Memphis, Tennessee

BACKGROUND: High throughput metabolomics makes it possible to measure the relative abundances of numerous metabolites in biological samples, which is useful to many areas of biomedical research. However, missing values (MVs) in metabolomics datasets are common and can arise due to both technical and biological reasons. Typically, such MVs are substituted by a minimum value, which may lead to different results in downstream analyses. RESULTS: Here we present a modified version of the K-nearest neighbor (KNN) approach which accounts for truncation at the minimum value, i.e., KNN truncation (KNN-TN). We compare imputation results based on KNN-TN with results from other KNN approaches such as KNN based on correlation (KNN-CR) and KNN based on Euclidean distance (KNN-EU). Our approach assumes that the data follow a truncated normal distribution with the truncation point at the detection limit (LOD). The effectiveness of each approach was analyzed by the root mean square error (RMSE) measure as well as the metabolite list concordance index (MLCI) for influence on downstream statistical testing. Through extensive simulation studies and application to three real data sets, we show that KNN-TN has lower RMSE values compared to the other two KNN procedures as well as simpler imputation methods based on substituting missing values with the metabolite mean, zero values, or the LOD. MLCI values between KNN-TN and KNN-EU were roughly equivalent, and superior to the other four methods in most cases. CONCLUSION: Our findings demonstrate that KNN-TN generally has improved performance in imputing the missing values of the different datasets compared to KNN-CR and KNN-EU when there is missingness due to missing at random combined with an LOD. The results shown in this study are in the field of metabolomics but this method could be applicable with any high throughput technology which has missing due to LOD.

Background High throughput technology makes it possible to monitor metabolites on different experiments and has been widely used to detect differences in metabolites in many areas of biomedical research. Mass spectrometry has become one of the main analytical technique for profiling a wide array of compounds in the biological samples. Extracting relevant biological information from large datasets is one of the challenges. Missing values in metabolomics datasets occur widely and can arise from different sources, including both technical and biological reasons. Mostly the missing value is substituted by the minimum value, and this substitute may lead to different results in the downstream analysis. Different methods tend to give different results. In this study we summarize the statistical analysis of metabolomics data with no missing values and with missing values. With the missing values, we compare the different methods and examine the outcomes based on each method.

A growing body of literature suggests that there is an optimal size for software components. This means that components that are too small or too big will have a higher defect content (i.e., there is a U-shaped curve relating defect content to size). The U-shaped curve has become known as the "Goldilocks Conjecture." Recently, a cognitive theory has been proposed to explain this phenomenon and it has been expanded to characterize object-oriented software. This conjecture has wide implications for software engineering practice. It suggests 1) that designers should deliberately strive to design classes that are of the optimal size, 2) that program decomposition is harmful, and 3) that there exists a maximum (threshold) class size that should not be exceeded to ensure fewer faults in the software. The purpose of the current paper is to evaluate this conjecture for object-oriented systems. We first demonstrate that the claims of an optimal component/class size (1) above) and of smaller components/classes having a greater defect content (2) above) are due to a mathematical artifact in the analyses performed previously. We then empirically test the threshold effect claims of this conjecture (3) above). To our knowledge, the empirical test of size threshold effects for object-oriented systems has not been performed thus far. We performed an initial study with an industrial C++ system and repeated it twice on another C++ system and on a commercial Java application. Our results provide unambiguous evidence that there is no threshold effect of class size. We obtained the same result for three systems using four different size measures. These findings suggest that there is a simple continuous relationship between class size and faults, and that, optimal class size, smaller classes are better and threshold effects conjectures have no sound theoretical nor empirical basis.

Much effort has been devoted to the development and empirical validation of object-oriented metrics. The empirical validations performed thus far would suggest that a core set of validated metrics is close to being identified. However, none of these studies allow for the potentially confounding effect of class size. We demonstrate a strong size confounding effect and question the results of previous object-oriented metrics validation studies. We first investigated whether there is a confounding effect of class size in validation studies of object-oriented metrics and show that, based on previous work, there is reason to believe that such an effect exists. We then describe a detailed empirical methodology for identifying those effects. Finally, we perform a study on a large C++ telecommunications framework to examine if size is really a confounder. This study considered the Chidamber and Kemerer metrics and a subset of the Lorenz and Kidd metrics. The dependent variable was the incidence of a fault attributable to a field failure (fault-proneness of a class). Our findings indicate that, before controlling for size, the results are very similar to previous studies. The metrics that are expected to be validated are indeed associated with fault-proneness.

A practical application of object oriented measures is to predict which classes are likely to contain a fault. This is contended to be meaningful because object oriented measures are believed to be indicators of psychological complexity, and classes that are more complex are likely to be faulty. Recently, a cognitive theory was proposed suggesting that there are threshold effects for many object oriented measures. This means that object oriented classes are easy to understand as long as their complexity is below a threshold. Above that threshold their understandability decreases rapidly, leading to an increased probability of a fault. This occurs, according to the theory, due to an overflow of short-term human memory. If this theory is confirmed, then it would provide a mechanism that would explain the introduction of faults into object oriented systems, and would also provide some practical guidance on how to design object oriented programs. The authors empirically test this theory on two C++ telecommunications systems. They test for threshold effects in a subset of the Chidamber and Kemerer (CK) suite of measures (S. Chidamber and C. Kemerer, 1994). The dependent variable was the incidence of faults that lead to field failures. The results indicate that there are no threshold effects for any of the measures studied. This means that there is no value for the studied CK measures where the fault-proneness changes from being steady to rapidly increasing. The results are consistent across the two systems. Therefore, we can provide no support to the posited cognitive theory.