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. Author manuscript; available in PMC: 2016 Jul 1.
Published in final edited form as: JAMA Psychiatry. 2015 Jul 1;72(7):735–736. doi: 10.1001/jamapsychiatry.2015.0212

LETTER TO THE EDITOR: Penrose Hypothesis not supported

Alexander C Tsai 1,2, Atheendar S Venkataramani 3
PMCID: PMC4500632  NIHMSID: NIHMS705569  PMID: 25945426

Dear Editor

Mundt et al. (1) should be applauded for attempting to bring new data to bear on a research question of substantive policy significance. We are concerned, however, that their analysis overlooked a point of critical significance. While they argued that their findings “cannot be explained by a simple overall trend to reduce numbers of beds and increase prison populations” (p.E6), they failed to adjust for secular changes in the underlying determinants of crime (3). Neither did Lamb (2), who argued in the accompanying editorial that longitudinal data are needed to appropriately test the Penrose Hypothesis, comment on the need to do so. Such adjustment would be considered standard practice in the analysis of panel data (4), particularly given the challenges of drawing causal inferences from cross-national panel data (5).

Using the information reported in Figures 1 and 2, we reconstructed the authors’ dataset (see Supplementary Materials). Fitting the same regression model with country fixed effects and robust standard errors, we replicated the authors’ main finding to a close approximation (b=-5.11; 95% CI, -6.61 to -3.60; P<0.001). Next, we added year fixed effects to the model. The estimated association between beds and prisoners was reduced in magnitude by more than 80%, was not statistically significant, and the lower confidence limit nearly excluded the upper confidence limit of the authors’ point estimate (b = -1.09; 95% CI, -3.37 to 1.19; P=0.27). Adding a linear time trend instead of year fixed effects yielded a similar result (b=-1.02; 95% CI, -3.49 to 1.46; P=0.34), suggesting that the weakened association cannot simply be attributed to the degree-of-freedom demands of the year fixed effects.

The correlation between beds and the linear time trend was relatively low (Spearman’s ρ=-0.38; 95% CI, -0.59 to -0.13), with the linear time trend explaining little of the variation in beds (R-squared=0.23). Thus, our finding cannot simply be attributed to collinearity between the two covariates. Consistent with this argument, Figure 1 in Mundt et al. (1) shows that the rates of change in beds differs for each country. Therefore, accounting for average sample time trends should not have attenuated the association between beds and prisoners if the association were (contrary to fact) robust. Even if our conclusion were simply driven by collinearity, it would not absolve the authors of their responsibility to adjust their estimates for secular trends (4).

The Penrose Hypothesis does not appear to be supported in these data.

Acknowledgments

Funding/Support: The authors received no specific funding for this study. Dr. Tsai acknowledges salary support from the U.S. National Institutes of Health K23MH096220 and the Robert Wood Johnson Health and Society Scholars Program.

Role of the Funder/Sponsor: The sponsors had no role in the design and conduct of the study; collection, management, analysis, or interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

Footnotes

Author Contributions: Drs. Tsai and Venkataramani contributed equally to this work. Both had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.

Conflict of Interest Disclosures: None reported.

Contributor Information

Alexander C. Tsai, Chester M. Pierce, MD Division of Global Psychiatry and Center for Global Health, Massachusetts General Hospital, Boston, United States; Mbarara University of Science and Technology, Mbarara, Uganda.

Atheendar S. Venkataramani, Department of Medicine and Center for Global Health, Massachusetts General Hospital, Boston, United States.

References

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