|Andersen, Andreas. 2012. Statistical Analysis of Population-Based Immunological Studies. Bandim Health Project, Statens Serum Institut. Faculty of Health and Medical Sciences, University of Copenhagen. 131 p.
Many infant still die from infectious diseases in low-income countries. Mortality has declined in the recent decades to a large extend due to vaccines. However, vaccines may have non-specific effects besides the prevention of the specific diseases. The Bandim Health Project has conducted population-based immunological studies within controlled randomized trials to study specific and non-specific vaccine effects. These studies examined the effects of vaccines on in-vitro stimulated cytokine production and the association between this production and child mortality.
The laboratory methods used to measure cytokine production are subject to detection limits (DL) and non-detectable (ND) cytokine concentrations. ND concentrations are censored observations and they pose several challenges for the subsequent statistical analysis, when analyzing ratios of cytokines, when comparing cytokine levels pre- and post-vaccination and when cytokines are included in Cox-models of child survival. The main objective of the present thesis was to address these statistical challenges and to find practical solutions.
First, when dealing with DL and ND, a frequent solution is to delete the NDs or to substitute them with DL, DL/2 or DL/Ö2. However, this is likely to give biased estimates of e.g. the treatment effect. No papers have directly addressed the challenge of comparing a ratio like TNF-α/IL-10 when both variables have censored observations. We addressed this challenge in paper I and compared a univariate method to a multivariate method.
Second, some immunological studies evaluate vaccination effect in randomized trials with prevaccination and post-vaccination measurements in both randomization groups. In this type of design, analysis of covariance (ANCOVA) is the most powerful to detect a vaccination effect. ANCOVA is a linear regression with the post-vaccination measurement as outcome and the prevaccination measurement and the vaccination variable as covariates. However, there may be censored observations of both the pre- and the post-vaccination measurements and thereby both a censored outcome and a censored covariate. We explored methods to conduct ANCOVA with censored variables in paper II.
Two immunological studies were analyzed in this thesis, as a proof of concept. In the REVAC study (paper III), the objective was to compare cytokine production between a group of BCG revaccinated children and a control group. A further objective was to assess the effect of BCG revaccination on the pro-/anti-inflammatory balance measured by the TNF-α/IL-10 ratio. In a study of neonates with low-birth-weight (LBW) (paper IV), the children were randomized to receive BCG at birth or later according to local practice. The objective was to examine associations between the child’s immune response potential, as measured by in-vitro stimulated cytokine production, and the risk of death. A specific objective was to explore non-linear associations. In this case it posed a challenge to conduct a survival analysis with a censored covariate which is allowed to have a non-linear effect.
The literature has shown that Tobit regression and multiple imputation (MI) are two valid methods to analyze univariate censored cytokine distributions. To analyze a ratio like TNF-α/IL-10 when both variables can be censored, we compared a multivariate Tobit method to a univariate Tobit method that uses clustered variance estimation to account for the inter-variable correlation. The two methods give almost identical results. To conduct ANCOVA with ND concentrations of both the pre- and post-vaccination measurements, we found that Tobit regression on the outcome combined with simple DL substitution of the covariate gives unbiased estimates of the vaccination effect. Compared to other analyzes, ANCOVA has the highest power also in the censored case. In the LBW study we applied MI of the ND concentrations to estimate and visualize non-linear associations between cytokine production and the risk of death.
In the REVAC study, BCG revaccination affected the pro-/anti-inflammatory balance in a manner that depended on DTP-booster vaccination and sex. In the LBW study, we found that both very low and very high cytokine responses were associated with increased mortality risk.
In the present thesis we assessed various methods to analyze cytokine data subject to DL and ND as single variables or ratios, in cross-sectional and pre-post vaccination designs and as exposure variables in survival analyzes. We found that Tobit regression is a good and fairly simple solution when dealing with cytokine data in cross-sectional studies. Univariate and multivariate Tobit regression give almost similar results in the analysis of the ratio. When dealing with pre- and postvaccination data, ANCOVA applying Tobit and simple DL substitution is unbiased with high power. MI can be used to include a censored covariate in a complex Cox-model.
Using these statistical tools we analyzed two immunological studies and showed non-specific immunological effects of BCG revaccination and that cytokine production in-vitro was correlated with subsequent mortality. Both very low and very high cytokine responses to LPS and PHA were associated with increased mortality, suggesting that a well-functioning immune system is balanced between strength and moderation in responsiveness to intruding pathogens.