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ISCB 2014 Vienna, Austria • Abstracts - Oral Presentations 73Wednesday, 27th August 2014 • 14:00-15:30 Monday25thAugustTuesday26thAugustThursday28thAugustAuthorIndexPostersWednesday27thAugustSunday24thAugust C40.3 A unified approach for testing goodness of fit in binary, multinomial, and ordinal logistic regression models MW Fagerland1 , DW Hosmer2 1 Oslo University Hospital, Oslo, Norway, 2 University of Massachusetts, Amherst, United States   Evaluating goodness of fit is an important step in the assessment of the adequacy of a regression model. Logistic regression models are popular because of their availability in software packages and the fact that the ex- ponential form of the regression coefficients can be interpreted as odds ratios. For binary logistic models, the Hosmer-Lemeshow (HL) test is in widespread use. The test is based on a strategy of sorting and grouping the observations according to their estimated probabilities of event. The test statistic is the Pearson chi-squared statistic on a contingency table where the groups form the rows and the observed and estimated frequen- cies form the columns. The HL approach for constructing a goodness-of-fit test can also be used for the multinomial logistic model and several ordinal logistic models: the proportional odds, adjacent category, and constrained continuation-ratio models. The required modifications of the HL test from the binary case to the multinomial and ordinal cases involve finding a suitable function of the estimated probabilities to use for sorting the observations and deter- mining the appropriate degrees of freedom for the chi-squared reference distribution. Simulations pit the HL tests against other goodness-of-fit tests and show that the HL tests are capable of detecting several different types of poorly fit models and can be recommended with moderate and large sample siz- es.The recommendation comes with a warning: no single test can provide a complete assessment of model fit. Ideally, a battery of tests and case- wise diagnostic tools should be used.   C40.4 Nonparametric estimation of covariate-specific summary indices of ROC curves through regression models JC Pardo-Fernández1 , EM Molanes-López2 , E Leton3 1 Universidade de Vigo, Vigo, Spain, 2 Universidad Carlos III de Madrid, Madrid, Spain, 3 UNED, Madrid, Spain   The receiver operating characteristic (ROC) curve is a statistical tool of ex- tensive use in diagnostic studies. The ROC curve allows for the visualiza- tion of the effect of different thresholds of the diagnostic variable in terms of sensitivity (probability of classifying a diseased individual as diseased) and specificity (probability of classifying a healthy individual as healthy). Some summary indicators, such as the area under the curve (AUC) or the Youden index, are often employed to describe the main features of the ROC curve. In many studies, a covariate is available along with the diagnostic variable. The behaviour of the ROC curve may depend on the values of the covari- ate, and therefore it is interesting to study the impact of the covariate on the covariate-specific ROC curve. This work will be devoted to the study of a nonparametric estimatior of the covariate-specific ROC curve and its as- sociated summary indices, specifically, the covariate-specific AUC and the covariate-specific Youden index. The incorporation of the information of the covariate over the diagnostic variable is modelled through nonpara- metric location-scale regression models.   C40.5 On bias of measures of explained variation for survival data J Stare1 , D Maucort Boulch2 , N Kejžar1 1 Faculty of Medicine, Ljubljana, Slovenia, 2 University of Lyon, Lyon, France   Papers evaluating measures of explained variation, or similar indices, in- variably use independence from censoring as the most important crite- rion. And they invariably end up suggesting that some measures meet this criterion, and some don’t, leading to a conclusion that the first are better than the second. As a consequence, users are offered measures that can- not be used with time-dependant covariates and effects, not to mention extensions to repeated events or multi state models. We explain in this paper that the above mentioned criterion is of no use in studying such measures, since it simply favours those that make an im- plicit assumption of a model being valid everywhere. Measures not mak- ing such an assumption are disqualified, even though they are better in every other respect. We show that if these, allegedly inferior, measures are allowed to make the same assumption, they are easily corrected to sat- isfy the `independent-from-censoring´ criterion. Even better, it is enough to make such an assumption only for the times greater than the last ob- served failure time τ. Which, in contrast with the `preferred´ measures, makes it possible to use all the modelling flexibility up-to τ, and assume whatever one wants after τ. As a consequence, we claim that measures being proffered as better in the existing reviews, are exactly those that are inferior.   C41 Survival analysis II C41.1 Conference Award for Scientists Kernel estimation of hazard function for orthopedic data J Zelinka1 , I Horová1 , S Katina1 , I Selingerová1 1 Masaryk University, Faculty of Science, Brno, Czech Republic   The hazard function is an important tool in survival analysis and reflects the instantaneous probability that an individual will die within the next time instant. The hazard function can depend on any covariates as age, gender, etc. In the present paper the kernel estimators of the hazard func- tion and of the conditional hazard function are discussed. These methods are applied to the real data from Slovak Arthroplasty Register about implants of an artificial hip joint replacement implement- ed in all 40 orthopaedic and traumatology departments in the Slovak Republic (coverage of 99.9%) with a maximum duration of follow-up of ten years from Jan 1 2003 to Dec 31 2013. The set of 35 182 operations with 665 implant failures is stratified based on types of fixation, diagnosis, and gender. The hazard function conditioned on age in years is calculated for pre-specified data-subsets and visualized as color-coded surfaces. These results will lead to an improvement of the quality of care for patients after artificial joint replacements.

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