On Sugon, McNamara and Intengan (2012): A Case for the RH Bill

On 26 March 2012, Sugon, McNamara and Intengan of the Ateneo de Manila University web-published a paper on Estimating abortion rates from contraceptive failure rates via risk compensation: a mathematical model, which puts forward a theoretical model linking the abortion rate and contraception (more on this later). More technically inclined readers can download the pdf here. It would probably have gone unnoticed, but Mr. Antonio Montalvan III of the Inquirer featured it in his column and sung it high praises. Bottom line, it presents a mathematical argument for not passing the controversial RH bill, at least at this time, because there is a chance that contraceptives can actually increase the abortion rate.

The paper presents a model for the number of abortions as a function of six determinants: how frequently a woman has intercourse, when she begins sexual activity, cumulative time she is pregnant (infertile time on top of the monthly infertile period), cumulative time she is breastfeeding (they assume a woman is infertile while she is breastfeeding), the contraceptive failure rate, and the risk compensation factor. Notwithstanding the other problems with the paper, this post will just take a look at their model and the conclusions they gather from that.

The Model in Brief (no pun intended)

In a nutshell, their contraception-to-abortion argument hinges on the risk compensation mechanism they set forth in their paper. They argue, using maths, that women (curiously, they make no reference to men in their paper) will be more sexually active if contraception is available (economists will easily recognise this as the moral hazard problem). Sugon, McNamara and Intengan begin by building a model of a woman's likely number of abortions (they couch the discussion in individual language, although I would presume they are referring to population averages) in equation (10):

Na = (1/s)[10(ns - np - nb)(1 - ce)]

where Na = number of abortions with contraception (this is actually the number of pregnancies, which the authors say may be aborted; later on this is just the number of abortions); s = interval between sexual intercourse in weeks (the lower this number, the more frequently she is having sex); ns = number of "womb years" (a proxy for fertile period depending on time being sexually active, so the earlier a woman starts having sex the higher this number); np = number of womb years a woman is pregnant; nb  = number of womb years a woman is breastfeeding (she is assumed to be infertile during this time, even though LAM doesn't apply to all breastfeeding mothers); and ce = the success probability of contraception, with 0 < ce < 1, so (1 - ce) is the contraceptive failure rate.

The authors then lay out their model of risk compensation in section 5 of their paper (page 7). The crucial link between contraceptive use and frequency of sexual intercourse can be seen in equation (12) under hypothesis 3:

s = k(1 - ce)^m

where k is a constant and the other variables are as earlier defined. In describing Hypothesis 3 and equation (12), the authors say that "we propose that a woman's intercourse interval s is proportional to the mth power of the contraceptive failure rate 1 - ce" (page 7). The boundary of equation (12) for s is then analysed when ce approaches zero, or (1 - ce) approaches one. This is done to examine the frequency of sexual intercourse when contraceptives fail miserably such that it is as if one is not using contraceptives at all. They find in equation (14) that

lim (ce -> 0) s = k = s0

where s0 = interval between sexual intercourse in the absence of contraception, or when ce = 0.  Thus, equation (12) becomes equation (15):

s =  s0(1 - ce)^m

Plugging in equation (15) into (10) and doing some algebra, they derive an equation linking the number of abortions with contraceptive use in equation (18):

Na = Na0 / (1 - ce)^(m - 1)

where Na = number of abortions with contraception; Na0 = number of abortions without contraception; and ce and m are as before. One can see that

Na'(ce) = Na0(m - 1) / (1 - ce)^m

so that the sign of  Na'(ce) depends on the sign of (m - 1): any value of m > 1 and we get Na'(ce) > 0, so contraceptive use will increase abortions. In other words, the way contraceptives affect the abortion rate depends on the magnitude of m.

The s(ce) Function and the RH Bill

The value of m is crucial for the paper because this is used to argue that the country should hold off on passing the RH bill.  Since contraceptives could reduce, increase, or have no impact on abortions depending on the value of m, they argue that the government should hold off on the RH bill pending an estimation of m. After all, if m happens to be empirically greater than unity then the RH bill will increase abortions, rather than decrease them as the bill's supporters argue. Other than the obvious line of critique against this argument (risk compensation also applies to seat belts and health insurance), the problem is that there is no explanation for the functional relationship between sexual frequency and contraceptive effectiveness.

Their argument against the RH bill hinges on their arbitrary definition of the risk compensation mechanism as seen in equation (12), which introduces m and leads to equation (18). It is arbitrary because it is neither derived from other equations, the outcome of an optimisation exercise, nor taken from previous literature. While the other parts of the model were derived from other equations, they just assumed a functional form for s(ce) and went from there. There is also no reason, theoretical or empirical, to say that the risk compensation mechanism should follow the power law.

That said, their incorporation of the risk compensation mechanism is a valid exercise: it is reasonable to say that intervals between sexual intercourse could be inversely proportional to the effectiveness of contraception, especially those who do not wish to have children at the moment. Looking at equation (12), one can see that the risk compensation mechanism, through the s(ce) function, needs to satisfy two conditions:

Condition 1: s'(ce) < 0

Condition 2: lim (ce -> 0) s(ce) = k = s0

Taken together, the two conditions state that (1) contraceptive effectiveness is inversely related to the intercourse interval and (2) if contraceptives are totally ineffective s(ce) should revert to the no-contraception case of s0. This would be a more general formulation of their Hypothesis 3.

Using their exact same model, but being just as arbitrary as the authors in defining s(ce), one can define the risk compensation mechanism as

s*(ce) = k / (1 + ce)

which one can easily verify satisfies the two conditions above. This then becomes

s*(ce) =  s0 / (1 + ce)

after the limits operation. The equation implies that, on average, women (men are not part of the authors' model) will be twice as sexually active with 100% effective contraception as they are without them. Plugging this into equation (10) gives us the following function for the number of abortions:

Na* = (1/s0)[10(ns - np - nb)(1 - ce^2)] = Na0(1 - ce^2)

So how does increasing contraceptive effectiveness affect the number of abortions relative to the no-contraceptives situation? One can easily see that

Na*'(ce) = - 2Na0ce < 0

so promoting contraceptive use will unambiguously reduce the number of abortions. In other words, using their same model while slightly changing the risk compensation function, but keeping the same properties, one can arrive at a totally opposite conclusion: approve the RH bill now because it will reduce abortions. In fact, if contraceptives were 100% effective there would be zero abortions!

So What's the Point?

The Sugon, McNamara and Intengan paper essentially sets out a thought experiment with the aim of bolstering the argument that contraceptives can increase, rather than decrease, the number of abortions. However, what we show here is that the driver of their thesis-- their formulation of the risk compensation mechanism-- is an arbitrary assertion meant to arrive at their desired conclusion. There was no attempt to buttress this formulation through a risk minimisation (or sexual utility maximisation) operation, or to generalise the functional form of the mechanism. What we show here is that, using essentially their same model and being as arbitrary as the authors, one can do a similar thought experiment and arrive at a totally different conclusion and policy prescription. Upon closer examination, the authors' conclusions are really just assertions dressed in the language of mathematics. Take out those assertions and the paper falls apart.

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[Postscript: As a critique, it would have been easy to just point out their unfounded assumptions, especially in equation (12), and do away with the paper, but it would be unfair to the authors. I really admire their effort to further their side through the use of hard logic-- this is really much better than the fear mongering and name-calling we have been hearing from other anti-RH campaigners. A bit more of this, and a lot less of Sotto's unoriginal dramatics, would be much appreciated.]

Why is the Catholic Church so stubborn on RH? Really?

If you know me then you know where I stand on reproductive health issues. This post is not to defend the Catholic Church's stand on artificial contraception, but to explain why she takes such a strong stance against it. I also hope to clarify some misconceptions on the Church's stance. If you wish to engage the Church on this issue you need to first understand where she's coming from and what motivates her. Maybe it will also help you evaluate the (f)utility of debating with the Church on this issue in the first place. This post is written with a lay (even irreligious) audience in mind, so I will dispense with the Bible quotes and Magisterial references. 

It is no secret that the Catholic Church believes in the existence of God who created the universe. Duh. But corollary to this belief in a sentient and benevolent God is the assumption that everything He created has a purpose: nothing is random in God's creation therefore everything has to have been made for a purpose. So the Sun isn't just an amalgamation of cosmic particles brought together by gravity and heated by nuclear fusion; it was created to eventually sustain life on Earth. This belief system applies to all of creation, including the human body. Everything in the human body from the heart to the toenail you clip off has a purpose willed and designed by God. So far so good. No problem.

The problem begins when we start talking about the reproductive system. The Catholic Church believes that the reproductive system-- not just the womb and testes but also the pleasure-giving glans penis and clitoris-- have a dual purpose: to express mutual love and to procreate. The reproductive system was created to enable humans to express their mutual love for each other through sexual intercourse and to encourage procreation. Now take note of the "and". The Catholic Church's issue with contraception begins when that "and" becomes an "or". Artificial contraception, by removing any possibility of procreation, turns sexual intercourse into an exclusively love-making pleasurable affair. This, believe the Church, is contrary to God's will and purpose for creating the reproductive system.

But how about natural family planning? Or when one spouse is infertile due to natural causes or a needed medical operation (e.g., hysterectomy due to a tumour)? Won't sexual intercourse in those situations be divorced from the procreation purpose too, and therefore against God's will? Well, no. Natural family planning, by virtue of being natural, is part of God's plan: in God's wisdom He recognised the need for families to plan and space their offspring, but also recognised the need for spouses to make love, so He provided windows of opportunity to make love while vastly minimising the chance of conception. As for infertility due to natural causes or a needed medical operation, well, God had reasons for giving someone that affliction, and it definitely wasn't His intention to prevent spouses from expressing their love for each other. So in these cases any dichotomy between love-making and procreation was not man's will but God's, which is fine for the Church.

So the Church's real problem with artificial contraception is that man is divorcing love-making with procreation. In the case of artificial contraception, man wants the love-making part while eliminating the procreation part. Note that the same problem arises when man wants the procreation part while eliminating the love-making part, thus the Church's similar opposition to in-vitro fertilisation. Man cannot, should not, separate the expression of mutual love from the possibility of procreation. God can do it, but not man.

It is thus easy to see why no amount of medical, social, economic, democratic, etc. arguments or evidence will change the Church's position on artificial contraception-- they all pale in comparison to God's will and purpose for creating the reproductive system. Practical circumstances may mitigate the gravity of going against God's will through the use of artificial contraception (or in-vitro fertilisation, for that matter), but it is a sin nonetheless and bishops will be remiss in their duty if they tolerate it. So changing their stance on artificial contraception will require a change in their understanding of God's purpose for creating the reproductive system. It hasn't changed in 2,000 years, so it is quite unlikely that it will change any time soon.

Sex, Schism, and Excommunication

Seems religions are exceptionally prominent in the news these days. The Pope in Australia, the Anglican Church in the brink of a schism, Islamophobia in America and Europe.

Today was expecially abuzz with these news. Here are three articles on sex, schism and excommunication that range from the disturbing to the absurd:

Abortion: don't even think about it.

Gay bishop: to beat it or not to beat it?

Outside the white shirt and black necktie there is no salvation.

Crime and the withdrawal of human rights

By now you've probably heard about the horrendous crime that happened in Laguna. We hear about violent crime everyday and mostly we are desensitised to them, taking refuge in abstraction, anonymity, and distance. But the events in Laguna really jar the psyche-- the magnitude of violence, the cold calculation of the murderers, the everydayness of the victims.

My condolences to the families of the victims-- their cries for vengeance are understandable and, I say, justified. As for the perpetrators, they should be punished in the most painful and protracted way possible.

That said, let me discuss human rights, which I'm sure the perpetrators will seek refuge in if they are caught and found guilty. Of course the accused, who are presumed innocent, should be accorded due process and all the protection under the law. But what do we do with those who are guilty of the most violent and heinous of crimes? What basis is there to say that the death penalty should be off the table? Generally, what rights of criminals, who despite their actions remain biologically human, may or may not be withdrawn?

Human rights are the set of rights and freedoms that everyone is endowed with by virtue of being born human. No one is born without human rights, and no action is required to acquire these rights. Everyone is entitled to the protection of their human rights, and no one may deny others these rights. However, one can do actions (i.e., criminal activity) that result in the State's (as the representative of society) legitimate and just withdrawal of some of these rights. For example, Article 13 of the Universal Declaration of Human Rights (UDHR) declares that "everyone has the right to freedom of movement". But incarceration-- a withdrawal of this right-- is a universally accepted penalty for criminal activity. So if Article 13 of the UDHR can be withdrawn as a consequence of certain crimes, why not, say, Article 3 (right to life) or Article 5 (protection from torture or cruel punishment)?

One argument is that some human rights are inalienable (e.g., right to life) and others are not (e.g., right to free movement). Alston (2005), who famously visited our country last year, puts it softer as the prioritisation of human rights, that some rights are more important than others and should thus be pursued more rigourously. Accepting that such a dichotomy of human rights exists, how do we detrmine which ones are inalienable (or more important) and thus cannot be withdrawn as a consequence of criminal activity?

Answers based on the Divine, religion, or some "self-evident" truths are flimsy because they cease to persuade once the underlying assertions and dogmas are disputed-- they are only persuasive for the converted. Natural law, social contract, Kantian morality, and evolutionary game theoretic arguments provide sound bases for the universal existence and protection of human rights, but give no objective limits on the punishment for those who violate them.

The strongest argument against the withdrawal of some human rights is the imperfection of the judicial system-- errors can occur and the innocent may be convicted. In this case, certain rights should not be withdrawn if there is a nonzero probability that the convict is actually innocent, especially if the withdrawal of such rights cannot be reversed. Indeed, it is better to err on the side of protecting human rights than withdrawing them. [I use a similar line of argument in my stand on abortion.] However, this is a practical argument that has no bearing on the merits of what punishments should or should not be allowed. After all, this argument falters if there is absolute certainty that the convicted criminal is guilty (say, there is untampered video of him shooting the victims).

The way I see it, the set of human rights that can be withdrawn as a consequence of criminal activity is a matter of social choice. There is no objective reason why some punishments should be allowed and others should be prohibited-- it all depends on the preferences of society. Thus, if society decides that violent criminals like the Laguna robbers should receive capital punishment (i.e., their right to life should be withdrawn), there is no objective reason to say that this should not be done; the only real constraint is society's sensibilities and public opinion.

Violent crimes like the Laguna robberies strain the rationale behind the limits on their punishment. If we subscribe to the social contract theory of human rights, a criminal should be deemed to have surrendered all his human rights if he decides to use violence on his victim. Perpetrators of heinous and violent crimes, if we are absolutely certain of their guilt, should be punished harshly, severely, and mercilessly.

If you disagree with me, do leave a reply and set me right.

Advice for Your Excellencies

Just read this story over at Inquirer: Bishop opposes QC birth control ordinance. Now, Bishop Ongtioco isn't the first bishop to oppose such measures, and I'm pretty sure he won't be the last. So to help the Magisterium engage the "anti-life" propagandists over at City Hall and various reproductive health centres, let me offer Their Excellencies some pieces of advice:

1. Stop confusing the laity by abortion-baiting (i.e., lumping contraception and abortion in the hope of transferring the distaste for the latter towards the former). There is a clear line between contraception and abortion-- even abortifacient drugs don't blur this line-- and you know this. Abortion-baiting is dishonest and condescending, something I'm sure Your Excellencies don't want to be.

2. Avoid making medical claims because, however we look at it, DD does not equal MD. Also, if Your Excellencies will point out that some contraceptives can raise the risk of certain cancers, you will be hard pressed to explain away the fact that contraceptives can reduce the risk of some cancers, and sex without contraceptives raises the risk of other cancers.

3. Emulate the great apologists like Justin Martyr and Irenaeus of Lyons by avoiding name-calling and sloganeering. Do you think the Athenians would have listened to St. Justin if he called them "boy-lovers", Your Excellencies?

4. Do not use "freedom of conscience" in your argument if you are trying to stop the dissemination of certain, even destructive, information. Free will can only be directed towards God if the conscience is given complete information, Your Excellencies. How holy is choosing the strait and narrow if the wide and broad was never shown?

5. Drop the argument that a teacher should be allowed to choose what she teaches based on her conscience-- this is a very treacherous slope. What applies to the Catholic teacher will also apply to the Jehovah's Witness teacher and the Iglesia ni Cristo teacher. Think about it, Your Excellencies.

6. Do not oppose humane, non-judgemental counselling and health care for anyone, even those you consider automatically excommunicated. Being humane and non-judgemental are good things, Your Excellencies.

7. Stop telling the laity how to have sex, Your Excellencies. Celibate men do not exactly make the best sex therapists, just like Stephen Hawking doesn't make the best track coach.

Nao Obrigada

"Nao Obrigada"-- "No Thank You" in Portuguese-- is the rallying cry of the pro-life movement in Portugal, which has just finished a referendum on abortion. The referendum asked voters whether or not women should be given more leeway in terminating their pregnancy (Portugal has one of the strictest anti-abortion laws in the EU, just a little more lax than that in the Philippines). To cut a long story short, the referendum failed to overturn current policy due to low voter turnout.

First, let me lay down my position: I am against abortion (at least the way pro-choicers want it). I think abortion should only be allowed when the pregnancy poses a medical risk to the mother's life, making abortion a legitimate form of self-defense. Let me explain.

Arguments for or against abortion often boil down to whether or not the fetus is a human being with its own right to life. Pro-life advocates argue that the fetus is a human being at the point of conception. Their reasons for believing this range from "God says so" (a weak argument appealing only to the converted) to pointing out that the embryo is a separate life with human DNA distinct from the mother (therefore, it is not part of the mother's body). Pro-choice advocates, on the other hand, argue that the fetus should still be considered part of the woman's body because it is not viable outside of it (therefore, she should have free rein over what to do with it).

I will not presume to know when human life starts, and neither should the pro-lifers or pro-choicers. The beginning of "human life" is something that cannot be materially proven because it is a metaphysical concept. Science can only tell us when certain aspects of human life are present (e.g., human DNA, beating heart, brainwaves), but it can't tell us when the fetus attains human consciousness (or a soul, for the religiously inclined). Science can't tell us when we should give the fetus the rights equal to ours.

What we can say is that human life starts at some point between fertilisation and birth-- when exactly, we do not know. Therefore, at any point during the pregnancy there is a probability 0 < h < 1 that the fetus is human, and a probability (1 - h) that it is not. So if we abort a fetus there is an h chance what we are killing another human being, and (1 - h) chance that we are not. Given the gravity of the act, this risk (h) is not something that society should take lightly, especially if we claim to value a person's right to life. Better to not kill a fetus and live with the (1 - h) chance that it could have been killed guilt-free, rather than kill it and bear the h chance that a human being was actually killed. Given h > 0, we have to err on the side of life and accord the fetus human rights.

Of course, self-defense is a valid argument for killing another person. If the fetus poses a clear and present danger to the life of the mother, she should be allowed to eliminate the threat. This goes for any person that threatens her life willingly or unwillingly, even those that have been out of the womb for some time.