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Background: Previous estimates of risk of progressive multifocal leukoencephalopathy (PML) in patients with multiple sclerosis receiving natalizumab were stratified by three risk factors: anti-John Cunningham virus (JCV) antibodies in serum, previous immunosuppressant use, and treatment duration, which were estimated using population-based assumptions. We aimed to calculate PML risk estimates from patient-level risk-factor data and to stratify risk by concentrations of anti-JCV antibody in serum (anti-JCV antibody index).Methods: Data on natalizumab-treated patients were pooled from four large, observational, open-label studies: STRATIFY-2, STRATA, TOP, and TYGRIS. Data were analysed with and without imputation for missing values of anti-JCV antibody status and previous immunosuppressant use. For anti-JCV antibody-positive patients in this pooled cohort, cumulative PML risk with or without previous immunosuppressant use was estimated using Kaplan-Meier analysis. Annual PML risks (per 12 natalizumab infusions) for patients without PML in the preceding year were estimated using conditional probability based on the life table method. For anti-JCV antibody-positive patients without previous immunosuppressant use, risk estimates were further stratified using a probability distribution for anti-JCV antibody index values, separately for patients with or without PML. Anti-JCV antibody index cutoffs were selected via sensitivity and specificity assessments for identifying PML cases in an index cohort.Findings: 156 (<1%) of 37 249 patients in the pooled cohort had PML. We imputed missing values on anti-JCV antibody status (3912 patients) and on previous immunosuppresant use (544 patients) using a multiple imputation method. For anti-JCV antibody-negative patients (n=13 996), estimated PML risk was less than 0·07 per 1000 patients (95% CI 0·00-0·40). In anti-JCV antibody-positive patients (n=21 696), estimated cumulative PML probability over 6 years (72 infusions of natalizumab) was 2·7% (95% CI 1·8-4·0) in patients with previous immunosuppressant use and 1·7% (1·4-2·1) in those without. In patients without previous immunosuppressant use (n=18 616), estimated annual PML risks per 1000 patients, conditional on having no PML before that year, ranged from 0·01 (0·00-0·03) in year 1 (1-12 infusions) to 0·6 (0·0-1·5) in year 6 (61-72 infusions) for people with an index of 0·9 or less; from 0·1 (0·0-0·2) in year 1 to 3·0 (0·2-5·8) in year 6 for those with an index of more than 0·9 up to and including 1·5; and from 0·2 (0·0-0·5) in year 1 to 10·0 (5·6-14·4) in year 6 for those with an index of more than 1·5.Interpretation: Our risk estimates calculated from patient-level clinical data allow individualised annual prediction of risk of PML in patients receiving natalizumab for multiple sclerosis, supporting yearly benefit-risk re-evaluation in clinical practice. Further, our estimates are generally consistent with previously calculated estimates. Incorporating anti-JCV antibody index allows further risk stratification for anti-JCV antibody-positive patients who have not previously taken immunosuppressants.Funding: Biogen. [ABSTRACT FROM AUTHOR]