Mendelian randomization suggests a bidirectional, causal relationship between physical inactivity and adiposity.

Physical inactivity and increased sedentary time are associated with excess weight gain in observational studies. However, some longitudinal studies indicate reverse causality where weight gain leads to physical inactivity and increased sedentary time. As observational studies suffer from reverse causality, it is challenging to assess the true causal directions. Here, we assess the bidirectional causality between physical inactivity, sedentary time, and adiposity by bidirectional Mendelian randomization analysis. We used results from genome-wide association studies for accelerometer-based physical activity and sedentary time in 91,105 individuals and for body mass index (BMI) in 806,834 individuals. We implemented Mendelian randomization using CAUSE method that accounts for pleiotropy and sample overlap using full genome-wide data. We also applied inverse variance-weighted, MR-Egger, weighted median, and weighted mode methods using genome-wide significant variants only. We found evidence of bidirectional causality between sedentary time and BMI: longer sedentary time was causal for higher BMI [beta (95% CI) from CAUSE method: 0.11 (0.02, 0.2), p = 0.02], and higher BMI was causal for longer sedentary time (0.13 (0.08, 0.17), p = 6.3 x 10-4). Our analyses suggest that higher moderate and vigorous physical activity are causal for lower BMI (moderate: -0.18 (-0.3,-0.05), p = 0.006; vigorous: -0.16 (-0.24,-0.08), p = 3.8 × 10-4), but indicate that the association between higher BMI and lower levels of physical activity is due to horizontal pleiotropy. The bidirectional, causal relationship between sedentary time and BMI suggests that decreasing sedentary time is beneficial for weight management, but also that targeting adiposity may lead to additional health benefits by reducing sedentary time.

Introduction

Obesity and physical inactivity are major risk factors for a number of chronic diseases, such as type 2 diabetes, cardiovascular diseases and several types of cancer. Today’s epidemic of obesity and sedentary lifestyle is thus a major burden on public health systems worldwide (GBD 2019 Risk Factors Collaborators, 2020).

Many observational studies suggest that physical inactivity and increased sedentary time are associated with a higher risk of obesity (Lee et al., 2010; Du et al., 2013; Silva et al., 2019; Myers et al., 2017). However, other studies have indicated a reverse effect, where obesity leads to physical inactivity and increased sedentary time (Petersen et al., 2004; Mortensen et al., 2006; Bak et al., 2004; Barone Gibbs et al., 2020; Ekelund et al., 2008; Myers et al., 2017). Furthermore, randomized clinical trials of physical activity interventions have indicated that the causal effects of physical activity on body weight are modest (Church et al., 2009; Rosenkilde et al., 2012; Golubic et al., 2015) compared to the strong inverse relationship between physical activity and body weight observed in cross-sectional epidemiological studies. This suggests that the observational results may be affected by bias, such as reverse causality or confounding by other lifestyle or environmental factors (Schnurr et al., 2021). To date, the causal relationships between physical inactivity, sedentary time and adiposity remain unclear and warrant further investigation. It is important to assess the causal relationship with adiposity separately for physical activity and sedentary time, as individuals can be physically active even if they engaged a substantial part of their time to sedentary behaviors, and vice versa (Panahi and Tremblay, 2018).

Mendelian randomization is a powerful method to minimize the influence of reverse causality and confounding on causal estimates derived from observational data. Since genotypes are randomly allocated at conception, genetic alleles associated with physical activity, sedentary behavior, and body mass index (BMI) can be used to assign individuals according to higher or lower mean levels of these exposures in a randomized manner (Figure 1).

Figure 1.

Mendelian randomization assumptions and directional associations between physical activity, sedentary time and adiposity.

Panel A shows Mendelian randomization assumptions when estimating the causal association between a given exposure and outcome: (1) The instruments are associated with the exposure, (2) the instruments do not cause the outcome independently from the exposure (horizontal uncorrelated pleiotropy), and (3) the effects of the exposure on the outcome are not influenced by any confounders (horizontal correlated pleiotropy). Panel B indicates a unidirectional causal effect of physical activity or sedentary time on adiposity, whereas panel C indicates a unidirectional causal effect of adiposity on physical activity or sedentary time. Panel D indicates a bidirectional causal relationship where physical activity or sedentary time has a causal effect on adiposity, but at the same time, adiposity has a causal effect on physical activity or sedentary time. Figure icons were created with BioRender.com.

Here, we aimed to assess the causality between the genetic liability of physical inactivity, sedentary time and BMI by applying bidirectional Mendelian randomization analyses on summary results of accelerometer-based physical activity and sedentary time for 91,105 adults and of BMI for 806,834 adults.

Results

We used the Mendelian randomization CAUSE method to take advantage of the full genome-wide summary results (Morrison et al., 2020). We found evidence of causality between higher vigorous and moderate physical activity and lower BMI (p = 3.8 × 10–4 and p = 0.006, respectively), and between more sedentary time and higher BMI (p = 0.02) (Table 1, Figure 2, and Appendix 1—table 1 and Appendix 1—table 2). In absolute units, we approximate that each one hour daily increase in moderate physical activity or decrease in sedentary time causally decreased BMI by 0.27 kg/m2 (~0.8 kg) or 0.14 kg/m2 (~0.4 kg) (Appendix 1—table 3). The median shared effect, which reflects the effect induced by correlated horizontal pleiotropy, ranged from –0.01 to 0 for all trait pairs, indicating that there was no bias induced by horizontal pleiotropy. The low q values under the causal model (q = 0.18–0.20), which reflect the proportion of variants that show correlated horizontal pleiotropy, also suggested that horizontal pleiotropy was limited. We checked for the existence of possible outlier variants that could have a large effect on the exposure but no effect on the outcome, by producing a scatter plot for CAUSE test statistics on the causal association between BMI and sedentary time (Appendix 1—figure 1). While CAUSE is not sensitive to outliers as such, the existence of outlier variants could provide evidence against the causal model. However, we found no evidence of outlier variants. As we found high shared model q values in our CAUSE analyses (q=0.7-0.9), which may suggest that the genetic effects between the two traits are highly correlated and causality will be difficult to establish, we also assessed the genetic correlation between BMI and sedentary time. However, the genetic correlation analysis suggested only a modest genetic correlation between BMI and sedentary time (rg=0.27), which provides further reassurance that our CAUSE results are valid.

Table 1.

Results for Mendelian randomization analyses using the CAUSE method.

Causal model better fit for the data
Direction	Median causal effect (95% CI)	Median q (CI)	P causal vs sharing
Vigorous PA→ BMI	–0.16 (-0.24,–0.08)	0.19 (0, 0.86)	3.8 × 10–04
Moderate PA→ BMI	–0.18 (-0.3,–0.05)	0.20 (0.01, 0.86)	0.006
Sedentary time → BMI	0.11 (0.02, 0.20)	0.19 (0, 0.86)	0.02
BMI → Sedentary time	0.13 (0.08, 0.17)	0.18 (0, 0.85)	6.3 × 10–4
Sharing model better fit for the data
Direction	Median shared effect (CI)	Median q (CI)	P causal vs sharing
BMI → Vigorous PA	–0.16 (-0.19,–0.14)	0.90 (0.77, 0.98)	0.35
BMI → Moderate PA	–0.14 (-0.19,–0.11)	0.77 (0.55, 0.95)	0.31

BMI, Body mass index (BMI); SE, standard error; N SNPs, number of single-nucleotide polymorphism; P, P-value; PA, physical activity; IVW, inverse variance weighted; CI, 95% confidence interval.

The results display the data according to the goodness-of-fit for the causal or the sharing model. The median q value indicates the proportion of variants with correlated pleiotropy.

Figure 2.

Causal estimates for Mendelian randomization analyses using the CAUSE, inverse-variance-weighted (IVW), weighted median, and weighted mode methods.

Median causal estimates for Mendelian randomization analyses using the CAUSE method are shown in the left panel and mean causal estimates from the inverse variance weighted (IVW), weighted median (Wmedian) and weighted mode (Wmode) methods are shown in the right panel after outlier removal and accounting for horizontal pleiotropy. A diamond (♢) in the estimate for CAUSE indicates that the sharing model fit the data better than the causal model, that is that the association between the traits was more likely to be explained by horizontal correlated pleiotropy than causality. PA, physical activity; BMI, body mass index. Figure icons were created with BioRender.com.

Appendix 1—table 1.

CAUSE expected log pointwise posterior density (ELPD) results for each combination of traits.

		Vigorous physical activity → BMI			BMI → vigorous physical activity
Model 1	Model 2	Delta_ELPD	SE_delta_ELPD	z	Delta_ELPD	SE_delta_ELPD	Z
Null	Sharing	–17.47	4.24	–4.12	–251.88	21.54	–11.69
Null	Causal	–18.98	4.68	–4.05	–252.22	21.65	–11.65
Sharing	Causal	–1.51	0.45	–3.36	–0.35	0.90	–0.38
		Moderate physical activity → BMI			BMI → Moderate physical activity
Null	Sharing	–8.50	2.86	–2.97	–119.39	15.15	–7.88
Null	Causal	–9.83	3.39	–2.90	–119.77	15.34	–7.81
Sharing	Causal	–1.34	0.53	–2.52	–0.38	0.77	–0.49
		Sedentary time → BMI			BMI → Sedentary time
Null	Sharing	–6.51	2.57	–2.53	–137.84	157.46	–8.75
Null	Causal	–7.67	3.14	–2.44	–138.89	15.88	–8.75
Sharing	Causal	–1.16	0.57	–2.05	–1.06	0.33	–3.22

BMI, Body mass index; SE, standard error; NA, not applicable; CI, 95% confidence interval.

Appendix 1—table 2.

CAUSE posterior probabilities and q values for the causal effect and the shared effect.

Model	Causal effect (CI)	Shared effect (CI)	q (CI)	Sharing vs causal model p-value
	Vigorous physical activity → BMI
Sharing	NA	–0.18 (-0.25,–0.12)	0.85 (0.57, 0.98)	3.80E-04
Causal	–0.16 (-0.24,–0.08)	0 (-0.31, 0.31)	0.19 (0.00, 0.86)
	Moderate physical activity → BMI
Sharing	NA	–0.2 (-0.33,–0.11)	0.75 (0.35, 0.96)	5.80E-03
Causal	–0.18 (-0.3,–0.05)	–0.01 (-0.44, 0.39)	0.2 (0.01, 0.86)
	Sedentary time → BMI
Sharing	NA	0.13 (0.06, 0.23)	0.69 (0.25, 0.95)	2.00E-02
Causal	0.11 (0.02, 0.20)	0 (-0.32, 0.32)	0.19 (0, 0.86)
	BMI → Vigorous physical activity
Sharing	NA	–0.16 (-0.19,–0.14)	0.9 (0.77, 0.98)	0.35
Causal	–0.15 (-0.2,–0.08)	0.01 (-0.18, 0.21)	0.21 (0.01, 0.83)
	BMI → Moderate physical activity
Sharing	NA	–0.14 (-0.19,–0.11)	0.77 (0.55, 0.95)	0.31
Causal	–0.11 (-0.19,–0.03)	0 (-0.28, 0.2)	0.23 (0.01, 0.84)
	BMI → Sedentary time
Sharing	NA	0.14 (0.12, 0.17)	0.9 (0.73, 0.98)	6.30E-04
Causal	0.13 (0.08, 0.17)	0 (-0.23, 0.26)	0.18 (0.00, 0.85)

BMI, Body mass index; NA, not applicable; CI, 95% confidence interval.

Appendix 1—table 3.

Approximation of the causal estimates in absolute units.

	Original causal estimates (weighted median)				Conversion of causal estimates			Converted causal estimates
Analysis	N SNPs	Beta	SE	p	Equation	SDexposure	SDoutcome
Vigorous physical activity → BMI	1,036	–0·09 SD	0·006 SD	9.28E-57	(Beta*SDoutcome)/SDexposure /(0,01*24 hours)	NA	4·807 kg/m2	–0·48 kg/m2 per hour of moderate physical activity per day
Moderate physical activity → BMI	914	–0·05 SD	0·005 SD	1.21E-20	(Beta*SDoutcome)/SDexposure /(0,01*24 hours)	3.76%	4·807 kg/m2	–0·27 kg/m2 per hour of moderate physical activity per day
Sedentary time → BMI	1,036	0·06 SD	0·005 SD	6.33E-30	(Beta*SDoutcome)/SDexposure /(0,01*24 hours)	7.38%	4·807 kg/m2	0,14 kg/m2 per hour of sedentary time per day
BMI → Sedentary time	11,849	0·16 SD	0·009 SD	2.87E-68	(Beta*SDoutcome)/SDexposure *(0·01*24 hours)	4·807 kg/m2	7.38%	3·54 min of sedentary time per kg/m2 per day
Original units of the traits:Moderate physical activity: Probability of moderate physical activity in a 30s-epoch frame (Doherty et al., 2018)Sedentary time: Probability of sedentary time in a 30s-epoch frame (Doherty et al., 2018)BMI: kg/m2 (Pulit et al., 2019)Note: For vigorous physical activity, SD exposure could not be found, thus we use the same as for moderate physical activity, i.e. 3·76%

SNP, single nucleotide polymorphism; BMI, SE, standard error; SD, standard deviation; Body mass index (BMI).

Appendix 1—figure 1.

Scatter plot for CAUSE test statistics on the causal association between BMI and sedentary time.

Effect estimates for body mass index (x-axis) are plotted against estimates for sedentary time (y-axis). Error bars indicate 95% confidence intervals and the dotted line indicates the median causal effect of BMI on sedentary time.

In the reverse direction, we found no evidence of a causal effect of BMI on vigorous physical activity (p = 0.35) or moderate physical activity (p = 0.31) using CAUSE (Table 1, Figure 2, and Appendix 1—table 1 and Appendix 1—table 2). However, we found evidence of a causal effect of BMI on more sedentary time (p = 6.3 × 10–4), indicating bidirectional causality between the traits. The median shared effect in the causal association between BMI and sedentary time was zero and the q value was 0.18, suggesting that the causal association between sedentary time and BMI was unlikely to be biased by horizontal pleiotropy. In absolute units, we approximate that each kg/m2 (~3 kg) increase in BMI was causally associated with a 3.5 min increase in sedentary time per day (Appendix 1—table 3).

We also estimated the causal effects of moderate physical activity, vigorous physical activity and sedentary time on BMI with four commonly used Mendelian randomization methods, including IVW, Egger, weighted median and weighted mode methods. Due to the low number of independent, genome-wide significant loci for vigorous physical activity, moderate physical activity and sedentary time that were present in the GWAS results for BMI, we used a less stringent threshold of p < 5 × 10–7 to identify genetic instruments for these traits, resulting in 5, 3, and 5 independent loci, respectively. The directions of causal estimates were consistent with the findings from CAUSE, but the evidence for causality was weaker (Table 2, Figure 2, Appendix 1, and Appendix 1—table 4). To estimate the causal effect of BMI on moderate physical activity, vigorous physical activity and sedentary time, we used genome-wide significant BMI loci (p < 5 × 10–8) as instruments (n = 57, n = 55 and n = 57, respectively). Again, the directions of causal estimates were consistent with the CAUSE results, but the associations were weaker (Table 2, Figure 2, Appendix 1, and Appendix 1—table 5).

Table 2.

Mendelian randomization results for inverse variance weighted, weighted median, weighted mode, and MR-Egger methods.

Direction	Vigorous physical activity → BMI				Moderate physical activity → BMI				Sedentary time → BMI
MR method	beta	SE	p-value	N SNPs	beta	SE	p-value	N SNPs	beta	SE	p-value	N SNPs
IVW	–0.17	0.08	0.04	5	–0.24	0.12	0.05	3	0.11	0.08	0.16	5
Weighted median	–0.18	0.10	0.08	5	–0.18	0.12	0.13	3	0.10	0.10	0.29	5
Weighted mode	–0.19	0.12	0.19	5	–0.14	0.15	0.43	3	0.08	0.14	0.59	5
MR-Egger	1.33	2.21	0.59	5	0.12	0.45	0.84	3	0.49	0.36	0.26	5
Direction	BMI → Vigorous physical activity				BMI → Moderate physical activity				BMI → Sedentary time
IVW	–0.07	0.02	0.01	57	–0.06	0.03	0.03	55	0.07	0.03	0.01	57
Weighted mode	–0.01	0.06	0.83	57	0.02	0.06	0.68	55	–0.06	0.08	0.46	57
Weighted median	–0.04	0.03	0.27	57	0.003	0.04	0.93	55	0.03	0.04	0.48	57
MR-Egger	0.13	0.07	0.06	57	0.16	0.07	0.04	55	–0.02	0.08	0.76	57
BMI, Body mass index (BMI); SE, standard error; N SNPs, number of single nucleotide polymorphism; IVW, inverse variance weighted; CI, 95% confidence interval.

The results display the data according to the goodness-of-fit for the causal or the sharing model. The median q value indicates the proportion of variants with correlated pleiotropy. CI, confidence interval; PA, physical activity; BMI, body mass index; P, P-value.

Appendix 1—table 4.

Mendelian randomization results using the IVW, Egger, weighted median and weighted mode methods of for the causal effect of moderate or vigorous physical activity or sedentary time on BMI.

	Before outlier extraction
	Vigorous physical activity → BMI				Moderate physical activity → BMI				Sedentary time → BMI
MR method	SNP	beta	SE	p-value	SNP	beta	SE	p-value	SNP	beta	SE	p-value
Egger	5	1.33	2.21	0.59	3	0.12	0.45	0.84	8	0.46	0.64	0.50
Weighted median	5	–0.18	0.10	0.08	3	–0.18	0.12	0.13	8	0.02	0.09	0.82
IVW	5	–0.17	0.08	0.04	3	–0.24	0.12	0.05	8	0.04	0.11	0.72
Weighted mode	5	–0.19	0.12	0.19	3	–0.14	0.15	0.43	8	–0.05	0.18	0.78
Sensitivity test	Estimate		p-value/CI		Estimate		p-value/CI		Estimate		p-value/CI
Q (p-value)	1.65		0.8		3.6		0.17		23.08		1.70E-03
I2 (CI)	0.00%		(0,0%; 49,5%)		44.30%		(0,0%; 83,4%)		69.70%		(36,8%; 85,4%)
Q-Q' (p-value)	0.46		0.5		1.75		0.19		1.96		0.16
Egger intercept (p-value)	–0.04		0.29		–0.01		0.19		–0.01		0.75
Rucker Test	IVW				IVW				IVW
	After outlier extraction
	Vigorous physical activity → BMI				Moderate physical activity → BMI				Sedentary time → BMI
MR method	SNP	beta	SE	p-value	SNP	beta	SE	p-value	SNP	beta	SE	p-value
Egger	NA	NA	NA	NA	NA	NA	NA	NA	5	0.49	0.36	0.26
Weighted median	NA	NA	NA	NA	NA	NA	NA	NA	5	0.10	0.10	0.29
IVW	NA	NA	NA	NA	NA	NA	NA	NA	5	0.11	0.08	0.16
Weighted mode	NA	NA	NA	NA	NA	NA	NA	NA	5	0.08	0.14	0.59
Sensitivity test	Estimate		p-value/CI		Estimate		p-value/CI		Estimate		p-value/CI
Q (p-value)	NA		NA		NA		NA		4.7		0.32
I2 (CI)	NA		NA		NA		NA		15		(0·0%; 82·3%)
Q-Q' (p-value)	NA		NA		NA		NA		1.41		0.24
Egger intercept (p-value)	NA		NA		NA		NA		–1.00E-02		0.24
Rucker Test	NA				NA				IVW

BMI, Body mass index (BMI); MR, Mendelian randomization; SNP, single nucleotide polymorphism; SE, standard error; NA, not applicable; IVW, inverse variance weighted; CI, 95% confidence interval. NA: not applicable. Note: No outlier extraction was performed for moderate physical activity → BMI and vigorous physical activity → BMI directions, since Q test and I2 did not indicate heterogeneity.

Appendix 1—table 5.

Mendelian randomization results using the IVW, Egger, weighted median and weighted mode methods of BMI on moderate PA, vigorous PA, or sedentary time.

Before outlier extraction
	BMI → Vigorous physical activity				BMI → Moderate physical activity				BMI → Sedentary time
MR method	SNP	beta	SE	p-value	SNP	beta	SE	p-value	SNP	beta	SE	p-value
Egger	64	0.09	0.08	0.22	65	0.17	0.08	0.04	65	–0.10	0.09	0.28
Weighted median	64	–0.04	0.03	0.21	65	0.004	0.04	0.92	65	0.03	0.04	0.44
IVW	64	–0.08	0.03	0.005	65	–0.05	0.03	0.09	65	0.07	0.03	0.02
Weighted mode	64	–0.01	0.07	0.86	65	0.02	0.05	0.72	65	–0.05	0.10	0.59
Sensitivity test	Estimate		p-value/CI		Estimate		p-value/CI		Estimate		p-value/CI
Q (p-value)	92.4		9.30E-03		83.73		0.05		97.5		4.40E-03
I2 (CI)	31.80%		6·9%; 50·00%		23.60%		(0·00%; 44·20%)		34.40%		10·80%; 51·70%
Q-Q' (p-value)	8.36		3.80E-03		10.86		9.81E-04		6.59		1.00E-02
Egger intercept (p-value)	–4.99E-03		9.90E-01		–6.40E-03		9.81E-04		4.96E-03		2.00E-02
Rucker test	Egger				Egger				Egger
After outlier extraction
	BMI → Vigorous physical activity				BMI → Moderate physical activity				BMI → Sedentary time
MR method	SNP	beta	SE	p-value	SNP	beta	SE	p-value	SNP	beta	SE	p-value
Egger	57	0.13	0.07	0.06	55	0.16	0.07	0.04	57	–0.02	0.08	0.76
Weighted median	57	–0.04	0.03	0.27	55	2.95E-03	0.04	0.93	57	0.03	0.04	0.48
IVW	57	–0.07	0.02	0.01	55	–0.06	0.03	0.03	57	0.07	0.03	0.01
Weighted mode	57	–0.01	0.06	0.83	55	0.02	0.06	0.68	57	–0.06	0.08	0.46
Sensitivity test	Estimate		p-value/CI		Estimate		p-value/CI		Estimate		p-value/CI
Q (p-value)	61.88		0.27		40.51		0.91		56.29		0.46
I2 (CI)	9.50%		0·00%–35·10%		0.00%		(0·0%; 8·9%)		0.50%		0·0%; 31·50%
Q-Q' (p-value)	9.79		1.75E-03		9.6		1.94E-03		1.62		2.00E-01
Egger intercept	–5.70E-03		1.75E-03		–6.44E-03		9.15E-05		2.60E-03		2.00E-01
Rucker test	IVW				IVW				IVW

BMI, Body mass index; MR, Mendelian randomization; SNP, single nucleotide polymorphism; SE, standard error; NA, not applicable; IVW, inverse variance weighted; CI, 95% confidence interval.

The results from CAUSE analyses for BFP were consistent with those for BMI, that is there was evidence of a causal effect of higher vigorous and moderate physical activity on lower BFP (p = 1.4 × 10–6 and p = 0.004, respectively), and a causal effect of more sedentary time on higher BFP (p = 0.009) (Figure 2, Appendix 1—table 6 and Appendix 1—table 7, Appendix 1—figure 2). We found no evidence of a causal relationship between physical activity or sedentary time and measures of central adiposity, including WCadjBMI and WHRadjBMI (Figure 2, Appendix 1—table 6 and Appendix 1—table 7, Appendix 1—figure 2).

Appendix 1—table 6.

CAUSE expected log pointwise posterior density (ELPD) results for central adiposity and fat percentage.

		Vigorous physical activity → BFP			BFP → vigorous physical activity
Model 1	Model 2	Delta_ELPD	SE_delta_ELPD	z	Delta_ELPD	SE_delta_ELPD	z
Null	Sharing	–23.55	4.67	–5.04	–360.48	24.46	–14.74
Null	Causal	–25.11	5.00	–5.02	–361.77	24.49	–14.77
Sharing	Causal	–1.56	0.33	–4.68	–1.30	0.17	–7.77
		Moderate physical activity → BFP			BFP → Moderate physical activity
Null	Sharing	–8.71	2.60	–3.34	–170.46	17.46	–9.76
Null	Causal	–10.11	3.13	–3.23	–171.50	17.63	–9.73
Sharing	Causal	–1.40	0.53	–2.65	–1.03	0.54	–1.90
		Sedentary time → BFP			BFP → Sedentary time
Null	Sharing	–9.74	3.30	–2.95	–143.04	15.86	–9.02
Null	Causal	–11.01	3.83	–2.87	–144.25	16.13	–8.94
Sharing	Causal	–1.27	0.54	–2.38	–1.21	0.36	–3.41
		Vigorous physical activity → WCadjBMI			WCadjBMI → Vigorous physical activity
		Delta_ELPD	SE_delta_ELPD	z	Delta_ELPD	SE_delta_ELPD	z
Null	Sharing	0.57	0.07	7.71	–6.37	3.13	–2.03
Null	Causal	1.36	0.15	9.28	–7.16	3.65	–1.96
Sharing	Causal	0.79	0.07	10.60	–0.79	0.54	–1.46
		Moderate physical activity → WCadjBMI			WCadjBMI → Moderate physical activity
Null	Sharing	0.50	0.56	0.89	–4.83	2.96	–1.63
Null	Causal	1.01	0.87	1.16	–5.40	3.58	–1.51
Sharing	Causal	0.51	0.36	1.44	–0.56	0.65	–0.87
		Sedentary time → WCadjBMI			WCadjBMI → Sedentary time
Null	Sharing	0.55	0.07	7.56	–7.59	3.34	–2.27
Null	Causal	1.39	0.16	8.55	–8.61	3.97	–2.17
Sharing	Causal	0.83	0.09	9.21	–1.02	0.65	–1.56
		Vigorous physical activity → WHRadjBMI			WHRadjBMI → Vigorous physical activity
		Delta_ELPD	SE_delta_ELPD	z	Delta_ELPD	SE_delta_ELPD	z
Null	Sharing	–0.91	1.19	–0.77	0.06	0.84	0.07
Null	Causal	–1.68	2.10	–0.80	0.31	1.52	0.21
Sharing	Causal	–0.77	0.91	–0.85	0.26	0.68	0.37
		Moderate physical activity → WHRadjBMI			WHRadjBMI → Moderate physical activity
Null	Sharing	0.48	0.16	3.00	0.22	0.77	0.28
Null	Causal	0.92	0.56	1.63	0.44	1.44	0.30
Sharing	Causal	0.44	0.41	1.09	0.22	0.67	0.32
		Sedentary time → WHRadjBMI			WHRadjBMI → Sedentary time
Null	Sharing	0.57	0.11	5.29	–6.72	3.44	–1.95
Null	Causal	1.37	0.28	4.83	–7.31	4.03	–1.81
Sharing	Causal	0.80	0.18	4.48	–0.59	0.61	–0.97

BFP, body fat percentage; WCadjBMI, waist cirumference adjusted for body mass index; WHRadjBMI, waist-to-hip ratio adjusted for body mass index, SE, standard error; NA, not applicable; CI, 95% confidence interval.

Appendix 1—table 7.

CAUSE posterior probabilities and q values for the causal and sharing models for central adiposity and body fat percentage.

Model	Causal Effect (CI)	Shared effect (CI)	Q (CI)	Sharing vs causal model p-value
	Vigorous physical activity → BFP
Sharing	NA	–0.18 (-0.23,–0.13)	0.89 (0.67, 0.98)	1.4e-06
Causal	–0.17 (-0.24,–0.09)	0 (-0.28, 0.26)	0.19 (0, 0.86)
	Moderate physical activity → BFP
Sharing	NA	–0.17 (-0.26,–0.09)	0.78 (0.39, 0.97)	0.0041
Causal	–0.15 (-0.24,–0.05)	0 (-0.32, 0.31)	0.2 (0, 0.86)
	Sedentary time → BFP
Sharing	NA	0.11 (0.06, 0.17)	0.75 (0.37, 0.96)	0.0088
Causal	0.09 (0.03, 0.15)	0 (-0.26, 0.27)	0.19 (0, 0.86)
	BFP → Vigorous physical activity
Sharing	NA	–0.27 (-0.29,–0.25)	0.97 (0.92, 1)	3.9e-15
Causal	–0.26 (-0.31,–0.22)	0 (-0.26, 0.22)	0.18 (0, 0.85)
	BFP → Moderate physical activity
Sharing	NA	–0.21 (-0.25,–0.18)	0.91 (0.77, 0.99)	0.029
Causal	–0.19 (-0.26,–0.12)	0 (-0.3, 0.31)	0.19 (0, 0.86)
	BFP → Sedentary time
Sharing	NA	0.2 (0.17, 0.24)	0.91 (0.76, 0.99)	0.00032
Causal	0.19 (0.12, 0.25)	0 (-0.33, 0.31)	0.18 (0, 0.86)
	Vigorous physical activity → WCadjBMI
Sharing	NA	–0.01 (-0.62, 0.59)	0.12 (0, 0.72)	1
Causal	0 (-0.15, 0.14)	0 (-0.55, 0.52)	0.2 (0.01, 0.86)
	Moderate physical activity → WCadjBMI
Sharing	NA	–0.14 (-0.98, 0.6)	0.13 (0.01, 0.69)	9.20E-01
Causal	–0.03 (-0.36, 0.27)	–0.03 (-0.83, 0.7)	0.26 (0.01, 0.84)
	Sedentary time → WCadjBMI
Sharing	NA	0.01 (-0.44, 0.57)	0.12 (0, 0.71)	1
Causal	0 (-0.13, 0.14)	0.01 (-0.41, 0.52)	0.21 (0.01, 0.85)
	WCadjBMI → Vigorous physical activity
Sharing	NA	–0.1 (-0.21,–0.05)	0.59 (0.19, 0.92)	0.072
Causal	–0.07 (-0.14, 0)	0 (-0.31, 0.36)	0.19 (0, 0.86)
	WCadjBMI → Moderate physical activity
Sharing	NA	–0.11 (-0.27,–0.04)	0.47 (0.11, 0.88)	0.19
Causal	–0.06 (-0.14, 0.03)	0 (-0.34, 0.36)	0.19 (0, 0.86)
	WCadjBMI → Sedentary time
Sharing	NA	0.1 (0.05, 0.2)	0.63 (0.23, 0.93)	0.059
Causal	0.07 (0.01, 0.14)	0.01 (-0.3, 0.48)	0.17 (0, 0.85)
	Vigorous physical activity → WHRadjBMI
Sharing	NA	–0.1 (-0.39, 0.07)	0.36 (0.01, 0.86)	0.2
Causal	–0.06 (-0.16, 0.04)	0 (-0.37, 0.44)	0.19 (0, 0.86)
	Moderate physical activity → WHRadjBMI
Sharing	NA	–0.04 (-0.48, 0.39)	0.15 (0, 0.76)	8.60E-01
Causal	–0.03 (-0.14, 0.09)	0 (-0.41, 0.4)	0.2 (0, 0.86)
	Sedentary time → WHRadjBMI
Sharing	NA	0.01 (-0.26, 0.34)	0.12 (0, 0.72)	1
Causal	0 (-0.06, 0.07)	0 (-0.22, 0.28)	0.2 (0, 0.86)
	WHRadjBMI → Vigorous physical activity
Sharing	NA	–0.04 (-0.3, 0.12)	0.16 (0, 0.76)	0.65
Causal	–0.01 (-0.06, 0.03)	0 (-0.25, 0.21)	0.18 (0, 0.85)
	WHRadjBMI → Moderate physical activity
Sharing	NA	–0.04 (-0.31, 0.14)	0.16 (0, 0.75)	6.30E-01
Causal	–0.01 (-0.06, 0.03)	0 (-0.25, 0.22)	0.18 (0, 0.85)
	WHRadjBMI → Sedentary time
Sharing	NA	0.07 (0.03, 0.18)	0.49 (0.13, 0.89)	0.17
Causal	0.04 (-0.01, 0.09)	0 (-0.29, 0.4)	0.17 (0, 0.83)

BFP, Body Fat Percentage; WCadjBMI, waist circumference adjusted for BMI; WHRadjBMI,waist-to-hip ratio adjusted for BMI; NA, not applicable; CI, 95% confidence interval.

Appendix 1—figure 2.

Estimates from the CAUSE method for the causal relationship between physical activity or sedentary time and waist-hip ratio, waist circumference, or body fat percentage.

Median causal estimates for Mendelian randomization analyses using the CAUSE method. A diamond (♢) in the estimate for CAUSE indicates that the sharing model fit the data better than the causal model, that is that the association between the traits was more likely to be explained by horizontal correlated pleiotropy than causality. PA, physical activity; WHRadjBMI, waist-to-hip ratio adjusted for body mass index; WCadjBMI, waist circumference adjusted for body mass index; BFP, body fat percentage. Figure icons were created with BioRender.com.

Discussion

The present Mendelian randomization analyses suggest a bidirectional causal relationship between higher sedentary time and higher BMI, implying that decreasing sedentary time is beneficial for weight management, but also that reducing adiposity may lead to additional health benefits by reducing sedentary time. The analyses also suggest there is a causal association between higher levels of physical activity and lower BMI, supporting the view that preventive programs for increasing physical activity and decreasing sedentary time are beneficial for weight management.

Based on the causal effect size in our analysis, we estimated that each 1 hr daily increase in moderate physical activity or 1 hr decrease in sedentary time was associated with a 0.27 kg/m2 (~ 0.8 kg) or 0.14 kg/m2 (~0.4 kg) decrease in BMI or body weight, respectively. Our results also suggest that each 1 kg/m2 (~3 kg) higher BMI increases daily sedentary time by ~3.5 min, but do not suggest a causal effect of BMI on physical activity (Appendix 1 and Appendix 1—table 3). Our results are well in accordance with a previous observational study that aimed to assess the bidirectional relationship between physical activity and weight change during a 10-year period (Barone Gibbs et al., 2020). Examining associations between accelerometer-based activity measures and weight change in 866 men and women, the study suggested a bidirectional relationship where higher sedentary time at baseline increased 10-year weight gain and higher baseline weight was associated with an unfavorable 10-year change in sedentary time. The effect sizes indicated that 1 hr lower sedentary time at baseline was associated with ~0.3 kg decrease in body weight over the 10-year follow up, whereas 3 kg higher baseline body weight was associated with ~2 min increase in sedentary time, closely resembling the causal estimates we observed in the present Mendelian randomization analyses. Our results are also in accordance with randomized clinical trials of physical activity interventions which generally suggest that increasing physical activity leads to a moderate loss of body weight in overweight or obese participants (Church et al., 2009; Rosenkilde et al., 2012; Golubic et al., 2015; Kim et al., 2019; Biddle et al., 2015). Resembling the causal estimates we observed, meta-analyses of randomized clinical trials have suggested weight losses ranging from 0.3 kg to 1.8 kg for various physical activity interventions ranging from 2 to 52 weeks (Twells et al., 2021). However, it is important to note that the causal estimates from Mendelian randomization are not fully comparable to those from randomized clinical trials, because they represent lifelong effects rather than effects lasting a defined length of an intervention, and furthermore, physical activity interventions may operate on body weight through other pathways than those affected by the genotypes. The causal effect of higher adiposity on sedentary time has not been to date assessed in randomized clinical trials, likely due to the ethical and practical limitations of performing such a study.

In a previous Mendelian randomization analysis of adult populations, evidence for a causal, bidirectional relationship between overall activity levels and higher BMI was observed using the maximum likelihood method, but the results showed evidence of horizontal pleiotropy that could not be fully accounted for and the role of activity intensity level remained unclear (Doherty et al., 2018). Here, using a method that takes advantage of full genome-wide summary results and corrects for sample overlap between the exposure and the outcome traits to maximize statistical power and correct for pleiotropy, we showed that the causal bidirectional relationship is particularly evident for the relationship between sedentary time and adiposity. Our results may also be compared with two independent one-sample Mendelian randomization studies performed in children (Richmond et al., 2014; Schnurr et al., 2018). The first study, including 4296 children at 11 years of age from the United Kingdom, indicated a causal association between higher BMI and lower accelerometer-based moderate and moderate-to-vigorous physical activity and more sedentary time (Richmond et al., 2014). The second study, including 679 children at age 3–8 years from Denmark, also indicated that higher BMI is causal for higher accelerometer-based sedentary time, but did not find a causality for moderate or moderate-to-vigorous physical activity (Schnurr et al., 2018). Consistent with the latter study of children, our results indicate a causal effect of BMI on sedentary behavior, but not on physical activity, in adults. The differences between studies could be due to different applied methods, or methodological limitations, such as weak instrument bias when smaller sample sizes are used, which may lead to estimated causal effects towards the observational association. One could also expect differences between children and adults given the distinct patterns by which they engage in physical activity. For example, while physical activity in adults consists of commuting, occupational and structured leisure-time activities, children primarily engage in spontaneous, play-oriented activities. Higher BMI leads to higher perceived exertion during physical activity (Groslambert and Mahon, 2006), which could reduce the natural inclination of children to engage in play-oriented activities, whereas adults exert more conscious control over their daily activities.

The strengths of the present studies include the use of genome-wide summary results for objectively measured physical activity and sedentary time, which avoided misreporting bias evident for self-reported measures, as well as the use of newly developed Mendelian randomization method that utilizes full genome-wide summary results to improve statistical power, correct for sample overlap, and assess horizontal pleiotropy, successfully applied in recent Mendelian randomization studies (Jäger et al., 2020; Mitchell et al., 2020). The limitations are that we cannot exclude other sources of bias in the measurement of physical activity and sedentary time that could influence the observed causal estimates, including the observer effect and the limited 7-day period of the measurement, which may not be representative of long-term activity habits. Furthermore, even if we used the largest available data on objectively measured physical activity, the statistical power was limited, as very few genome-wide significant loci have thus far been identified. When larger sample sizes for accelerometer-based physical activity become available, the results should be replicated. The present study is also limited in the fact that the findings are not generalizable across different age-groups or populations. Moreover, further research is needed to investigate causal relationships at various BMI thresholds.

In conclusion, the present Mendelian randomization analyses indicate a bidirectional causal relationship between higher sedentary time and higher BMI. Thus, decreasing sedentary time is likely to be beneficial for weight management, but reducing adiposity may also lead to additional health benefits by reducing sedentary time. Our analyses also suggest that there is a causal association between higher levels of physical activity and lower BMI, supporting the view that lifelong preventive programs for increasing physical activity and decreasing sedentary time are beneficial for weight management.

Materials and methods

Data sources and populations

We used summary results from the largest published genome-wide association studies (GWAS) of objectively assessed physical activity, sedentary behavior, and BMI in individuals of European ancestry. The physical activity GWAS included up to 91,105 individuals for accelerometer-based vigorous physical activity, moderate physical activity, or sedentary time from the UK Biobank (Klimentidis et al., 2018; Doherty et al., 2018). In these studies, accelerometer was worn continuously for at least 72 hr and up to 7 days. Vigorous physical activity was defined as the fraction of accelerations > 425 milli-gravities, and moderate physical activity was predicted using a machine-learning method for moderate intensity activity time (Doherty et al., 2018). Sedentary time was defined as the time spent in activities with metabolic equivalent of task (MET) ≤1.5 during sitting, lying, or in reclining posture, except for driving and certain non-desk work instances where MET ≤2.5 was applied (Doherty et al., 2018). For BMI, we utilized GWAS results from a meta-analysis of the Genetic Investigation of Anthropometric Traits (GIANT Consortium) and the UK Biobank data, including altogether 806,834 individuals of European ancestry (Pulit et al., 2019). For Mendelian randomization analyses using the inverse variance-weighted (IVW), weighted median, weighted mode, and MR-Egger regression methods, we used only the GIANT Consortium BMI meta-analysis data of 339,224 individuals without the UK Biobank data to avoid sample overlap between the exposure and outcome traits as these methods are sensitive to bias from overlapping samples (Locke et al., 2015).

In addition to BMI, we assessed causal effects of physical activity and sedentary time on body fat percentage (BFP) and on two measures of central adiposity, including waist circumference and waist-hip ratio adjusted for BMI (WCadjBMI and WHRadjBMI, respectively). GWAS results for BFP were available from an analysis of 454,633 participants of European ancestry in the UK Biobank (Elsworth et al., 2020). GWAS results for WCadjBMI and WHRadjBMI were available from GIANT Consortium meta-analyses of 231,355 and 694,649 individuals of European ancestry, respectively (Justice et al., 2017; Pulit et al., 2019).

Mendelian randomization using full genome-wide summary results for the exposure trait

Only few genetic loci have been found to be associated with accelerometer-based moderate physical activity (n = 2), vigorous physical activity (n = 1) or sedentary time (n = 4) at genome-wide significance (p < 5 × 10–8) (Klimentidis et al., 2018; Doherty et al., 2018), and the loci thus provide a limited power to study causal associations with BMI using Mendelian randomization. The recently published Causal Analysis Using Summary Effect Estimates (CAUSE) Mendelian randomization method (Morrison et al., 2020) improves statistical power in such cases, by utilizing full genome-wide summary results instead of genome-wide significant loci only. Furthermore, the CAUSE method is able to correct for sample overlap between the exposure and the outcome trait, which allows using the largest sample sizes available for both traits. CAUSE has also been found to be less prone to identify false positive associations compared to other commonly used Mendelian randomization methods (Burgess et al., 2019; Morrison et al., 2020).

The CAUSE method calculates the posterior probabilities of the causal effect and the shared (non-causal) effect, where the causal effect reflects the effect of the variants on the outcome trait through the exposure and the shared effect reflects correlated horizontal pleiotropy (Figure 1), that is the effect of the variants on the outcome through confounders. The distinction between a causal effect and correlated horizontal pleiotropy follows the assumption that a causal effect leads to non-zero genetic correlation between the exposure and the outcome where the correlation is driven by all variants associated with the exposure. If only a subset of variants contributes to the genetic correlation between the exposure and the outcome, it is considered the result of correlated horizontal pleiotropy. The CAUSE method also provides an estimate of the proportion of variants that are likely to show correlated horizontal pleiotropy, the q value.

We used the CAUSE settings and procedures originally recommended by the authors (Morrison et al., 2020), with the exception of q priors that were set to fit the strictest model possible (q_alpha = 1 and q_beta = 2) in order to avoid false positive findings. A thorough explanation of the steps used to perform CAUSE analysis is included in the supplementary text (Appendix 1).

Mendelian randomization using genome-wide significant loci for the exposure trait

In addition to the CAUSE method that implements Mendelian randomization analyses using full genome-wide summary results for the exposure trait, we implemented four commonly used Mendelian randomization methods that utilize genome-wide significant loci only: the IVW, MR-Egger, weighted median and weighted mode methods (Appendix 1). We performed sensitivity analyses using Steiger filtering to remove variants that showed stronger association with the outcome than the exposure trait and that were thus not considered suitable as instruments for the exposure trait. To create the genetic instrument for the exposure trait, we only included the lead variants that showed genome-wide significant associations with the trait (p < 5 × 10–8) and with a pairwise linkage disequilibrium (LD) r2 <0.001 with their neighboring variants, in a window of 10,000 kb. Variants that were not available in the outcome trait GWAS were substituted by their LD proxies (r2 >0.8). Palindromic variants (A/T, G/C) were excluded. If less than three genetic variants were identified with these parameters, we used a less stringent p-value threshold of p < 5 × 10–7 to identify enough genetic instruments. In order to assess the strength of the genetic instrument, we obtained F-statistics for each trait. The analyses were performed using the TwoSampleMR package in R and are described in detail in the Appendix 1 (Hemani et al., 2018).

We estimated heterogeneity across the causal estimates of the SNPs using the Meta R package (Schwarzer et al., 2015). The causal estimates were considered heterogeneous if the p value for Cochran’s Q test was significantly different from zero (p < 0.05) and I2 was above 0.25. We assessed bias introduced by horizontal pleiotropy by implementing the Egger’s intercept test using the TwoSampleMR package in R (Hemani et al., 2018). An Egger’s intercept that deviated significantly from zero (p < 0.05) was considered as evidence of horizontal pleiotropy. We used the Rucker framework (Bowden et al., 2018) to assess whether Egger regression that accounts for horizontal pleiotropy but limits statistical power should be applied instead of the standard IVW model. To visually assess heterogeneity and horizontal pleiotropy, we observed forest plots and funnel plots (Figure 2, Appendix 1—figure 3). To detect individual pleiotropic variants that might bias the results, we applied the RadialMR package in R using an iterative Cochran’s Q method and setting a strict outlier P value threshold of <0.05 (Bowden et al., 2018). The iterative Cochran’s Q, either IVW’s Q or Egger’s Q was chosen depending on Rucker framework results. After removing outlier variants detected with RadialMR, we re-run the Mendelian randomization and sensitivity tests and plots, to make sure that the variants introducing horizontal pleiotropy (Figure 1) had been removed. The analysis plan for this study is described in the supplementary text (Appendix 2).

Appendix 1—figure 3.

Leave-one-out forest and funnel sensitivity plots after outlier extraction.

The CAUSE method’s median posterior probability of the causal effect cannot be easily transformed to absolute units. To convert the causal estimates to absolute units, we calculated a causal effect with weighted median method using independent variants identified in CAUSE that were not removed by the outlier extraction protocol described above, in order to mimic CAUSE control for correlated and uncorrelated pleiotropy (Appendix 1).

This paper is of potential interest to those researchers and clinicians working in the area of physical activity and obesity. The authors have presented strong evidence of a causal relationship between physical activity and higher BMI. The conclusions that have been made are supported by the data and are translationally relevant.

Our editorial process produces two outputs: i) public reviews designed to be posted alongside the preprint for the benefit of readers; ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

Thank you for submitting your article "Mendelian randomization suggests a bidirectional, causal relationship between physical inactivity and obesity" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by Y M Dennis Lo as the Senior Editor/Reviewing Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Xin He (Reviewer #2); Ashley Budu-Aggrey (Reviewer #3).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

1) It is mentioned in the abstract and shown in Table 1 that BMI lead to increase in sedentary but not moderate/more vigorous activities. Could the authors explain why it may be the case (one may expect no associations for all or consistent associations for these 3)?

2) The use of BMI is reasonable but did the authors consider other measures of (central) obesity, eg waist circumference, waist-hip ratio, fat % etc., for which GWAS summary data should be available.

3) The no. of SNPs should be presented in table 2.

4) How do the MR estimate in this study compare to effect sizes of physical exercise (or interventions of exercise program) from previous clinical (epidemiology) studies? How does this study support or refute findings from previous works? Please kindly elaborate further.

5) Typo? in the conclusion part: increasing sedentary time is likely to be beneficial for weight management.

6) Supp Text p21 line 471

I don't think the inside assumption can be checked by I-squared (it addresses NOME assumption mainly). Please refer to

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5446088/.

7) It may be useful to visualize the MR analysis with scatter plot of the effect sizes of variants on the exposure (BMI) and outcome (sedentary time). In the plot, the variants can be colored by their contribution to the CAUSE statistics, see Figure 4 of the CAUSE paper. This plot would help show, for example, whether there are outlier variants; or whether the results are largely driven by just a small number of variants.

8) CAUSE is susceptible to false positives when the value of q, a measure of the proportion of shared variants, is high. The authors stated that q is about 0.2, which is pretty small. However, it is unclear if this is q under the causal model or the sharing model. If q is small under the sharing model, the result would be quite convincing. This needs to be clarified.

9) For transparency, it would be useful to make the genetic instruments, the summary data and the scripts used to perform the analysis publicly available. It would be useful to emphasize in the manuscript that it is the causal effect of genetic liability for these traits that have been investigated. In addition, the authors may want to mention that further study would be warranted to investigate causal relationships at various BMI thresholds.

Reviewer #1 (Recommendations for the authors):

The author employed a causal inference method known as Mendelian randomization (MR) to evaluate potential causal relationships between physical activities and obesity. The strengths and part of the limitations are given in the public review part.

Here are my further suggestions/comments for authors' consideration

1) It is mentioned in the abstract and shown in Table 1 that BMI lead to increase in sedentary but not moderate/more vigorous activities. Could the authors explain why it may be the case (one may expect no associations for all or consistent associations for these 3)?

2) The use of BMI is reasonable but did the authors consider other measures of (central) obesity, eg waist circumference, waist-hip ratio, fat % etc. , for which gwas summary data should be available

3) I suggest the no. of snps be presented in table 2

4) How do the MR estimate in this study compare to effect sizes of physical exercise (or interventions of exercise program) from previous clinical (epidemiology) studies? How does this study support or refute findings from previous works? Please kindly elaborate further.

5) typo? in the conclusion part: increasing sedentary time is likely to be beneficial for weight management.

6) Supp Text p21 line 471

I don't think the inside assumption can be checked by I-squared (it addresses NOME assumption mainly). Please refer to

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5446088/.

Reviewer #2 (Recommendations for the authors):

None.

Reviewer #3 (Recommendations for the authors):

The authors have presented a well written and conclusive study, where strong evidence suggests a causal bidirectional relationship between BMI and physical inactivity.

The methods used and results presented do support the conclusions that have been claimed in this study.

For transparency, I would suggest making the genetic instruments, the summary data and the scripts used to perform the analysis publicly available. I would also stress that it is the causal effect of genetic liability for these traits that have been investigated. In addition, the authors may want to mention that further study would be warranted to investigate causal relationships at various BMI thresholds.

Essential revisions:

1) It is mentioned in the abstract and shown in Table 1 that BMI lead to increase in sedentary but not moderate/more vigorous activities. Could the authors explain why it may be the case (one may expect no associations for all or consistent associations for these 3)?

This is a very relevant point to clarify. Sedentary time reflects the time spent awake in sedentary behaviors involving a sitting, reclining or lying posture. Moderate physical activity reflects the time spent in brisk walking, slow bicycling or other behaviors that affect heart rate and breathing. Sedentary time and physical activity are thus not opposite of each other, and individuals can be physically active even if they would increase their daily time spent in sedentary behaviors. Therefore, it is important to address the causal relationship with obesity separately for sedentary time and physical activity.

We have now clarified this aspect in the Abstract and Introduction:

Lines 58-60: “It is important to assess the causal relationship with adiposity separately for physical activity and sedentary time, as individuals can be physically active even if they engaged a substantial part of their time to sedentary behaviors, and vice versa (Panahi and Tremblay, 2018).”

2) The use of BMI is reasonable but did the authors consider other measures of (central) obesity, eg waist circumference, waist-hip ratio, fat % etc., for which GWAS summary data should be available.

Thank you, this is a very good suggestion. We have now expanded our analyses using CAUSE to other measures of obesity and central obesity, including body fat percentage (BFP) and waist circumference and waist-hip ratio adjusted for BMI (WCadjBMI and WHRadjBMI). Overall, we find that BFP shows consistent results with BMI, but find no evidence of causality between physical inactivity or sedentary time and WCadjBMI or WHRadjBMI.

We have reported these new results in Lines 235-241:

“The results from CAUSE analyses for BFP were consistent with those for BMI, i.e. there was evidence of a causal effect of higher vigorous and moderate physical activity on lower BFP (P=1.4x10-6 and P=0.004, respectively), and a causal effect of more sedentary time on higher BFP (P=0.009) (Appendix 1-table 6 and 7, Figure 2, Appendix 1-figure 2). We found no evidence of a causal relationship between physical activity or sedentary time and measures of central adiposity, including WCadjBMI and WHRadjBMI (Appendix 1-table 6 and 7, Figure 2, Appendix 1-figure 2).”

We have described the methods used in these new analyses in Lines 373-379:

“In addition to BMI, we assessed causal effects of physical activity and sedentary time on body fat percentage (BFP) and on two measures of central adiposity, including waist circumference and waist-hip ratio adjusted for BMI (WCadjBMI and WHRadjBMI, respectively). GWAS results for BFP were available from an analysis of 454,633 participants of European ancestry in the UK Biobank (Elsworth et al., 2020). GWAS results for WCadjBMI and WHRadjBMI were available from GIANT Consortium meta-analyses of 231,355 and 694,649 individuals of European ancestry, respectively (Justice et al., 2017, Pulit et al., 2019).”

To note, since we are now examining four different continuous measures of adiposity in the manuscript, we have changed the word “obesity” to “adiposity” in the title and elsewhere in the manuscript, whenever needed and justified.

3) The no. of SNPs should be presented in table 2.

We have now added the number of SNPs in Table 2.

4) How do the MR estimate in this study compare to effect sizes of physical exercise (or interventions of exercise program) from previous clinical (epidemiology) studies? How does this study support or refute findings from previous works? Please kindly elaborate further.

We have now elaborated further on the effect sizes of physical activity and exercise interventions on weight loss in previous studies, and compared these findings with the causal estimates observed in the present Mendelian randomization analyses:

Lines 278-294: “Our results are well in accordance with a previous observational study that aimed to assess the bidirectional relationship between physical activity and weight change during a 10-year period (Barone Gibbs et al., 2020). Examining associations between accelerometer-based activity measures and weight change in 866 men and women, the study suggested a bidirectional relationship where higher sedentary time at baseline increased 10-year weight gain and higher baseline weight was associated with an unfavorable 10-year change in sedentary time. The effect sizes indicated that 1 hour lower sedentary time at baseline was associated with ~0.3 kg decrease in body weight over the 10-year follow up, whereas 3 kg higher baseline body weight was associated with ~2 min increase in sedentary time, closely resembling the causal estimates we observed in the present Mendelian randomization analyses. Our results are also in accordance with randomized clinical trials of physical activity interventions which generally suggest that increasing physical activity leads to a moderate loss of body weight in overweight or obese participants (Church et al., 2009, Rosenkilde et al., 2012, Golubic et al., 2015, Kim et al., 2019, Biddle et al., 2015). Resembling the causal estimates we observed, meta-analyses of randomized clinical trials have suggested weight losses ranging from 0.3 kg to 1.8 kg for various physical activity interventions ranging from 2-52 weeks (Twells et al., 2021).”

5) typo? in the conclusion part: increasing sedentary time is likely to be beneficial for weight management.

Thank you for noting this error. We have now corrected the sentence to “decreasing sedentary time is likely to be beneficial for weight management” (lines 347-348).

6) Supp Text p21 line 471

I don't think the inside assumption can be checked by I-squared (it addresses NOME assumption mainly). Please refer to

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5446088/.

We agree and have now clarified that we checked the NOME assumption, not the inside assumption, using I-squared and used the suggested reference (PMC5446088) in Lines 670-672:

“The no measurement error (NOME) assumption, which assumes no measurement error between the genetic instrument and the exposure, was checked by calculating the mean F-statistic and the variation of the I2 statistic [3].”

7) It may be useful to visualize the MR analysis with scatter plot of the effect sizes of variants on the exposure (BMI) and outcome (sedentary time). In the plot, the variants can be colored by their contribution to the CAUSE statistics, see Figure 4 of the CAUSE paper. This plot would help show, for example, whether there are outlier variants; or whether the results are largely driven by just a small number of variants.

We agree and have now added a scatter plot of the expected log pointwise posterior density (ELPD) contributions of each variant to BMI and sedentary time, and the contributions of the variants to selecting either the causal model or the shared model (Supplementary Figure 1 panel A). We identified one clear outlier variant (red circle) that we thus decided to remove before re-running the CAUSE analysis (panel B). We found that the causal effect of BMI on sedentary time remained of similar magnitude before and after the removal of this outlier variant (β=0.13, P=6x10-4 and β=0.13, P=3x10-5, respectively) (Appendix 1-table 1 and 2).

We have added a paragraph in the Results section to describe these new findings:

Lines 204-210: “We checked for outlier variants by producing a scatter plot of expected log pointwise posterior density (ELPD) contributions of the variants to BMI and sedentary time (Appendix 1-table 1), identifying one clear outlier variant (rs6567160 in MC4R gene) (Figure 2, Appendix 1-figure 1). However, the causal effect of BMI on sedentary time remained consistent even after removing this outlier variant from the CAUSE analysis (Appendix 1-table 1 and 2).”

8) CAUSE is susceptible to false positives when the value of q, a measure of the proportion of shared variants, is high. The authors stated that q is about 0.2, which is pretty small. However, it is unclear if this is q under the causal model or the sharing model. If q is small under the sharing model, the result would be quite convincing. This needs to be clarified.

We thank the reviewer for a very relevant question. We have now clarified in the manuscript that all of the reported q values (~0.2) were under the causal model (lines 202-203). We applied the strict parameters for the priors in CAUSE in all of our analyses, which leads to high shared model q values (q=0.7-0.9). To examine whether our bidirectional causal findings for BMI and sedentary time may represent false positive results, we performed a further analysis to identify and exclude outlier variants, as described in our response to Question 7. I.e. we produced a scatter plot of expected log pointwise posterior density (ELPD) contributions of each variant to BMI and sedentary time, and the contributions of the variants to selecting either the causal model or the shared model (Supplementary Figure 1 panel A). We identified one clear outlier variant (red circle) that we thus removed (panel B), but the magnitude of the causal estimates was not affected by the exclusion of the variant (Appendix 1-table 1 and 2).

9) For transparency, it would be useful to make the genetic instruments, the summary data and the scripts used to perform the analysis publicly available. It would be useful to emphasize in the manuscript that it is the causal effect of genetic liability for these traits that have been investigated. In addition, the authors may want to mention that further study would be warranted to investigate causal relationships at various BMI thresholds.

Thank you for the valuable comments. We fully agree that making the data and scripts publicly available is important. Thus, we have now added a data sharing statement in the end of the manuscript along with the web-link and github repositories where the summary data, genetic instruments and R scripts are freely available

Lines 461-466: “Data sharing: All analyses were performed using R statistical package freely available at https://cran.r-project.org/mirrors.html. The CAUSE R package and instructions are available at https://jean997.github.io/cause/. The Two-sample MR package is available at https://mrcieu.github.io/TwoSampleMR/. The RadialMR package is available at https://github.com/WSpiller/RadialMR. The code and curated data for the current analysis are available at https://github.com/MarioGuCBMR/MR_Physical_Activity_BMI.”

As suggested by the reviewers, we have now also clarified that we investigated the causal effect of genetic liability for physical activity and adiposity traits.

Lines 24-25: “We assessed genetic liability using results from genome-wide association studies for accelerometer-based physical activity and sedentary time…”

Lines 67-68: “Here, we aimed to assess the causality between the genetic liability of physical inactivity, sedentary time and BMI…”

Lines 266-267: “The present Mendelian randomization analyses suggest a bidirectional causal relationship between higher genetic liability of sedentary time and higher BMI…”

We have now also added a sentence in the Discussion section to state that future research is needed to investigate the casual relationships in connection to different BMI thresholds.

Lines 342-343: “Moreover, further research is needed to investigate causal relationships at various BMI thresholds.”

Reviewer #1 (Recommendations for the authors):

The author employed a causal inference method known as Mendelian randomization (MR) to evaluate potential causal relationships between physical activities and obesity. The strengths and part of the limitations are given in the public review part.

Here are my further suggestions/comments for authors' consideration

1) It is mentioned in the abstract and shown in Table 1 that BMI lead to increase in sedentary but not moderate/more vigorous activities. Could the authors explain why it may be the case (one may expect no associations for all or consistent associations for these 3)?

This is a very relevant point to clarify. Sedentary time reflects the time spent awake in sedentary behaviors involving a sitting, reclining or lying posture. Moderate physical activity reflects the time spent in brisk walking, slow bicycling or other behaviors that affect heart rate and breathing. Sedentary time and physical activity are thus not opposite of each other, and individuals can be physically active even if they would increase their daily time spent in sedentary behaviors. Therefore, it is important to address the causal relationship with obesity separately for sedentary time and physical activity.

We have now clarified this aspect in the Abstract and Introduction:

Lines 58-60: “It is important to assess the causal relationship with adiposity separately for physical activity and sedentary time, as individuals can be physically active even if they engaged a substantial part of their time to sedentary behaviors, and vice versa (Panahi and Tremblay, 2018).”

2) The use of BMI is reasonable but did the authors consider other measures of (central) obesity, eg waist circumference, waist-hip ratio, fat % etc. , for which gwas summary data should be available

Thank you, this is a very good suggestion. We have now expanded our analyses using CAUSE to other measures of obesity and central obesity, including body fat percentage (BFP) and waist circumference and waist-hip ratio adjusted for BMI (WCadjBMI and WHRadjBMI). Overall, we find that BFP shows consistent results with BMI, but find no evidence of causality between physical inactivity or sedentary time and WCadjBMI or WHRadjBMI.

We have reported these new results in Lines 235-241:

“The results from CAUSE analyses for BFP were consistent with those for BMI, i.e. there was evidence of a causal effect of higher vigorous and moderate physical activity on lower BFP (P=1.4x10-6 and P=0.004, respectively), and a causal effect of more sedentary time on higher BFP (P=0.009) (Appendix 1-table 6 and 7, Figure 2, Appendix 1-figure 2). We found no evidence of a causal relationship between physical activity or sedentary time and measures of central adiposity, including WCadjBMI and WHRadjBMI (Appendix 1-table 6 and 7, Figure 2, Appendix 1-figure 2).”

We have described the methods used in these new analyses in Lines 373-379:

“In addition to BMI, we assessed causal effects of physical activity and sedentary time on body fat percentage (BFP) and on two measures of central adiposity, including waist circumference and waist-hip ratio adjusted for BMI (WCadjBMI and WHRadjBMI, respectively). GWAS results for BFP were available from an analysis of 454,633 participants of European ancestry in the UK Biobank (Elsworth et al., 2020). GWAS results for WCadjBMI and WHRadjBMI were available from GIANT Consortium meta-analyses of 231,355 and 694,649 individuals of European ancestry, respectively (Justice et al., 2017, Pulit et al., 2019).”

To note, since we are now examining four different continuous measures of adiposity in the manuscript, we have changed the word “obesity” to “adiposity” in the title and elsewhere in the manuscript, whenever needed and justified.

3) I suggest the no. of snps be presented in table 2

We have now added the number of SNPs in Table 2.

4) How do the MR estimate in this study compare to effect sizes of physical exercise (or interventions of exercise program) from previous clinical (epidemiology) studies? How does this study support or refute findings from previous works? Please kindly elaborate further.

We have now elaborated further on the effect sizes of physical activity and exercise interventions on weight loss in previous studies, and compared these findings with the causal estimates observed in the present Mendelian randomization analyses:

Lines 278-294: “Our results are well in accordance with a previous observational study that aimed to assess the bidirectional relationship between physical activity and weight change during a 10-year period (Barone Gibbs et al., 2020). Examining associations between accelerometer-based activity measures and weight change in 866 men and women, the study suggested a bidirectional relationship where higher sedentary time at baseline increased 10-year weight gain and higher baseline weight was associated with an unfavorable 10-year change in sedentary time. The effect sizes indicated that 1 hour lower sedentary time at baseline was associated with ~0.3 kg decrease in body weight over the 10-year follow up, whereas 3 kg higher baseline body weight was associated with ~2 min increase in sedentary time, closely resembling the causal estimates we observed in the present Mendelian randomization analyses. Our results are also in accordance with randomized clinical trials of physical activity interventions which generally suggest that increasing physical activity leads to a moderate loss of body weight in overweight or obese participants (Church et al., 2009, Rosenkilde et al., 2012, Golubic et al., 2015, Kim et al., 2019, Biddle et al., 2015). Resembling the causal estimates we observed, meta-analyses of randomized clinical trials have suggested weight losses ranging from 0.3 kg to 1.8 kg for various physical activity interventions ranging from 2-52 weeks (Twells et al., 2021).”

5) Typo? in the conclusion part: increasing sedentary time is likely to be beneficial for weight management.

Thank you for noting this error. We have now corrected the sentence to “decreasing sedentary time is likely to be beneficial for weight management” (lines 347-348).

6) Supp Text p21 line 471

I don't think the inside assumption can be checked by I-squared (it addresses NOME assumption mainly). Please refer to

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5446088/.

We agree and have now clarified that we checked the NOME assumption, not the inside assumption, using I-squared and used the suggested reference (PMC5446088) in Lines 670-672:

“The no measurement error (NOME) assumption, which assumes no measurement error between the genetic instrument and the exposure, was checked by calculating the mean F-statistic and the variation of the I2 statistic [3].”

Reviewer #3 (Recommendations for the authors):

The authors have presented a well written and conclusive study, where strong evidence suggests a causal bidirectional relationship between BMI and physical inactivity.

The methods used and results presented do support the conclusions that have been claimed in this study.

For transparency, I would suggest making the genetic instruments, the summary data and the scripts used to perform the analysis publicly available. I would also stress that it is the causal effect of genetic liability for these traits that have been investigated. In addition, the authors may want to mention that further study would be warranted to investigate causal relationships at various BMI thresholds.

Thank you for the valuable comments. We fully agree that making the data and scripts publicly available is important. Thus, we have now added a data sharing statement in the end of the manuscript along with the web-link and github repositories where the summary data, genetic instruments and R scripts are freely available

Lines 461-466: “Data sharing: All analyses were performed using R statistical package freely available at https://cran.r-project.org/mirrors.html. The CAUSE R package and instructions are available at https://jean997.github.io/cause/. The Two-sample MR package is available at https://mrcieu.github.io/TwoSampleMR/. The RadialMR package is available at https://github.com/WSpiller/RadialMR. The code and curated data for the current analysis are available at https://github.com/MarioGuCBMR/MR_Physical_Activity_BMI.”

As suggested by the reviewers, we have now also clarified that we investigated the causal effect of genetic liability for physical activity and adiposity traits.

Lines 24-25: “We assessed genetic liability using results from genome-wide association studies for accelerometer-based physical activity and sedentary time…”

Lines 67-68: “Here, we aimed to assess the causality between the genetic liability of physical inactivity, sedentary time and BMI…”

Lines 266-267: “The present Mendelian randomization analyses suggest a bidirectional causal relationship between higher genetic liability of sedentary time and higher BMI…”

We have now also added a sentence in the Discussion section to state that future research is needed to investigate the casual relationships in connection to different BMI thresholds.

Lines 342-343: “Moreover, further research is needed to investigate causal relationships at various BMI thresholds.”