2. The legal setting

In 1987, the Oregon legislature enacted a statute which imposed a $500,000 cap on non-economic damages in tort lawsuits [OR Rev Stat §18.560(1) subsequently renumbered 31.710(1)]. Non-economic damages include damages for which an individual did not incur a direct, out-of-pocket cost, such as damages for pain and suffering. On 9 October 1996, the Oregon Court of Appeals found that the cap violated the Oregon Constitution (Lakin et al. vs Senco Products, Inc. 144 OR App 52, 925 P.2d 107). The Court of Appeals decision was appealed to the Oregon Supreme Court. On 15 July 1999, the Oregon Supreme Court upheld the Court of Appeals decision, rendering the cap unconstitutional (Lakin et al. vs Senco Products, Inc. 329 Ore. 62, 987 P.2d 463).

3. Theoretical model of physician decision making

We adapt the Currie and MacLeod (Reference Currie and MacLeod2008) theoretical model of physician decision making to our analysis. Currie and MacLeod (Reference Currie and MacLeod2008) model a physician's decision to perform a medical procedure. Physician utility is

(1)$$U( {\alpha , \;s, \;p, \;law} ) = B( {\alpha , \;s, \;p} ) \;\ndash \;H( {s, \;p, \;law} ) \times \alpha $$

where ‘s’ represents a patient's condition, ‘law’ represents the existing tort law, ‘p’ represents either not using the procedure (NP) or using the procedure (P), α is a medical ‘error rate’ chosen by the physician, $B({\bullet} )$ is benefits to the physician and $H({\bullet} )$ is the physician's expected malpractice liability. A patient's condition may vary from s  =  0 (a patient with no medical conditions or difficulties) to s  =  S (a patient with the most severe conditions). In the context of a pregnancy, a patient's condition includes maternal and fetal conditions. In terms of our analysis, we might think of a low-risk woman as having a low s, a woman with a plural pregnancy as having a mid-level value of s, a woman with a prior c-section as having a higher s and, for example, a situation in which the fetus presents with an umbilical cord prolapse which cannot be managed through manipulation as one of the highest conditions. In the present context, ‘no procedure’ is a vaginal birth (v) and the procedure is a c-section (cs). Physician benefits from performing (not performing) a procedure ‘include the intrinsic reward from treating the patient, any pecuniary rewards from treatment, and the opportunity cost of care, α’ (Reference Currie and MacLeod2008: 805).

For a given set of tort laws and a given value of p, the physician first chooses the optimal error rate for each possible patient condition. The physician then chooses a c-section if their optimal utility from performing a c-section $( U^\ast ( \alpha _{cs}^\ast , \;\;s, \;\;law, \;\;cs) )$ is greater than their optimal utility from a vaginal birth $( U^\ast ( \alpha _v^\ast , \;\;s, \;\;law, \;\;v) )$ and vice-versa. If we assume that as s increases the increase in optimal utility associated with a c-section is greater than the increase (or decrease) in their optimal utility associated with a vaginal delivery and if we assume that when s  =  0 the optimal utility from a vaginal birth exceeds the optimal utility from a c-section there will be a critical cutoff value of s $( \bar{s})$ above which a c-section is chosen and below which a vaginal birth is chosen. We may represent the physician decision in terms of the difference in their utility between a c-section and vaginal birth: ΔU(s, law) = $U^\ast ( {\alpha_{cs}^\ast , \;\;s, \;\;law, \;\;cs} ) -\;U^\ast ( {\alpha_v^\ast , \;\;s, \;\;law, \;\;v} )$. A physician chooses a c-section when ΔU(s, law) ⩾ 0. Patient condition $\bar{s}$ is the patient condition where ΔU(s, law) = 0. Letting ‘Law’ refer to the tort law before the Oregon court decisions and ‘Law′’ to the tort law after an Oregon court decision, we may represent the impact of a change in law as ΔU(s, Δlaw)  =  [ΔU(s, Law ^′)  −  ΔU(s, Law)].Footnote ²

The Currie and MacLeod (Reference Currie and MacLeod2008) model implies that the impact of a change in tort law on physician use of c-sections depends on relative optimal error rates of a procedure (e.g. a c-section) at $\bar{s}$ and of not using the procedure (e.g. a vaginal birth) at $\bar{s}$. If the error rate of the procedure is greater than the error rate of not using the procedure, an increase in expected malpractice liability associated with, say, the removal of a cap on damages will result in a decrease in use of the procedure. If the opposite is true with respect to the optimal error rates at $\bar{s}$, we would observe an increase in the physician's use of c-sections.

Whether the optimal error rate of a c-section is less than (or exceeds) the optimal error rate of a vaginal birth for the woman with the $\bar{s}\;$condition depends on how the optimal error rates of c-sections and of vaginal births vary as s increases and on their relative magnitudes. Generally, we view the error rate for c-sections as relatively stable across values of s because the medical risks associated with a c-section are relatively stable across maternal and fetal conditions (Ecker and Frigoletto, Reference Ecker and Frigoletto2007; Yang et al., Reference Yang, Mello, Subramanian and Studdert2009). Although the c-section procedure is not without risk, it is widely perceived among physicians as effective at minimizing the severe birth injuries that invite litigation (Yang et al., Reference Yang, Mello, Subramanian and Studdert2009). In fact, a common saying among obstetricians is that ‘no one gets sued for doing a c-section’ (Lake, Reference Lake2012).Footnote ³ On the contrary, we might expect the error rate for vaginal births to increase dramatically as we move from low values of s to high values of s. Consider, for example, the error rate associated with having a vaginal delivery when a fetus is deprived of oxygen (which could lead to cerebral palsy). In such a case, the risks to the fetus are high, especially relative to the risks associated with a c-section, a procedure meant to address such potentially dire outcomes. These observations suggest that it is likely that the optimal error rate for a vaginal birth is greater than the optimal error rate for a c-section at $\bar{s}$. For our purposes, an important aspect of the Currie and MacLeod (Reference Currie and MacLeod2008) model is that it implies heterogeneous impacts of a change in tort law across patient conditions. In discussing their model, Currie and MacLeod (Reference Currie and MacLeod2008) observe ‘[o]ur model predicts that doctors should have less discretion over high-risk births so that tort reforms should have smaller effects in these cases’ (814). Specifically, an increase in expected malpractice liability will have a greater impact on the probability that a woman with a lower value of s receives a c-section than on that probability for a higher s woman (if it has any impact on them). Stated in terms of our model, ΔU(s, Δ law) is decreasing in s, where it may effectively equal zero at the highest s.

The result makes sense theoretically and intuitively. In terms of the theoretical model, a change in law will have little or no impact on physician utility in equation (1) at high s because medical concerns dominate economic incentives. Intuitively, when, for example, a physician is presented with a mechanical obstruction involving a baby with severe hydrocephalus, the medical risks to a fetus associated with a vaginal delivery are so high (prohibitively high) that a change in malpractice liability should not affect a physician's decision (to perform a c-section). At low values of s, on the contrary, a physician has greater discretion in performing a c-section because such medical risks are absent and we might expect a physician to be more responsive to changes in legal liability. In light of these observations, if the change in law increases expected malpractice liability we would expect ΔU(s, Δ law) to be positive at low values of s, approaching zero as s increases.

Finally, the timing of Oregon court decisions regarding the cap on non-economic damages also provides an opportunity to obtain some insight into the impact of expected malpractice liability on physician decision making. During the 2-year, 9-month Appellate Period, the constitutional fate of Section 18.560 was uncertain. Under the foregoing model, the uncertainty associated with the Court of Appeals decision would increase a physician's expected medical malpractice liability cost but not by as much as the Oregon Supreme Court decision. Thus, if we observed an effect of the change in tort law arising out of the Oregon courts' decisions, we would expect the effect during the Appellate Period to be smaller, compared with the period after the Oregon Supreme Court decision.

4. Analysis of potential bias in the DD estimator

We use Heckman et al. (Reference Heckman, Ichimura, Smith and Todd1998a) to identify the bias in the DD estimator which may arise out of changing marginal distributions of patient conditions in treatment and control groups. Assume that there are two legal regimes in the Portland area: the legal regime prior to the change in Oregon tort law and the legal regime after the change (the treatment). Let y ₁ = 1 if a c-section was performed under the treatment and equal 0 otherwise, and y ₀ = 1 if a c-section was performed when not subject to the treatment and equal 0 otherwise. Let g = 1 if a mother is in the treatment group (they live in Oregon) and equal 0 otherwise (they live in Washington state). A patient's condition (s) is the unaccounted-for variable. We have assumed that s lies on [0, S] with cumulative distribution function F(s).

We seek to estimate the (conditional on s) average effect of treatment on the treated (δ(s)) by comparing outcomes in the treatment and control groups; i.e.

(2)$${\rm Pr}( y_1 = 1\vert g = 1, \;s) \;-\;{\rm Pr}( y_0 = 1\vert g = 0, \;s) .$$

We can show that equation (2) equals

(3)$$\delta ( s) + B( s) $$

where B(s) is a conditional bias term identified by Heckman, et al. (Reference Heckman, Ichimura, Smith and Todd1998a: 1022).

The conventional bias term, which does not condition on s, is B = Pr (y ₀ = 1|g = 1) − $\Pr ( {y_0 = 1{\rm \vert }g = 0} )$. We relate B to equation (3) by integrating across s. First, we define several terms. Let a ‘ ^′ ’ mark designate the period prior to the change in law, with the absence of such a mark indicating the period after the change in law. Next, let

$$\Delta F( {s{\rm \vert }g} ) {\rm d}s = [ {F( {s{\rm \vert }g} ) \;\ndash \;{F}^{\prime}( {s{\rm \vert }g} ) } ] {\rm d}s, \; and \eqno $$

$$\Delta \displaystyle{{\partial \Pr ( {y_0 = 1{\rm \vert }g = 0, \;s} ) } \over {\partial s}} = \displaystyle{{\partial \Pr ( {y_0 = 1{\rm \vert }g = 0, \;s} ) } \over {\partial s}}\;-\;\displaystyle{{\partial P {r}^{\prime}( {y_0 = 1{\rm \vert }g = 0, \;s} ) } \over {\partial s}}$$

In the Appendix, we show that for the DD estimator B equals

$$\int_0^S {\Delta \displaystyle{{\partial \Pr ( {y_0 = 1{\rm \vert }g = 0, \;{\rm s}} ) } \over {\partial {\rm s}}}\cdot [ {F( {s{\rm \vert }g = 0} ) {\rm d}s\;\ndash F( {s{\rm \vert }g = 1} ) \;{\rm d}s} ] } $$

(4)$$-\int_0^S {\displaystyle{{\partial P {r}^{\prime}( {y_0 = 1{\rm \vert }g = 0, \;{\rm s}} ) } \over {\partial {\rm s}}}\cdot \;[ \Delta F( s\vert g = 1) {\rm d}s\;\ndash \;\Delta F( s\vert g = 0) {\rm d}s] } $$

Because the bias term can have any sign or be of any size, the estimated treatment effect may be greater or smaller than the actual effect, or it might have the opposite sign. Obtaining an OM result in the presence of DM is an example of the latter case. Such a situation will arise when equation (4) is negative and greater in absolute value than the average treatment effect (the expected value of δ(s)). Elsewhere in the literature, such a result has been called Simpson's paradox (Samuels, Reference Samuels1993).

Because we have no a priori beliefs about the sign of F(s|g = 0)–F(s|g = 1), we focus on the second component of equation (4). Since the probability of a c-section increases with s, ∂Pr^′(y ₀ = 1|g = 0, s)/∂s is positive. Equation (4), thus, will be negative when ΔF(s|g = 1)ds is positive and/or ΔF(s|g = 0)ds is negative. The former is positive when there is more density at lower values of s in the period after the treatment (i.e. the density shifts left) for the treatment group. The latter is negative when there is more density at higher values of s in the period before the treatment. Furthermore, wider variation in c-section rates across patient conditions makes the bias larger.

5. Econometric model

We use a Probit model to represent a physician's decision to perform a c-section and model the impacts of the Oregon court decisions using the DD estimator. Since consistency of the DD estimator depends on a common trends assumption, we check whether our groups differ with respect to unobserved factors by estimating a Probit discrete factor model (Probit DFM). We account for different possible impacts of the court decisions by allowing the DD estimator to differ during the Appellate period and the period after the Supreme Court decision. Thus, we estimate the following model:

(5)$$\eqalign{Y_{it} = & \beta _1 + \beta _2Oregon_{it} + \beta _3SCt_{it} + \beta _4Oregon_{it} \times SCt_{it} \cr & + \beta _5Appellate_{it} + \beta _6Oregon_{it} \times Appellate_{it} + {\bf X}_{{\boldsymbol it}}{\boldsymbol \beta } + \lambda \mu _i + \varepsilon _{it}}$$

where Y _it equals 1 if a woman had a c-section (and equals 0 if they had a vaginal birth), Oregon _it is a dummy variable which equals 1 if the birth was in Oregon, SCt _it is a dummy variable for a birth being in a month after the Oregon Supreme Court decision, Appellate _it is a dummy variable for the birth occurring in a month during the Appellate period, ${\bf X}_{{\boldsymbol it}}$ represent other independent variables in the analysis, μ _i is an unobserved variable with load factor λ and ɛ_it is a disturbance with a standard normal distribution.Footnote ⁴ We assume that μ _i has a discrete distribution with two points of support, one for each of the two groups. We assume that the points of support are {0, 1} and estimate their probabilities non-parametrically. We test for the presence of unobserved heterogeneity using the ‘upward-testing approach’ suggested by Mroz (Reference Mroz1999).

6. Data and descriptive statistics

We use primarily data from the Natality Files. Our population is births in the Portland-Vancouver PMSA (PMSA 6440) between 1992 and 2002 which were attended by a medical doctor or by a Doctor of Osteopathy (we refer to them collectively as ‘physicians’). Our data start in 1992 because Washington state (Clark county) was first incorporated into the PMSA in that year. A birth was associated with its State of occurrence.

We estimate the econometric model for sub-groups of women and for the Full Sample (all of the mothers together). We identify four primary sub-groups of women plus two other sub-groups which serve as a check on our results. Our ‘low-risk’ (low s) sub-group consists of women who had (1) a full term (i.e. between weeks 37 and 41 of the pregnancy), singleton birth, (2) not had a prior c-section and (3) none of maternal and fetal complications listed in the Natality Files.Footnote ⁵ The second sub-group is women in our low-risk group who were first-time mothers. These women face higher c-section rates than low-risk women who have had a prior birth. The third sub-group is women who had a plural birth and had not had a prior c-section. Since physicians are more likely to perform c-sections for these births, a physician's failure to use a c-section in this context exposes them to greater legal risks (Ecker and Frigoletto, Reference Ecker and Frigoletto2007). In order to obtain a reasonable sample size, we combined women with no complications and women with complications. The fourth sub-group is women who have had a prior c-section, and have a full-term, singleton birth with no complications. Women with a prior c-section represent, to physicians, greater medical and legal risks. Finally, we separated the maternal and fetal complications reported in the Natality Files into those complications whose likelihood of having a c-section was less than 50% (we might think of these as being lower risk) and those complications whose likelihood of having a c-section was greater than 50%. The latter group includes women with seven different complications (cephalopelvic disproportion, breech birth, dysfunctional labor, cord prolapse, fetal distress, placenta previa and seizure during labor) for which the medical risks associated with a vaginal birth were high. The former group includes women with 23 different complications. We include these two groups as a test of consistency with results obtained for the sub-groups.

Table 1 identifies the total number of observations in our dataset and the number of observations in each of the six sub-groups analyzed. The low-risk group of women represents a large portion of the births in our sample. The percent of women in the group with a prior c-section is relatively small (10.8% of the Full Sample had a prior c-section), as is the percent of women with plural births. Table 1 also reports c-section rates for the sub-groups analyzed. Consistent with national statistics (Menacker, Reference Menacker2005; Lee et al., Reference Lee, Gould, Boscardin, EL-Sayed and Blumenfeld2011), the c-section rates across the sub-groups of women vary considerably.

Table 1. C-section rates for sub-groups analyzed

Notes: Most of the observations in the Full Sample but not in one of the sub-groups analyzed were (i) women with no prior c-section, a singleton and non-full term birth and birth complications (n = 17,363), (ii) women with no complications and no prior c-section, who had a singleton, non-full term birth (n = 14,393) and (iii) women with a prior c-section and with complications who were having a singleton birth (n = 11,925).

Table 2 compares mean values of the maternal demographic variables in the two groups. Overall, the two groups of women are similar. Education rates differ somewhat, with the greater percentages of women in Oregon having a college degree and more women in Washington having a high school diploma. The difference in Hispanic origin is also notable.

Table 2. Mean values of maternal demographic variables

As a final matter, Figure 1 reflects the trends in c-section rates in Washington and Oregon over the 11-year period of our analysis for the Full Sample. The overall rates suggest an upward trend in both states starting in the late-1990s.

Figure 1. C-section rates for the Portland-Vancouver PMSA by state.

7. Empirical analysis

7.1 Regression results

Table 3 presents regression results for sub-groups of women. Probit DFM results are reported when testing suggested the presence of unobserved heterogeneity. Otherwise, Probit results are reported. In light of the impact of nonlinearity on interpreting the marginal effect of interaction variables (see Ai and Norton, Reference Ai and Norton2003), we calculate treatment effects using the results in Puhani (Reference Puhani2012), who identifies the formula for calculating a treatment effect with the DD estimator in a Probit model. The effects in the Appellate period were generally statistically insignificant and positive. The Post-Supreme Court Period DD estimates for sub-groups reveal results consistent with the theoretical prediction that changes in tort laws will have greater effects on physicians presented with low-risk women. The average partial effects for low-risk mothers, and low-risk, first-time mothers were positive and statistically significant, suggesting the presence of DM for these women. On the contrary, the results suggest no effect for women with a prior c-section or a plural birth.

Table 3. DD estimate average partial effects for sub-groups of women

Notes: The DD estimates were calculated using the results in Puhani (Reference Puhani2012). Standard errors are in parentheses below parameter estimates. The standard errors for the average partial effects were calculated using the Delta method (Greene Reference Greene2012: 698).

*Statistically significant (SS) 10% level of significance, two-sided test.

**SS 5% level of significance, two-sided test.

***SS 1% level of significance, two-sided test.

Turning to the regressions which served as a consistency check, the average partial effect of the Post-Supreme Court Period DD estimator is positive and statistically insignificant for mothers with complications whose c-section rates were less than 50%. The statistically significant negative effect for women with a complication whose c-section probability exceeds 50% is surprising. Our analysis in the next section provides insights into this result.

Table 4 includes regression results when we estimate the Probit model for the Full Sample. The second column of the table identifies the average partial effects of the DD estimates when we do not include patient condition dummy variables in the regression. The results suggest an OM result after the Oregon Supreme Court decision. The OM result disappears when we add dummy variables for the different conditions: the third column of the table. The sizes of the average partial effects for the patient condition dummy variables indicate that women with these conditions are notably different than women without the conditions.

Table 4. Probit DD estimate average partial effects for the Full Sample

Notes: Standard errors are in parentheses below parameter estimates.

***Statistically significant at 1% level of significance, two-sided test.

Figure 2 presents ‘standardized’ average partial effects (the DD average partial effect for a sub-group divided by the unconditional c-section rate for the sub-group reported in Table 1) and their 95% confidence intervals. The condition of the patient is on the horizontal axis, from low risk (s) conditions on the left to higher risk conditions on the right. The point estimate for the Full-Sample regression (with no patient condition dummy variables) is reported as ‘aggregate estimate’. The confidence intervals reflect large positive effects for lower-risk mothers, with those effects being indistinguishable from zero for higher-risk mothers.

Figure 2. Standardized average partial effects for sub-groups of women.

7.2 Evidence suggesting bias in treatment effect estimates

We now analyze our regression results in light of our analysis of bias in Section 4. We note first that the variation in c-section rates across patient conditions from 3.3 to 75% presents a situation in which the ∂Pr ^′(y ₀ = 1|g = 0, s)/∂s term in equation (4) is larger, making any bias in the DD estimates due to changing marginal patient conditions larger.

The distributions of patient conditions in Oregon and Washington over the time period considered changed in a manner consistent with Simpson's paradox (SP) (Samuels, Reference Samuels1993). The distribution did not change much in Oregon, while the distribution of conditions in Washington shifted toward higher s conditions. We summarize the changes in Figure 3, which identifies the relative changes in the distributions of certain conditions in Oregon and Washington over time. Specifically, the reported changes are

$$\Delta _s = \displaystyle{{P_{st}^{OR} -\;P_{s1}^{OR} } \over {P_{s1}^{OR} }}-\;\displaystyle{{P_{st}^{WA} -\;P_{s1}^{WA} } \over {P_{s1}^{WA} }}\;\;$$

where $P_{st}^i$ is the probability that a patient in state i and period t presents with condition s. A positive value of Δ_s indicates that over time Oregon had a relatively larger percentage of patients with condition s than did Washington. Figure 3 indicates that Oregon had a greater relative percentage of low-risk patients over time, while Washington had relatively a greater percentage of the higher-risk patients with some type of complication. These are the types of shifts in distributions of conditions which can produce an SP result.Footnote ⁶

Figure 3. Relative changes in the marginal distributions of patient medical conditions in the Oregon and Washington parts of the Portland-Vancouver PMSA.

We sought to gain further insight into the importance of the changes in the distributions of patient conditions to our regression results by estimating the Probit model for the Full Sample using narrower time frames. Narrowing the time frame examined minimizes the impact on regression results of changes in the distributions of conditions. The estimated average partial effects of the Supreme Court DD and the Appellate period DD estimators were statistically insignificant and close to zero for the (1997–2001), (1997–2002), (1998–2001) and (1998–2002) time frames.

The change in distribution of patient conditions in Washington over time suggested the possibility of bias in the DD estimates for sub-groups of women reported in Table 3 because of changes in our control group. For several reasons, we do not believe that the DD estimates are biased. First, since the DFM is supposed to capture the type of unobserved heterogeneity represented by a differing trends over time, our Probit DFM estimates being substantially similar to the Probit estimates suggests that such a bias is not present. Second, since most of the change in distribution of patient conditions in Washington involved mothers moving from the low risk group to the complications with less than a 50% probability of c-section group, we merged the two groups and estimated the Probit model for the merged group of mothers. The regression results were basically the same; the average partial effect of the DD estimate for the post Supreme Court period was positive and statistically significant and the average partial effect for the Appellate period was statistically insignificant and close to 0. Third, we thought that excluding midwife-attended births from our population might bias our results if midwife-attended births were more prominent in one state. We would expect midwives to attend low-risk births. To that end, we re-estimated the Probit model regressions with midwife births included in the sample. The regression results were substantially the same.

7.3 Sources of changes in marginal distributions of patient conditions

As a final matter, we consider possible causes of the changes in the distributions of patient conditions in Washington and Oregon. Although our population continues to be births attended by a physician, we focus on the impact of midwives on the distributions of patient conditions which present to physicians. We focus on the role of midwives as substitute caregivers for low-risk births. We focus on low-risk births because midwives are generally restricted from attending higher-risk births. Low-risk births are the types of births for which a midwife is a substitute for a physician. The essence of our argument is that an increased supply of midwives will result in fewer lower-risk mothers using a physician, causing the distribution of patient conditions for births attended by a physician to shift with more mass at higher-risk patients. This dynamic occurred in the Oregon side of Portland. A decreased supply of midwives will have the opposite effect. This dynamic occurred in the Washington side of Portland.

These changes in the distributions of patient conditions in both states may have been endogenous in that they were a product of the Oregon Supreme Court decision. The Oregon Supreme Court decision increased the potential liability of medical caregivers in Oregon.Footnote ⁷ In response to the change in expected liability and costs of practice in Oregon, midwives in the Portland area may have shifted the focus of their practices to Washington. The increased supply of midwives in Washington and decreased supply of midwives in Oregon would produce the types of changes in the distributions of patient conditions observed in Section 6. One possible exogenous change in Washington might also have contributed to an increased supply of midwives there. In 2000, the Washington legislature ‘added licensed midwives to a Washington State law that require[d] private health insurers to provide direct access to health-care services for women’ (Midwives Association of WA State, 2011).

Figure 4 identifies the share of deliveries of low-risk mothers which were attended by a midwife in Washington and Oregon between 1992 and 2002. In both states, there were no notable changes between 1992 and 1998. Between 1998 and 2002, the percentage increase in Washington was substantially larger. The percentage of low-risk births attended by a midwife in Oregon increased from 16.8 to 23.4% between 1998 and 2002 whereas in Washington the percentage increased from 23.5 to 40.3%. The changes in Washington between 1999 and 2002 suggest two separate impacts in that period. There was an increase between 1999 and 2001 (consistent with the Oregon Supreme Court decision) and a larger increase between 2001 and 2002 (consistent with the added effect of the change in Washington laws regarding health insurance policies covering midwifery).

Figure 4. Share of deliveries of low-risk mothers attended by a midwife in the Oregon and Washington parts of the Portland-Vancouver MSA