Category Archives: causal networks

Using Math to Cure Cancer

There are a couple of takes on this.

One is like “big data and data analytics supplanting doctors.”

So Dr. Cary Oberije certainly knows how to gain popularity with conventional-minded doctors.

In Mathematical Models Out-Perform Doctors in Predicting Cancer Patients’ Responses to Treatment she reports on research showing predictive models are better than doctors at predicting the outcomes and responses of lung cancer patients to treatment… “The number of treatment options available for lung cancer patients are increasing, as well as the amount of information available to the individual patient. It is evident that this will complicate the task of the doctor in the future,” said the presenter, Dr Cary Oberije, a postdoctoral researcher at the MAASTRO Clinic, Maastricht University Medical Center, Maastricht, The Netherlands. “If models based on patient, tumor and treatment characteristics already out-perform the doctors, then it is unethical to make treatment decisions based solely on the doctors’ opinions. We believe models should be implemented in clinical practice to guide decisions.”


Dr Oberije says,

Correct prediction of outcomes is important for several reasons… First, it offers the possibility to discuss treatment options with patients. If survival chances are very low, some patients might opt for a less aggressive treatment with fewer side-effects and better quality of life. Second, it could be used to assess which patients are eligible for a specific clinical trial. Third, correct predictions make it possible to improve and optimise the treatment. Currently, treatment guidelines are applied to the whole lung cancer population, but we know that some patients are cured while others are not and some patients suffer from severe side-effects while others don’t. We know that there are many factors that play a role in the prognosis of patients and prediction models can combine them all.”

At present, prediction models are not used as widely as they could be by doctors…. some models lack clinical credibility; others have not yet been tested; the models need to be available and easy to use by doctors; and many doctors still think that seeing a patient gives them information that cannot be captured in a model.

Dr. Oberije asserts, Our study shows that it is very unlikely that a doctor can outperform a model.

Along the same lines, mathematical models also have been deployed to predict erectile dysfunction after prostate cancer.

I think Dr. Oberije is probably right that physicians could do well to avail themselves of broader medical databases – on prostate conditions, for example – rather than sort of shooting from the hip with each patient.

The other approach is “teamwork between physicians, data and other analysts should be the goal.”

So it’s with interest I note the Moffit Cancer Center in Tampa Florida espouses a teamwork concept in cancer treatment with new targeted molecular therapies.


The IMO program’s approach is to develop mathematical models and computer simulations to link data that is obtained in a laboratory and the clinic. The models can provide insight into which drugs will or will not work in a clinical setting, and how to design more effective drug administration schedules, especially for drug combinations.  The investigators collaborate with experts in the fields of biology, mathematics, computer science, imaging, and clinical science.

“Limited penetration may be one of the main causes that drugs that showed good therapeutic effect in laboratory experiments fail in clinical trials,” explained Rejniak. “Mathematical modeling can help us understand which tumor, or drug-related factors, hinder the drug penetration process, and how to overcome these obstacles.” 

A similar story cropped up in in the Boston Globe – Harvard researchers use math to find smarter ways to defeat cancer

Now, a new study authored by an unusual combination of Harvard mathematicians and oncologists from leading cancer centers uses modeling to predict how tumors mutate to foil the onslaught of targeted drugs. The study suggests that administering targeted medications one at a time may actually insure that the disease will not be cured. Instead, the study suggests that drugs should be given in combination.

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Causal and Bayesian Networks

In his Nobel Acceptance Lecture, Sir C.J.W. Granger mentions that he did not realize people had so many conceptions of causality, nor that his proposed test would be so controversial – resulting in its being confined to a special category “Granger Causality.’

That’s an astute observation – people harbor many conceptions and shades of meaning for the idea of causality. It’s in this regard that renewed efforts recently – motivated by machine learning – to operationalize the idea of causality, linking it with both directed graphs and equation systems, is nothing less than heroic.

However, despite the confusion engendered by quantum theory and perhaps other “new science,” the identification of “cause” can be materially important in the real world. For example, if you are diagnosed with metastatic cancer, it is important for doctors to discover where in the body the cancer originated – in the lungs, in the breast, and so forth. This can be challenging, because cancer mutates, but making this identification can be crucial for selecting chemotherapy agents. In general, medicine is full of problems of identifying causal nexus, cause and effect.

In economics, Herbert Simon, also a Nobel Prize recipient, actively promoted causal analysis and its representation in graphs and equations. In Causal Ordering and Identifiability, Simon writes,


For example, we cannot reverse the causal chain poor growing weather → small wheat crops → increase in price of wheat by an attribution increase in price of wheat → poor growing weather.

Simon then proposes that the weather to price causal system might be represented by a series of linear, simultaneous equations, as follows:


This example can be solved recursively, first by solving for x1, then by using this value of x1 to solve for x2, and then using the so-obtained values of x1 and x2 to solve for x3. So the system is self-contained, and Simon discusses other conditions. Probably the most important is assymmetry and the direct relationship between variables.

Readers interested in the milestones in this discourse, leading to the present, need to be aware of Pearl’s seminal 1998 article, which begins,

It is an embarrassing but inescapable fact that probability theory, the official mathematical language of many empirical sciences, does not permit us to express sentences such as “”Mud does not cause rain”; all we can say is that the two events are mutually correlated, or dependent – meaning that if we find one, we can expect to encounter the other.”

Positive Impacts of Machine Learning

So far as I can tell, the efforts of Simon and even perhaps Pearl would have been lost in endless and confusing controversy, were it not for the emergence of machine learning as a distinct specialization

A nice, more recent discussion of causality, graphs, and equations is Denver Dash’s A Note on the Correctness of the Causal Ordering Algorithm. Dash links equations with directed graphs, as in the following example.

DAGandEQS Dash shows that Simon’s causal ordering algorithm (COA) to match equations to a cluster graph is consistent with more recent methods of constructing directed causal graphs from the same equation set.

My reading suggests a direct line of development, involving attention to the vertices and nodes of directed acyclic graphs (DAG’s) – or graphs without any backward connections or loops – and evolution to Bayesian networks – which are directed graphs with associated probabilities.

Here is are two examples of Bayesian networks.

First, another contribution from Dash and others


So clearly Bayesian networks are closely akin to expert systems, combining elements of causal reasoning, directed graphs, and conditional probabilities.

The scale of Bayesian networks can be much larger, or societal-wide, as this example from Using Influence Nets in Financial Informatics: A Case Study of Pakistan.


The development of machine systems capable of responding to their environment – robots, for example – are a driver of this work currently. This leads to the distinction between identifying causal relations by observation or from existing data, and from intervention, action, or manipulation. Uncovering mechanisms by actively energizing nodes in a directed graph, one-by-one, is, in some sense, an ideal approach. However, there are clearly circumstances – again medical research provides excellent examples – where full-scale experimentation is simply not possible or allowable.

At some point, combinatorial analysis is almost always involved in developing accurate causal networks, and certainly in developing Bayesian networks. But this means that full implementation of these methods must stay confined to smaller systems, cut corners in various ways, or wait for development (one hopes) of quantum computers.

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