README file: Panel Count Data Programs 1. "PanelCount" is a collection of C applications written by Ying Zhang, Piet Groeneboom, and Jon Wellner to implement the methods discussed in the technical reports Wellner, J. A. and Zhang, Y. (1998) Large sample theory for an estimator of the mean of a counting process with panel count data. Technical Report 327, Department of Statistics, Univ. of Wash. and Wellner, J. A. and Zhang, Y. (1998) A Nonparametric Maximum Likelihood Estimator for Panel Count Data Technical Report ???, Department of Statistics, Univ. of Wash. (go the the URL http://www.stat.washington.edu/jaw/RESEARCH/PAPERS/available.html for more information. 2. The model for "Panel Count Data" treated here means that: (a) For each individual $i, i =1, ... , n$ there is a counting process $N^{(i)}(t), t \ge 0$ with mean function $\Lambda (t) = EN^{(i)} (t)$. (b) For each individual $i$, there is a random integer $K^{(i)}$, the number of times at which we get to observe $N^{(i)}$. (c) For each individual $i$, there is a triangular array $T^{(i)}$ of "potential observation times"; if $K^{(i)} = k$ we observe $N^{(i)}$ at the times $T_{k1}^{(i)} , \ldots , T_{kk}^{(i)}$ . Thus we observe the counts $(N^{(i)} (T_{K^{(i)},1}^{i}) , ... , N^{(i)} (T_{K^{(i)},K^{(i)}}^{i}))$ . We assume that $N^{(i)}$, $K^{(i)}$, $T^{(i)}$ are independent. (c) The observations for the $i$th individual consist of $X_i = ( K^{(i)} , T_{K^{(i)},1}^{(i)} , ... , T_{K^{(i)},K^{(i)}}^{(i)} , (N^{(i)} (T_{K^{(i)},1}^{i}) , ... , N^{(i)} (T_{K^{(i)},K^{(i)}}^{i})) $. The object is to estimate the unknown mean function $\Lambda $ nonparametrically. The estimators computed in the program are the Non-Parametric Maximum Pseudo Likelihood Estimator (NPMPLE) and the Non-Parametric Maximum Likelihood Estimator (NPMLE) under the assumption that the underlying counting process for each individual is a Non-homogeneous Poisson process. 2. Methods available in the program: CM (convex minorant, one-step) algorithm for the NPMPLE. ICM algorithm; the iterative convex minorant algorithm as described in Wellner and Zhang (1998). ?? One can choose to do Pseudo MLE or Full MLE in the menu ?? "Algorithms". The default is set on the Pseudo MLE estimator. ?? One can also switch between the two by the keyboard equivalents ?? "command-1" and "command-2". 3. Data generated in the application: Two types of counting processes are currently generated in npmle.sim.exe and npmple.sim.exe: --- Counts generated from Poisson(2t). --- One jump counting process with the distribution function of the on jump time distributed as exp(0.2). Users are allowed to select: (1) Sample size (<5000). (2) Maximum number of looks (K) on each process. (The number of looks is generated by Unif[1,2,...K]) (3) The time interval, [a,b] in which the observation times are generated. (The observation time points are generated by taking the order statistics of $K^{(i)}$ random observation from unif[a,b]). (4) Data type: Poisson or One Jump Counting process. One can choose to use input files or to generate random samples by the menu "Samples". 4. User-specified data is allowed; input files should be in the form as the follows index time count 1 0.2 0 1 2.3 2 1 3.2 1 2 2.3 1 2 4.5 2 2 6.3 4 2 7.2 0 3 0.4 1 3 4.5 3 . . . . . . . . . where index stands for the counting process for the index i individual's counting process, and where the count in the third column is the number of events which happened since the last observation time (the increment of the counting process). 5. For running one of the algorithms on either input files or randomly generated data, press "command-r" or use the menu "Run". 6. Output: (i) values of the Fenchel conditions and log-likelihood for successive iterations of the algorithm. For more information on the Fenchel conditions, see the reference above: Groeneboom and Wellner (1992). The iterations can be stopped at any time (particularly needed for the EM algorithm) by pressing "command-period" (="apple-period"). The iterations are stopped automatically if the criteria are zero in 6 decimals. The text output of the iterations can be saved if desired, the name can be specified in the dialog box that will appear. The value of the estimator at the end of the iterations is written to a file called "NPMLE" giving the NPMLE at the jump times (not at all observations). (ii) a plot of the estimated d.f., which can be saved as a PICT file via the menu or "command-s". The PICT file can be opened by SimpleText or applications like Adobe Illustrator or Mathematica. One can exit the plot by pressing return or clicking the "go-away" box. Because the output files are large for big n, usually bigger than 32K, the program uses a freeware replacement of the Apple toolbox Text Edit routines. At the time that the program was written (1996), the toolbox Text Edit routines still had the limitation of 32K. Since in Mac OS 8.1 SimpleText still refuses to open files bigger than 32K, we fear that the situation in this respect still has not changed, which is an absolute disgrace in this day and age! The replacement of the Apple toolbox Text Edit routines is called TE32K.c and was written by Roy Wood and Michael J. Lowe, whose contribution (given unknowingly) is gratefully acknowledged. The text files that are produced can be read by any editor that can handle text files bigger than 32K (in which case they cannot be read by SimpleText!), like BBEdit or Textures. 7. For more information on Macintosh compatible C source code for this program, please contact either Ying Zhang or Jon Wellner. (Copyright issues are involved in making source code available.) Written by Ying Zhang, Jon Wellner, and Piet Groeneboom, June 1998.