Statistical Methods for Correlated Data: Application to Severe Malaria Case Management Evaluation in Kenya

Abstract

Correlated data arise when clusters of observations are similar to each other. This is common in public health research where measurements on the same subject are repeatedly tracked over time and space. Health facility surveys are routinely implemented to monitor severe malaria case management. The dataset from this kind of surveys have hierarchical structure and requires statistical methods that can properly account for correlated data. This study developed a statistical model for analyzing correlated data by evaluating severe malaria case management in Kenya. This was secondary analysis using data from repeated cross-sectional inpatient malaria case management surveys undertaken at the government (GOK) and the Faith Based Organization (FBO) health facilities in Kenya from 2016 to 2019. The number of health facilities, health workers and suspected malaria admissions ranged from; 86 to 94, 330 to 367 and 2243 to 2485 respectively, across the survey period. Three methods of data collection were applied; retrospective data was extracted from the patients‘ files, health workers (clinicians and nurses) from the paediatric and medical ward were interviewed and, health facilities were assessed for readiness. Firstly, to evaluate the impact of correlation on outcomes, multilevel mixed effect logistic regression modelling was performed to identify the predictors of the health workers‘ knowledge about artesunate-based severe malaria treatment recommendations in Kenya. During modeling, the random effects and intracluster correlation were examined. Secondly, a Bayesian hierarchical spatial model beyond predictor analysis was applied to predict subnational estimates of knowledge levels. Three hierarchical models were fitted with ordinal logistic regression. The best fitting models were overlaid on a map showing all counties in Kenya. Lastly, to model factors related to hospital length of stay for severe malaria patients, competing risk approach was applied based on usual clinical setting in Kenya. Two models were fitted and their parameter estimates examined; conventional Cox regression model to obtain a cause-specific hazard (CSH) ratio and Fine and Gray competing risks method to obtain a subdistribution hazard (SDH) ratio. Evaluating the impact of correlation while adjusting for health facility and county structures, the parameter estimates were slightly varied and some of the variables that were significant in unadjusted analyses lost their significance. With respect to the treatment policy knowledge, clinicians compared to nurses were more likely to have high knowledge, both at the GOK (adjusted Odds Ratio [aOR] =1.86; 95% CI: 1.18-2.91) and FBO health facilities (aOR=2.27; 95% CI=1.41-3.65). Health workers‘ knowledge about recommended artesunate dosing was significantly associated with displayed artesunate administration posters (aOR=2.17; 95% CI=1.24-3.79) at the GOK health facilities. The knowledge of artesunate dosing intervals was significantly associated with the availability of artesunate (aOR=2.18; 95% CI=1.20-3.94) at the FBO health facilities. Health workers in the paediatric ward had high knowledge about artesunate preparation compared to those in medical ward (aOR=1.99; 95% CI=1.33-2.99) at the GOK health facilities. The knowledge of preferred route of artesunate administration was significantly higher in high malaria risk areas compared to low areas. Conditional on the fixed effects covariates, the health worker knowledge on severe malaria treatment policy and artesunate preparation were slightly correlated within the same county. The random effects composed about 4% to 11% of the total residual variance. Artesunate dose and dosing interval were slightly correlated within the same health facilty. The random effects composed about 7% and 26% of the total residual variance. While, artesunate route of administration was slightly correlated within the same county in the GOK sector, and within the same health facility in the FBO sector. The random effects composed about 26% and 39% of the total residual variance in the GOK and FBO sector respectively. Adjusting for county structures in Bayesian hierarchical spatial approach, the best model fitted with spatially structured random effects and the spatial variations of the knowledge level across the 47 counties exhibited neighborhood influence. The likelihood of having high knowledge on severe malaria treatment policy was lower among nurses relative to clinicians (aOR=0.48, 95% CI: 0.25 to 0.87), health workers older than 30 years were 61% less likely to have high dosing knowledge compared to younger health workers (aOR=0.39, 95% CI: 0.22 to 0.67) while those exposed to artesunate poster had 2.4-fold increased odds of higher dosing knowledge compared to non-exposed health workers (aOR=2.38, 95% CI: 1.22 to 4.74). Based on the spatial maps, the health workers in Kisii county had high knowledge levels (>10%) on severe malaria treatment policy. In addition, Muranga, Embu, Uasin Gishu, Kiambu, and Kisumu counties had high knowledge levels (>10%) about artesunate dose, and slightly more than a third of the counties had high knowledge levels (>10%) on artesunate preparation. Modelling factors associated with the length of stay (LOS) among the severe malaria patients, the median LOS was 4 days. The factor estimates and the confidence interval spans between the SDH and CSH models were slightly varied. Among the factors assessed for influencing LOS, respiratory rate (Subdistribution-Hazard ratio [SDHR]: 0.873; 95% CI: 0.789–0.967), oxygen saturation (SDHR: 0.859; 95% CI: 0.754–0.978), Hemoglobin(Hb)/Hematocrit (HCT) (SDHR: 0.769; 95% CI: 0.709–0.833), glucose/Random Blood Sugar(RBS) (SDHR: 0.766; 95% CI: 0.704–0.833) and documentation of at least one clinical feature of severe malaria (SDHR: 0.696; 95% CI: 0.626–0.774) were significantly associated with shortened LOS. Conversely, patients with confirmed severe malaria (SDHR: 1.214; 95% CI: 1.082–1.362) and those treated with injectable artesunate (SDHR: 1.339; 95% CI: 1.184–1.515) were significantly associated with prolonged LOS. The malaria program can utilize multilevel mixed effect logistic regression modelling to account for the hierarchical structure of the survey data. Further, Bayesian hierarchical spatial model can be used to account for the substantial heterogeneity among the health workers at various levels. In the presence of a competing risk and correlation, SDH model is the best model. The program should target on interventions likely to improve health workers‘ knowledge about severe malaria case management; artesunate availability, access to guidelines and exposure of artesunate poster in the wards. Based on the spatial maps, focused multidisciplinary interventions implemented can bridge the knowledge gaps identified at the subnational levels. Measurement of temperature, respiratory rate, oxygen saturation and laboratory tests (Hb/HCT, glucose/RBS) were significantly associated with shortened LOS. Treating severe malaria patients with artesunate boosted survival and increased LOS. The statistical models developed can be applied to analyse similar correlated data.