trying to get it right?

1. Statistical challenges in hospital acquired infection data trying to get it right? INFERENCE FOR EPIDEMIC-RELATED RISK InFER2011 CONFERENCE Emma McBryde Royal Melbourne Hospital & University of Melbourne & Burnet Institute Australia March 2011

2. RMH

3. Intensive Care

4. Methicillin-resistant Staphylococcus aureus

5. HAIs Hospital acquired infections • High morbidity • High mortality • Greater duration of stay* • Greater cost • …. Large burden Engemann, J. J., Y. Carmeli, et al. (2003). "Adverse clinical and economic outcomes attributable to methicillin resistance among patients with Staphylococcus aureus surgical site infection." Clin Infect Dis 36(5): 592-598

7. Challenges in statistical inference • Serial dependence of transmission data • Data have a complex relational structure • bidirectional causality • confounding • Experimental options are limited • randomised Control Trial infeasible, unethical • may not answer any valuable question • Interrupted Time Series • has some advantages • numerous ways they can lead to incorrect inference • Partial observation

8. Challenges in statistical inference • Serial dependence of transmission data • Data have a complex relational structure • bidirectional causality • confounding • Experimental options are limited • randomised Control Trial infeasible, unethical • may not answer any valuable question • Interrupted Time Series • has some advantages • numerous ways they can lead to incorrect inference • Partial observation

9. Basic science informs transmission models Hand to hand (contact) transmission is the commonest way the Staphylococcus aureusspreads In the ICU, most of patient to patient transmission is from colonised to uncolonised patients via the hands of HCW Environmental contamination certainly plays a role in some hospital pathogens Must be considered if it is an influential transmission dynamic driver and particularly if the environment remains contaminated after the colonised patient is gone

10. Ross-MacDonald Model

12. HCW

14. Serial Dependence in data • RCT: contaminated by effect of treatment in neighbouring patients • Cluster RCT; ok but • feasibility how many similar ICUs are there? • some effects can’t be ethically compared in RCT • Hand hygiene, for example • inference can limited (variance of events >> mean) • Interrupted time series is a more convenient alternative but has potential to lead to false inference

16. ITS common mistakes • Wait until there is an epidemic • Institute numerous measures at once • Disregard • important confounding effects • that observations are partial • dependency in the data

18. Simulation SI model

22. Challenges in statistical inference • Serial dependence of transmission data • Data have a complex relational structure • bidirectional causality • confounding • Experimental options are limited • randomised Control Trial infeasible, unethical • may not answer any valuable question • Interrupted Time Series • has some advantages • numerous ways they can lead to incorrect inference • Partial observation

23. Length of stay-> Infection • Estimate effect of hospital infection on length of stay • Confounds effect of other covariates on infection

24. Many solutions • Different approaches taken • Competing risk models • Instrumental variables • Survival analysis with discharge day as the “failure event” • Infection and other known factors as covariates • If day of infection is known, can model this as a time-dependent covariate • Assumes the hazard ratio due to infection on discharge odds per day is constant over time • Data imputation (risk model for day of acquisition) if time of infection is unknown

25. Some common mistakes • Take LOS as a “time invariant” covariate or binary covariate “risk factors for the development of HA-MRSA on multivariate analysis multivariate analysis included length of stay >7 days” • Use a statistical model that allows LOS to confound other potential risk factors for HAI, such as antibiotics

26. A 0.1 A Infec Uncol 0.1 10 days Infec 50 days

27. Results of simple univariate regression

28. Hazard is not constant Marshall, C., D. Spelman, et al. (2009). "Daily hazard of acquisition of methicillin-resistant Staphylococcus aureus infection in the intensive care unit." Infect Control Hosp Epidemiol 30(2): 125-129.

30. Challenges in statistical inference • Serial dependence of transmission data • Data have a complex relational structure • bidirectional causality • confounding • Experimental options are limited • randomised Control Trial infeasible, unethical • may not answer any valuable question • Interrupted Time Series • has some advantages • numerous ways they can lead to incorrect inference • Partial observation

31. Partial observation in hospital data • Colonisation unseen • date of colonisation • Presence of colonisation • Missing data • Infections not correctly diagnosed, for example • When and from whom the transmission occurred • With perfect data we could learn a lot about transmission • Solutions? • Assume perfect data • Underestimate true effects, overestimate false effect

32. Missing data imputation • Impute missing data using the partial likelihood given the state of the model and the partial likelihood values as the sampling distribution • Calculating likelihood is difficult on observed data • observed infection times • Fully observed dataset is readily soluble using a model • actual infection times

33. RMH

34. Does detection and isolation work?

35. Study • Planned ITS at Melbourne Hospital Intensive Care Unit • Pre-intervention 15 months • standard care • add swabs form MRSA on admission, discharge and Mondays, Thursdays • no reporting of results back to treating team • no routine isolation for MRSA colonisation (unethical?) • Post-intervention 15 months • Swabs and rapid PCR, returned within hours, but only on swab days • Report results of colonised patients, within the day • Patient isolation; add in contact precautions, put sign on patient room, aprons and gloves, single room (or cohorting)

36. Complexities • Censored data; 3-4 days between swabs • Covariates • Patient factors: age, treating unit, risk of death • Ward factors: infection control compliance • Colonised patients: new versus old, antibiotic exposure

38. Statistical model: hazard of colonisation • Patient factors: antibiotic use, age, sex, admitting unit • Colonised patients, • Total number or all or nothing • New colonisation or known to be colonised • Antibiotic exposure • Ward factors: • staff ratio, • adherence to infection control precautions; • Treatment (phase of trial) • Nuisance? • Baseline hazard changes due to time since admission

39. Results: segmental regression model

40. Segmented regression • Negative binomial regression • 4 parameters • Using vague priors • Estimated expected rate at end of intervention compared with change-point • Estimated expected rate at end compared with extrapolated rate

41. Segmented regression model: posteriors for change in MRSA rates Change in MRSA incidence rate During phase 2 Change in MRSA incidence rate During phase 2

42. Back to the richer dataset

43. Making most out of the data • first attempts at incorporating full patient histories • Just concentrating on colonisation pressure (the numberof other patients on the ward who were colonised) • Reed-Frost • Greenwood • Phase • Interaction between phase and colonisation

44. Mathematical model S I S I Q

45. Method of likelihood estimation • Piecewise hazard • Time interval of one day • Hazard calculated based on patient factors, ward factors, phase of intervention and colonised patient factors • Hazard of a transmission for patient p on day t given data, augmented data (exact transmission times of patients) and parameters

46. Day of acquisition was imputed using partial likelihood:Components of the likelihood that depend on the imputed value Time

48. Method of data augmentation: MCMC • Calculate likelihood and update augmented dataset, using a Gibbs step • Recalculate likelihood update parameters, using a Metropolis, Metropolis-Hastings

49. Assumptions • Fully sensitive test • New colonisation in first 48 hours must be pre-colonised • Individual Infectiousness unchanged with time, except in presence of time dependent covariate = antibiotic use • All of these assumptions could be relaxed

50. Methods Effect of phase 2 Factors included Colonised patients phase of study Phase x colonised • Alone • On colonised S I Q background