Models for cost analysis in health care

Department of Bioinformatics Ljubljana, 1st April 2005 Models for cost analysis in health care: a critical and selective review Dario Gregori Department of Public Health and Microbiology, University of Torino Giulia Zigon, Department of Statistics, University of Firenze Rosalba Rosato, Eva Pagano, Servizio di Epidemiologia dei Tumori, Università di Torino, CPO Piemonte Simona Bo, Gianfranco Pagano, Dipartimento di Medicina Interna, Università di Torino Alessandro Desideri, Service of Cardiology, Castelfranco Veneto Hospital University of Torino Department of Public Health and Microbiology Outline • Cost-effectiveness and cost-analisys • Problems in cost analisys of clinical data – zero costs – skewness – censoring • Models for cost data • Two case studies – Diabetes costs in the Molinette cohort – COSTAMI trial Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 2 The Molinette Diabetes Cohort 3892 subjects, including all type 2 diabetic patients, resident in region Piedmont, attending the Diabetic Clinic of the San Giovanni Battista Hospital of the city of Torino (region Piedmont, Italy) during 1995 and alive at 1st January 1996. A mortality and hospitalization follow-up was carried over up to 30th June 2000. A sub-cohort of 2550 patients having at least one hospitalization in the subsequent years was also identified. Demographic data (age, sex) and clinical data relative to the year 1995 ( duration of disease or years of diabetes and number of other comorbidities) were recorded. Costs (in euros) for the daily and the ordinary hospitalizations have been calculated referring to the Italian DRG system. Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 3 The COSTAMI study • 487 patients with uncomplicated AMI were randomly assigned to three different strategies: – (132 patients) early (Day 3-5) use of pharmacological stress echocardiography and discharge on days 7-9 in case of a negative test result ; – (130 patients) pre-discharge exercise ECG, that is a maximum, symptom limited test on days 7-9, followed by discharge in case of a negative test result; – (225 patients) clinical evaluation and hospital discharge in Day 79. • The suggested strategy in case of a positive test for the strategy 1 and 2 was coronary angiography followed by ischaemia guided revascularisation (Desideri et. al, 2003). A follow up of 1 year for medical costs was carried out. Cost of hospitalization was estimated referring to mean reimbursement for the diagnosis-related groups (DRG). Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 4 The CE Incremental Ratio Goal is to compare efficacy with costs T1, T2 treatment-groups of patients C1  C 2 12  E1  E 2 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 5 The Cost-Efficacy plane ΔC R1 R1c Upper Threshold Lower Threshold R1B R2A R1A R2B R2c ΔE R2 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 6 Dominance Laska & Wakker work (late 80’s) ΔC < 0, ΔE > 0 T1 is dominant ΔC > 0, ΔE < 0 T2 is dominant ΔC > 0, ΔE > 0 T1 more effective and more costly ΔC < 0, ΔE < 0 T1 less costly but less effective If effects are equivalent or of no interest, then the approach is the analysis of costs alone Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 7 Typical goals in cost-analysis •To get an estimate of the mean costs of treating the disease –In experimental settings: to test for differences among two or more groups –In observational settings: to identify patients/structure characteristics influencing costs •To get an estimate of the expected costs, at a fixed time point, for specific types of patients (cost profiling) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 8 Typical problems in cost-analysis • • • The possible large mass of observations with zero cost; The asymmetry of the distribution, given that there is a minority of individuals with high medical cost compared to the rest of the population Possible presence of censoring: – Right censoring due to loss at follow-up or administrative rule (O’Hagan 2002) – Death censoring: dead patients are seen as lost at follow-up, to compensate for higher/earlier mortality at lower costs (Dudley et al, 1993) General requisite are – the censoring must be independent or non informative. This condition is needed because the individuals still under observation must be representative of the population at risk in each group, otherwise the observed failure rate in each group will be biased – the assumption of proportional hazards may be violated by the medical costs due to accumulation at different rates • Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 9 Proportionality on cost accumulation and censoring Etzioni, 1999 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 10 Accumulation under alternatives (without covariates) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 11 Censoring: some conflicting definitions Analysis Censoring definition Caveats Administrative Cost till death (O’Hagan, 2003) Only dead patients Cost and survival have complete are closely related follow-up history Loss at follow-up Cost till death Only dead patients Possible have complete informative follow-up history censoring Only patients Informative arrived alive at the censoring end of follow-up are uncensored Downward bias in cost estimation Death censoring Cost up to a prespecified time (Harrell, 1993) Observed costs No-censoring (actual data) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 12 Cost distribution 3000 # zero-cost patients: 2226 1500 Min 99.42 1st Q 1938 Median 3913 Mean 7278 3rd Q 9014 Max 89650 2000 0 1000 0 40000 80000 120000 0 0 500 1000 40000 80000 120000 Costs (€) full cohort Costs (€) sub-cohort with one hospitalization (no-zero) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 13 Accumulation of costs over time 50000 Cumulative cost up to time of event 40000 30000 20000 10000 0 0 1 2 Follow-up 3 4 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 14 Studies with no-zero mass • • • • • • • • • • OLS on untransformed use or expenditures OLS for log(y) to deal with skewness Box-Cox generalization Gamma regression model with log link Generalized Linear Models (GLM) Robustness to skewness Reduce influence of extreme cases Good forecast performance No systematic misfit over range of predictions Efficiency of estimator Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 15 Linear models Ordinary Least Square (OLS) model assumes the following form for the costs ci    j x j   i estimated via Gauss-Markov or ML, in this case requiring normality and constant variance on residuals To reduce skewness in the residuals, the Box-Cox transform of ci can be used ci  1 Problems: – normality is still assumed – bias is 2 log(ci )    j x j   i     j x j  i if   0 if   0 thus, heteroscedasticity, if present, raises additional efficiency and inference problems on the transformed scale   xi  xi Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 16 Log-normal models A particular case of transformation is the ln(C ij) ~ N(γj, σj2) for two treatments j=0,1 In this case, E(Cij)=exp(γj+0.5 σj2) and a test of H0: γ1 – γ2=0 is a test for the geometric means. This was argued to be less interesting for policy makers, but observing H0: exp(γ1+0.5 σ12) = exp(γ2+0.5 σ22) implies H0: γ1 – γ2=0 iff σ12= σ22 Making a test for the geometric means being equivalent to one on arithmetic means only in case of homogeneity of variances in the treatment groups Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 17 Box-Cox transform varying λ 100 200 300 400 500 600 6 8 lambda=0 (log) 10 12 0 100 200 300 400 0 0 200 400 lambda=1/2 600 100 200 300 400 500 600 0 15 20 25 lambda=1/8 30 35 0 100 200 300 400 500 26 28 30 32 34 36 lambda=1/20 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 18 The threshold-logit model Utilized to model the probability of having costs in excess of a given threshold, usually chosen as the median q2 or the third quartile q3 in the cost distribution 1 p(ci  q23 )  h 1  exp( j 1  j x j ) It does not requires normality, and can work also for very skewed costdistributions. Problems: • it does not give an estimate of the mean costs, although it estimates the covariates’ effects on costs • conclusions are sensitive to the threshold chosen, which, in addition is sample-based Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 19 GLM models To avoid bias in transforming the costs directly, since g 1 E ci   E g 1 ci    the idea is to model the transformation of the expectation g Eci     j x j Where the distribution for the response is usually taken to be Gamma() and the link function – for additive effects as the identity function I() – for multiplicative models as the log() allowing in this case back-transformation to avoid bias Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 20 GLM and QL/GEE estimate • • • • Use data to find distributional family and link Family “down weights” noisy high mean cases Link can handle linearity Note difference in roles from Box-Cox – Box-Cox power addresses mostly symmetry in error. – GLM with power function addresses linearity of response on scale to be chosen GLM/GEE/GMM modeling approach’s estimating equations • Given correct specification of E[y|x] = µ(xβ), key issues relate to secondorder or efficiency effects This requires consideration of the structure of v(y|x) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 21 Variance determination Accommodates skewness & related issues via variance weighting rather than transform/retransform methods Assumes Var[y|x] = α × [E(y|x)]γ = α × [exp(xβ)]γ For GLM, solutions are • Adopt alternative "standard" parametric distributional assumptions, – γ = 0 (e.g. Gaussian NLLS) – γ = 1 (e.g. Poisson) – γ = 2 (e.g. Gamma) – γ = 3 (e.g. Wald or inverse Gaussian) • Estimate γ via: – linear regression of log((y- µ)2) on [1, log( µ)] (modified "Park test" by least squares) – gamma regression of (y- µ)2 on [1, log( µ)] (modified "Park test" estimated by GLM) – nonlinear regression of (y- µ)2 on αµγ – Given choice of γ, can form V(x) and conduct (more efficient) second-round estimation and inference Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 22 Monte Carlo Simulation (Mannings, 2000) • Data Generation – Skewness in dependent measure • Log normal with variance 0.5, 1.0, 1.5, 2.0 • Heavier tailed than normal on the log scale • Heteroscedastic responses • Std. dev. proportional to x • Variance proportional to x • monotonically declining or bell-shaped • Gamma with shapes 0.5, 1.0, 4.0 – Mixture of log normals – Alternative pdf shapes • Estimators considered – Log-OLS with – – – – • homoscedastic retransformation • heteroscedastic retransformation Generalized Linear Models (GLM), log link Nonlinear Least Squares (NLS) Poisson Gamma Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 23 Effect of skewness on the raw scale Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 24 Effects of heavy tails on the log scale Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 25 Effects of shape for Gamma Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 26 Effect of heteroschedasticity on the log scale Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 27 Simulation summary • All consistent, except Log-OLS with homoscedastic retransformation if the log-scale error is actually heteroscedastic • GLM models suffer substantial precision losses in face of heavy-tailed (log) error term. If kurtosis > 3, substantial gains from least squares or robust regression. • Substantial gains in precision from estimator that matches data generating mechanism Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 28 The “zero” problem • Problems with standard model – OLS may predict negative values – Zero mass may respond differently to covariates – These problems may be bigger when higher mass at 0 • Alternative estimators – Ignore the problem – ln(c+k) – Tobit and Adjusted Tobit models (Heckman type model) – Two-part models Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 29 The log(c+k) solution Solution: add positive constant k to costs • Advantages – Easy – Log addresses skewness, constant deals with ln(0) • Disadvantages – Zero mass may respond differently to covariates – Many set k=1 arbitrarily – Value of k matters, need grid search for optimum – Poorly behaved (Duan 1983) – Retransformation problem aggravated at low end Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 30 Latent Variables Sometimes binary dependent variable models are motivated through a latent variables model The idea is that there is an underlying variable y*, that can be modeled as y* =  0 +x + e, but we only observe y = 1, if y* > 0, and y =0 if y* ≤ 0, Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 31 The Tobit Model Can also have latent variable models that don’t involve binary dependent variables Say y* = x + u, u|x ~ Normal(0,2) But we only observe y = max(0, y*) The Tobit model uses MLE to estimate both  and  for this model Important to realize that  estimates the effect of x on y*, the latent variable, not y Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 32 Interpretation of the Tobit Model Unless the latent variable y* is what’s of interest, can’t just interpret the coefficient E(y|x) = F(x/)x + x/, so ∂E(y|x)/∂xj =  j F(x/) If normality or homoskedasticity fail to hold, the Tobit model may be meaningless Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 33 Tobit fit to diabetes data (Intercept) Age Sex Years.Diabetes Pat.1 Log(scale) Value Std. Error z 5510.8 1474.4643 3.737 16.94 22.2739 0.761 -62.85 424.3257 -0.148 50.48 25.0192 2.018 2134.09 605.1603 3.526 9.09 0.0167 544.008 p 0.000186 0.446917 0.88225 0.043613 0.000421 0 Deviance residuals -4 -2 0 2 8.2 8.4 Linear predictor 8.6 8.8 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 34 Tobit – some notes • Only works well if dependent variable is censored Normal • Places many restrictions on parameters, error term • Hypersensitive to minor departures from normality • (Almost) never recommended for health economics Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 35 Mixed models On the basis of the basic rule of expectation one can partition E ci | x   Pci  0E ci | ci  0 Thus, expectation is splitted in two parts, 1. Pr(any use or expenditures) Full sample Use logit or probit regression 2. Level of use or expenditures Conditional on c > 0 (subsample with c >0) Use appropriate continuous model Estimates of mean costs are obtained using the Duan’s (1983) smearing estimator (mean of the exponentiated residuals) E ci | x   Fx  expx  Department of Public Health and Microbiology University of Torino 1  expln(ci )  x  n 16/04/2008 Slide 36 Diabetes two-part model Logit model Value (Intercept) -2.17186743 Age 0.02991614 Sex 0.10780381 Years.Diabetes 0.02408149 Pat.1 0.6860717 OLS model Value (Intercept) 5125.61 Age 28.02 Sex 483.89 Years.Diabetes 49.83 Pat.1 2596.41 Department of Public Health and Microbiology University of Torino Std. Error t value 0.229258 -9.473445 0.003507 8.531373 0.067253 1.602964 0.004125 5.837866 0.1064 6.448012 Std. Error t value 1428.88 21.33 413.26 24.24 566.67 3.59 1.31 1.17 2.06 4.58 16/04/2008 Slide 37 Marginal effect in the two-part model Continuous variable x P(y>0)=0.54 E(Y|Y>0)=7509.82 For year of diabetes, this means Βlogit = 0.025 Βols=49.83 Marginal effect is 208€ per year of diabetes Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 38 Weighted-regression models To adjust for censoring, the basic idea is to weight the costs for the inverse of the probability of being alive, mimicking the basic Horvitz-Thompson estimator. Thus, the Bang-Tsiatis (2000) basic estimator is 1 n iM i E (ci )   n i 1 K (Ti ) where δ is the censoring indicator, M(t) is the cumulative cost up to time t and K() is the Kaplan-Meier estimate Bang-Tsiatis (2000) proposed an improved version accounting for cost-history lost due to censoring, allowing the cost function M() and the Kaplan-Meier to be estimated in each of the K intervals, defined optimally according to Lin (1993) j 1 n K  i M i t j   M i t j 1  E ci    n i 1 j 1 K j Ti j  Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 39 Improving estimation (Jiang, 2004) Bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution. When there is light censoring on medical costs (<25%) the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy. For heavily censored cost data (censoring rate >30%) with larger sample sizes (n>200), the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 40 Censored estimation (diabetes cohort) Mean estimate Lin estimate (administrative censoring) Cox estimate (death censoring at 4 years) No-censoring estimate SE 249 5856 33896 4488.18 1249 129.44 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 41 Survival models The cost function is defined as S ci   Pci  c   (c)  f (c) (1  F (c)) and the hazard of having an “excess” of costs is modeled avoiding (Cox’s model) or not (Weibull model) the full specification of the baseline λ0  (ci  xh )  0 (c)exp(  j x j ) j 1 h to avoid assumption of proportional accumulation over time (Etzioni, 1999), an alternative model can be the Aalen additive regression (Zigon, 2005)  (ci  xh )  0    j (c) x j (c) j 1 h where the hazard rate is a linear combination of the variables x(c) and α(c) are functions estimated from the data Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 42 Survival approach – some notes Coefficients are interpretable as the “risk” of having costs greater than actual ones If proportionality does not hold, then • • • • Baseline cost-hazard with strata Partition of the costs axis Model non-proportionality by cost-dependent covariates β(c)X = βX(c) Refer to other models (accelerated failure or additive hazards) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 43 Diabetes Full cohort Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 44 Issues and models in cost-analysis Skweness Original scale models OLS (ci) Tobit/adjusted tobit GLM (gamma, loggamma) Transformed response OLS log(ci+k) Threshold logit models Survival models Parametric (Weibull) Semiparametric (Cox Proportional hazard) Mixed models Weighted regression Robis-Rotnizky 1995 Chao-Tsiatis 1997 Bang-Tsiatis 2000 X= satisfied, o = partially satisfied Department of Public Health and Microbiology University of Torino Zero-cost Censoring Mean estimation E (ci | x) X X X X X X O X X X X X O X X X O X O X X X X 16/04/2008 Slide 45 Estimates on the Molinette Cohort We compared performances of the survival models with two “benchmarks” widely (and often inappropriately) used in the literature, OLS and Threshold-logit model, using the non-zero costs cohort Sex Co-morbidities Female Male No Yes [0, 4) [4, 10) [10, 18) [18, 48] [22.1, 59.2) [59.2, 66.2) [66.2, 72.6) [72.6, 90.8] N 1270 1280 2187 363 480 594 691 785 638 638 637 637 2550 Median 3617 4290 3704 5943 3552 3728 4007 4307 2891 3684 4844 4517 3913 1 q, 3 q 1872, 8424 2047, 9700 1850, 8386 2765, 12950 1641, 8452 1922, 8009 1886, 9363 2142, 9671 1425, 7261 1872, 8121 2395, 10940 2333, 9411 1938, 9014 st rd 1 Years of Diabetes Age Overall Both normality (Shapiro-Wilk test p<0.0001) and proportionality in hazards (Grambsch-Therneau test p<0.001) assumptions refused Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 46 Covariates effects 1 Intercept OLS Logistic 2 nd Models 2 Age 53.70 (SE=18.50) 0.026 (SE=0.004) 0.017 (SE=0.004) 0.0577 (SE=0.005) -0.0196 (SE=0.001) 0.023 (SE=0.067) 3 Sex (M vs F) 829.80 (SE=360.65) 0.346 (SE=0.081) 0.233 (SE=0.093) 0.2032 (SE=0.107) -0.0938 (SE=0.03) 0.873 (SE=1.503) 4 Years of diabetes 59.02 (SE=21.36) 0.006 (SE=0.004) 0.005 (SE=0.005) 0.0439 (SE=0.006) -0.0149 (SE=0.001) -0.078 (SE=0.118) 5 N. comorbidities 2946.98 (SE=474.93) 0.539 (SE=0.110) 0.682 (SE=0.111) 1.3073 (SE=0.160) -0.4829 (SE=0.051) -1.504 (SE=0.576) q Logistic 3 q Weibull Cox Aalen rd 2155.15 (SE=1220.02) -2.102 (SE=0.283) -2.565 (SE=0.330) 3.0683 (SE=0.348) – – 4.611 (SE=5.744) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 47 Estimates of the mean Models OLS nd Logistic 2 q rd Logistic 3 q Weibull Cox Aalen Estimated expectation 7278 0.500 0.2502 8269 8717.984 8077.735 95% C.I. 7222.88, 7333.12 0.480, 0.519 0.2334, 0.2670 8154.698, 8383.302 7881.01, 9554.95 7493.737, 8661.733 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 48 Cost profiling Crude costs OLS (95% C.I.) Age=40 4421 (4365.88 4476.12) Age=40 7840 (7784.88 7895.12) Age=70 10870 (10814.88 10925.12) Age=60 9209 (9153.88 9264.12) Age=65 8246 (8190.88 8301.12) Weibull (95% C.I.) Years of Diabetes=2 236.40 (102.3689 370.4311) Years of Diabetes=10 1242 (1107.969 1376.031) Years of Diabetes=20 13347 (13212.97 13481.03) Years of Diabetes=15 4909 (4774.969 5043.031) Years of Diabetes=30 4199 (4064.969 4333.031) Cox (95% C.I.) Sex=F 1517.058 (1229.894 1804.222) Sex=F 4594.555 (3521.434 5667.676) Sex=M 16401.33 (13488.79 19313.88) Sex=F 9806.214 (8006.951 11605.477) Sex=M 8835.986 (7363.122 10308.850) Aalen (95% C.I.) Co-morbidities=0 3936.722 (3272.815 4600.629) Co-morbidities =1 5108.192 (4043.500 6172.884) Co-morbidities =1 7637.626 (6401.272 8873.980) Co-morbidities=1 6411.435 (5374.243 7448.626) Co-morbidities=0 5377.089 (4574.917 6179.260) 3388 7894 8077.704 5724.294 5527.482 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 49 Effect of covariates (Aalen model) on Λ(c) Cumulative regression function Cumulative regression function Constant 15 Age 0.05 -0.15 0 10 0 5 0 10000 20000 30000 Time 40000 50000 -0.05 10000 20000 30000 Time 40000 50000 Cumulative regression function Cumulative regression function Sex 0.5 Years.Diabetes -0.5 -1.5 0 10000 20000 30000 Time 40000 50000 -0.10 0 0.0 10000 20000 30000 Time 40000 50000 Cumulative regression function Pat.1 0.0 -2.5 0 -1.0 10000 20000 30000 Time 40000 50000 Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 50 One-year cost distribution Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 51 Cost distribution Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 52 Cost accumulation over time Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 53 Model coefficients Significant coefficients in italic Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 54 Mean cost estimates Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 55 Patient profiling Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 56 Relative accuracy Deviation (%) for the fitted model from the observed data Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 57 Remarks - I First papers appeared in late ’80 in medical literature, and a decade before in the econometrical literature Censored costs estimators appeared in Lin, 1997 and still growing research (Bang, 2002, 2003) Still high interest is in the statistical aspects of no-censoring fitting approaches (Basu, HE, 2004, Etzioni, HE, 2005) Need for a comprehensive simulation study under complex situations (censoring and non proportional accumulation in particular) Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 58 Remarks - II Modeling costs is basically an exercise of fitting adequacy and bias reduction however, it does also have strong impact on public health aspects, like economic planning and resource allocation, based on optimal prediction of future costs (patient profiling). Nevertheless, caution has to be used in choosing the model and interpreting results, which can be a finding due to an artifactual representation of real cost process, as a consequence of inappropriate assumptions made on data Department of Public Health and Microbiology University of Torino 16/04/2008 Slide 59