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Log-rank and Wilcoxon tests of equality of the survivorship functions across the two drug strata. Graphs of the Nelson-Aalen and Kaplan-Meier estimators of the survivorship function from the hmohiv data. Survival Analysis is a branch of statistics that takes care of representing development of an event during a period of time. Hazard Curve’s notion could resemble another useful banking indicator, vintage absorbing, because the concept is the same: ratio between number of “dead contract” at time t and total number of contracts.
But their trends are completely different due to 2 reasons: vintage numerator is not decreasing (“dead contracts” continue to be considered, differing from Hazard Curve), while denominator is constant (starting portfolio, differing from Hazard Curve where population is decreasing).
SAS program produces automatically graphics and statistics: this study could be useful to understand temporal trends or the way these variables influence credit risk in portfolio.
In the first case, we’ll have a model as a function of n+1 variables (time t and n significant variables), while in the other, it will depend only by time (through a method similar to linear regression). The ability of PGAMs to estimate the log-baseline hazard rate, endows them with the capability to be used as smooth alternatives to the Kaplan Meier curve. From the above definition it is obvious that the value of the survival distribution at any given time point is a non-linear function of the PGAM estimate.
The function makes use of another function, Survdataset, that expands internally the vector of time points into a survival dataset. To illustrate the use of these functions we revisit the PBC example from the 2nd part of this blog series. Subsequently, we fit the log-hazard rate to the coarsely (5 nodes) and more finely discretized (using a 10 point Gauss Lobatto rule) versions of the PBC dataset, created in Part 2. In all cases 1000 Monte Carlo samples were obtained for the calculation of survival probability estimates and their pointwise 95% confidence intervals.
STATISTICA 10 (released November 2010) features further, significant performance improvements achieved by automatically taking advantage of the 64-bit CPU technology (if available on the currently used hardware), as well as highly optimized multithreading. The input into (and output from) STATISTICA 10 has now been integrated with the fastest growing standard for data exchange and integration – Microsoft SharePoint. STATISTICA imports directly native Office 2007 and 2010 files including the formatting information.
STATISTICA Query can now retrieve data from OLAP cube providers such as the Microsoft OLE DB Provider for Analysis Services or SAP Business Warehouse. It is now easier to install and manage the STATISTICA PI Connector in STATISTICA 10; the PI connector is distributed as part of version 10, and a separate installer is no longer necessary. The STATISTICA Graph display technology has been substantially upgraded to automatically detect and take advantage of the high-performance hardware acceleration, which is now available not only in the high-end, but also in many mid-range video display controllers available in both desktop and laptop computer workstations. The resulting output is not only generated faster, but also supports more advanced smoothing and gradient display options. Also, all STATISTICA Graph windows (both stand-alone and integrated into workbooks) now feature interactive graphics controls (a bar with sliders and other controls placed at the bottom of the graph window), which enable you to interactively adjust these new display features.
You can now directly interact with the scaling on the graph by hovering the mouse pointer above the axis labels toward the end of the axis and pulling left or right to change the scaling.
You can now directly interact with the graph axis to pan to the right or the left by hovering the mouse pointer above the axis labels toward the center of the axis. STATISTICA 10 supports transparency (interactively controlled with on-screen sliders) for controlling plot areas and desaturating overlapping markers (requires Windows Vista SP 2 or Windows 7). Reference lines can be added to graphs much more easily in STATISTICA 10 through dedicated Reference Lines options, accessible in the Graph Options dialog. Text can now be interactively edited on-screen (by simply clicking and typing in the edits), without a need to open the editor window. All ribbon bars have been updated and they now include completely redesigned symbols [the traditional, pull-down menu user interface (classic menus) continues to be supported for compatibility purposes].
The STATISTICA Distribution & Simulation module and functionality introduced with version 9 has been further refined and enhanced.
Now you can find the distribution that best fits the variables, and then use that information, along with the correlation structure of the data, to simulate a specified number of cases.
Another example is the Quality by Design initiative from the US Food and Drug Administration (FDA) and the use of multivariate simulation. A comprehensive and highly scalable implementation of the Cox Proportional Hazards Models (a powerful modeling technique for lifetime data) has been added to STATISTICA 10.
Numerous minor improvements were made to the computation of descriptive statistics, often yielding significant speed improvements for large data volumes.



In STATISTICA 10, the STATISTICA MSPC Online option makes it easier to deploy multivariate analysis (PCA, PLS) models to STATISTICA Enterprise for real-time-updating, monitoring, and interactive drill-down from component scores, to contribution plots, and univariate charts.
Profit charts can now be created with STATISTICA’s Rapid Deployment of Predictive Models. ROC curves can now be created with STATISTICA’s Rapid Deployment of Predictive Models.
In response to the recent trends in text mining, where enormously large data sets are being submitted for exploration and modeling, the main computational engine of STATISTICA Text Miner has been substantially redesigned and further optimized to improve its scalability and performance.
The scorecard-builder wizard is now fully integrated into the STATISTICA solution platform and includes further improvements.
STATISTICA Scorecard is a dedicated solution for developing, evaluating, and monitoring scorecards including steps for Feature Selection, Attribute Building, Scorecard Building, Cutoff Point Selection, Reject Inference, and Population Stability. Additional significant performance improvements have been achieved for various predictive modeling algorithms when working with very large data sets. Application navigation in the STATISTICA 10 Enterprise Manager application is simpler and more efficient with the new ribbon bar. The Database Migration tool is updated for the STATISTICA 10 Enterprise database schema, and is now available directly within STATISTICA Enterprise. Enterprise Manager now allows more flexibility in defining the names of STATISTICA Enterprise configurations. Analysis Configurations that are set to auto-update will now also auto-update when run in a Web browser; the user can adjust the auto-update interval from the browser, or initiate a manual update.
Data are aggregated and cleaned and models are trained and validated using the STATISTICA Data Miner software. STATISTICA Live Score provides multi-threaded, efficient, and platform-independent scoring of data from line-of-business applications. STATISTICA Scorecard is a dedicated solution for development, evaluating, and monitoring Scorecards including steps for Feature Selection, Attribute Building, Scorecard Building, Cutoff Point Selection, Reject Inference, and Population Stability.
Some survival models have been created to produce principally 2 functions: Survival Function S(t), which represents the odds that the event would happen after time t, and Hazard Curve h(t), that describes probability of the phenomenon at time t. In concrete terms, the event “death” happens when a contract has n outstanding installments (in other terms, having current delinquency equal to n). If we assume for the shake of simplicity that there are no proportional co-variates in the PGAM regression, then the quantity modeled  corresponds to the log-hazard of the  survival function.
Consequently, the predicted survival value, , cannot be derived in closed form; as with all non-linear PGAM estimates, a simple Monte Carlo simulation algorithm may be used to derive both the expected value of and its uncertainty. This dataset is used to obtain predictions of the log-hazard function by calling the predict function from the mgcv package. STATISTICA documents can now be conveniently checked in and checked out of SharePoint from within the STATISTICA user interface. MDX queries can be generated with a drag-and-drop environment, or the MDX code can be entered directly (currently offered in Beta release). The benefits include not only a vastly improved appearance of all graphs, but also new analytic and exploratory options, such as tools to reveal hidden trends by gradually desaturating dense displays and to rotate 3D graphs vertically and horizontally. Interactive Scaling is a powerful graphical exploratory technique that enables you to reveal hidden trends by stretching or compressing the desired parts of the display.
Interactive Panning is a powerful graphical exploratory technique that assists you to explore trends hidden in the data.
Transparency control is a powerful graphical exploratory technique that enables you to reveal trends hidden in the dense concentrations of data points (especially scatterplots and scatterplot matrices generated from extremely large data sets).
Additionally, making plot areas transparent allows portions of the plot to overlap while still being visible. The graph text editor controls are still available and support the more advanced editing options. STATISTICA 10 offers a better and more efficient user interface, achieved by completely redesigned display technology as well as new iconography.
Developers can now customize the ribbon bar through API (Application Programming Interface) calls. STATISTICA 10 makes it easier to generate simulated data from a specific distribution with Design Simulation. Instead of having to wait to accrue the required data, you can fit theoretical distributions to the observed data, simulate from those distributions, and then draw conclusions based upon the simulation.
For example, the multithreading of by-group statistics, including percentile computations, has been further improved to achieve extremely fast performance for very large data volumes.


The profit chart summarizes the costs and the estimated profit for the current model, and can be used in a wide variety of data mining application as one of the tools to evaluate the models. The internal database handling procedures have been redesigned and the module can now handle extremely large data set very efficiently by extensive use of multithreading. The latter also includes the ability to generate C# code in a form that can be directly incorporated into a SQL Server user-defined function, which can then be used in a stored-procedure to score the model directly inside the database. Scorecard also supports various specialized analyses and graphical exploration tools for scoring of new cases and evaluation of model accuracy. It can be run by an administrator to copy configurations from one database to another database. This is a simpler method to create SVB Analysis Configurations, and works not only for SVB but also for R scripts. STATISTICA Live Score is STATISTICA Server software within the STATISTICA Data Analysis and Data Mining Platform. This analysis is absorbing, because when the contract goes into this bad situation, it will definitively exit from portfolio population. Note that the only assumptions made by the PGAM is that the a) log-hazard is a smooth function, with b) a given maximum complexity (number of degrees of freedom) and c) continuous second derivatives. For the case of the survival function, the simulation steps are provided in Appendix (Section A3) of our paper. Furthermore, the 95% confidence interval of each estimator (dashed lines) contain the expected value of the other estimator. To the best of our knowledge, STATISTICA 10 is currently the only analytics or data mining application that offers this (seamlessly integrated) functionality. Deployment of the survival functions on new data is available with STATISTICA Rapid Deployment.
Similar scalability and significant performance improvements have been achieved for the C&RT and CHAID algorithms. To access this new option, after creating the macro in STATISTICA, switch to the Enterprise tab and click Deploy Macro. Another way to go out from community is the censor: the contract finishes in advance or it has no outstanding installments during the period of analysis.
The following R function can be used to predict the survival function and an associated confidence interval at a grid of points. This suggests that there is no systematic difference between the KM and the PGAM survival estimators. Below is a correlation matrix for the defect rate and sample completion times for these precision parts. Side note: Interestingly, the ROC curve method has its roots in early days of radar technology, when it was used during World War II.
These can be used to predict the value of the survival function, , by approximating the integral appearing in the definition of by numerical quadrature. It accepts as arguments a) the vector of time points, b) a PGAM object for the fitted log-hazard function, c) a list with the nodes and weights of a Gauss-Lobatto rule for the integration of the predicted survival, d) the number of Monte Carlo samples to obtain and optionally e) the seed of the random number generation. This correlation is estimated based on previous processes and information about this specific process. The main advantage of this deployment method is performance gains; the inside database deployment can be executed by an order of magnitude faster, compared to external processing. Of note, the order of the quadrature used to predict the survival function is not necessarily the same as the order used to fit the log-hazard function. The means and standard deviations are estimates as well, as the production runs have not yet begun. Using the Design Simulation tool, data are simulated from the theoretical distributions for each variable, their parameter values and correlation. The correlation structure between the variables, -0.45, is maintained in the simulated data as well as the specified distributions and parameters.




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