Bayesian statistics in oncology: a guide for the clinical investigator

The rise of evidence-based medicine as well as important progress in statistical methods and computational power have led to a second birth of the >200-year-old Bayesian framework. The use of Bayesian techniques, in particular in the design and interpretation of clinical trials, offers several substantial advantages over the classical statistical approach. First, in contrast to classical statistics, Bayesian analysis allows a direct statement regarding the probability that a treatment was beneficial. Second, Bayesian statistics allow the researcher to incorporate any prior information in the analysis of the experimental results. Third, Bayesian methods can efficiently handle complex statistical models, which are suited for advanced clinical trial designs. Finally, Bayesian statistics encourage a thorough consideration and presentation of the assumptions underlying an analysis, which enables the reader to fully appraise the authors' conclusions. Both Bayesian and classical statistics have their respective strengths and limitations and should be viewed as being complementary to each other; we do not attempt to make a head-to-head comparison, as this is beyond the scope of the present review. Rather, the objective of the present article is to provide a nonmathematical, reader-friendly overview of the current practice of Bayesian statistics coupled with numerous intuitive examples from the field of oncology. It is hoped that this educational review will be a useful resource to the oncologist and result in a better understanding of the scope, strengths, and limitations of the Bayesian approach.

Immune reconstitution inflammatory syndrome in patients starting antiretroviral therapy for HIV infection: a systematic review and meta-analysis

In patients with HIV-1 infection who are starting combination antiretroviral therapy (ART), the incidence of immune reconstitution inflammatory syndrome (IRIS) is not well defined. We did a meta-analysis to establish the incidence and lethality of the syndrome in patients with a range of previously diagnosed opportunistic infections, and examined the relation between occurrence and the degree of immunodeficiency. Systematic review identified 54 cohort studies of 13 103 patients starting ART, of whom 1699 developed IRIS. We calculated pooled cumulative incidences with 95% credibility intervals (CrI) by Bayesian methods and did a random-effects metaregression to analyse the relation between CD4 cell count and incidence of IRIS. In patients with previously diagnosed AIDS-defining illnesses, IRIS developed in 37.7% (95% CrI 26.6-49.4) of those with cytomegalovirus retinitis, 19.5% (6.7-44.8) of those with cryptococcal meningitis, 15.7% (9.7-24.5) of those with tuberculosis, 16.7% (2.3-50.7) of those with progressive multifocal leukoencephalopathy, and 6.4% (1.2-24.7) of those with Kaposi's sarcoma, and 12.2% (6.8-19.6) of those with herpes zoster. 16.1% (11.1-22.9) of unselected patients starting ART developed any type of IRIS. 4.5% (2.1-8.6) of patients with any type of IRIS died, 3.2% (0.7-9.2) of those with tuberculosis-associated IRIS died, and 20.8% (5.0-52.7) of those with cryptococcal meningitis died. Metaregression analyses showed that the risk of IRIS is associated with CD4 cell count at the start of ART, with a high risk in patients with fewer than 50 cells per microL. Occurrence of IRIS might therefore be reduced by initiation of ART before immunodeficiency becomes advanced.

Mortality from road traffic accidents in Switzerland: longitudinal and spatial analyses

Road traffic accidents (RTA) are an important cause of premature death. We examined socio-demographic and geographical determinants of RTA mortality in Switzerland by linking 2000 census data to RTA mortality records 2000-2005 (ICD-10 codes V00-V99). Data from 5.5 million residents aged 18-94 years, 1744 study areas, and 1620 RTA deaths were analyzed, including 978 deaths (60.4%) in motor vehicle occupants, 254 (15.7%) in motorcyclists, 107 (6.6%) in cyclists, and 259 (16.0%) in pedestrians. Weibull survival models and Bayesian methods were used to calculate hazard ratios (HR), and standardized mortality ratios (SMR) across study areas. Adjusted HR comparing women with men ranged from 0.04 (95% CI 0.02-0.07) in motorcyclists to 0.43 (95% CI 0.32-0.56) in pedestrians. There was a u-shaped relationship with age in motor vehicle occupants and motorcyclists. In cyclists and pedestrians, mortality increased after age 55 years. Mortality was higher in individuals with primary education (HR 1.53; 95% CI 1.29-1.81), and higher in single (HR 1.24; 95% CI 1.05-1.46), widowed (HR 1.31; 95% CI 1.05-1.65) and divorced individuals (HR 1.62; 95% CI 1.33-1.97), compared to persons with tertiary education or married persons. The association with education was particularly strong for pedestrians (HR 1.87; 95% CI 1.20-2.91). RTA mortality increased with decreasing population density of study areas for motor vehicle occupants (test for trend p<0.0001) and motorcyclists (p=0.0021) but not for cyclists (p=0.39) or pedestrians (p=0.29). SMR standardized for socio-demographic and geographical variables ranged from 82 to 190. Prevention efforts should aim to reduce inequities across socio-demographic and educational groups, and across geographical areas, with interventions targeted at high-risk groups and areas, and different traffic users, including pedestrians.

Patterns of morphological changes and hybridization between sympatric whitefish morphs (Coregonus spp.) in a Swiss lake: a role for eutrophication?

Whitefish, genus Coregonus, show exceptional levels of phenotypic diversity with sympatric morphs occurring in numerous postglacial lakes in the northern hemisphere. Here, we studied the effects of human-induced eutrophication on sympatric whitefish morphs in the Swiss lake, Lake Thun. In particular, we addressed the questions whether eutrophication (i) induced hybridization between two ecologically divergent summer-spawning morphs through a loss of environmental heterogeneity, and (ii) induced rapid adaptive morphological changes through changes in the food web structure. Genetic analysis based on 11 microsatellite loci of 282 spawners revealed that the pelagic and the benthic morph represent highly distinct gene pools occurring at different relative proportions on all seven known spawning sites. Gill raker counts, a highly heritable trait, showed nearly discrete distributions for the two morphs. Multilocus genotypes characteristic of the pelagic morph had more gill rakers than genotypes characteristic of benthic morph. Using Bayesian methods, we found indications of recent but limited introgressive hybridization. Comparisons with historical gill raker data yielded median evolutionary rates of 0.24 haldanes and median selection intensities of 0.27 for this trait in both morphs for 1948-2004 suggesting rapid evolution through directional selection at this trait. However, phenotypic plasticity as an alternative explanation for this phenotypic change cannot be discarded. We hypothesize that both the temporal shifts in mean gill raker counts and the recent hybridization reflect responses to changes in the trophic state of the lake induced by pollution in the 1960s, which created novel selection pressures with respect to feeding niches and spawning site preferences.

Therapeutic drug monitoring of once daily aminoglycoside dosing: comparison of two methods and investigation of the optimal blood sampling strategy.

PURPOSE Therapeutic drug monitoring of patients receiving once daily aminoglycoside therapy can be performed using pharmacokinetic (PK) formulas or Bayesian calculations. While these methods produced comparable results, their performance has never been checked against full PK profiles. We performed a PK study in order to compare both methods and to determine the best time-points to estimate AUC0-24 and peak concentrations (C max). METHODS We obtained full PK profiles in 14 patients receiving a once daily aminoglycoside therapy. PK parameters were calculated with PKSolver using non-compartmental methods. The calculated PK parameters were then compared with parameters estimated using an algorithm based on two serum concentrations (two-point method) or the software TCIWorks (Bayesian method). RESULTS For tobramycin and gentamicin, AUC0-24 and C max could be reliably estimated using a first serum concentration obtained at 1 h and a second one between 8 and 10 h after start of the infusion. The two-point and the Bayesian method produced similar results. For amikacin, AUC0-24 could reliably be estimated by both methods. C max was underestimated by 10-20% by the two-point method and by up to 30% with a large variation by the Bayesian method. CONCLUSIONS The ideal time-points for therapeutic drug monitoring of once daily administered aminoglycosides are 1 h after start of a 30-min infusion for the first time-point and 8-10 h after start of the infusion for the second time-point. Duration of the infusion and accurate registration of the time-points of blood drawing are essential for obtaining precise predictions.