[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119590-en":3,"doc-seo-119590-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119590,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Likelihood contrasts - a machine learning algorithm for binary classification of longitudinal data","Likelihood contrasts (LC) is introduced as a robust machine learning method for biomedical longitudinal data when observation times are unaligned across individuals. LC performs binary classification by combining linear mixed models for modelling with maximized log-likelihoods for decision making. The approach was evaluated against widely used classifiers and longitudinal regression baselines across four simulated and three real datasets, where LC achieved the highest accuracy in simulations and demonstrated reliable performance on real studies. The method is computationally efficient and straightforward to use.","[www. nature.com/scientificreports](www. nature.com/scientificreports)  \nopen  \nLikelihood contrasts: a machine learning algorithm for binary classification of longitudinal data  \nRiku Klén1,2,3, Markku Karhunen1,3 & Laura L. elo1*  \nMachine learning methods have gained increased popularity in biomedical research during the recent years. However, very few of them support the analysis of longitudinal data, where several samples are collected from an individual over time. Additionally, most of the available longitudinal machine learning methods assume that the measurements are aligned in time, which is often not the case in real data. Here, we introduce a robust longitudinal machine learning method, named likelihood contrasts (LC), which supports study designs with unaligned time points. Our LC method is a binary classifier, which uses linear mixed models for modelling and log-likelihood for decision making. To demonstrate the benefits of our approach, we compared it with existing methods in four simulated and three real datasets. In each simulated data set, LC was the most accurate method, while the real data sets further supported the robust performance of the method. LC is also computationally efficient and easy to use.  \nMany biomedical studies consist of longitudinal data, i.e. data with multiple samples for each individual, taken at different time points. Here, we define longitudinal data so that the covariates are measured repeatedly, but not necessarily at even intervals or at the same time points for each individual. This type of data turns out to yield substantial modelling challenges. For example, the most widely used binary classifiers, such as Lasso1, random forest2 and artificial neural networks3, are not designed for this type of data. Therefore, they cannot fully benefit from the repeated measurements. Moreover, those machine learning methods which support longitudinal data typically assume that the time points are aligned between the individuals4.  \nMany statistical methods are available for longitudinal data, especially within the discipline of econometrics5, but these methods typically also assume the time points to be aligned and evenly spaced. The only main exception suitable for biomedical data is the linear mixed-effects model (LME) and its modifications6–9, which support data with non-aligned time points. However, the LME model is a regression model for a continuous response variable. Many different solutions to turn the model into binary classifier can be envisaged10, 11. Here, we present one such solution: the method of likelihood contrasts (LC). We introduce this novel method because it exploits all longitudinal data in classification instead of a single time point or average. LC is fast and easy to calculate, and secondly, our results show its good performance in simulated and real data sets alike.  \nWe take the univariate LME as the starting point and use it as a building block for our LC algorithm. Briefly, we fit LMEs using a standard software package (lme4 version 3.1–131.1) 12, and then use their maximised log-likelihood functions for inference. We assign each sample to the group where the log-likelihood changes most favourably. Thus, this method amounts to a binary classifier. However, contrary to many other machine learning methods, LC is computationally very efficient, easy to implement and the need to fine-tune parameters is minimal. We provide an open-source implementation of LC at [https://elolab.utu.fi/software/](https://elolab.utu.fi/software/) .  \nIn this paper, we demonstrate the performance of LC in four simulated and three publicly available real datasets. In each data set, we test the discriminatory power of LC regarding the case-control status of the study subjects and compare it to that of widely used machine learning and predictive algorithms, including Lasso1, random forest (RF)2, support vector machines (SVM)13, neural networks (NN)3, and LME regression models. Two of the real d","cbCairvpBpWpHotc","https://ap.wps.com/l/cbCairvpBpWpHotc","pdf",1844896,1,10,"English","en",105,"# Methods\n## Likelihood contrasts\n## Model comparison and evaluation","[{\"question\":\"What problem does likelihood contrasts (LC) solve in longitudinal biomedical data?\",\"answer\":\"LC targets binary classification when individuals have repeated measurements but observation times are unaligned. It avoids relying on time alignment assumptions common in existing longitudinal machine learning methods.\"},{\"question\":\"How does LC make its classification decision?\",\"answer\":\"LC fits two separate linear mixed models for case and control groups, computes maximized log-likelihoods, and assigns each individual to the group where the log-likelihood contrast favors that group.\"},{\"question\":\"How was LC evaluated in the study?\",\"answer\":\"Performance was tested on four simulated datasets and three publicly available real datasets. LC was compared with standard machine learning classifiers such as Lasso, random forest, SVM, and neural networks as well as LME regression baselines.\"}]","Likelihood contrasts - a machine learning algorithm for binary classification of longitudinal data | PDF",1785725158,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"likelihood-contrasts-a-machine-learning-algorithm-for-binary-classification-of-longitudinal-data","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/likelihood-contrasts-a-machine-learning-algorithm-for-binary-classification-of-longitudinal-data/119590/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does likelihood contrasts (LC) solve in longitudinal biomedical data?","Question",{"text":75,"@type":76},"LC targets binary classification when individuals have repeated measurements but observation times are unaligned. It avoids relying on time alignment assumptions common in existing longitudinal machine learning methods.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does LC make its classification decision?",{"text":80,"@type":76},"LC fits two separate linear mixed models for case and control groups, computes maximized log-likelihoods, and assigns each individual to the group where the log-likelihood contrast favors that group.",{"name":82,"@type":73,"acceptedAnswer":83},"How was LC evaluated in the study?",{"text":84,"@type":76},"Performance was tested on four simulated datasets and three publicly available real datasets. LC was compared with standard machine learning classifiers such as Lasso, random forest, SVM, and neural networks as well as LME regression baselines.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]