Ok, thank you very much for your help. Actually, the current model I have built works not bad. Still, some of the parameters that have been proved to be associated with the independent variables by professional knowledge have been tested as statistically insignificant in my analysis. Therefore, for the sake of improving my model, I have come to seek help to examine if the insignificances were caused by collinearities, by the lack of samples, or by other issues (e.g. outliers). You have repeated reminded me that in the circumstance I am consulting, principal component analysis may not be the best choice. Thank you for your reminder. Actually, I have only systematically studied statistics and the mathematical knowledge it bases upon for an entire year. Therefore, I can only use SAS right now. I will try Logistic Partial Least Squares method if principal component analysis failed to tackle this problem. Thank you very much again! ... View more

Thank you very, very much, Paige, for your kind help! Actually, I have not been that familiar with principal component analysis as well as PROC PRINCOMP. Therefore, I previously thought that PROC PRINCOMP only supports principal component analysis for models whose independent variable is a continuous one. One issue that bothers me much is the lack of information on how to perform principal component analysis for logistic regression via SAS. Since SAS Help has not provided an example on how to perform principal component analysis for logistic regression and I retrieved no results for my question after browsing SAS Community Library, could you please provide some hint on the detailed procedure of doing so? Or perhaps a tutorial written by someone else? Many thanks! ... View more

Hello, Rick. Upon raising my question in early December last year, I had not revised the knowledge regarding model validation and Bootstrap resampling. After revising knowledge concerning this topic and tried to find information regarding using Bootstrap resampling to perform model internal validation, I found that the information you offered was of the greatest utility. As you have mentioned, Bootstrap resampling was not a statistical method specially designed for model validation. But currently Bootstrap resampling can be deemed as the top choice when it comes to the internal validation of prediction models. To the best of my knowledge, using Bootstrap resampling as a means of prediction model internal validation follows the following procedures: (1) Suppose that we have n observations. Use Bootstrap resampling to generate B samples, with B being the times Bootstrap resampling is performed repeatedly and each and every of the sample generated contains n observations. (2) Perform internal validation for each sample. (3) "Average" the statistics that assess the discrimination and calibration of the prediction model (e.g., C-statistic, Brier score). By the way, I am still not sure about the way to "average" the statistics (e.g., whether the final statistics of the prediction model is a weighted average of each and every of the statistics of the sample generated by Bootstrap resampling or an arithmetic average).  Therefore, after consulting SAS Help, the blog you have mentioned, and discussions posted on other communities. I have generated the SAS code to perform prediction model internal validation using Bootstrap resampling. proc surveyselect data=a out=b method=balbootstrap reps=1000;/*let B=1000 here, which is a number frequently used when it comes to Bootstrap resampling*/ run; proc hplogistic data=b; by replicate;/*instructs the SAS to perform B=1000 times of PROC HPLOGISTIC, using the observations of the same number of replicate at one time*/ model x(event='1')=y z/lackfit; partition fraction(test=0.5 validate=0);/*perform model validation*/ output out=c/allstats; run; In brief, the user should perform Bootstrap resampling prior to build and validate the prediction model. By running the SAS code mentioned above, SAS can perform Bootstrap resampling first and generate 1000 samples, then generate and perform internal validation of the prediction model sample by sample. But SAS will ultimately produce B (which equals to 1000 here) groups of statistics regarding the discrimination and calibration of the prediction model. I wonder (1) if my code were correct and (2) the means of generating "overall statistics" on the discrimination and calibration of the prediction model after finishing the process above. Thanks! ... View more

Thank you, @Ksharp, for your suggestion! ... View more

After searching for literatures in the past month, I successfully found out that there currently is a model using longitudinal data to do survival analysis. To be more explicit, a joint model of longitudinal and time-to-event data, which in many cases is abbreviated as "joint model") has been proposed, with a few monographs pertaining to this joint model having been published, including those that only introduces statistical theory and those that also introduces the method of building joint models via statistical softwares (such as Rizopoulos, D. . (2012). Joint Models for Longitudinal and Time-to-Event Data). But almost all of the literatures currently published discussing the way to build joint models via statistical softwares are performed via R. So, my question is: can I perform the building and correction of joint models via SAS? If so, via what module (PROC XXX)? Many thanks! ... View more

Thank you for the tip you have offered. Actually, I opened the editing page by following your instructions. But I had been doing something else at the same time and left the page unchanged for some time. When I edited my sentences and clicked the "Post" button, the system refused to let me change the contents I had posted, saying that I had run out of time. I tried to enter the editing page again, but failed to find the "edit reply" option this time. So I simply deleted my original reply and posted my corrected version. ... View more

Thank you for the help you have offered. In a respect, yes, what I want to put in the model is a covariate that changes over time. Actually, I have used the Cox model with time-dependent variable using PROC PHREG before. After receiving your reply, I revised the theory of the model and found that it does not fully satisfy my expectation. The reasons are as follows. First, using Cox model with time-dependent covariates is not unconditional. Violation of proportional hazards assumption of the covariate(s) is a prerequisite of using the model. Were the assumption not rejected, the Cox proportional hazards model is preferred. In this case, the change of hazard ratio over time cannot be observed. Second, explanatory variables in Cox model with time-dependent covariates are "considered" only once. To make my ideas clearer, let me compare Cox models with ANOVA of longitudinal data. Let us suppose that we are dividing a sample into two groups by their age: senior citizens and youngsters. The variable I am interested in is called "X". By using ANOVA of longitudinal data, data from each and every time point can be considered, eventually reaching conclusion like "the curve of the variable X of the population where the sample was from follows a quadratic pattern", "in the second time point, the level of X is 'statistically different' between senior citizens and youngsters", "the mean of X of the entire population in the first time point is 'statistically different' from that of the entire population in the third time point". However, Cox models with time-dependent variables cannot accommodate levels of X in each and every time point. You can put the baseline level of X when in the model, you can put the level of X when the follow-up terminates in the model, you can put whether X changes a threshold during follow-up (e.g. X rises more than 50% from baseline) in the model, but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates simultaneously. Moreover, it cannot deduce the pattern of the change in covariates as time passes by, let alone reaching conclusions like "if the level of X rises exponentially, then a patient will have an extra 50% of risk of developing stroke during follow-up, compared to those whose level of X rises in a linear pattern". It may be hard to deduce the pattern of the curve of change, but what I am actually looking for is a model that can put virtually all of the data I collected inside, just like ANOVA of longitudinal data. But since a major defect of ANOVA of longitudinal data is its inability to consider loss of follow-up, which is quite common in time-to-event data; I am looking for a "blend mixture" of methods dealing with longitudinal data (like ANOVA) and methods dealing with time-to-event data (like Cox model). I wonder if that kind of model exists and if there really is one, if I can perform this on SAS. Many thanks! ... View more

I missed a word in one sentence in the fourth paragraph. "but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates" should be "but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates simultaneously". I missed the word "simultaneously" when I was typing. ... View more

Thank you very much, Steve, for your patient explanation on the concepts. Actually, what I am wondering is something more pragmatic-how does the degrees of freedom influence the model? As you have explained, the sum of the trace of the smoothing matrices asymptotically approximates the degrees of freedom of the GAM. But as a researcher, what I am concerned is something more practical. To put my ideas in oral English, my reaction upon hearing the definition of the degrees of freedom may be like "OK, I know that. So what? Does that bring trouble to me?" （I am not a native English speaker, sorry for any offense the "So what" may cause, but it really reflects my concerns) More specifically, I am looking for a tactic or a flow chart that deals with matters regarding the degrees of freedom of GAM. I am like a tourist traveling to an alien place and has got lost. Therefore, what I badly need right now is how I could find the place I am going. I hope that somebody who is familiar with the area act as a guide to help me find the place. I am not that interested in the history or architecture of the buildings that surrounds me, at least not now. This "lost tourist" sentiment is the one I, as a researcher with not that much mathematical proficiency, am experiencing when it comes to a question I must tackle. I know it may be hard for others to do this if the person in need is too ignorant on the topic, just like it is hard for a university professor to teach a first-grade primary school student calculus. But that is the case for me. I will work hard to learn more mathematical knowledge to deal with problem on my own, but before I succeed in doing so, perhaps asking for the help of more experienced experts is the only choice left for me.   ... View more

Thank you, Rick, for kindly offering me help! Actually, I haven't heard about PROC SEVERITY before. Thank you for your suggestion. ... View more

Thank you, Sylvain, for the help you offered! ... View more

Thank you, Steve, for your kind help! ... View more

Thank you, Steve, for your kind help. Unfortunately, I had already accepted @StatDave 's reply as the solution. I am pretty new at the forum, so I do not know how I could select all of your replies as the solution to this problem. Sorry for any inconvenience it may cause. I should have selected the solution later. I noticed the description of the degrees of freedom that was given in a "matrix algebra" fashion. In SAS Help, the degree of freedom for the jth smoothing parameter is the trace of Aj(λj). But as a medical researcher who had barely received any education on matrix algebra and calculus before (in fact, I have successfully taught myself some basic linear algebra in the past few months and has already mastered the definition of the trace of matrix, but I know no more about that), I find myself still confused after consulting SAS Help, for I do not know what the trace of Aj(λj) stands for. I know that it may be too "greedy" to let statisticians express concepts in plain English (e.g. P value of a parameter means the probability that the null hypothesis is true), but unfortunately I knew nothing about the significance of the concept after consulting SAS Help alone. Now that you have given me a more clarified explanation about the concept, I have mastered more about that concept (but I am still not fully clear about the significance of the trace of the degrees-of freedom matrix and is therefore still confused by questions like "If the trace is high, what does it mean? Will it have an impact on the model? If so, what impact? How should I "maximize" the positive impacts while "minimize" the negative ones?", sorry...) I will continue to work hard on more advanced and sophisticated matrix algebra (which may seem basic to statisticians like you, of course) to understand statistics better, but it takes time to do so... Anyway, thank you for your help! ... View more