Leukocyte esterase means there's neutrophils in the urine which means there's likely a bacterial infection.
The Gram negative enterobactericeae (such as E.coli, citrobacter, klebsiella, proteus, and serratia; note that Psudomonas is not in the list) capable of transforming nitrates to nitrite (via the enzyme nitrate reductase) and therefore they give a Nitrite positive test. Importantly, this is not true with Gram positive bacteria.
Causes of false negative nitrite test:
A- Fresh urine and recently emptied bladder
B- Small number of microorganisms
C- Vitamin C supplementation
D- Low Nitrogen diet
Causes of false positive nitrite test:
A- Vaginal contamination
B- Test strips exposed to air
C- Phenazopyridine treatment
D- Gross hematuria
E- Alkaline urine
Common USMLE question; female presented with clinical picture of UTI but her Nitrite test was negative. Think Staphyloccocus saprophyticus (Gram positive) or other false negative causes mentioned above.