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Abstract
The purpose was to identify risk factors for bacteremia in febrile episodes occurring during chemotherapy for acute lymphoblastic leukemia (ALL) in children, and to develop a risk score permitting risk-adapted antibiotic therapy. We reviewed a total of 172 febrile episodes occurring during chemotherapy in 31 children and adolescents with ALL. Temperature, hematological parameters, culture findings, and antibiotic therapy were recorded. Bacteremias were classified as transmucosal or CVC-dependent. Blood cultures were positive with mucosal pathogens in 15 cases (9%) and with skin/environmental bacteria in 34 (20%). CVC-dependent infections occurred throughout the treatment phases, while transmucosal primarily during induction therapy. Transmucosal bacteremia was associated with induction therapy, leukocyte count ≤0.5 × 109/L, neutrophil count ≤0.1 × 109/L, monocyte count ≤0.01 × 109/L, and platelet count ≤50 × 109/L. Based on logistic conversion of the odds ratios for the five factors, a weight of 2 was assigned to induction therapy and leukocyte count ≤0.5 × 109/L, and a weight of 1 to the remaining three parameters. The weights were included in a simple additive score ranging from 0 to 7, which defined groups with 4%, 6%, 24%, and 40% risk of transmucosal bacteremia. CVC-dependent bacteremia was not associated with markers of poor bone marrow function. In conclusion, transmucosal bacteremia in children with ALL is related to infiltration or suppression of the bone marrow. A score reflecting the condition of the marrow can define low-risk and high-risk groups and may prove clinically useful
Appendix
Bayes theorem is stated most simply in terms of odds, the probability that a disease is present relative to the probability that it is absent, as follows:
(1) Post-test odds = pre-test odds × likelihood ratio (LR) of the observed test result,
where LR is the ratio between the frequency of the result in patients with the disease and the frequency in patients with other diseases. For example, a clinical finding occurring in 80% vs. 10% will increase odds by a factor of 8.
The following formula can be derived:
(2) Odds if test positive = odds if test negative × odds ratio (OR).
The OR is a measure of the association of the test characteristic with the disease, showing how many times odds are higher when the finding is present than when it is absent and taking the value 1 when the test is negative. OR is equal to LR for a positive result divided by LR for a negative result. In the above example, OR = (80:10)/ (20:90) = 36.
If a combination or a sequence of three tests is performed, the following formula applies, assuming that the test outcomes are independent of each other:
(3) Odds given the profile of results = odds if all tests negative × OR1 × OR2 × OR3,
i.e., odds are multiplied by the ORs for positive findings (signs of the disease).
The multiplicative formula can be converted to an additive formula by logarithmic transformation:
(4) Odds/profile of results = odds/all tests negative + log OR1 + log OR2 + log OR3.
Log OR can be taken as a measure of the weight of evidence (W) in favor of disease supplied by the sign in question and takes the value 0 when it is absent. Conventionally the natural log to base e is used. Using log to base 2 is more practical, giving W a specific meaning that is easy to understand: the number of times odds are doubled (multiplied by 2) when the sign is found. It also makes approximate estimation of W from OR easy: an OR of 36 is rapidly seen to correspond to a W between 5 (25 = 32) and 6 (26 = 64).
The sum of log ORs indicates the total weight of evidence in favor of the diagnosis that has been accumulated in the test sequence. This sum can be used as a diagnostic or predictive score. For ease of computation, weights are rounded off to the nearest lower integer (i.e., any decimals are dropped), which also serves to partially counteract interdependence between test outcomes.
The score cannot be converted to diagnostic odds, since an intercept corresponding to odds if all tests are negative is not included. This value depends on the prevalence of the disease in the test population and may be unknown. The score reflecting the total amount of evidence in favor of the diagnosis can be assumed to be independent of disease prevalence.
Scores summing diagnostic weights of clinical findings and test results are in perfect correspondence with the process of diagnosis used intuitively by most clinicians: presence of a disease is suspected, you look for evidence (signs) of the disease, weighing the importance of each piece of information, adding up the evidence, and deciding that the disease is present if the amount of evidence is sufficient.