Variables with time-varying effects and the Cox model: Some statistical concepts illustrated with a prognostic factor study in breast cancer

International audienceBACKGROUND: The Cox model relies on the proportional hazards (PH) assumption, implying that the factors investigated have a constant impact on the hazard - or risk - over time. We emphasize the importance of this assumption and the misleading conclusions that can be inferred if it is violated; this is particularly essential in the presence of long follow-ups. METHODS: We illustrate our discussion by analyzing prognostic factors of metastases in 979 women treated for breast cancer with surgery. Age, tumour size and grade, lymph node involvement, peritumoral vascular invasion (PVI), status of hormone receptors (HRec), Her2, and Mib1 were considered. RESULTS: Median follow-up was 14 years; 264 women developed metastases. The conventional Cox model suggested that all factors but HRec, Her2, and Mib1 status were strong prognostic factors of metastases. Additional tests indicated that the PH assumption was not satisfied for some variables of the model. Tumour grade had a significant time-varying effect, but although its effect diminished over time, it remained strong. Interestingly, while the conventional Cox model did not show any significant effect of the HRec status, tests provided strong evidence that this variable had a non-constant effect over time. Negative HRec status increased the risk of metastases early but became protective thereafter. This reversal of effect may explain non-significant hazard ratios provided by previous conventional Cox analyses in studies with long follow-ups. CONCLUSIONS: Investigating time-varying effects should be an integral part of Cox survival analyses. Detecting and accounting for time-varying effects provide insights on some specific time patterns, and on valuable biological information that could be missed otherwise

Seroprevalence of malaria in inhabitants of the urban zone of Antananarivo, Madagascar

BACKGROUND: Antananarivo, the capital of Madagascar, is located at an altitude of over 1,200 m. The environment at this altitude is not particularly favourable to malaria transmission, but malaria nonetheless remains a major public health problem. The aim of this study was to evaluate exposure to malaria in the urban population of Antananarivo, by measuring the specific seroprevalence of Plasmodium falciparum. METHODS: Serological studies specific for P. falciparum were carried out with an indirect fluorescent antibody test (IFAT). In a representative population of Antananarivo, 1,059 healthy volunteers were interviewed and serum samples were taken. RESULTS: The seroprevalence of IgG+IgA+IgM was 56.1% and that of IgM was 5.9%. The major risk factor associated with a positive IgG+IgA+IgM IFAT was travel outside Antananarivo, whether in the central highlands or on the coast. The abundance of rice fields in certain urban districts was not associated with a higher seroprevalence. CONCLUSION: Malaria transmission levels are low in Antananarivo, but seroprevalence is high. Humans come into contact with the parasite primarily when travelling outside the city. Further studies are required to identify indigenous risk factors and intra-city variations more clearly