Identifying unusual performance in Australian and New Zealand intensive care units from 2000 to 2010
© Solomon et al.; licensee BioMed Central Ltd. 2014
Received: 6 March 2014
Accepted: 14 April 2014
Published: 22 April 2014
The Australian and New Zealand Intensive Care Society (ANZICS) Adult Patient Database (APD) collects voluntary data on patient admissions to Australian and New Zealand intensive care units (ICUs). This paper presents an in-depth statistical analysis of risk-adjusted mortality of ICU admissions from 2000 to 2010 for the purpose of identifying ICUs with unusual performance.
A cohort of 523,462 patients from 144 ICUs was analysed. For each ICU, the natural logarithm of the standardised mortality ratio (log-SMR) was estimated from a risk-adjusted, three-level hierarchical model. This is the first time a three-level model has been fitted to such a large ICU database anywhere. The analysis was conducted in three stages which included the estimation of a null distribution to describe usual ICU performance. Log-SMRs with appropriate estimates of standard errors are presented in a funnel plot using 5% false discovery rate thresholds. False coverage-statement rate confidence intervals are also presented. The observed numbers of deaths for ICUs identified as unusual are compared to the predicted true worst numbers of deaths under the model for usual ICU performance.
Seven ICUs were identified as performing unusually over the period 2000 to 2010, in particular, demonstrating high risk-adjusted mortality compared to the majority of ICUs. Four of the seven were ICUs in private hospitals. Our three-stage approach to the analysis detected outlying ICUs which were not identified in a conventional (single) risk-adjusted model for mortality using SMRs to compare ICUs. We also observed a significant linear decline in mortality over the decade. Distinct yearly and weekly respiratory seasonal effects were observed across regions of Australia and New Zealand for the first time.
The statistical approach proposed in this paper is intended to be used for the review of observed ICU and hospital mortality. Two important messages from our study are firstly, that comprehensive risk-adjustment is essential in modelling patient mortality for comparing performance, and secondly, that the appropriate statistical analysis is complicated.
KeywordsHierarchical models Hospital comparisons Intensive care performance Multiple comparisons Risk-adjusted mortality Seasonal effects Variance components
Comparing the performance of intensive care units (ICUs) is important for health care provider accountability and for ensuring public safety. In this paper, we compare ICUs contributing to the Australian and New Zealand Intensive Care Society (ANZICS) Adult Patient Database (APD) from 2000 to 2010. The purpose of the comparison is to identify ICUs with unusual performance as characterised by risk-adjusted in-hospital mortality. Such a characterisation of performance is not without controversy, but we take the pragmatic view that comparisons of mortality will be undertaken, and that it is important the analysis be conducted in a statistically rigorous manner. In-hospital mortality is the only widely available mortality measure for the ANZICS APD, as population mortality databases are maintained by separate State and Territory jurisdictions in Australia and they are not currently linked. In any case, the analysis of 30-day mortality or patient survival is controversial in this context, [1, 2].
The ANZICS APD is one of the largest binational databases in the world. In 2010, 124 of the eligible 157 ICUs contributed to the database which currently contains more than one million intensive care patient submissions collected from ICUs in Australia and New Zealand. The ANZICS APD has been collecting data since 1987 on physiological and chronic health status variables at the point of ICU admission and over the subsequent 24 hours, . The specific variables are primarily relevant to the computation of hospital mortality probabilities for existing algorithms such as APACHE II and III, and SAPS II, [4–6]. Mortality outcome is recorded at ICU and hospital discharge.
Ours is the first comprehensive, risk-adjusted analysis of mortality in the ANZICS APD covering such an extended period and provides the most complete picture to date of critical care outcomes in Australia and New Zealand. Patient mortality is modelled using a risk-adjusted three-level hierarchical logistic regression model which clusters patients within years and years within ICUs. Hierarchical models are also known as multilevel models and the three levels of the hierarchy are: between ICUs (level three), between years within ICUs (level two, treating years as independent random effects, which we refer to as ICU-years) and between patients within ICU-years within ICUs (level one). Such models capture the hierarchical nature of the data and the fact that responses within clusters are correlated. The use of hierarchical models for the assessment of health care provider performance has been recommended as best practice [7–9], and is standard for the analysis of hospital outcomes data [10–12]. However, hierarchical models appear much less frequently in the critical care literature and ours is the first application of a three-level hierarchical model to ICU comparisons. Furthermore, our statistical approach using a three-stage analysis includes the estimation of a null distribution to describe ‘usual performance’. Our analysis extends the work of Ohlssen et al. from a Bayesian to a classical (frequentist) framework using empirical Bayes models, and from a two-level to a three-level hierarchical model and application to longitudinal data, .
We have chosen the standardized mortality ratio (SMR) as the performance indicator on which to base the ICU comparisons. For each ICU, this is the ratio of the observed to expected number of deaths, where a value of one implies that the two numbers are in agreement under the assumptions of the model. The SMR is widely used in applications of provider comparisons and in mortality studies generally, and has the attractive feature of incorporating both the observed and expected numbers of deaths. Typically when hierarchical models are used to characterise mortality, providers are compared using random effects estimators. These estimators provide shrinkage towards the overall mean and can be of substantial benefit when incorporating low-volume providers in the analysis. However, the estimates are also potentially biased, . Our study assumes a minimum annual volume of 150 patient admissions to each ICU in each year, thereby avoiding instability of estimation issues or potential bias due to excessive shrinkage. Bias can also arise when patient characteristics are associated with provider attributes and we expand on this further in the Discussion. Our overall statistical approach avoids problems apparently associated with simplistic (direct and indirect) casemix adjustment methods  and mis-interpretation which can arise when comparing hospitals using funnel plots (again under artificially abridged assumptions) with small observed numbers of deaths . Recent statistical work in the social sciences has shown that large numbers are required for valid inference at each level of the hierarchies modelled, , a condition our study of ICU performance in the ANZICS APD more than satisfies.
Patient data from 2000 to 2010 were extracted from the ANZICS APD, [3, 19]. The initial dataset contained 858,758 admissions from 1,354 ICU-year units from 161 ICUs. Exclusions were patients with: unknown hospital outcome (18,244); ICU length-of-stay (LOS) ≤4 hours (9,607); age <16 years (14,752); coronary artery bypass graft (CABG) (81,166); ICU admissions for the same and separate hospital admissions (123,151); and missing Acute Physiology and Chronic Health Evaluation (APACHE) III score, age, ventilation status, diagnostic category, or ICU source (40,507). Patients with CABG and uncomplicated acute myocardial infarction are not considered in the current dataset, and the exclusion of patients with LOS ≤ 4 hours was an original APACHE III requirement . To ensure stability of estimation, ICU-year units with fewer than 150 complete patient records were excluded; this corresponds to three or fewer admissions per week to an ICU in a year. The final dataset consisted of records for 523,462 patients from 984 ICU-year units from 144 ICUs. Access to the data was granted by the ANZICS Database Management Committee in accordance with standing protocols. The research was exempt from formal University of Adelaide Human Research Ethics Committee approval according to the Australian National Statement on Ethical Conduct in Human Research, 2007 and local hospital (The Queen Elizabeth Hospital, Adelaide) Human Research Ethics Committee approval was waived.
The performance indicator is the natural logarithm of the standardised mortality ratio (log-SMR), where the SMR is the ratio of the observed to expected numbers of in-hospital deaths. We prefer the log to the raw SMR, as it provides confidence intervals with better coverage probabilities and is approximately normally distributed, [14, 20].
Identifying unusual ICUs
Stage 1: Risk-adjusted model
The dataset was split randomly into 80% training and 20% test datasets for model building. Owing to the (very long) computing time required to fit three-level models to such a large dataset, the initial model selection was conducted using one-level models and the logistic command in Stata™ (Version 12, 2011, ). Continuous (fixed) covariates included APACHE III score, year of admission, and annual ICU volume. The inclusion of Year as a fixed effect enabled adjustment for a (systematic) trend in the response over time. The patient severity score APACHE III is the third revision of the Acute Physiology and Chronic Health Evaluation (APACHE III) score, which is computed using the patient’s worst values during the first 24 hours post-admission to the ICU, . The APACHE III score is the most referenced patient severity of illness score in the clinical literature and is an important predictor of mortality, . It has a range 0-299, and in the original paper, , the mean score was 50. A severely-ill patient would have an APACHE III score of between 50-70. It is an important (although not the sole) measure of patient illness, since it combines several physiological and chronic health status variables. Our previous work fitting random intercept and random coefficient logistic regression models to the ANZICS APD demonstrated that APACHE III is the most important predictor of mortality, [14, 19]. In the present study, APACHE III was fitted as a non-linear term (in particular, a degree four polynomial) with the inclusion of a random slope term for APACHE III as this significantly improved the goodness of fit. Additional random terms were not included to avoid increasing the complexity of the model and the associated computing time. Age was fitted as a grouped variable with six bins, which enabled better prediction for very elderly patients. Fitting splines or fractional polynomials, , did not improve the fit of age or APACHE III. Descriptors of ICU-admission primary-organ-system dysfunction and patient surgical status (i.e., patient diagnostic category) were generated by consolidating the diagnostic categories of the APACHE III algorithm. ICU-level variables locality and hospital level were also included in the model. The discrete explanatory variables were fitted as indicator variables. Increased mortality during the winter months and at weekends has previously been observed in the ANZICS APD [24, 25]. This was modelled here by sine and cosine trigonometric terms representing yearly and weekly periods and initially included harmonic terms at six months and 3.5 days, calculated from calendar day of admission, [26, 27]. However, the harmonic terms at six months and 3.5 days were not significantly associated with mortality and were dropped from the final model. Interactions between the periodic terms and locality were also included in the model, together with other clinically meaningful two-way interactions. Continuous explanatory variables were centred for model fitting and variables were removed stepwise if the estimated p-value was >0.05, excepting the pairs of sine and cosine terms which were always retained together in the model. Annual volume was retained in the final model because it is important, and Year squared was included to allow for a (systematic) nonlinear trend over time. Fitted models were compared using AIC (for nested models only), BIC, area under the ROC curve, and the Hosmer-Lemeshow test statistic (the latter used with caution in this large dataset, ). Binned residual plots were used to assess both the covariate modelling and the overall model fit and to help select a final model, .
where X itjk contains the observed (fixed-effects) explanatory variables for patient j, U it is the random intercept for year t in ICU i, U i is the random intercept for ICU i, and U i1 is the random coefficient for APACHE III score. The indices range from i = 1,…,144 ICUs, t = 1,…,n i years within ICU i, and j = 1,…,n it patients within ICU-year t. The level-three (ICU-level, or between ICUs) random intercepts are assumed to be normally distributed with zero mean and variance ; the APACHE III slopes are also assumed normally distributed with variance , and there is a component of covariance, σ I,A P , assumed at level three. The level-two (ICU-year, or between years within ICUs) random effects are assumed to be independently normally distributed with variance , independently of the level-three random effects. The level-three random intercepts represent (potentially unknown) differences between ICUs and the random slopes for APACHE III allow the dependence of in-hospital mortality on patient severity to vary between hospitals. The component of covariance accommodates potential dependence between the intercept and APACHE III slope terms within ICUs. The normality assumptions for the random effects were assessed using estimated gradient graphs, .
where I is the indicator function. This gave an approximate p-value for each ICU under the nominal null hypothesis that the SMR is equal to one. Under this null hypothesis, we would expect the simulated number of deaths to exceed the observed number in approximately half of the simulations, . Thus p-approx measures how well the estimated model predicts the observed number of deaths for each ICU. We chose a nominal 20% significance level for this first stage of screening for potential outliers. When p-approx < 0.1, an ICU was assessed to be potentially over-performing (i.e., has low mortality), and when p-approx > 0.9, a site was potentially under-performing (i.e., has high mortality). It may be helpful to plot a histogram of the p-values, or transformed p-values, to detect the presence of outliers. If the variability amongst the providers is very small with no obvious outliers, one might decide on a much lower nominal level of significance such as 5% or to proceed with a different analysis for comparison, or no analysis.
Stage 2: A null model
The Stage 2 model was estimated by excluding the potentially unusual ICUs identified in Stage 1, then re-fitting the final model. This provided a null ‘reference’ distribution for describing usual ICU performance. Log-SMRs and their variances were again estimated for each ICU, according to the methods described in  and Additional file 1. The estimation of the variances of the log-SMRs is somewhat technical, but an outline of the calculations to obtain the approximate variance of the log-SMR for ICU i in year t is given in Additional file 1. The uncertainty in estimating the expected number of deaths for each ICU is therefore accounted for in our analysis, whereas this is usually treated as given. Treating the estimated expected number of deaths as a constant in the calculations under-estimates the true variance of the log-SMRs, so our analysis offers an advantage over what is usually done. Note that the potentially unusual ICUs were modelled without random effects, so for each unusual ICU, a usual ICU was randomly selected and the random effects predictions from that ICU used to calculate the expected number of deaths for the potentially unusual ICU. Extensive sensitivity analyses demonstrated that randomly selecting the random effects from the ‘usual’ distribution in this way gave the same results as stratifying on ICU level, for example.
Stage 3: Unusual ICUs
The funnel plot was constructed as described previously, . ICUs with log-SMRs lying outside the funnel were identified as performing unusually, with either higher or lower mortality than usual. All ICUs have been randomly allocated a random identity number which is shown for those lying outside the thresholds. Confidence intervals controlling the false coverage-statement rate (FCR) at 5% were also constructed for the ICUs identified as unusual, . The FCR is the expected proportion of false discovery rate (FDR) selected  confidence intervals which do not cover their true parameter values. FCR is a property of the set of confidence intervals not covering zero and does not involve confidence intervals for the non-selected parameters. However, all confidence intervals may be plotted together by applying visual impact to distinguish the two sets of intervals (selected and non-selected) and we use bold lines to distinguish the FDR-selected intervals. The remaining intervals have FCR coverage of at most 0.05 for all parameters because the FCR offers marginal coverage of at least 0.95. We further evaluated the performance of the outlying ICUs by posing the question: is the worst ICU worse than expected, given it has arisen from the null (usual) predictive distribution, ? This question is answered by simulating the distribution of the predicted true worst number of deaths and comparing it to the observed worst number of deaths.
Characteristics of the 523,462 ANZICS APD patients analysed
APACHE III score
ICU mortality (%)
Hospital mortality (%)
ICU hospital level
New South Wales
Australian Capital Territory
Characteristics of ANZICS APD study patients by year, 2000-2010
Hosp. admit year
Hosp. mort. (%)
ICU mort. (%)
APIII mean (sd)
Age mean (sd)
ICU characteristics by year and geographical locality of Australia, or New Zealand
Hosp. admit year
Identifying unusual ICUs
Stage 1: Risk-adjusted model
Components of variance and covariance from the Stage 1 and Stage 2 models
Cov(ICU-level intercept, APIII)
Hospital level and locality for the 27 ICUs identified as unusual at Stage 1
New South Wales
New South Wales
New South Wales
New South Wales
Australian Capital Territory
New South Wales
2001, 04, 08-10
New South Wales
New South Wales
New South Wales
New South Wales
Stage 2: A null model
The concern is that the potentially unusual ICUs are inflating the estimates of the random effects distribution at Stage 1. The 27 potentially unusual ICUs identified in Stage 1 were therefore excluded from the Stage 2 analysis, which resulted in n=430,049 patients in 816 ICU-years from 117 ICUs. The three-level hierarchical logistic regression model was then re-fitted to the reduced dataset. This resulted in good agreement between the fixed effects parameter estimates from both Stages as shown in Additional file 2. However, the variance component estimate corresponding to the Stage 2 ICU-level random intercept was reduced by more than half from Stage 1, as shown in Table 4. The ICU-year intercepts variance component estimates were little changed between the two stages, and similarly for the between-ICU APACHE III slope variance components estimates. The estimated component of covariance between the ICU-level intercept and slope was slightly reduced at Stage 2, and remained rather small (-0.022, Table 4). This indicates that the ICU-level random intercepts are representing unexplained differences between ICUs, whereas differences between-years within-ICUs are similar across sites. The approach used here to attenuate the effects of the potentially unusual ICUs differs from that in  where all ICUs contributed to the estimation of the fixed effects component of the model, and has been taken primarily for computational reasons. As discussed below, the results here are in excellent agreement with those obtained previously.
Stage 3: Unusual ICUs
Seven ICUs were identified with unusually high mortality by our analysis. ICUs 16,44 and 93 have been previously identified in an analysis of data from 2009-2010, , and the present longitudinal study confirms those findings. ICU 81 was also identified with unusually high mortality in , and was labelled as potentially unusual at Stage 1. We note that ICUs 16,44 and 93 are in private hospitals in Queensland. A total of 23% of patient admissions were to private sector ICUs which cover most areas of care (medical and surgical) and includes end-of-life care. A recent study comparing conventional risk-adjusted fixed and random effects models analysing the 2009-2010 data was unable to detect any outliers (Moran and Solomon, preprint submitted for publication, 2014).
The ‘Swiss cheese’ nature of the ANZICS APD is apparent from Figure 6, which shows that several ICUs contribute data in some years only. This effect is partly compounded by the minimum 150 patient-volume requirement, and we discuss below issues of missing data and data quality with regard to the particular ICUs identified as unusual. We note that it is by no means assured that the 144 ICUs analysed in this study are representative of the entire adult ICU experience in Australia and New Zealand, and it is likely that the ability to sustain the effort of continuous (and complete) contribution is concentrated in larger, well-resourced ICUs. However, smaller peripheral units are encouraged to participate in the database, and future longitudinal analyses using an instrumental variables approach to participation will help address this issue. Generally, problems with missing data in large observational databases have received a great deal of attention in the literature, and multiple imputation (MI) is the primary technique for handling missing data. However, little of this literature is directed towards MI in the context of hierarchical models, and by way of a caution, a recent simulation study by Twisk et al. showed that MI applied to mixed models may be misleading, . Given these observations, the complete case-record analysis we have undertaken is a reasonable way to proceed as a first analysis.
ICUs with unusual casemix, and data quality
ICU 140 had a very low proportion of ventilated patients compared to comparable ICUs during the three years it contributed data to the ANZICS APD (3.2% versus 32.4%, p-value < 0.0001), and the lowest proportion of ventilated patients of all ICUs in 2000 and 2001. Given ventilation is associated with increased mortality risk, the large log-SMR is associated with the small proportion of ventilated patients. This (historical) outcome could be related to data quality: since ventilation is only inferred from documentation of ventilation at the time an arterial blood gas is taken, there may have been ventilated patients with no blood gas measurement, but we do not know. ICU 54 had the highest proportion of deaths in each year in South Australia. This ICU had a significantly higher proportion of non-surgical patients compared to the other two South Australian tertiary ICUs (72.5% versus 51.1%, p-value < 0.0001) and a higher proportion of deaths amongst non-surgical patients (30.0% versus 22.1%, p-value < 0.0001). However, ICU 54 also had a high proportion of patients with missing APACHE III scores during 2004-2006, and the log-SMRs in 2004 and 2005 were high compared to later years, as shown in Figure 6. ICU 134 also had a high proportion of patients with missing APACHE III scores. It is possible that poor record keeping and high mortality are common causes, for example, of poor ‘process of care’. No association between mortality and important covariates, including APACHE III, could be established at these sites however. Of the remaining ICUs identified with poor performance in our analysis, none had identifiable anomalous casemix, missing data, or other data quality issues. ANZICS CORE analyses outcomes data from ICUs contributing to the APD in a given year using a simple predictive mortality model, based exclusively on the APACHE III algorithm. ICUs identified as outliers by this process are normally followed up according to the Outlier Management Policy .
The variance component estimates demonstrate that the staged modelling approach has appropriately accommodated the effects of outliers. The reduction in the Stage 2 ICU-level variance component indicates that the presence of potentially unusual ICUs is inflating the variance component at Stage 1. This component of variance represents differences between ICUs, and the fact that we cannot explain the high mortality for all of the identified ICUs by unusual casemix or other known factors, indicates that there are unexplained differences in mortality between ICUs. At Stage 1, the estimated component of correlation is -0.52. The direct interpretation of this modest correlation is that lower mortality ICU-intercepts are associated with higher APACHE III slopes. This observation is reflecting the fact that the overall average APACHE III score in this dataset increased over the decade at the same time as mortality decreased; a correlation of 0.8 was observed in a normal model of APACHE III on year. Note too that the fitted model, which was estimated using xtmelogit in Stata, allowed for an unstructured covariance matrix and would have detected any important correlations in the random effects distribution. We also note that random effects models are often self-consciously deployed in the literature, and variance components typically treated as nuisance parameters, which they are not here.
Using our Stage 1 mixed model, we have demonstrated for the first time yearly and weekly seasonal effects across Australian jurisdictions. Since it was not the primary purpose of the present paper to study seasonal effects, we have restricted our attention to a comparison conditional on the model baseline variables and baseline patient diagnostic category (i.e., respiratory disease) which is of interest in its own right. Note that the mortality cycles estimated refer to the day of admission, so for example, NSW, the ACT, the NT, VIC, SA and WA all have higher mortality associated with weekend admissions. Tasmania is the only state which has a statistically significant different peak on Wednesday but we do not have an explanation for this yet. New Zealand also has a weekly Wednesday admissions peak, but this was not statistically significantly different from NSW. Interestingly, New Zealand is geographically most similar in climate to Tasmania. Not surprisingly, peak mortalities also tend to occur in the southern hemisphere winter months, which are June, July and August in south-eastern Australia. The tropical Northern Territory has little or no apparent annual seasonal respiratory cycle, and Queensland has a much earlier annual peak mortality. Queensland is a large geographically-diverse state, being tropical in the north and temperate (similar to NSW) in the south. The ACT on the other hand, is located inland, and elevated. It has an annual peak mortality which is later in the year (in August) than anywhere else in Australia.
The ICUs identified with unusual performance may merit consideration in any future analysis, albeit the observation period studied here is historical. The distinct seasonal mortality patterns identified across regions in Australia undoubtedly warrant further study, from both policy and planning viewpoints. The statistical methods proposed are intended for reviewing and monitoring the performance of ICUs contributing to the ANZICS APD but are appropriate for application to comparable mortality databases. Two key messages from our analysis are firstly, that comprehensive risk-adjustment for patient casemix and factors such as hospital level and locality is essential, and secondly, that the appropriate statistical analysis is complicated.
This research was supported by Australian Research Council Discovery Project DP110102028 awarded to PJS and JLM. JK thanks the University of Adelaide, where she was employed when the work was undertaken.
- Schoenfeld D: Survival methods, including those using competing risk analysis, are not appropriate for intensive care unit outcome studies. Crit Care. 2006, 10: 103-View ArticlePubMedGoogle Scholar
- Freemantle N, Richardson M, Wood J, Ray D, Khosla S, Shahian D, Roche W, Stephens I, Keogh B, Pagano D: Weekend hospitalization and additional risk of death: an analysis of inpatient data. J R Soc Med. 2012, 105: 74-84. 10.1258/jrsm.2012.120009.View ArticlePubMedPubMed CentralGoogle Scholar
- Stow PJ, Hart GK, Higlett T, George C, Herkes R, McWilliam D, Bellomo R: Development and implementation of a high-quality clinical database: the Australian and New Zealand Intensive Care Society Adult Patient Database. J Crit Care. 2006, 21: 133-41. 10.1016/j.jcrc.2005.11.010.View ArticlePubMedGoogle Scholar
- Knaus WA, Draper EA, Wagner DP, Zimmerman JE: APACHE II: a severity of disease classification system. Crit Care Med. 1985, 13: 818-29. 10.1097/00003246-198510000-00009.View ArticlePubMedGoogle Scholar
- Knaus WA, Wagner DP, Draper EA, Zimmerman JE, Bergner M, Bastos PG, Sirio CA, Murphy DJ, Lotring T, Damiano A: The APACHE III prognostic system. Risk prediction of hospital mortality for critically ill hospitalized adults. Chest. 1991, 100: 1619-36. 10.1378/chest.100.6.1619.View ArticlePubMedGoogle Scholar
- Le Gall JR, Lemeshow S, Saulnier F: A new simplified acute physiology score (SAPS II) based on a European/North American multicenter study. JAMA. 1993, 270: 2957-63. 10.1001/jama.1993.03510240069035.View ArticlePubMedGoogle Scholar
- Ash AS, Feinberg SE, Louis TA, Norman SL, Stukel TA, Utts J: Statistical Issues in Assessing Hospital Performance. Commissioned by the Committee of Presidents of Statistical Statistical Societies for the Centers for Medicare and Medicaid Services (CMS), January 27, 2012. [http://www.cms.gov/Medicare/Quality-Initiatives-Patient-Assessment-Instruments/HospitalQualityInits/Downloads/Statistical-Issues-in-Assessing-Hospital-Performance.pdf],
- Gallagher MP, Krumholz HM: Public reporting of hospital outcomes: a challenging road ahead. MJA. 2011, 194: 658-60.PubMedGoogle Scholar
- Goldstein H, Spiegelhalter DJ: League tables and their limitations: statistical issues in comparisons of institutional performance. JRSS A. 1996, 159: 285-443.Google Scholar
- DeLong ER, Peterson ED, DeLong DM, Muhlbaier LH, Hackett S, Mark DB: Comparing risk-adjustment methods for provider profiling. Statist Med. 1997, 16: 2645-64.View ArticleGoogle Scholar
- Jones HE, Spiegelhalter DJ: The identification of ‘unusual’ health-care providers from a hierarchical model. Am Stat. 2011, 65: 154-63. 10.1198/tast.2011.10190.View ArticleGoogle Scholar
- Normand S-LT, Shahian DM: Statistical and clinical aspects of hospital outcomes profiling. Stat Sci. 2007, 22: 206-26. 10.1214/088342307000000096.View ArticleGoogle Scholar
- Ohlssen DI, Sharples L, Spiegelhalter DJ: A hierarchical modelling framework for identifying unusual performance in health care providers. JRSS A. 2007, 170: 265-90.Google Scholar
- Kasza J, Moran JL, Solomon PJ: Evaluating the performance of Australian and New Zealand intensive care units in 2009 and 2010. Statist Med. 2013, 13: 3720-36.View ArticleGoogle Scholar
- Kalbfleisch JD, Wolfe R: On monitoring outcomes of medical providers. Stat Bio. 2013, 5: 286-302. 10.1007/s12561-013-9093-x.View ArticleGoogle Scholar
- Pouw ME, Peelen LM, Lingsma HF, Pieter D, Steyerberg E, Kalkman CJ, Moons KGM: Hospital standardized mortality ratio: consequences of adjusting hospital mortality with indirect standardization. PLOS One. 2013, 8 (4): e59160-10.1371/journal.pone.0059160. doi:10.1371/journal.pone.0059160View ArticlePubMedPubMed CentralGoogle Scholar
- Seaton SE, Barker L, Lingsm HF, Steyerberg EW, Manktelow BN: What is the probability of detecting poorly performing hospitals using funnel plots?. BMJ Qual Saf. 2013, doi:10.1136/bmjqs-2012-001689Google Scholar
- Bryan ML, Jenkins SP: Regression analysis of country effects using multilevel data: a cautionary tale. ISER Working Paper Series. 2013-14, Colchester, University of Essex. [https://www.iser.essex.ac.uk/publications/workingpapers/iser/2013-14],Google Scholar
- Moran JL, Bristow P, Solomon PJ, George C, Hart G: Mortality and length-of-stay outcomes, 1993-2003 in the binational Australian and New Zealand intensive care Adult Patient Database. Crit Care Med. 2008, 36: 46-61. 10.1097/01.CCM.0000295313.08084.58.View ArticlePubMedGoogle Scholar
- Hosmer DW, Lemeshow S: Confidence interval estimates of an index of quality performance based on logistic regression models. Statist Med. 1995, 14: 2161-72. 10.1002/sim.4780141909.View ArticleGoogle Scholar
- StataCorp: Stata™: Release 12. 2011, College Station, TX, USA: StataCorp LP, Statistical SoftwareGoogle Scholar
- Iezzoni L: The risks of risk-adjustment. JAMA. 1997, 278: 1600-7. 10.1001/jama.1997.03550190064046.View ArticlePubMedGoogle Scholar
- Sauerbrei W, Royston P, Binder H: Selection of important variables and determination of functional form for continuous predictors in multivariable model building. Stat Med. 2007, 26: 5512-8. 10.1002/sim.3148.View ArticlePubMedGoogle Scholar
- Moran JL, Solomon PJ: Conventional and advanced time series estimation: application to the Australian and New Zealand Intensive Care Society Adult Patient Database 1993-2006. JECP. 2011, 17: 45-60.Google Scholar
- Bhonagiri D, Pilcher DV, Bailey MJ: Increased mortality associated with after-hours and weekend admission to the intensive care unit: a retrospective analysis. MJA. 2011, 194: 287-92.PubMedGoogle Scholar
- Diggle PJ: Time Series: a Biostatistical Introduction. 1990, Oxford: Oxford University PressGoogle Scholar
- Stolwijk AM, Straatman H, Zielhuis GA: Studying seasonality by using sine and cosine functions in regression analysis. J Epid Comm H. 1999, 53: 235-38. 10.1136/jech.53.4.235.View ArticleGoogle Scholar
- Paul P, Pennell ML, Lemeshow S: Standardizing the power of the Hosmer-Lemeshow goodness of fit test in large data sets. Stat Med. 2013, 32: 67-80. 10.1002/sim.5525.View ArticlePubMedGoogle Scholar
- Gelman A, Hill J: Data Analysis Using Regression and Multilevel/hierarchical Models. 2007, Cambridge: Cambridge University PressGoogle Scholar
- Verbeke G, Molenberghs G: The gradient function as an exploratory goodness-of-fit assessment of the random-effects distribution in mixed models. Biostat. 2013, 14: 477-90. 10.1093/biostatistics/kxs059.View ArticleGoogle Scholar
- Benjamini Y, Yekutieli D: False discovery rate-adjusted multiple confidence intervals for selected parameters. JASA. 2005, 100: 71-93. 10.1198/016214504000001907.View ArticleGoogle Scholar
- Benjamini Y, Hochberg Y: Controlling the false discovery rate: a practical and powerful approach to multiple testing. JRSS B. 1995, 57: 289-300.Google Scholar
- Harrison DA, Lertsithichai P, Brady AR, Carpenter JR, Rowan K: Winter excess mortality in intensive care in the UK: an analysis of outcome adjusted for patient casemix and unit workload. Int Care Med. 2004, 30: 1900-7. 10.1007/s00134-004-2390-6.View ArticleGoogle Scholar
- Twisk J, de Boer M, de Vente W, Heymans M: Multiple imputation of missing values was not necessary before performing a longitudinal mixed-model analysis. J Clin Epi. 2013, 66: 1022-28. 10.1016/j.jclinepi.2013.03.017.View ArticleGoogle Scholar
- ANZICS CORE: ANZICS Centre for Outcome and Resource Evaluation. 2011, Outlier management policy at: [http://www.anzics.com.au/core/core-management-governance],Google Scholar
- The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2288/14/53/prepub
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