurement scales was estimated by measuring the internal consistency of each of the dimensions using Cronbach’s alpha, with an acceptable alpha value of 0.60 or higher (28).
The total membership-years of follow-up with an average follow-up time and the annual dropout rate were computed. For categorical variables, the time to drop out of a CBHI membership was described using the Kaplan-Meier estimate. To investigate the effect of covariates on the time to drop out of CBHI members, a univariate analysis was performed by fitting separate models for each covariate before proceeding to the multivariate analysis. Variables that were found to be significant in the univariate analysis at a p-value of less than 0.20 were included in the multivariable analysis. A multivariable analysis was done using the accelerated failure time shared frailty models to identify the predictors of time to drop out.
The proportional hazards assumption specifies that the ratio of the hazards between any two individuals is constant over time. However, in many applications, the study population cannot be considered homogeneous. In this study, the time to drop out of a CBHI membership is assumed to be different between clusters (kebeles) due to variations in the performance of the kebele health insurance committee which is mainly responsible for retaining scheme members. The intra-cluster correlation is assumed to be due to unobservable covariates specific to the cluster. One approach to account for such unobserved heterogeneity is the use of a shared frailty model which introduces a random effect into the model that induces dependence within clusters. In a shared frailty model, individuals in a cluster are assumed to share the same frailty value (29).
Frailty is an unobservable random effect shared by subjects within a cluster. It acts multiplicatively on the hazard function assumed to follow some distribution. When a shared frailty term with a Weibull distribution is assumed, the hazard function at time t for the jth individual, j = 1, 2,. . ., ni, in the ith group, i = 1, 2,. . ., g, is given by:
$${h}_{ij}\left(t\right)={z}_{i}\text{exp}({\beta \text{'}x}_{ij})\rho {t}^{\rho -1}$$
,
Where xij is a vector of explanatory variables for the jth individual in the ith group, β the vector of regression coefficients, ρtρ − 1 is the baseline hazard function, ρ a shape parameter and the zi are frailty effects that are common for all ni individuals within the ith group (30).
The hazard function can also be written in the form:
\({h}_{ij}\left(t\right)=\text{exp}({\beta \text{'}x}_{ij}+{u}_{i})\rho {t}^{\rho -1}\) , where ui = log(zi),
The corresponding survivor function for a Weibull model that incorporates a shared frailty component is:
\({S}_{ij}\left(t\right)=\text{e}\text{x}\text{p}\{-\text{e}\text{x}\text{p}({\beta \text{'}x}_{ij+}{u}_{i}){t}^{p}\) }
The frailty is generally assumed to follow a gamma or inverse Gaussian distribution with a mean equal to 1, and variance θ which is estimated from the data. The estimate for the variance parameter θ in a shared frailty model can be thought of as a measure of the degree of correlation, where θ > 0 indicates the presence of heterogeneity. Large values of θ reflect a greater degree of heterogeneity among clusters and a stronger association within clusters (30).
An accelerated failure time (AFT) model is a parametric model that provides a useful alternative to the commonly used proportional hazards models in survival analysis owing to its ease of interpretation. In addition, the regression parameters in AFT models are robust towards omitted covariates unlike that of the proportional hazards models (31). The AFT model is a general model for survival data in which explanatory variables measured on an individual are considered to act multiplicatively on the timescale. It allows researchers to measure the direct effect of predictor variables on survival time. In contrast to the proportional hazards model, the AFT model can best be interpreted in terms of the survival function (32). The AFT model is defined by the relationship:
S 1 (t) = S 0 (t/δ), for t ≥ 0,
Where δ is a constant called the acceleration factor, which tells the researcher how the change in the value of the covariate changes the time scale relative to the baseline time scale. The acceleration factor is the ratio of the survival time corresponding to any fixed value of S(t). In the regression framework, the acceleration factor δ can be parameterized as exp (α), where α is the parameter to be estimated from the data. With this parameterization, the general form of the survivor function for the ith individual in an AFT model is:
S i (t) = S 0 {t/exp(α′x i )},
In this version of the model, exp(α′xi) is the acceleration factor for the ith individual.
The general parametric AFT model that incorporates a shared frailty component is of the form:
S ij (t) = S 0 {t/ exp(η ij )},
Where ηij = α′xij + ui, and exp (ηij) is the acceleration factor for the jth individual in the ith group. This model can be expressed in log-linear form as:
$$\text{l}\text{o}\text{g}{T}_{ij}=\mu +{\alpha }_{1}{x}_{1ij}+{\alpha }_{2}{x}_{2ij}+\dots +{\alpha }_{p}{x}_{pij}+{u}_{i}+\gamma {ϵ}_{ij}$$
,
Where Tij is the random variable associated with the survival time of the jth individual in the ith group, µ and γ are intercept and scale parameters respectively and ui’s are the cluster-specific random effects. The quantity ϵij is a random variable used to model the deviation of the values of logTij from the linear part of the model, and ϵij is assumed to have a particular parametric distribution (33). In this formulation of the model, the α-parameters reflect the effect that each explanatory variable has on the survival times; positive values suggest that the survival time increases with increasing values of the explanatory variable and vice versa.
The common baseline distributions of the AFT models include exponential AFT, Weibull AFT, log-logistic AFT, and log-normal AFT distributions. In this study, Akaike’s Information Criterion (AIC) was used for model comparison and to choose the one that best fits the data. The overall fit of the final AFT model was checked by using the Cox-Snell residuals plot. Finally, the variance of the random effect (θ), Kendall’s Tau (τ), the regression coefficients, and the acceleration factor (δ) with 95% confidence interval were estimated.