Small sample GEE estimation of regression parameters for longitudinal data

Abstract

Longitudinal (clustered) response data arise in many bio-statistical applications which, in general, cannot be assumed to be independent. Generalized estimating equation (GEE) is a widely used method to estimate marginal regression parameters for correlated responses. The advantage of the GEE is that the estimates of the regression parameters are asymptotically unbiased even if the correlation structure is misspecified, although their small sample properties are not known. In this paper, two bias adjusted GEE estimators of the regression parameters in longitudinal data are obtained when the number of subjects is small. One is based on a bias correction, and the other is based on a bias reduction. Simulations show that the performances of both the bias-corrected methods are similar in terms of bias, efficiency, coverage probability, average coverage length, impact of misspecification of correlation structure, and impact of cluster size on bias correction. Both these methods show superior properties over the GEE estimates for small samples. Further, analysis of data involving a small number of subjects also shows improvement in bias, MSE, standard error, and length of the confidence interval of the estimates by the two bias adjusted methods over the GEE estimates. For small to moderate sample sizes (N ≤50), either of the bias-corrected methods GEEBc and GEEBr can be used. However, the method GEEBc should be preferred over GEEBr, as the former is computationally easier. For large sample sizes, the GEE method can be used.

Associations between fruit and vegetable consumption and depressive symptoms: evidence from a national Canadian longitudinal survey

“…A healthy diet, including adequate consumption of fruits and vegetables may engender improvements in mental health, possibly due to the impact of essential nutrients such as folate, magnesium, selenium and vitamin b6 5–7. Following a healthy diet may also facilitate engagement in other positive health behaviours, such as exercise and quitting smoking,23 34 which may in turn contribute to improved mental health 20–21 23 38–40. However, symptoms of depression and distress may also make it more difficult to engage in positive health behaviours 24 25.…”

“…Models were fitted using an autoregressive correlation structure—that is, assuming that repeated measures closer in time will be more highly correlated than more temporally distant measures. However, coefficients obtained from GEE modelling are unbiased even when the correlation structure is misspecified 34. To account for the complex survey design, we included normalised longitudinal sampling weights in the analysis.…”

Long-term outcomes following lower extremity press-fit bone-anchored prosthesis surgery: a 5-year longitudinal study protocol

“…Generalised estimating equations (GEE) for repeated measurements with an exchangeable correlation structure will be used [59–61]. Back pain will be dichotomised for this analysis into ‘no back pain’ and ‘back pain’ (representing the classes ‘yes, with episodes’ and ‘yes, chronic (daily)’).…”

“…For the significantly changed outcomes of interest over time (change of coronal plane kinematics, prosthetic use, walking ability, HRQoL and prosthesis comfort) and for stump pain at follow-up, multivariate GEE [59, 61] will be used to examine which potential predictors are of added value in the prediction of these outcomes (Additional file 1). Potential predictors are age, BMI, time from primary amputation to inclusion, cause of amputation, level of amputation, length of the residual limb, baseline hip abductor strength, baseline prosthetic use, baseline mobility level, baseline walking ability and baseline prosthesis comfort.…”

Feasibility, Acceptability, and Tolerability of Targeted Naltrexone for Nondependent Methamphetamine-Using and Binge-Drinking Men Who Have Sex with Men

“…Moreover, these exploratory analyses utilized GEE models which have been shown to result in standard errors that are too small for small studies, and may bias findings away from the null. 82 Taken together, the significant results from these exploratory analyses (reductions in binge drinking days in as-treated analyses; meth using days in sub-group analyses; and serodiscordant receptive anal intercourse events) should be interpreted with caution, as they may be subject to both type-I error and error from bias. While we did not find significant differences between those enrolled versus those excluded during screening, our small sample size and use of non-probability sampling may nevertheless limit the generalizability of our findings.…”