Nunkui

In this study, we applied a flexible tool for estimating biomarker exposure effects in observational data, taking into account covariates information. The list of biomarkers deemed significant as well as the direction of the associations noted - as suggested by the sign of the log hazards ratio or by a visual inspection of the adjusted survival curves (not shown) - is consistent with current clinical and medical

knowledge of HIV infection. For instance, a negative log hazards ratio was expected - and found - for increases in lymphocytes counts. It is known that total lymphocytes counts (TLC) tend to decrease as a result of HIV infection and disease progression. Also, the significant association found with the outcome is consistent with research findings of a relatively high positive correlation between absolute values of TLC and CD4 cell counts or between changes in TLC and CD4 cell counts (Badri and Wood, 2003; Mwamburi et al., 2005). This finding could have practical applications for HIV medical care. As a measure of a patient’s immune capacity, CD4 cell count is considered as a standard method for determining eligibility for highly active antiretroviral therapy (HART) and HIV disease progression. However, its measurements require highly skilled personnel and costly maintenance of

sophisticated equipment, and these costs could be prohibitive in resource-deprived countries. Cheaper alternatives identified in this study (e.g. TLC), upon further evaluation, could potentially support decision-making with regards to the initiation of antiretroviral therapy or could help monitor patients’ immune status during therapy in the absence of expensive CD4 measurements. Overall, the application of the weighted Cox proportional hazards model to the GS study data provides valuable

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information for HIV medical care, and should be considered in the panoply of techniques used in biomarker assessment.

In addition to its ability to produce a consistent estimate of the effect of a given exposure, the Weighted Cox proportional hazards model is appealing because it makes it easier to create adjusted survival curves, which can be viewed as a graphic summary of the data averaged over the covariates used in the weights models. While adjusted estimates from the Cox proportional hazards model have been ubiquitously used in the reporting of results from survival analysis, survival curves have been used less frequently in observational studies (Hernán, 2010) due to the lack of a standard method for dealing with confounding. There have been attempts in the literature to generate adjusted survival curves from the conventional Cox model, but these applications were fraught with problems (Nieto and Coresh, 1996). One

notable shortcoming identified in Nieto and Coresh’s paper was the inability to adjust for continuous covariates. In their 2004 paper, Cole and Hernán proposed and demonstrated the idea of using survival estimates from the weighted Cox model to generate adjusted survival curves. This method was simple, easily implemented using standard statistical software, did not involve stratification on any covariate, and accommodated both continuous and time-varying covariates. Thus, even when results and conclusions from standard covariate adjustment through the

conventional Cox proportional hazards model are identical to those from a Weighted Cox proportional hazards model performed on the same data, the latter method has the advantage of readily generating adjusted survival curves. Certainly, the use of survival curves to report results from time to events analyses is encouraged (Hernán,

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2010) because survival curves have served as effective tools for displaying

informative and meaningful summary of study findings over the span of the entire study period.

This study has limitations. We applied the weighted Cox proportional hazards model under the assumption of no unmeasured confounders for biomarker exposure and censoring. There is no direct way to verify whether there remained any putative confounders that were not part of the vector of covariates (W) used in this study. All measured confounders are controlled for in the weights, and bias could still exist if some important confounding variables were not measured and, therefore, were not included in the weighted models. To guard against violation of this assumption, we included process a number of covariates believed to be related to the exposure of interest and the outcome (based on existing literature and expert knowledge) in the modeling process (Van Der Pol, 2008). Another potential limitation could be the occurrence of practical violations of ETA. Research by Wang et al (2006),

Neugebauer and van der Laan (2005), and by Moore et al (2010) has demonstrated how ETA violations could result in significant bias in the inverse probability

weighted estimator of causal effect models. In real life applications, it is not uncommon for an exposure to occur with a small probability or even with 0 probability within a given stratum of subjects. Also there may just be practical violations of ETA, defined as the occurrence of random 0 or 1 probability by chance. In this study, we have used a number of biomarkers measured on continuous scales, and it is known that ETA violation tends to be frequently associated with the use of continuous exposure variables. To reduce the impact of practical violations of ETA

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on the stability of our estimator and to ensure an adequate bias-variance trade-off, we set all estimated probabilities from both the censoring and exposure models below 0.01 to 0.01, as suggested in Bembom et al. (2008). Another technique implemented in this analysis to mitigate the effects of possible ETA violations was the use of stabilized weights, which allowed for a weaker form of the ETA

assumption (Wang et al, 2006).